1 Nicolaas Vroom  The two postulates in Special Relativity  Wednesday 6 may 2015 
2 robert bristowjohnson  Re :The two postulates in Special Relativity  Thursday 7 may 2015 
3 Gerry Quinn  Re :The two postulates in Special Relativity  Saturday 9 may 2015 
4 Tom Roberts  Re :The two postulates in Special Relativity  Wednesday 13 may 2015 
5 Nicolaas Vroom  Re :The two postulates in Special Relativity  Tuesday 19 may 2015 
6 robert bristowjohnson  Re :The two postulates in Special Relativity  Wednesday 20 may 2015 
7 Tom Roberts  Re :The two postulates in Special Relativity  Thursday 21 may 2015 
8 Hendrik van Hees  Re :The two postulates in Special Relativity  Saturday 23 may 2015 
9 al...@interia.pl  Re :The two postulates in Special Relativity  Sunday 24 may 2015 
10 robert bristowjohnson  Re :The two postulates in Special Relativity  Monday 25 may 2015 
11 Roland Franzius  Re :The two postulates in Special Relativity  Monday 25 may 2015 
12 al...@interia.pl  Re :The two postulates in Special Relativity  Wednesday 27 may 2015 
13 Jos Bergervoet  Re :The two postulates in Special Relativity  Wednesday 27 may 2015 
14 Roland Franzius  Re :The two postulates in Special Relativity  Wednesday 27 may 2015 
15 Nicolaas Vroom  Re :The two postulates in Special Relativity  Friday 29 may 2015 
16 al...@interia.pl  Re :The two postulates in Special Relativity  Saturday 30 may 2015 
17 al...@interia.pl  Re :The two postulates in Special Relativity  Saturday 30 may 2015 
18 Nicolaas Vroom  Re :The two postulates in Special Relativity  Monday 1 june 2015 
19 Gary Harnagel  Re :The two postulates in Special Relativity  Monday 1 june 2015 
20 Nicolaas Vroom  Re :The two postulates in Special Relativity  Friday 5 june 2015 
21 Nicolaas Vroom  Re :The two postulates in Special Relativity  Saturday 6 june 2015 
22 Gary Harnagel  Re :The two postulates in Special Relativity  Saturday 6 june 2015 
23 Gerry Quinn  Re :The two postulates in Special Relativity  Saturday 6 june 2015 
24 Nicolaas Vroom  Re :The two postulates in Special Relativity  Tuesday 9 june 2015 
25 Nicolaas Vroom  Re :The two postulates in Special Relativity  Tuesday 9 june 2015 
26 Gerry Quinn  Re :The two postulates in Special Relativity  Thursday 11 june 2015 
27 al...@interia.pl  Re :The two postulates in Special Relativity  Saturday 13 june 2015 
28 Nicolaas Vroom  Re :The two postulates in Special Relativity  Saturday 20 june 2015 
29 Roland Franzius  Re :The two postulates in Special Relativity  Saturday 20 june 2015 
30 al...@interia.pl  Re :The two postulates in Special Relativity  Saturday 20 june 2015 
31 Tom Roberts  Re :The two postulates in Special Relativity  Saturday 20 june 2015 
32 Gerry Quinn  Re :The two postulates in Special Relativity  Saturday 27 june 2015 
33 Nicolaas Vroom  Re :The two postulates in Special Relativity  Sunday 28 june 2015 
34 Nicolaas Vroom  Re :The two postulates in Special Relativity  Monday 29 june 2015 
35 Tom Roberts  Re :The two postulates in Special Relativity  Friday 3 july 2015 
36 Gerry Quinn  Re :The two postulates in Special Relativity  Monday 6 july 2015 
37 John Heath  Re :The two postulates in Special Relativity  Saturday 11 july 2015 
38 Tom Roberts  Re :The two postulates in Special Relativity  Wednesday 5 augustus 2015 
39 Nicolaas Vroom  Re :The two postulates in Special Relativity  Wednesday 12 augustus 2015 
40 Gregor Scholten  Re :The two postulates in Special Relativity  Monday 17 augustus 2015 
41 Tom Roberts  Re :The two postulates in Special Relativity  Saturday 22 augustus 2015 
42 Nicolaas Vroom  Re :The two postulates in Special Relativity  Tuesday 8 september 2015 
43 Nicolaas Vroom  Re :The two postulates in Special Relativity  Thursday 10 september 2015 
44 Gregor Scholten  Re :The two postulates in Special Relativity  Thursday 10 september 2015 
45 Nicolaas Vroom  Re :The two postulates in Special Relativity  Saturday 12 september 2015 
46 Gregor Scholten  Re :The two postulates in Special Relativity  Saturday 12 september 2015 
47 Nicolaas Vroom  Re :The two postulates in Special Relativity  Tuesday 29 september 2015 
48 Gregor Scholten  Re :The two postulates in Special Relativity  Sunday 11 october 2015 
49 Nicolaas Vroom  Re :The two postulates in Special Relativity  Saturday 17 october 2015 
50 Gregor Scholten  Re :The two postulates in Special Relativity  Saturday 17 october 2015 
51 Gregor Scholten  Re :The two postulates in Special Relativity  Sunday 25 october 2015 
52 Oliver Jennrich  Re :The two postulates in Special Relativity  Sunday 25 october 2015 
53 Nicolaas Vroom  Re :The two postulates in Special Relativity  Saturday 28 november 2015 
54 Gregor Scholten  Re :The two postulates in Special Relativity  Tuesday 1 december 2015 
55 John Heath  Re :The two postulates in Special Relativity  Monday 7 december 2015 
56 Gregor Scholten  Re :The two postulates in Special Relativity  Tuesday 8 december 2015 
57 John Heath  Re :The two postulates in Special Relativity  Thursday 10 december 2015 
58 Gregor Scholten  Re :The two postulates in Special Relativity  Friday 11 december 2015 
59 Gary Harnagel  Re :The two postulates in Special Relativity  Friday 11 december 2015 
60 John Heath  Re :The two postulates in Special Relativity  Friday 11 december 2015 
61 Jonathan Thornburg  Re :The two postulates in Special Relativity  Saturday 12 december 2015 
62 Gregor Scholten  Re :The two postulates in Special Relativity  Saturday 12 december 2015 
63 Gregor Scholten  Re :The two postulates in Special Relativity  Saturday 12 december 2015 
64 Gregor Scholten  Re :The two postulates in Special Relativity  Sunday 13 december 2015 
65 Gerry Quinn  Re :The two postulates in Special Relativity  Sunday 13 december 2015 
66 Gary Harnagel  Re :The two postulates in Special Relativity  Sunday 13 december 2015 
67 Gregor Scholten  Re :The two postulates in Special Relativity  Sunday 13 december 2015 
68 Steven Carlip  Re :The two postulates in Special Relativity  Monday 14 december 2015 
69 John Heath  Re :The two postulates in Special Relativity  Tuesday 15 december 2015 
70 Jos Bergervoet  Re :The two postulates in Special Relativity  Tuesday 15 december 2015 
71 John Heath  Re :The two postulates in Special Relativity  Tuesday 15 december 2015 
72 Tom Roberts  Re :The two postulates in Special Relativity  Wednesday 16 december 2015 
73 Gregor Scholten  Re :The two postulates in Special Relativity  Wednesday 16 december 2015 
74 Gregor Scholten  Re :The two postulates in Special Relativity  Friday 18 december 2015 
75 John Heath  Re :The two postulates in Special Relativity  Friday 18 december 2015 
76 Gerry Quinn  Re :The two postulates in Special Relativity  Friday 18 december 2015 
77 Gregor Scholten  Re :The two postulates in Special Relativity  Saturday 19 december 2015 
78 Gary Harnagel  Re :The two postulates in Special Relativity  Sunday 20 december 2015 
79 Tom Roberts  Re :The two postulates in Special Relativity  Sunday 20 december 2015 
80 Gregor Scholten  Re :The two postulates in Special Relativity  Sunday 20 december 2015 
81 Gerry Quinn  Re :The two postulates in Special Relativity  Sunday 20 december 2015 
82 Gerry Quinn  Re :The two postulates in Special Relativity  Monday 21 december 2015 
83 Gerry Quinn  Re :The two postulates in Special Relativity  Monday 21 december 2015 
84 Jonathan Thornburg  Re :The two postulates in Special Relativity  Thursday 31 december 2015 
85 Jonathan Thornburg  Re :The two postulates in Special Relativity  Thursday 31 december 2015 
86 Gerry Quinn  Re :The two postulates in Special Relativity  Friday 1 january 2016 
87 John Heath  Re :The two postulates in Special Relativity  Friday 1 january 2016 
88 Jonathan Thornburg  Re :The two postulates in Special Relativity  Saturday 2 january 2016 
89 Tom Roberts  Re :The two postulates in Special Relativity  Monday 11 january 2016 
90 Gerry Quinn  Re :The two postulates in Special Relativity  Tuesday 12 january 2016 
91 John Heath  Re :The two postulates in Special Relativity  Wednesday 13 january 2016 
92 Jos Bergervoet  Re :The two postulates in Special Relativity  Wednesday 13 january 2016 
93 Gerry Quinn  Re :The two postulates in Special Relativity  Friday 15 january 2016 
94 Jos Bergervoet  Re :The two postulates in Special Relativity  Sunday 17 january 2016 
95 Gary Harnagel  Re :The two postulates in Special Relativity  Sunday 17 january 2016 
96 Mike Fontenot  Re :The two postulates in Special Relativity  Sunday 17 january 2016 
97 Tom Roberts  Re :The two postulates in Special Relativity  Sunday 17 january 2016 
98 Jos Bergervoet  Re :The two postulates in Special Relativity  Monday 18 january 2016 
99 Jos Bergervoet  Re :The two postulates in Special Relativity  Monday 18 january 2016 
100 Tom Roberts  Re :The two postulates in Special Relativity  Tuesday 19 january 2016 
101 John Heath  Re :The two postulates in Special Relativity  Wednesday 20 january 2016 
102 Tom Roberts  Re :The two postulates in Special Relativity  Wednesday 20 january 2016 
103 Mike Fontenot  Re :The two postulates in Special Relativity  Wednesday 20 january 2016 
104 erkd...@gmail.com  Re :The two postulates in Special Relativity  Sunday 28 february 2016 
105 Eric Baird  Re :The two postulates in Special Relativity  Tuesday 10 may 2016 
106 Ralph Frost  Re :The two postulates in Special Relativity  Friday 13 may 2016 
107 Nicolaas Vroom  Re :The two postulates in Special Relativity  Monday 16 may 2016 
108 Jos Bergervoet  Re :The two postulates in Special Relativity  Monday 16 may 2016 
109 Poutnik  Re :The two postulates in Special Relativity  Friday 20 may 2016 
110 Nicolaas Vroom  Re :The two postulates in Special Relativity  Friday 20 may 2016 
111 Poutnik  Re :The two postulates in Special Relativity  Saturday 21 may 2016 
112 Tom Roberts  Re :The two postulates in Special Relativity  Sunday 22 may 2016 
113 Nicolaas Vroom  Re :The two postulates in Special Relativity  Tuesday 24 may 2016 
114 Tom Roberts  Re :The two postulates in Special Relativity  Wednesday 1 june 2016 
115 Nicolaas Vroom  Re :The two postulates in Special Relativity  Sunday 5 june 2016 
116 John Heath  Re :The two postulates in Special Relativity  Wednesday 22 june 2016 
117 Nicolaas Vroom  Re :The two postulates in Special Relativity  Thursday 30 june 2016 
118 Phillip Helbig  Re :The two postulates in Special Relativity  Friday 1 july 2016 
119 Oliver Jennrich  Re :The two postulates in Special Relativity  Saturday 2 july 2016 
120 Phillip Helbig  Re :The two postulates in Special Relativity  Saturday 2 july 2016 
121 Dr J R Stockton  Re :The two postulates in Special Relativity  Sunday 3 july 2016 
122 Nicolaas Vroom  Re :The two postulates in Special Relativity  Sunday 3 july 2016 
123 Gregor Scholten  Re :The two postulates in Special Relativity  Sunday 3 july 2016 
124 Nicolaas Vroom  Re :The two postulates in Special Relativity  Thursday 7 july 2016 
125 Gregor Scholten  Re :The two postulates in Special Relativity  Sunday 10 july 2016 
126 Gregor Scholten  Re :The two postulates in Special Relativity  Sunday 10 july 2016 
127 Tom Roberts  Re :The two postulates in Special Relativity  Wednesday 13 july 2016 
128 Nicolaas Vroom  Re :The two postulates in Special Relativity  Monday 18 july 2016 
129 Gregor Scholten  Re :The two postulates in Special Relativity  Tuesday 19 july 2016 
130 Tom Roberts  Re :The two postulates in Special Relativity  Thursday 21 july 2016 
131 Nicolaas Vroom  Re :The two postulates in Special Relativity  Friday 22 july 2016 
132 Tom Roberts  Re :The two postulates in Special Relativity  Friday 22 july 2016 
133 Phillip Helbig  Re :The two postulates in Special Relativity  Saturday 23 july 2016 
134 Nicolaas Vroom  Re :The two postulates in Special Relativity  Saturday 23 july 2016 
135 Nicolaas Vroom  Re :The two postulates in Special Relativity  Monday 25 july 2016 
136 Dr J R Stockton  Re :The two postulates in Special Relativity  Sunday 31 july 2016 
137 Gregor Scholten  Re :The two postulates in Special Relativity  Sunday 7 augustus 2016 
138 Nicolaas Vroom  Re :The two postulates in Special Relativity  Monday 15 augustus 2016 
139 Gregor Scholten  Re :The two postulates in Special Relativity  Monday 29 augustus 2016 
140 Nicolaas Vroom  Re :The two postulates in Special Relativity  Saturday 29 october 2016 
141 Tom Roberts  Re :The two postulates in Special Relativity  Tuesday 8 november 2016 
142 Nicolaas Vroom  Re :The two postulates in Special Relativity  Sunday 13 november 2016 
143 Phillip Helbig  Re :The two postulates in Special Relativity  Sunday 13 november 2016 
144 Roland Franzius  Re :The two postulates in Special Relativity  Sunday 13 november 2016 
145 Gregor Scholten  Re :The two postulates in Special Relativity  Wednesday 16 november 2016 
146 Poutnik  Re :The two postulates in Special Relativity  Wednesday 16 november 2016 
147 Gregor Scholten  Re :The two postulates in Special Relativity  Friday 18 november 2016 
148 Nicolaas Vroom  Re :The two postulates in Special Relativity  Friday 18 november 2016 
149 Gregor Scholten  Re :The two postulates in Special Relativity  Friday 18 november 2016 
150 Poutnik  Re :The two postulates in Special Relativity  Monday 21 november 2016 
151 Maryann Tonn  Re :The two postulates in Special Relativity  Monday 21 november 2016 
152 Nicolaas Vroom  Re :The two postulates in Special Relativity  Wednesday 30 november 2016 
153 Gregor Scholten  Re :The two postulates in Special Relativity  Saturday 1 october 2016 
154 Nicolaas Vroom  Re :The two postulates in Special Relativity  Monday 5 december 2016 
>  We NOW know this is NOT what relativity says. In relativity, all clocks tick at their usual rates, regardless of how they might move or where they might be located (e.g. in a gravitational field). 
In the book "Subtle is the Lord..." by Abraham Pais at page 140
and 141 we read:
The two postulates:
1. The laws of physics take the same form in all inertial frames.
2. In any given inertial system the velocity of light c is the same
whether the light be emitted by a body at rest or by a body in uniform
motion.
At page 138 we read: "By definition, any two of these (inertial frames) are in uniform motion with respect to each other"
Consider the following three situations: 1. a light at rest which emits a flash at position p1 at t1. 2. an uniform moving light which also emits a flash at p1 at t1. 3. an accelerating moving light which does the same. Question: for any observer at a certain distance are this one or three distinquished physical events? IMO: It is one physical event. From a frequency point of view this is a different story.
[[Mod. note  Assuming that when you say "at rest" or "uniformly moving" or "accelerating" you really mean "... with respect to some specified inertial frame", then you're correct: neglecting any doppler shift of the light, a distant observer can't distinguish between situation 1, situation 2, and situation 3. (This remains true regardless of the distant observer's state of motion with respect to the inertial frame.)  jt]]
When I study postulate 1 immediate certain some thoughts pop up: Which type of physical processes are we discussing here? Are this all physical processes or only some (i.e. subset)? Laws are descriptions of physical processes. That means (if my interpretation is correct) that all physical processes are indepent of uniform movement until the speed of light. This sounds "too optimistic" specific if you consider these clocks which inner working uses light signals to operate (i.e. counts)
The following article is very interesting: http://www.nist.gov/pml/div689/20150421_strontium_clock.cfm. It writes: "Precision refers to how closely the clock approaches the true resonant frequency at which the strontium atoms oscillate between two electronic energy levels." Also here the question arises to which extend these oscillations are independent of the speed of the clock and does not influence the ticking rate.
A whole different thought is: why are accelarations not discussed?
Nicolaas Vroom Click here to Reply
> 
In the book "Subtle is the Lord..." by Abraham Pais at page 140 and 141 we read: The two postulates: 1. The laws of physics take the same form in all inertial frames. 2. In any given inertial system the velocity of light c is the same whether the light be emitted by a body at rest or by a body in uniform motion. 
this doesn't seem to be widely accepted (not sure why), but i've always felt that postulate #2 comes directly from postulate #1. if the laws of physics are the same for all inertial frames of reference, every observer has the same epsilon_0 and mu_0 in their laws of physics. so c=(epsilon_0*mu_0)^(1/2) is the same for every inertial observer hanging around in a vacuum.
and all postulate #1 says is that if a vacuum is physically nothing, you can't tell if a vacuum is whizzing past you at a speed of c/2 or not. the relative speed of a physical nothing is meaningless. so you could be whizzing past me at a constant relative speed of c/2, but there is no aether wind blowing in your face nor in mine. we both have equal claim to being "at rest". when we look at the **same** flash or beam of light, since we both have the same physics (because we're *both* "at rest"), then we both measure the speed of that flash of light to be the same speed. the only way for that to happen is if we both observe the other's clock as ticking more slowly than our own.
so, in my opinion, there is only one necessary postulate to special relativity and it is the first postulate.
> 
At page 138 we read: "By definition, any two of these (inertial frames)
are in uniform motion with respect to each other"
Consider the following three situations: 1. a light at rest which emits a flash at position p1 at t1. 2. an uniform moving light which also emits a flash at p1 at t1. 3. an accelerating moving light which does the same. Question: for any observer at a certain distance are this one or three distinquished physical events? IMO: It is one physical event. From a frequency point of view this is a different story. 
once the EM wave departs the mechanism that created it (the emitter), all we have is a changing electric field which causes a changing magnetic field which, in turn, causes a changing electric field which causes another changing magnetic field, etc.
the light is a propagating EM field and, once emitted, has no idea about the emitter including what the velocity or motion the emitter had.

r bj r...@audioimagination.com
"Imagination is more important than knowledge."
>  On 5/5/15 9:24 PM, Nicolaas Vroom wrote: 
> > 
In the book "Subtle is the Lord..." by Abraham Pais at page 140 and 141 we read: The two postulates: 1. The laws of physics take the same form in all inertial frames. 2. In any given inertial system the velocity of light c is the same whether the light be emitted by a body at rest or by a body in uniform motion. 
> 
this doesn't seem to be widely accepted (not sure why), but i've always felt that postulate #2 comes directly from postulate #1. if the laws of physics are the same for all inertial frames of reference, every observer has the same epsilon_0 and mu_0 in their laws of physics. so c=(epsilon_0*mu_0)^(1/2) is the same for every inertial observer hanging around in a vacuum. 
The first postulate doesn't tell us what the limiting velocity, if any, is. Newtonian physics, in which the velocity of a massless particle is infinite, would be compatible with it.
 Gerry Quinn
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>  [Einstein's postulates for SR] When I study postulate 1 immediate certain some thoughts pop up: Which type of physical processes are we discussing here? 
All types.
>  Laws are descriptions of physical processes. That means (if my interpretation is correct) that all physical processes are indepent of uniform movement until the speed of light. This sounds "too optimistic" specific if you consider these clocks which inner working uses light signals to operate (i.e. counts) 
Instead of inertial frames, consider this proposition: all physical phenomena are independent of coordinates. This must be true if physics is possible, because coordinates are arbitrary human constructs; they are part of the model, not the world. Once you accept this, then it's easy to see that inertial frames are just a subset of possible coordinates.
So this is not "too optimistic".
>  Also here the question arises to which extend these oscillations are independent of the speed of the clock and does not influence the ticking rate. 
Assuming Einstein's first postulate is valid, then the physics that governs the clock's ticking is the same regardless of which inertial frame it finds itself at rest in. So the "speed of the clock" (relative to any coordinates one might choose) does not affect its ticking rate.
>  A whole different thought is: why are accelarations not discussed? 
In 1905 Einstein did not get that far. Modern textbooks on SR certainly do discuss acceleration. Many experiments have shown that acceleration does not affect a clock's ticking rate, as long as the clock is not damaged. Commercial clocks come with a specification of how large an acceleration they can sustain without damage.
Tom Roberts
>  On 5/5/15 5/5/15  8:24 PM, Nicolaas Vroom wrote: 
> >  Which type of physical processes are we discussing here? 
> 
All types. 
> >  Laws are descriptions of physical processes. That means that all physical processes are indepent of uniform movement until the speed of light. This sounds "too optimistic" specific if you consider these clocks which inner working uses light signals to operate (i.e. counts) 
> 
Instead of inertial frames, consider this proposition: all physical phenomena are independent of coordinates. 
>  Once you accept this, then it's easy to see that inertial frames are just a subset of possible coordinates. 
>  So this is not "too optimistic". 
[[Mod. note  Pendulum clocks and hourglasses both have the property that they depend on the local "little g" acceleration with respect to an inertial frame, and *don't* work in an inertial frame. Thus for present purposes, they're not good clocks.  jt]]
https://books.google.be/books?id=Z7chuo4ebUAC&pg=PA61&sig=r7PLMbI4rhAgfGkfBSMCJEBkVs&hl=nl#v=onepage&q&f=false This document at page 64 raises the question: Can we always build a better clock?
> >  Also here the question arises to which extend these oscillations are independent of the speed of the clock and does not influence the ticking rate. 
> 
Assuming Einstein's first postulate is valid, then the physics that governs the clock's ticking is the same regardless of which inertial frame it finds itself at rest in. So the "speed of the clock" (relative to any coordinates one might choose) does not affect its ticking rate 
The issue is the ticking rate (tr) of two clocks (as measured by the final clock count = fcc) relative to each other.
Consider two identical clocks.
A) IMO if both clocks are not "moved" the fcc will be the same
B) IMO if both clocks are moved from A to B following the same
path the fcc will be the same.
C) IMO if both clocks are moved from A to B following a different path
there are two options:
C1) The fcc is the same. IMO this has a low chance.
C2) The fcc is different. IMO this has a high chance.
C2 IMO implies that the ticking rate is different.
> >  A whole different thought is: why are accelarations not discussed? 
> 
In 1905 Einstein did not get that far. 
>  Modern textbooks on SR certainly do discuss acceleration. Many experiments have shown that acceleration does not affect a clock's ticking rate, as long as the clock is not damaged. 
[[Mod. note  The standard way to assess this is to make comparisons amongst an ensemble of similar clocks, some of which have been accelerated and some not. If all the clocks are statistically "similar", then they're probably all undamaged. The Allen variance http://en.wikipedia.org/wiki/Allen_variance is a common way of characterizing the performance of (undamaged) clocks.  jt]]
Nicolaas Vroom
*only* dimensionless constants are fundamental.
all c needs to be is real, positive, and finite. no matter how "God" (or whatever hypothetical immortal being not governed by the laws of nature) perceives the speed of instantaneous interactions (EM, gravity, strong force) meditated by massless particles, we mortals would continue to perceive it as moving 299792456 of our meters in the time elapsed by one of our seconds. (we would also measure the same epsilon_0 and define the same mu_0.)
cut c in half (from the POV of the godlike being) and the rest of us get our length and time scaled in such a manner that c remains the same.
c will always be 1 Planck Length per Planck Time. and if none of the dimensionless fundamental constants change, then the number of Planck Lengths per meter will remain the same and the number of Planck Times per second will remain the same.  show quoted text 
>  It would be interesting to study a hourglas inside a spacecraft. 
Why? An hourglass is NOT a clock. Only hourglass+earth is a (modestly accurate) clock, and you cannot possibly put that into a spacecraft.
Ditto for pendulum clocks and sundials (etc.).
>  The question is: what is the influence on the accuracy of a pendulum clock when you move such a clock (fast?) from A to B. 
That question is useless, because you cannot move the earth with it.
> 
The issue is the ticking rate (tr) of two clocks (as measured by the
final clock count = fcc) relative to each other.
Consider two identical clocks. 
No to this last  you DID NOT MEASURE the tick rate of either clock, and therefore cannot make any conclusion about it.
In relativity this difference is modeled as being the difference in the "length of the paths", where "length" for such timelike paths is really the elapsed proper time.
When cars' odometers indicate different distances for different paths between A and B, do you really think the odometers' tick rates are different? OF COURSE NOT! The odometers increment 1 mile for every mile traveled  that is their (intrinsic) tick rate. The clocks increment 1 second for every second of elapsed proper time  that is their (intrinsic) tick rate.
Note your implicit assumption hidden in your conclusion: you are assuming your personal appreciation of "time" is important. That is, you have added a HIDDEN third clock, your mind, and you are really assessing "tick rate" relative to it, WITHOUT MENTIONING IT. Yes, if you measured the tick rates of those clocks RELATIVE TO A CLOCK COLOCATED and CO_MOVING WITH YOURSELF, then you could conclude their tick rates RELATIVE TO THAT CLOCK are different.
But as I have said before, when you just discuss the "tick rate of a clock", that phrase inherently refers to the INTRINSIC tick rate of the clock, because that is how words behave. The intrinsic rate of the clock never changes; only tick rates RELATIVE TO OTHER CLOCKS can change (really relative to other coordinate systems).
Bottom line: your "common sense" is insufficient to understand what is happening in relativity. The world is more complicated than your common sense can capture. Relativity models it well, "common sense" does not.
>>>  A whole different thought is: why are accelarations not discussed? 
>>  In 1905 Einstein did not get that far. 
>  IMO all experiments with moving clocks imply acceleration 
>> 
Modern textbooks on SR certainly do discuss acceleration. Many experiments have shown that acceleration does not affect a clock's ticking rate, as long as the clock is not damaged. 
>  What is the definition of damaged? 
A clock is not damaged if it continues ticking at its intrinsic tick rate.
>  When you first perform test C and than test A and the fcc is different than at least one clock is damaged. 
No. Had you measured each clock's (intrinsic) tick rate, you would have found them to be correct.
There is more going on here than you understand, and you keep making assumptions based on your personal experience, which is woefully inadequate because you have no personal experience with speeds approaching c. You need to study relativity, and its underlying geometry.
Tom Roberts
>  On 5/9/15 3:21 AM, Gerry Quinn wrote: 
> >  The first postulate doesn't tell us what the limiting velocity, if any, is. Newtonian physics, in which the velocity of a massless particle is infinite, would be compatible with it. 
> 
but that doesn't matter. (well, "if any" matters. but even in 1900, we already had a finite speed for c, so the point doesn't count.) 
So why write down ANY laws or postulates that are known to be true?
In any case, it's not obvious from first principles that c is the limiting speed, even if we haven't found anything that goes faster. Sure, you can deduce that based on observations too. But ultimately, you must state enough postulates to describe the physics that you want to describe.
> 
*only* dimensionless constants are fundamental.
all c needs to be is real, positive, and finite. no matter how "God" (or whatever hypothetical immortal being not governed by the laws of nature) perceives the speed of instantaneous interactions (EM, gravity, strong force) meditated by massless particles, we mortals would continue to perceive it as moving 299792456 of our meters in the time elapsed by one of our seconds. (we would also measure the same epsilon_0 and define the same mu_0.) cut c in half (from the POV of the godlike being) and the rest of us get our length and time scaled in such a manner that c remains the same. 
I can agree that the second postulate could have been stated as "there is a limiting speed", leaving it open to be deduced from observation that the speed of light fits the bill. [Assuming it does  it is not actually proven that the photon has zero mass, although numerous arguments constrain any photon mass to be extremely small.]  show quoted text 
>  So why write down ANY laws or postulates that are known to be true? 
Postulates are not any laws.
These are the supplementary assumptions only, and of a special type; for example, in the model of the collisions there are used two assumption usually: ideal elastic collision, or ideal inelastic.
And we know very well these both are false in any practical case. But this not a problem  the models works well... in some limited conditions, which are known commonly.
And the same rule applies to every postulate  to these of SR too.
Especially: the 'light speed is invariant' is not any discovery, but a modeledassumption only, on which the SR is based (or on the assumption of the relativity principle, which is equivalent, or maybe a superior, to the invariance of a light speed).
>  In any case, it's not obvious from first principles that c is the limiting speed, even if we haven't found anything that goes faster. Sure, you can deduce that based on observations too. But ultimately, you must state enough postulates to describe the physics that you want to describe. 
No. The postulates are suplementary always, therefore these are present in the models only, never in a theory itself.
There is none of postulates in a real theory, but just axioms only! And an axiom is not a postulate.
So, what is a difference between an axiom and postulate? It should be rather obvious...
> 
> 
There is none of postulates in a real theory, but just axioms only! And an axiom is not a postulate. So, what is a difference between an axiom and postulate? It should be rather obvious... 
it's not to me. seems to me that, operationally, postulates and axioms are the same. they are initial statements that are taken as true without proof and other substantive conclusions are made from those postulates or axioms.  show quoted text 
>  On 5/23/15 10:30 PM, al...@interia.pl wrote: 
>> 
> 
... 
>> 
There is none of postulates in a real theory, but just axioms only! And an axiom is not a postulate. So, what is a difference between an axiom and postulate? It should be rather obvious... 
> 
it's not to me. seems to me that, operationally, postulates and axioms are the same. they are initial statements that are taken as true without proof and other substantive conclusions are made from those postulates or axioms. 
There are no axioms in physics exept the axiom of "use logic and numbers, make an experiment and adapt the mathematical model to its outcomes".
Axioms can be formulated in an axiomatic theory as a mathematical framework to serve as a specific model describing the measurable observables of a given system.
Postulates are more general: They fomulate model independent features which all mathematical models of a physical reality have to incorporate, like use of a spacetime universe, Poincare invariance, probabilistic interpretation, gauge invariance, locality, causality, determinism aof system states by a given set of starting conditions at the time of preparation of experiments.
These postulates drive the development in quite different models like relativistic mechanics, cosmology, quantum theory, field theory or classical and quantum statistical mechanics.

Roland Franzius
> 
There are no axioms in physics exept the axiom of "use logic and numbers, make an experiment and adapt the mathematical model to its outcomes". 
Indeed, because the whole physics is not a theoretical domain in fact.
The physics is just about the models.
>  Axioms can be formulated in an axiomatic theory as a mathematical framework to serve as a specific model describing the measurable observables of a given system. 
No, axioms are just of a theory basis... a model is besed on a theory, of course, because there is nothig more to start!
>  Postulates are more general: They fomulate model independent features which all mathematical models of a physical reality have to incorporate, like use of a spacetime universe, Poincare invariance, probabilistic interpretation, gauge invariance, locality, causality, determinism aof system states by a given set of starting conditions at the time of preparation of experiments. 
Yes. Maybe a postulate can be a something more than an axiom.
But it's only because we have more freedom in this case... any axiom are independent of any our decision  it's just a fact, an obvious truth.
Finally: there are unlimited postulates possible, but an axioms set is very limited.
>  These postulates drive the development in quite different models like relativistic mechanics, cosmology, quantum theory, field theory or classical and quantum statistical mechanics. 
These all 'theories' are just the models only, in fact, because: the relativity, quantum, ect. are based on the general theory  the math itself, what is evident... and sametime on a specfic theory, like in the case of relativity: the Lorentz  Poincare's Theory.
>  Am 25.05.2015 um 10:02 schrieb robert bristowjohnson: 
>>  On 5/23/15 10:30 PM, al...@interia.pl wrote: ... 
>>> 
There is none of postulates in a real theory, but just axioms only!
And an axiom is not a postulate.
So, what is a difference between an axiom and postulate? It should be rather obvious... 
>> 
it's not to me. seems to me that, operationally, postulates and axioms are the same. they are initial statements that are taken as true without proof and other substantive conclusions are made from those postulates or axioms. 
> 
There are no axioms in physics exept the 
>  Postulates are more general: They fomulate model independent features 
There isn't much support for giving them different meanings:
http://math.stackexchange.com/questions/258346/whatisthedifferencebetweenanaxiomandapostulate
(Although stackexchange is of course less authoritative than sci.physics.research, let's postulate that first!)
 Jos
>  W dniu poniedziaLek, 25 maja 2015 15:45:18 UTC+2 uLLytkownik Roland Franzius 
>> 
There are no axioms in physics exept the axiom of "use logic and numbers, make an experiment and adapt the mathematical model to its outcomes". 
> 
Indeed, because the whole physics is not a theoretical domain in fact. The physics is just about the models. 
>> 
Axioms can be formulated in an axiomatic theory as a mathematical framework to serve as a specific model describing the measurable observables of a given system. 
> 
No, axioms are just of a theory basis... a model is besed on a theory, of course, because there is nothig more to start! 
You will find two unique truly axiomatic theories in physics and both have no working model, that proves its existence in the mathematical sense for a faily general rich set of observables and their time development:
1) Analytical Lagrangian mechanics: Plainly wrong physical, mathematical not existent because of lack of predictability for many pointparticle systems with interaction.
2) Axiomatic Quantum field theory: While starting with beautiful results in the 1950 after the work of Wigner, Wightman, Haag, Kastler there was little physical progress later on. Now it is a branch of pure mathematics applied to an physical motivated axiomatic setting.
Again there exists no mathematical realisation beyond free fields could be established in a physical acceptable number of spacetime dimensions.
Of course this is symptomatic for theoretical physics:
Physics is about time development of 3dgeometric systems with an indefinite bilinear form invariant under the local families of representations of the Poincare group.
The general lack of a unique canonical euclidean norm for systems in spacetime makes convergency theorems in relativistic mechanics and field theories extremely hard to prove.
In most cases one has to introduce smoothness conditions on series solutions in some much too rich taylored solution spaces that are by no means capable to select a unique mathematical model.
So finally the best thing one gets as an aximotic setting in physics is the selection of some interesting categories like continuous representations of Liegroups over tensor products.
In axiomatic field theories like General Relativity and QED and Quantum Field Theory it is not known until today if the choosen set of axioms is consistent and free of contradictions except perhaps for the toy theories of free test systems in external backgrounds.

Roland Franzius
Op woensdag 13 mei 2015 10:21:35 UTC+2 schreef Tom Roberts:
>  On 5/5/15 5/5/15  8:24 PM, Nicolaas Vroom wrote: 
> >  Which type of physical processes are we discussing here? 
> 
All types. 
> >  Laws are descriptions of physical processes. That means that all physical processes are indepent of uniform movement until the speed of light. This sounds "too optimistic" specific if you consider these clocks which inner working uses light signals to operate (i.e. counts) 
> 
Instead of inertial frames, consider this proposition: all physical phenomena are independent of coordinates. 
That is correct, but it does not say anything about (the inner working) of the processes them self
>  Once you accept this, then it's easy to see that inertial frames are just a subset of possible coordinates. 
Again that is correct, but etc (see above)
>  So this is not "too optimistic". 
When you study http://en.wikipedia.org/wiki/Clock you can see that it is a continuous struggle to make better, more accurate, clocks. It would be interesting to study a hourglas inside a spacecraft. The question is what is the influence on the accuracy of a pendulum clock when you moved.
https://books.google.be/books?id=Z7chuo4ebUAC&pg=PA61&sig=r7PLMbI4rhAgfGkfBSMCJEBkVs&hl=nl#v=onepage&q&f=false This document at page 64 raises the question: Can we always build a better clock?
> >  Also here the question arises to which extend these oscillations are independent of the speed of the clock and does not influence the ticking rate. 
> 
Assuming Einstein's first postulate is valid, then the physics that governs the clock's ticking is the same regardless of which inertial frame it finds itself at rest in. So the "speed of the clock" (relative to any coordinates one might choose) does not affect its ticking rate 
The issue is the ticking rate (tr) of two clocks (as measured in the final clock count = fcc) relative to each other.
Consider two identical clocks.
A) IMO if both clocks are not "moved" the fcc will be the same
B) IMO if both clocks are moved from A to B following the same
path the fcc will be the same.
C) IMO if both clocks are moved from A to B following a different path
there are two options:
C1) The fcc is the same. IMO this has a low chance.
C2) The fcc is different. IMO this has a high chance.
C2 IMO implies that the ticking rate is different.
> >  A whole different thought is: why are accelarations not discussed? 
> 
In 1905 Einstein did not get that far. 
>  Modern textbooks on SR certainly do discuss acceleration. Many experiments have shown that acceleration does not affect a clock's ticking rate, as long as the clock is not damaged. 
Nicolaas Vroom
W dniu sroda, 27 maja 2015 13:19:32 UTC+2 uzytkownik Jos Bergervoet napisal:
>  On 5/25/2015 3:45 PM, Roland Franzius wrote: 
>>  Am 25.05.2015 um 10:02 schrieb robert bristowjohnson: 
>>>  On 5/23/15 10:30 PM, al...@interia.pl wrote: ... 
>>>> 
There is none of postulates in a real theory, but just axioms only!
And an axiom is not a postulate.
So, what is a difference between an axiom and postulate? It should be rather obvious... 
>>> 
it's not to me. seems to me that, operationally, postulates and axioms are the same. they are initial statements that are taken as true without proof and other substantive conclusions are made from those postulates or axioms. 
>> 
There are no axioms in physics exept the 
>  ... ... 
>>  Postulates are more general: They fomulate model independent features 
> 
There isn't much support for giving them different meanings: (Although stackexchange is of course less authoritative than sci.physics.research, let's postulate that first!)  Jos 
Any postulate is some trick math trick in fact, which leads to more simplicity... of the equations... so, any model is based just on such trick.
The great example is the c = inv in the SR model: it's evident that: c' = c  v, due to the strict math: a gemetry principles, logics, ect.
But it's to poor fact, because a speed can't be measured directly, but omly indirect: by a time and a distance measure.
Therefore if there is in fact: c' = cv, then we still can assume it's: c = inv, but then we must transform a time or a distance adecuatelly, to cancel the obvious change of the speed of light.
A distance is rather hard to transform, because if we have some rod with a fixed length, say L = 1m, then we assume it's preserved unconditionaly (in any local system).
Thus we must transform a time  it's the one real possibility!
Therefore the relativity model, which is based on the postulate: c = inv, postulates in fact just that: a transformation of a light speed = tr. of a time.
And it's all obout this model, because such convention lands directly on the well known transformation:
x' = k(x  vt) and t' = k(t  xv)
>>  No, axioms are just of a theory basis... a model is besed on a theory, of course, because there is nothig more to start! 
> 
You will find two unique truly axiomatic theories in physics and both have no working model, that proves its existence in the mathematical sense for a faily general rich set of observables and their time development: 1) Analytical Lagrangian mechanics: Plainly wrong physical, mathematical not existent because of lack of predictability for many pointparticle systems with interaction. 
This is just a model, which is based explicityly on some postulates; and the model gives very good predictions... for example: a simulation of the Solar System, basing on this model, is possible, and rather easy, and the final results are quite good.
>  Again there exists no mathematical realisation beyond free fields could be established in a physical acceptable number of spacetime dimensions. 
The whole spacetime concempt is just a modelspecific postulate... and it depends totaly on an abstract mathematical space theory.
>  In axiomatic field theories like General Relativity and QED and Quantum Field Theory it is not known until today if the choosen set of axioms is consistent and free of contradictions except perhaps for the toy theories of free test systems in external backgrounds. 
There is no axioms in the GR, nor QM... similarily the hiperbolic geometry is not of SR domain at all, nor the complex algebra is a part of the waves theory.
>  On 5/18/15 5/18/15  9:35 PM, Nicolaas Vroom wrote: 
> >  It would be interesting to study a hourglas inside a spacecraft. 
> 
Why? An hourglass is NOT a clock. 
That is the question. What is a clock and what is not a clock. If SR describes all processes and all clocks and if that is the case than it should also describe a hourglass and a pendulum.
>  That question is useless, because you cannot move the earth with it. 
Than you cannot perform any experiment with any clock ? (because of the earth)
> > 
The issue is the ticking rate (tr) of two clocks (as measured by the
final clock count = fcc) relative to each other.
Consider two identical clocks. C2) The fcc is different. IMO this has a high chance. C2 IMO implies that the ticking rate is different. 
> 
No to this last  you DID NOT MEASURE the tick rate of either clock, and therefore cannot make any conclusion about it. 
I agree, but I did not write that. I specific use the word "implies". The issue is that the final clock counts are different. If you agree that that is possible, than the Q is: how do you explain that.
>  Note your implicit assumption hidden in your conclusion: you are assuming your personal appreciation of "time" is important. That is, you have added a HIDDEN third clock, your mind, and you are really assessing "tick rate" relative to it, WITHOUT MENTIONING IT. 
I'm comparing the result (counts) of an experiment with two clocks. My mind has nothing to do with this. You can add a third clock, (and call each count of that clock 1 second) but that does not really makes a difference.
>  But as I have said before, when you just discuss the "tick rate of a clock", that phrase inherently refers to the INTRINSIC tick rate of the clock, because that is how words behave. 
Exactly what is your definition of the INTRINSIC (tick rate)
>  The intrinsic rate of the clock never changes. 
Even in the case when you perform experiment C/C2 and the fcc is different?
>  Bottom line: your "common sense" is insufficient to understand what is happening in relativity. 
I would never use the words "common sense". Generally you should perform experiments without any (directly) people involved.
>  A clock is not damaged if it continues ticking at its intrinsic tick rate. 
I will come back to this remark when the meaning of the word intrinsic is clear.
> >  When you first perform test C and than test A and the fcc is different than at least one clock is damaged. 
> 
No. Had you measured each clock's (intrinsic) tick rate, you would have found them to be correct. 
The issue is the definition of damaged. When you supposedly have two identical clocks and when you perform experiment A (both clocks are not "moved") and the fcc is different than at least one clock is damaged.
Nicolaas Vroom
> 
Op donderdag 21 mei 2015 19:01:17 UTC+2 schreef Tom Roberts: 
> > 
On 5/18/15 5/18/15  9:35 PM, Nicolaas Vroom wrote: 
> > > 
It would be interesting to study a hourglas inside a spacecraft. 
> > 
Why? An hourglass is NOT a clock. 
> 
That is the question. What is a clock and what is not a clock. If SR describes all processes and all clocks and if that is the case than it should also describe a hourglass and a pendulum. 
Nick, Tom has explained to you that pendulum clocks by themselves are not clocks because they operate only in an acceleration field. Hourglasses are the same. Ideal clocks keep perfect time within their range of operation. Pendulum clocks and hourglasses are far from perfect even in their range of operation and don't work at all in free fall. The best clocks we have are atomic clocks.
> >  That question is useless, because you cannot move the earth with it. 
> 
Than you cannot perform any experiment with any clock ? (because of the earth) 
The earth, or rather its acceleration field, is PART of hourglasses and pendulum clocks. The earth is NOT part of an atomic clock. That's why they keep excellent time even in orbit.
Gary
> 
In article 
> >  On 5/5/15 9:24 PM, Nicolaas Vroom wrote: 
> > > 
In the book etc. we read: The two postulates: 1. The laws of physics take the same form in all inertial frames. 2. In any given inertial system the velocity of light c is the same whether the light be emitted by a body at rest or by a body in uniform motion. 
> 
The first postulate doesn't tell us what the limiting velocity, if any, is. 
>  Newtonian physics, in which the velocity of a massless particle is infinite, would be compatible with it. 
The above two postulates are not the total picture. In the same book at page 142 is written: Einstein spells out three additional assumptions which are made in this reasoning (See volume 7 doc 50) 3) Homogeneity: the properties of rods and clocks depend neither on position nor on the time at which they move, but only on the way in which they move. 4) Isotropy: the properties of rods and clocks are independent of direction. 5) these properties are also independent of their history. (in the text the 3 assumptions are idicated as 1. 2. and 3.)
Accordingly to Websters a postulate is a statement that is assumed and as such requires no proof of its validity. As such IMO relativity is based on 5 assumptions. The next step is to make testable (observable) predictions using a a common set of "logical" reasoning.
One important issue is that the assumptions should be clear.
IMO all the words or concepts: inertial system, at rest, in (uniform)
motion and properties require a clear definition.
As such assumption 3 should be divided in two assumptions:
3a) the properties of rods depend on the way in which they move.
3b) the properties of clocks depend on the way in which they move.
What does the word property in each instant mean?
Does "on the way in which clocks move" imply that clock count if two
identical clocks move from A to B (at a different path) could be
different?
Assumption 2 can be used to make the following prediction (?):
The speed of light in any inertial sytem is the same in (any)
two opposite directions.
Can this prediction being tested?
Nicolaas Vroom
> 
Nick, Tom has explained to you that pendulum clocks by themselves are not clocks because they operate only in an acceleration field. Hourglasses are the same. Ideal clocks keep perfect time within their range of operation. Pendulum clocks and hourglasses are far from perfect even in their range of operation and don't work at all in free fall. The best clocks we have are atomic clocks. 
Gary. I (almost) 100% agree with you. However the real question is what are ideal clocks. How do you know that they keep perfect time? That is why I raised the 3 question/experiments using two identical clocks. The assumption is that both clocks keep the same time when 1) not moved or 2) both moved together from A to B. The third possibility is that both are moved from A to B accordingly to a different path. The Q is: Do they both keep perfect time? IMO even when you use atomic clocks that is not always the case. IMO when both clocks meet and the time (count) is different than at least one clock does not indicate the perfect time.
If you agree than the next question is: How come? When your answer depents about "range of operation" then you have to explain what you mean. IMO when both clocks meet and the time (count) is different than always different accelerations are involved. (Those different accelerations are the cause that the clocks behave differently)
Nicolaas Vroom
> 
Op maandag 1 juni 2015 13:22:20 UTC+2 schreef Gary Harnagel: 
> > 
Nick, Tom has explained to you that pendulum clocks by themselves are not clocks because they operate only in an acceleration field. Hourglasses are the same. Ideal clocks keep perfect time within their range of operation. Pendulum clocks and hourglasses are far from perfect even in their range of operation and don't work at all in free fall. The best clocks we have are atomic clocks. 
> 
Gary. I (almost) 100% agree with you. However the real question is what are ideal clocks. How do you know that they keep perfect time? 
Hi Nick,
Well, there's no such thing as a perfect clock. USNO provides the time standard and NIST has a bank of atomic clocks. A large number is needed because atomic clocks have a tendency to randomly jump a nanosecond from time to time, and real clocks do have failure modes so you can't count on one particular clock.
>  That is why I raised the 3 question/experiments using two identical clocks. The assumption is that both clocks keep the same time when 1) not moved or 2) both moved together from A to B. 
The standard clocks are indeed "moving together" since the earth is moving. That should take care of that question.
>  The third possibility is that both are moved from A to B accordingly to a different path. The Q is: Do they both keep perfect time? IMO even when you use atomic clocks that is not always the case. IMO when both clocks meet and the time (count) is different than at least one clock does not indicate the perfect time. 
If two clocks travel different paths and then meet, they certainly will not indicate the same elapsed time. You seem to believe that there is some "universal time" a la Newton, but there is only proper time. If you took one bank of clocks (say, 100 of them) down one path and another bank down another path, all the clocks in one bank would agree among themselves but they would disagree with all the clocks in the other bank.
"Perfect" time is nonexistent, unless you want to define that as far from the influence of any gravitational field and "motionless" (whatever that means), but there is no such place.
>  If you agree than the next question is: How come? 
Relativity explains that.
>  When your answer depents about "range of operation" then you have to explain what you mean. 
That has been explained. Atomic clocks work as long as they aren't accelerated beyond 2g. This is a technological problem involving the atomic beam hitting the wall of the clock body instead of remaining in free fall.
>  IMO when both clocks meet and the time (count) is different than always different accelerations are involved. 
That is correct (unless, of course, they never parted from each other).
> 
(Those different accelerations are the cause that the clocks behave
differently)
Nicolaas Vroom 
But that's part of the cause but not the whole story. Half correct is not correct. In SR, distance between clocks when the acceleration occurs affects the outcome. If the distance is zero, there is no time dilation regardless of the acceleration.
Concerning your post to Gerry Quinn, you are correct about assumptions 3, 4 and 5. You might, in fact, add another: v = delta_x/delta_t, but that's more of a definition.
However, I must disagree with Websters. That may be true in mathematics but in physics everything is subject to experimental verification.
Gary
>  Op zaterdag 9 mei 2015 09:21:11 UTC+2 schreef Gerry Quinn: 
> > 
In article 
> > >  On 5/5/15 9:24 PM, Nicolaas Vroom wrote: 
> > > > 
In the book etc. we read: The two postulates: 1. The laws of physics take the same form in all inertial frames. 2. In any given inertial system the velocity of light c is the same whether the light be emitted by a body at rest or by a body in uniform motion. 
> > 
The first postulate doesn't tell us what the limiting velocity, if any, is. 
>  I agree. 
> >  Newtonian physics, in which the velocity of a massless particle is infinite, would be compatible with it. 
>  I do not expect that Newton makes any statement about the speed of a massless particle. 
Sure he does: F = MA. A massless particle subject to a finite force will undergo infinite acceleration. If you integrate the motion of a particle over a finite distance you will find that the terminal velocity rises proportional to the square root of the acceleration, so in the limiting case of infinite acceleration, the velocity would be infinite.
>  Also IMO newton's physics is independent about the speed of light. IMO his assumption is that gravity acts instantaneous. 
Yes. Newton actually knew well that there were problems with instantaneous gravity, but he could not see a way to avoid it.
> 
The above two postulates are not the total picture.
In the same book at page 142 is written: Einstein spells out three
additional assumptions which are made in this reasoning (See volume 7 doc 50) 3) Homogeneity: the properties of rods and clocks depend neither on position nor on the time at which they move, but only on the way in which they move. 4) Isotropy: the properties of rods and clocks are independent of direction. 5) these properties are also independent of their history. (in the text the 3 assumptions are idicated as 1. 2. and 3.) Accordingly to Websters a postulate is a statement that is assumed and as such requires no proof of its validity. As such IMO relativity is based on 5 assumptions. The next step is to make testable (observable) predictions using a a common set of "logical" reasoning. One important issue is that the assumptions should be clear. IMO all the words or concepts: inertial system, at rest, in (uniform) motion and properties require a clear definition. As such assumption 3 should be divided in two assumptions: 3a) the properties of rods depend on the way in which they move. 3b) the properties of clocks depend on the way in which they move. What does the word property in each instant mean? 
What it always means in relativity theory: the result of a measurement that could be made.
>  Does "on the way in which clocks move" imply that clock count if two identical clocks move from A to B (at a different path) could be different? 
Clearly it is intended to allow for that, since Einstein would have noticed if the consequences of his theory were in complete contradiction to one of his postulates!
>  Assumption 2 can be used to make the following prediction (?): The speed of light in any inertial sytem is the same in (any) two opposite directions. Can this prediction being tested? 
Seems reasonably testable. You can set up a coordinated system of clocks at two separate positions, and then fire light beams to and fro, comparing the clock readings for sent and received signals at your leisure. You will find that you measure the same speed whichever way the beam is going.
 Gerry Quinn
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>  On Saturday, June 6, 2015 at 5:24:12 AM UTC6, Nicolaas Vroom wrote: 
> > 
Gary. I (almost) 100% agree with you. However the real question is what are ideal clocks. How do you know that they keep perfect time? 
> 
Hi Nick, Well, there's no such thing as a perfect clock. 
Gary, I agree with you. Science should not use the wording perfect. In that sense "everything" is relatif because you are comparing either different working clocks under the same conditions or "identical" clocks under different conditions.
> >  The third possibility is that both are moved from A to B accordingly to a different path. The Q is: Do they both keep perfect time? IMO even when you use atomic clocks that is not always the case. IMO when both clocks meet and the time (count) is different than at least one clock does not indicate the perfect time. 
>  If two clocks travel different paths and then meet, they certainly will not indicate the same elapsed time. You seem to believe that there is some "universal time" a la Newton, but there is only proper time. If you took one bank of clocks (say, 100 of them) down one path and another bank down another path, all the clocks in one bank would agree among themselves but they would disagree with all the clocks in the other bank. 
which one is correct? Next I perform a test with three banks all going from A to B, accordingly to a different path and I get 1100, 1000 and 900 counts. Which one is "correct"? (or the best) Of course you can answer they are all correct because each behaves as it should behave. IMO the bank (of clocks) which the highest count is the best. All the other clocks are running behind.
> >  If you agree than the next question is: How come? 
> 
Relativity explains that. 
Which do you mean SR or GR? IMO inorder to understand the behaviour of clocks (pendulums) you can use
Newton's Law. IMO to fully understand the behaviour of clocks you should use GR. IMO when you can only use SR to do the same under a rather strict set of limitations i.e. lineair motion.
> >  (Those different accelerations are the cause that the clocks behave differently) 
>  But that's part of the cause but not the whole story. 
>  In SR, distance between clocks when the acceleration occurs affects the outcome. 
>  If the distance is zero, there is no time dilation regardless of the acceleration. 
> 
Concerning your post to Gerry Quinn, you are correct about assumptions
3, 4 and 5. You might, in fact, add another: v = delta_x/delta_t, but
that's more of a definition.
However, I must disagree with Websters. That may be true in mathematics but in physics everything is subject to experimental verification. 
In the book Newton's law by 's Chandrasekbar Chapter 2 Basic Concepts explains 8 definitions and 3 Laws. Law 3 can be stated as: Action is reaction. The text is: This Law is central to proving the important Corollaries IV and V etc. IMO it is not directly necessary to prove the assumptions but it is important that these assumptions lead to predictions which can be verified by means of observations.
Nicolaas Vroom
>  In article <87d4e9b82dc34621a772b5879f88824e@googlegroups.com>, nicolaas.vroom@pandora.be says... 
> > >  Newtonian physics, in which the velocity of a massless particle is infinite, would be compatible with it. 
> >  I do not expect that Newton makes any statement about the speed of a massless particle. 
> 
Sure he does: F = MA. A massless particle subject to a finite force will undergo infinite acceleration. etc 
Studying the book Newton's Principia by s'Chandrasekhar I can not find any mentioning of this. The issue is why should Newton study massless particles ?
> >  Also IMO newton's physics is independent about the speed of light. IMO his assumption is that gravity acts instantaneous. 
> 
Yes. Newton actually knew well that there were problems with instantaneous gravity, but he could not see a way to avoid it. 
> > 
One important issue is that the assumptions should be clear.
IMO all the words or concepts: inertial system, at rest, in (uniform)
motion and properties require a clear definition.
As such assumption 3 should be divided in two assumptions: 3a) the properties of rods depend on the way in which they move. 3b) the properties of clocks depend on the way in which they move. What does the word property in each instant mean? 
> 
What it always means in relativity theory: the result of a measurement that could be made. 
> >  Does "on the way in which clocks move" imply that clock count if two identical clocks move from A to B (at a different path) could be different? 
> 
Clearly it is intended to allow for that, since Einstein would have noticed if the consequences of his theory were in complete contradiction to one of his postulates! 
> >  Assumption 2 can be used to make the following prediction (?): The speed of light in any inertial sytem is the same in (any) two opposite directions. Can this prediction being tested? 
> 
Seems reasonably testable. You "C" can set up a coordinated system of clocks at two separate positions "A" and "B", and then fire light beams to and fro, comparing the clock readings for sent and received signals at your leisure. You "C" will find that you measure the same speed whichever way the beam is going. 
Assuming the observer C is half way between the two clocks at A and B, that means the distance AC and BC is the same and stays the same during the whole experiment. The speed in both (opposite) directions is the same when the arrival times of the two beams is the same at A and B. That means the counts of the clocks at A and B should be the same. In order to do that you first have to synchronise the clocks at A and B. How do you that? by using light signals. That means you use the same strategy to synchronise as to measure the speed, which ofcourse gives the same value in both directions.
The problem this test depents about the position and speed of "C". IMO you should perform a test indepent of "C"
Nicolaas Vroom.
>  Op zaterdag 6 juni 2015 17:21:05 UTC+2 schreef Gerry Quinn: 
> >  In article <87d4e9b82dc34621a772b5879f88824e@googlegroups.com>, nicolaa...@pandora.be says... 
> 
> > > > 
Newtonian physics, in which the velocity of a massless particle is infinite, would be compatible with it. 
> > >  I do not expect that Newton makes any statement about the speed of a massless particle. 
> > 
Sure he does: F = MA. A massless particle subject to a finite force will undergo infinite acceleration. etc 
> 
Studying the book Newton's Principia by s'Chandrasekhar I can not find any mentioning of this. The issue is why should Newton study massless particles ? 
Does he say anywhere that M should be greater than zero?
> > >  One important issue is that the assumptions should be clear. IMO all the words or concepts: inertial system, at rest, in (uniform) motion and properties require a clear definition. As such assumption 3 should be divided in two assumptions: 3a) the properties of rods depend on the way in which they move. 3b) the properties of clocks depend on the way in which they move. What does the word property in each instant mean? 
> > 
What it always means in relativity theory: the result of a measurement that could be made. 
>  For example the length of a rod? But why mention this as an assumption? 
Because in other theories properties could be defined differently. For example, in etherbased theories, the actual length of a rod is reduced when it is in motion with respect to the ether. But this actual length, although it is a property of the object, cannot be measured by any known method.
> > >  Does "on the way in which clocks move" imply that clock count if two identical clocks move from A to B (at a different path) could be different? 
> > 
Clearly it is intended to allow for that, since Einstein would have noticed if the consequences of his theory were in complete contradiction to one of his postulates! 
>  Again also here: Why mention clocks? Newton studies pendulums as a mechanical object, subject of gravity. 
You were the one to mention clocks!
> > >  Assumption 2 can be used to make the following prediction (?): The speed of light in any inertial sytem is the same in (any) two opposite directions. Can this prediction being tested? 
> > 
Seems reasonably testable. You "C" can set up a coordinated system of clocks at two separate positions "A" and "B", and then fire light beams to and fro, comparing the clock readings for sent and received signals at your leisure. You "C" will find that you measure the same speed whichever way the beam is going. 
There were no A, B and C in what I wrote. Please note when posting edited versions of what I say. I did not place A, B and C in equivalent statuses. A and B can be considered measuring devices. C is a scientist, not a measuring device. C studies the results of measurements made at A and B.
> 
Assuming the observer C is half way between the two clocks at A and B,
that means the distance AC and BC is the same and stays the same during
the whole experiment.
The speed in both (opposite) directions is the same when the arrival
times of the two beams is the same at A and B.
That means the counts of the clocks at A and B should be the same.
In order to do that you first have to synchronise the clocks
at A and B. How do you that? by using light signals.
That means you use the same strategy to synchronise as to measure
the speed, which ofcourse gives the same value in both directions.
The problem this test depents about the position and speed of "C". IMO you should perform a test indepent of "C" 
Unless you can find a way to synchronise them with does not ultimately depend on such signals, or other signals which also obey the Lorentz symmetries, then according to relativity theory, your point is irrelevant, because things that can't be measured are not physical properties.
 Gerry Quinn
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W dniu pitek, 5 czerwca 2015 14:59:20 UTC+2 uytkownik Nicolaas Vroom napisa:
>  In the same book at page 142 is written: Einstein spells out three additional assumptions which are made in this reasoning (See volume 7 doc 50) 3) Homogeneity: the properties of rods and clocks depend neither on position nor on the time at which they move, but only on the way in which they move. 4) Isotropy: the properties of rods and clocks are independent of direction. 5) these properties are also independent of their history. (in the text the 3 assumptions are idicated as 1. 2. and 3.) 
These are not any postulates, but a trivial facts, deduced from math directly, ie. from a theory.
>  Does "on the way in which clocks move" imply that clock count if two identical clocks move from A to B (at a different path) could be different? 
Yes. It is independent on the path. The experimantal data show this explicitly, a logics  theory also.
In the SR model it depends on path... because thes model is based on: c = inv, and on some other simplifications/idealisations.
>  Assumption 2 can be used to make the following prediction (?): The speed of light in any inertial sytem is the same in (any) two opposite directions.> Can this prediction being tested? 
Yes, it can be tested, but still superflous because Lorentz theory predicts this: c'(f) = k(c  vcosf) = c/k(1v/c cosf');
therefore the measured twoway speed of light, in the vacuum, is constant: c = inv.
And it's due to the first Lorentz's equation only: x' = k(x  vt); So, we catch at once the whole experimental data, from the 20 century without any superfluous postulates... the strict ans strong math is good enought.
> >  Studying the book Newton's Principia by s'Chandrasekhar I can not find any mentioning of this. The issue is why should Newton study massless particles ? 
> 
Does he say anywhere that M should be greater than zero? 
Newton at page 18 defines the notion of mass as a quantity of matter. Newton defines: quantity of motion = mass * velocity. (IMO) When mass = 0 the body or object does not exist.
> > >  What it always means in relativity theory: the result of a measurement that could be made. 
> >  For example the length of a rod? But why mention this as an assumption? 
> 
Because in other theories properties could be defined differently. For example, in etherbased theories, the actual length of a rod is reduced when it is in motion with respect to the ether. But this actual length, although it is a property of the object, cannot be measured by any known method. 
You make it even more complex. IMO assumption 3 is not very clear. Why not rewrite assumption 3 that the length? and mass? depend on the way in which they move. Of course the last part of this sentence is also not clear.
>  You were the one to mention clocks! 
> > >  You "C" will find that you measure the same speed whichever way the beam is going. 
> 
There were no A, B and C in what I wrote. 
>  Please note when posting edited versions of what I say. I did not place A, B and C in equivalent statuses. A and B can be considered measuring devices. C is a scientist, not a measuring device. C studies the results of measurements made at A and B. 
> > 
Assuming the observer C is half way between the two clocks at A and B,
that means the distance AC and BC is the same and stays the same during
the whole experiment.
The speed in both (opposite) directions is the same when the arrival
times of the two beams is the same at A and B.
That means the counts of the clocks at A and B should be the same.
In order to do that you first have to synchronise the clocks
at A and B. How do you that? by using light signals.
That means you use the same strategy to synchronise as to measure
the speed, which ofcourse gives the same value in both directions.
The problem this test depents about the position and speed of "C". IMO you should perform a test indepent of "C" 
> 
Unless you can find a way to synchronise them with does not ultimately depend on such signals, or other signals which also obey the Lorentz symmetries, then according to relativity theory, your point is irrelevant, because things that can't be measured are not physical properties. 
The problem is my question: how can you test or measure the speed of light in any inertial system in both directions and come to the conclusion that this speed is always the same. Of course if this can not be measured than this becomes a whole different story. You could also claim that this is true by definition i.e. that the speed of light is (physical) the same in both directions. But if that is the case why mention: "in any inertial system".
Nicolaas Vroom
Am 20.06.2015 um 05:41 schrieb Nicolaas Vroom:
>  Op donderdag 11 juni 2015 09:00:42 UTC+2 schreef Gerry Quinn: 
>> 
Does he say anywhere that M should be greater than zero? 
> 
Newton at page 18 defines the notion of mass as a quantity of matter. Newton defines: quantity of motion = mass * velocity. (IMO) When mass = 0 the body or object does not exist. 
Thats the question.
It originated with detection of the duality of the two mathematical concepts of waves and point particles as the possible nature of light.
Fermat Huyghens, Newton, Kirchhoff and even people like Goethe and Schopenhauer engaged in that widely philosophically shaped academic discussion.
The two generic Newtonian equations of motion of point particles m x'' = K = m g for acceleration in static gravity and m x'' = e E for charged particles clearly have simple limits m>0. The first equation is stating universality of gravitation independent of mass, the second aimes to conclude that classes of charged point particles in the limit m>0 should have constant specific charge per mass density.
That idea was the starting point of quantum theory and the redetection of Demokritos' and Leibniz' fundamental concept of the atomism of matter, where the atoms represent the smallest unit having the same physical and chemical identity as a pure macroscopic body composed of them.
In the times of the glorius physical revolution between Maxwell and Heisenberg/Schroedinger the idea of a point particle disappeared together with its velocity and acceleration.
The first doubt was raised by H.A. Lorentz who showed the impossibility to make the relativistic limit for charged point particles to diameter > 0 at fixed e/m.
Today we are left now with a widely algebraically equivalent Hamiltonian canonical picture of position and momentum variables in a quantised wave theory where the mass m is a fixed parameter in the relativistic Einstein wave dispersion relation
(E/c)^2  p^2 == (m c)^2
to be fulfilled at every space time point where E/c and p are the local frequency and wave number in units of hbar.
In this Qtheory mass m (and charge e and spin s) are fixed parameters of a group representation and the limit m>0 cannot be taken on representation spaces.
But representations with m=0, e=0 exist (scalar bosons, neutrinos, photons, gravitons). The limits to be taken are mathematically involved and notoriously difficult to understand.

Roland Franzius
> 
The problem is my question: how can you test or measure the speed of
light in any inertial system in both directions and come to the
conclusion that this speed is always the same.
Of course if this can not be measured than this becomes a whole
different story.
You could also claim that this is true by definition i.e. that the speed
of light is (physical) the same in both directions.
But if that is the case why mention: "in any inertial system".
Nicolaas Vroom 
There is no problem with a lightspeed, because it's: c' = c  v due to the fact: x' = x  vt;
But in a moving frame we measure a different quantity, due to the physical contraction, in a moving system, which rescale the unit of distance, like this: d' = kd, where k = gamma;
hence the Lorentz transform: x' = k(xvt); thus the light =velocity= must be rescaled in the same way: c'_vec = k(c  v)
thus a speed is: c'(f) = k(c  vcosf)
where the angle f is measured in a stationary frame; but we should use f'  the angle in the moving frame, which is: cosf' = ...
and finally the light speed (measured in a moving frame) is eq.: c'(f') = c/k(1v/c cosf'); ... so, we can measure just that quatnity only.
The twoway speed of light, ie. a harmonic mean of the: c'(f') and c'(f'+180) is constant, of course... therefore the SR model  as a very simplified version of the Lorentz's theory.
>  The problem is my question: how can you test or measure the speed of light in any inertial system in both directions and come to the conclusion that this speed is always the same. 
The measurements leading up to the redefinition of the meter in 1983 did precisely that, for all inertial frames occupied by laboratories on earth. As they are rotating and orbiting with the earth, a large number of different inertial frames were sampled, and the accuracy of the measurements was ~ 60,000 times better than the variations in velocities of the frames relative to the solar system rest frame.
Today (post 1983) standards organizations are not interested in measuring the speed of light, as it is a constant used to define the meter.
You may argue that those were all roundtrip measurements. True, but unimportant, because oneway measurements are conventional in that they require one to select an ARBITRARY convention for synchronizing clocks, and the result depends on your ARBITRARY choice.
Using pre1983 standards and modern equipment, direct measurements of the oneway speed of light suffer from large systematic errors, but there are many measurements of the isotropy of the oneway speed of light that are far more accurate; they use slow clock transport for synchronization. The combination of isotropy of oneway propagation and accurate measurements of the roundtrip speed is sufficient to test the various fundamental theories of physics, and the only theories that survive are SR and the other theories that are experimentally indistinguishable from it (none of which are useful or interesting other than historically).
Tom Roberts
>  Op donderdag 11 juni 2015 09:00:42 UTC+2 schreef Gerry Quinn: 
> > >  Studying the book Newton's Principia by s'Chandrasekhar I can not find any mentioning of this. The issue is why should Newton study massless particles ? 
> > 
Does he say anywhere that M should be greater than zero? 
> 
Newton at page 18 defines the notion of mass as a quantity of matter. Newton defines: quantity of motion = mass * velocity. (IMO) When mass = 0 the body or object does not exist. 
We certainly consider that entities with zero mas exist nowadays. I don't know what Newton thought about the issue, though perhaps we could get some clue from considering his various tyhoughts regarding infinitesimals etc. But in any case, it is clearly implicit in his equations that an object of zero mass would gain infinite velocity if impelled by a force. And even if zero mass objects cannot exist, there is no obvious limit on the velocities attainable by objects of very low mass subjected to large forces.
> > > >  What it always means in relativity theory: the result of a measurement that could be made. 
> > >  For example the length of a rod? But why mention this as an assumption? 
> > 
Because in other theories properties could be defined differently. For example, in etherbased theories, the actual length of a rod is reduced when it is in motion with respect to the ether. But this actual length, although it is a property of the object, cannot be measured by any known method. 
> 
You make it even more complex. IMO assumption 3 is not very clear. Why not rewrite assumption 3 that the length? and mass? depend on the way in which they move. Of course the last part of this sentence is also not clear. 
I would see assumption 3 as just partial. To say that length and mass do not depend on position or time is not to imply that they must necessarily vary with velocity.
> > >  The problem this test depents about the position and speed of "C". IMO you should perform a test indepent of "C" 
> > 
Unless you can find a way to synchronise them with does not ultimately depend on such signals, or other signals which also obey the Lorentz symmetries, then according to relativity theory, your point is irrelevant, because things that can't be measured are not physical properties. 
> 
The problem is my question: how can you test or measure the speed of light in any inertial system in both directions and come to the conclusion that this speed is always the same. Of course if this can not be measured than this becomes a whole different story. 
If you adopt the philosophy that what cannot be measured is not real, then there is no difference. My view is that the philosophy is justified by what we know of quantum theory. [That is not to imply that quantum theory says that the vacuum in principle cannot have a state of motion; our failure so far to find a way to detect any such motion is a matter of observation rather than theory.]  show quoted text 
>  We certainly consider that entities with zero mas exist nowadays. I don't know what Newton thought about the issue, though perhaps we could get some clue from considering his various thoughts regarding infinitesimals etc. But in any case, it is clearly implicit in his equations that an object of zero mass would gain infinite velocity if impelled by a force. And even if zero mass objects cannot exist, there is no obvious limit on the velocities attainable by objects of very low mass subjected to large forces. 
Reading the previous mentioned book objects of zero mass are no issue for Newton. At page 236 we read: "If the masses m1,m2,m3 etc are sufficiently tiny (compared to M) then the center of gravity will not be sensibly different from the location of M, which may, then, be considered to be at rest or moving uniformly forward in a right line; and about which the lesser bodies will revolve."
One of the most amazing chapters is #10 "On revolving orbits" In this chapter he discusses different "Laws of force". In example 1 (page 194) the situation close to the movement of the planet Mercury is discussed. Truly amazing.
> >  The problem is my question: how can you test or measure the speed of light in any inertial system in both directions and come to the conclusion that this speed is always the same. Of course if this can not be measured than this becomes a whole different story. 
> 
If you adopt the philosophy that what cannot be measured is not real, then there is no difference. 
>  My view is that the philosophy is justified by what we know of quantum theory. 
Nicolaas Vroom
>  On 6/19/15 6/19/15 10:41 PM, Nicolaas Vroom wrote: 
> >  The problem is my question: how can you test or measure the speed of light in any inertial system in both directions and come to the conclusion that this speed is always the same. 
> 
The measurements leading up to the redefinition of the meter in 1983 did precisely that, for all inertial frames occupied by laboratories on earth. 
How did they measure the speed in one direction ? I think it is rather difficult to measure the speed of light in a laboratory accurately, with the emphasis on accurate.
>  Today (post 1983) standards organizations are not interested in measuring the speed of light, as it is a constant used to define the meter. 
I can understand that you define the speed of light as a constant. However that is only a part of the problem. The first question is: is the speed of individual photons everywhere the same? Is the speed the same at "my" position as near a blackhole? The second question is when you draw a space time diagram, Is the space diagram the same at "my" position as on a moving train from the position of an observer on the moving train. See: https://en.wikipedia.org/wiki/Relativity_of_simultaneity#Spacetime_diagrams or: https://en.wikipedia.org/wiki/Relativity_of_simultaneity#/media/File:TrainAndPlatformDiagram1.svg
To be more specific: Is it always correct to draw the light lines at the same angle in both directions.
>  Using pre1983 standards and modern equipment, direct measurements of the oneway speed of light suffer from large systematic errors, but there are many measurements of the isotropy of the oneway speed of light that are far more accurate; they use slow clock transport for synchronization. 
As I wrote before there are three types of tests with identical clocks
in relation to their clock counts:
1) They both stay at the same position A (IMO the counts are the same)
2) They both are moved together from A to B (IMO the counts are the same)
3) They both are moved along different paths (length) from A to B
(IMO the clock counts (in general) are different)
4) A specific case is when the points A and B are the same and when
one clock stays at home.
(IMO the clock counts of the moving clock will be the least)
5) There is also a fifth test.
One clock #1 stays at point A.
A second clock is moved from point A to point B and back to A along
the same path at high speed. (the counts of #1 and #2 will be different)
A third clock follows exactly the same path as #2 but very slowly.
The issue are the counts of clock #1 and #3 the same or different.
(at point A)
The problem is even when the clock counts are the same, you are not sure if that is the case for the whole trip nor what the clock count is of clock #1 (at point A) when clock #3 is at point B. (is this correct ?)
Nicolaas Vroom
>  Op zaterdag 20 juni 2015 21:45:03 UTC+2 schreef Tom Roberts: 
>>  On 6/19/15 6/19/15 10:41 PM, Nicolaas Vroom wrote: 
>>>  The problem is my question: how can you test or measure the speed of light in any inertial system in both directions and come to the conclusion that this speed is always the same. 
>>  The measurements leading up to the redefinition of the meter in 1983 did precisely that, for all inertial frames occupied by laboratories on earth. 
> 
How did they measure the speed in one direction ? 
They didn't. They measured the speed over a roundtrip laboratory path (in vacuum), and verified isotropy in many different OTHER experiments. The many different roundtrip measurements were accurate to better than 1 m/s, and did not vary significantly over the location, year, month, or day.
>  I think it is rather difficult to measure the speed of light in a laboratory accurately, with the emphasis on accurate. 
Not at all. The accuracy back then was a few parts per billion; could do better today, but:
>>  Today (post 1983) standards organizations are not interested in measuring the speed of light, as it is a constant used to define the meter. 
> 
I can understand that you define the speed of light as a constant. However that is only a part of the problem. 
WHAT "problem"??? The definitions as of 1983 have proven to be robust and useful.
OK, YOU seem to have a problem understanding this. The only cure is to STUDY. Your "20 questions" approach here is USELESS. Get a good textbook; I recommend: Misner, Thorne, and Wheeler, _Gravitation_.
>  The first question is: is the speed of individual photons everywhere the same? 
If you actually knew what photons are, you would know that this question is meaningless. We measure the speed of LIGHT PULSES, not "individual photons".
In our best theory of all this, GR, the LOCAL speed of LIGHT PULSES (in vacuum) is indeed everywhere the same. And in all places we have managed to measure it, the measurements are consistent with this prediction.
>  Is the speed the same at "my" position as near a blackhole? 
Nobody has ventured near a black hole to measure. But in our only theory that describes black holes, GR, the LOCAL speed of light is equal to c EVERYWHERE, including near and even inside a black hole.
>  The second question is when you draw a space time diagram, Is the space diagram the same at "my" position as on a moving train from the position of an observer on the moving train. 
The diagrams themselves are of course the same, but the objects depicted in them can be displayed in different places, with different orientations. This is no different from "left" to you being "right" to me as we face different directions  remember that in relativity, relative motion is a change in orientation (in spaceTIME) as well as a (timedependent) change in (relative) position.
>  Is it always correct to draw the light lines at the same angle in both directions. 
Yes, as long as the diagram is drawn from the perspective of an inertial frame, and as long as the diagram is no larger than the domain of validity of that frame's coordinates.
>  [... more questions too complicated to parse] 
Tom Roberts
>  Op zaterdag 27 juni 2015 22:26:39 UTC+2 schreef Gerry Quinn: 
> >  If you adopt the philosophy that what cannot be measured is not real, then there is no difference. 
>  If you cannot measure what the proposition describes than you cannot validate the proposition. 
Not relevant if from your philosophical perspective the proposition (a 'true' eachway velocity that cannot be measured by any means) is meaningless! Meaningless propositions are neither susceptible to validation, nor needful of it.
It is perfectly legitimate to adopt another perspective in which the proposition is meaningful  this leads us to etherlike interpretations along the lines proposed by Lorentz and Poincare. If our physical intuitions invoke a prequantum world, in which every phenomenon must be explicable in terms of the workings of constituent local mechanisms, and counterfactual definiteness is a given, this approach is very attractive. For example, in this approach there is no such thing as the 'twin paradox'  regardless of the twins' motions, the aging of each twin is controlled at all times simply by his velocity with respect to the ether, and no other factor need be considered at all.
Unfortunately it's rather clear that we do not in fact live in such a world. In the world we live in, it has been demonstrated that quantities we choose not to measure are not meaningful, even if we could have measured them had we wanted to. For example, when we set up a two slit experiment, "the slit the particle goes through" is something we can measure if we choose, by monitoring one or both slits. But if we don't choose to monitor that, and we send a large number of particles through, the resulting distribution will be consistent only with the idea that each particle in some sense goes through both slits. Because we did not measure which slit, the question of 'which slit' has become meaningless.
In such a world, the existential status of something that we not only do not measure, but do not know how to measure, is precarious!
> >  My view is that the philosophy is justified by what we know of quantum theory. 
>  Certain aspects of the quantum theory are also different to measure i.e. to validate, but that is not the subject here. 
What parts of the quantum theory are asserted to be measureable, but cannot be measured?  show quoted text 
On Monday, July 6, 2015 at 1:56:45 AM UTC4, Gerry Quinn wrote:
> > >  My view is that the philosophy is justified by what we know of quantum theory. 
> 
> > 
Certain aspects of the quantum theory are also different to measure i.e. to validate, but that is not the subject here. 
> 
What parts of the quantum theory are asserted to be measureable, but cannot be measured? 
Hi Gerry
"Meaningless propositions are neither susceptible to validation, nor needful of it."
Well said.
Would like to touch on developmental psychology with respect to the 2 postulates.
There are two general types in science. A Faraday and an Oppenheimer.
A Faraday will compare the postulate with the math to verify the math. The postulates are of greater importance. I will venture a guess at 12 he required cloves tied to coat sleeves to keep them from being lost. Forgetful is the key leading to an intuitive thinker later in life.
An Oppenheimer will compare the math with the postulates to verify the postulates. The math is of greater importance. Oppy has no need for cloves tied to sleeves as they are in a draw organize chronologically. A well organized mind that is not forgetful is the key.
I would put myself in the Faraday camp. The postulates are heart of special relativity. If it turned out the math in SR is wrong then one simply corrects the math somewhat like a spelling mistake. It is the postulates that may not be violated.
This placers a greater burden on us. Dr Einstein could not violate Newtonian physics in 1905 as he would no longer have a floor to stand on. When the last dot was put on SR Newtonian physics was not violated with regards to energy and arrival times for a given frame of reference. Both theories render the same answer. This makes SR foundational to Newtonian physics. From a physics foundational position we today can not violate the two postulates as we will no longer have a floor to stand on in the same way Dr Einstein could not violate Newtonian physics.
> 
My understanding is that when there is curvature involved there
is also mass involved implying that you come in the region which
is described by GR and where light rays do not follow straight lines.
IMO to calculate the speed of light under such conditions is tricky. 
It's much worse than merely "tricky", it is AMBIGUOUS and therefore not well defined.
Consider a simple oneway measurement of the speed of light from a mountaintop to the adjacent valley, using two (ideal) clocks, neglecting air. The clocks must be synchronized, so imagine you do that using a light ray. Obviously if you make the measurement immediately thereafter, you will obtain c. Wait a while, and you will obtain a value smaller than c (due to the relative drift of the clocks due to "gravitational redshift"). Wait long enough, and you will obtain a NEGATIVE result! Use the same endpoints but measure in the other direction, and you can obtain an arbitrarily large answer!
That is why when physicists measure a speed, they always intend the measurement to be made in a locally inertial frame. The size of that frame, of course, depends on both the local curvature of spacetime and the measurement accuracy. For marathons and auto races this doesn't matter; for measuring the speed of light it can.
Note, however, if the two endpoints are on earth's geoid, then the measurement will be independent of time, even though the path is the same length as before. It would be disingenuous to claim this uses SR  one must apply GR, and for this case it predicts the constant value c.
But if one measures in a lab over a horizontal path of a few meters, then one CAN apply SR  a locally inertial (free falling) frame that is at rest with the apparatus when the measurement begins will fall much less than the measurement accuracy during the few nanoseconds of the measurement.
>  Of course the simplest solution is to declare the speed of light constant. 
HUH??? That is no "solution" at all.
Of course physicists don't do that  the constancy of the speed of light applies to SR, not GR, and SR is only APPROXIMATELY valid, and only in a locally inertial frame; the maximum size of that frame, of course, depends on both the local curvature of spacetime and the measurement accuracy.
>  If you cannot use GR what than? 
Then YOU must find another hobby.... Those of us who do this sort of thing for a living can and will use GR. Most likely in an appropriate approximation, of course.
Tom Roberts
>  On 8/4/15 8/4/15 7:48 AM, Nicolaas Vroom wrote: 
> >  IMO to calculate the speed of light under such conditions is tricky. 
> 
It's much worse than merely "tricky", it is AMBIGUOUS and therefore not well defined. Consider a simple oneway measurement of the speed of light from a mountaintop to the adjacent valley, using two (ideal) clocks, neglecting air. The clocks must be synchronized, so imagine you do that using a light ray. 
Just some thoughts. IMO this synchronisation process is already rather complex. IMO the mountaintop should issue a light signal at regular intervals. You get than a string like 6, 8, 10, 12 and 14. The next step is to record the arrival times of these signals at the valley clock. You could get than a string like 11, 13, 15, 17 and 19. (A) But also You could get than a string like 11, 12.9, 14.8, 16.7 and 18.6 (B) In case B the valley clock runs faster, which have to adjusted to take care that both clocks run at the same rate. After this adjustment the time to go from top to valley is always the same, which it physical should be. The next step consists of two parts: You must first reflect the received valley signals back to the top. You get a string like 10, 12, 14, 16 and 18 Secondly you must adjust the valley clocks such that their readings are a string like: (6+10)/2 = 8, 10, 12, 14 and 16 Now the clocks are synchronised?
However you do not know if the speed is constant during the whole trip. To test that you have to repeat the same process half way between top and valley.
>  That is why when physicists measure a speed, they always intend the measurement to be made in a locally inertial frame. 
But if you perform such a test at a locally inertial frame at the top and a second time at a locally inertial frame at the valley and the speeds are different what is the point of declaring the speed of light constant?
See also you posting at 20 June 2015: "Today (post 1983) standards organizations are not interested in measuring the speed of light, as it is a constant used to define the meter."
> >  Of course the simplest solution is to declare the speed of light constant. 
> 
HUH??? That is no "solution" at all. 
I agree
>  Of course physicists don't do that  the constancy of the speed of light applies to SR, not GR, and SR is only APPROXIMATELY valid, and only in a locally inertial frame; the maximum size of that frame, of course, depends on both the local curvature of spacetime and the measurement accuracy. 
The problem is what I want to do is to simulate the movements of the planets around the sun, specific the planet Mercury. Also I want to calculate a Galaxy Rotation Curve. In both cases I want to see what is involved when I use GR. Apperently SR is out of the question, including the two (five) postulates on which it is based. The question than remains: what is the purpose of SR?
> >  If you cannot use GR what than? 
> 
Then YOU must find another hobby.... 
>  Those of us who do this sort of thing for a living can and will use GR. Most likely in an appropriate approximation, of course. 
If you start from one mutual agreed reference frame and if you do not use moving clocks (after synchronisation) things are becoming simpler.
IMO one important question to answer is what is the function of the speed of light (ie photons) in relation to the laws of nature i.e. GR. This question is specific important in relation to dark matter.
Nicolaas Vroom
Nicolaas Vroom wrote:
>  Just some thoughts. IMO this synchronisation process is already rather complex. IMO the mountaintop should issue a light signal at regular intervals. You get than a string like 6, 8, 10, 12 and 14. The next step is to record the arrival times of these signals at the valley clock. You could get than a string like 11, 13, 15, 17 and 19. (A) But also You could get than a string like 11, 12.9, 14.8, 16.7 and 18.6 (B) In case B the valley clock runs faster, which have to adjusted to take care that both clocks run at the same rate. After this adjustment the time to go from top to valley is always the same, which it physical should be. 
What do you mean with "time to go from top to valley"? The time a signal takes to run from top to valley? In GR, this time can mean the proper time of the signal (what is zero in the case of a light signal) or the coordinate time interval in some coordinate system. The coordinate time interval is, assumed the coordinate system is time translation invariant like Schwarzschild coordinates are, always the same, fully independent from adjustments of the valley clock.
>  The next step consists of two parts: You must first reflect the received valley signals back to the top. You get a string like 10, 12, 14, 16 and 18 Secondly you must adjust the valley clocks such that their readings are a string like: (6+10)/2 = 8, 10, 12, 14 and 16 Now the clocks are synchronised? 
The clocks are synchronized in Schwarzschild coordinates if both run with the same running speed with respect to Schwarzschild coordinate time and show the same clock time at the same Schwarzschild coordinate time. I.e. on any spacelike hypersurface defined by t = const, where t is Schwarzschild coordinate time, they must show the same clock time.
The division by 2 in your procedure sounds as if you want to apply SR clock synchronization that assumes a constant speed of light. Since the speed of light with respect to Schwarzschild coordinates is not constant, your procedure will probably fail.
>  However you do not know if the speed is constant during the whole trip. 
Applying the Schwazschild solution, you know that the speed of light is not constant with respect to Schwarzschild coordinates.
>>  That is why when physicists measure a speed, they always intend the measurement to be made in a locally inertial frame. 
> 
But if you perform such a test at a locally inertial frame at the top and a second time at a locally inertial frame at the valley and the speeds are different 
No, they are not. The speeds measured in the particular local inertial frame are the same, namely c. Only the speeds indicated in a coordinate like Schwarzschild coordinates are different.
More mathematically: take two clocks A and B that are radially free falling. For each clock, you take a small spacetime region, so small that you can approximate each clock as resting in Schwarzschild coordinates, i.e. dr/dt = 0, where r ist Schwarzschild radial coordinate. So, in the particular spacetime region, you can imagine clock A as resting at radial coordinate rA, clock B at rB.
Now take a light ray passing clock A radially. In Schwarzschild coordinates, the speed of the light ray is
dr/dt = (1  rs/rA) c (1)
Now let's calculate the speed of that light ray in the local inertial frame of clock A. To do so, we at first have to calculate the proper time interval d(tauA) elapsing for clock A during the Schwarzschild coordinate time interval dt. We get
d(tauA) = sqrt(g_tt(rA)) = sqrt(1  rs/rA) dt
with g_tt(rA) = 1  rs/rA being the ttcomponent of the metric tensor in Schwarzschild coordinates at r = rA. Next, we need to calculate the spatial distance d(lA) in clock A's local inertial frame between the points rA and rA + dr between which the light ray is travelling during the Schwarzschild coordinate time interval dt. We get
d(lA) = sqrt(g_rr(rA)) = dr / sqrt(1  rs/rA)
with g_rr(rA) = 1/(1  rs/rA) being the rrcomponent of the metric tensor in Schwarzschild coordinates at r = rA. For dr, we insert (1):
dr = (1  rs/rA) c dt
=> d(lA) = (1  rs/rA) c dt / sqrt(1  rs/rA)
= sqrt(1  rs/rA) c dt
To get now the speed of light in the local inertial frame of clock A, we need to calculate
d(lA) / d(tauA) = sqrt(1  rs/rA) c dt / sqrt(1  rs/rA) dt
= c
So, in the local inertial frame of clock A, the speed of that light ray is c.
The procedure we apply to clock B: the speed of a light ray passing clock B radially is in Schwarzschild coordinates:
dr/dt = (1  rs/rB) c (2)
The elapsing proper time on clock B is
d(tauB) = sqrt(g_tt(rB)) = sqrt(1  rs/rB) dt
and the spatial distance in clock B's local inertial frame
d(lB) = sqrt(g_rr(rB)) = dr / sqrt(1  rs/rB)
We again insert (2):
d(lB) = sqrt(g_rr(rB)) = (1  rs/rB) c dt / sqrt(1  rs/rB)
= sqrt(1  rs/rB) c dt
and calculate the speed of the light ray in clock B's local inertial frame:
d(lB) / d(tauB) = sqrt(1  rs/rB) c dt / sqrt(1  rs/rB) dt
= c
We again get c as speed.
In other words: the speed of light slows down in Schwarzschild coordinates when r is decreasing, but clocks of local inertial frames are slowing down, too, with respect to Schwarzschild coordinate time, and in combination with the effects of spatial curvature, expressed by g_rr, this provides that the speed of light remains the same, namely c, in all local inertial frames.
In fact, the causality of GR is the other way round: the constancy of the speed of light in all local inertial frames is the fundamental principle, and the slowing down of the speed of light with respect to Schwarzschild coordinates in Schwarzschild solution is derived from that.
And it is important to note, that the speed of light in local inertial frames is, compared to the speed of light in Schwarzschild coordinates, the more fundamental one. Schwarzschild coordinates are just an arbitrarily chosen coordinate system, one could as well chose various different coordinate systems, like one does in the case of black holes, e.g. EddingtinFinkelstein coordinates, freefalling coordinates, or Kruskal coordinates, that yield totally different speeds of light.
>>  Of course physicists don't do that  the constancy of the speed of light applies to SR, not GR, and SR is only APPROXIMATELY valid, and only in a locally inertial frame; the maximum size of that frame, of course, depends on both the local curvature of spacetime and the measurement accuracy. 
> 
The problem is what I want to do is to simulate the movements of the planets around the sun, specific the planet Mercury. Also I want to calculate a Galaxy Rotation Curve. In both cases I want to see what is involved when I use GR. Apperently SR is out of the question, including the two (five) postulates on which it is based. 
In GR, the postulate of the constancy of the speed of light remains valid in that way that the speed of light measured in local inertial frames is constant.
>  The question than remains: what is the purpose of SR? 
Describing situation where gravity can be neglected.
>>>  If you cannot use GR what than? 
>> 
Then YOU must find another hobby.... 
>  I'm too old to learn fishing. 
>> 
Those of us who do this sort of thing for a living can and will use GR. Most likely in an appropriate approximation, of course. 
>  Of course if you remove too much, is it than still GR or does it become Newton+ 
That depends on how much too much is.
>  If you start from one mutual agreed reference frame and if you do not use moving clocks (after synchronisation) things are becoming simpler. 
If you want to use reference frames in a regime ruled by gravity, then you cannot use GR. But why don't you simply use GR and accept that you have to use coordinate systems instead of inertial frames?
And: your desire to use reference frames but not to use moving clocks, seems a little strange. Usually, using reference frames is combined with using moving clocks.
>  IMO one important question to answer is what is the function of the speed of light (ie photons) in relation to the laws of nature i.e. GR. 
I'm not sure whether I can make any sense in this question. In coordinate systems in which the speed of light is not constant, e.g. Schwarzschild coordinates in Schwarzschild solution, you can write the speed of light as function of some parameters, like r in the case of Schwarzschild coordinates:
v(r) = (1  rs/r) c
Or did you rather want to ask in what way the postulate of the constancy of the speed of light from SR remains valid in GR?
>  Op woensdag 5 augustus 2015 21:38:22 UTC+2 schreef Tom Roberts: 
>>  On 8/4/15 8/4/15 7:48 AM, Nicolaas Vroom wrote: when physicists measure a speed, they always intend the measurement to be made in a locally inertial frame. 
> 
But if you perform such a test at a locally inertial frame at the top and a second time at a locally inertial frame at the valley and the speeds are different what is the point of declaring the speed of light constant? 
If the speeds were measurably different then you would have refuted GR in a rather big way. To date that has not happened, and most physicists would give rather long odds that this sort of refutation won't ever happen.
>  The problem is what I want to do is to simulate the movements of the planets around the sun, specific the planet Mercury. 
Using Newtonian gravitation (NG) this is simple if you ignore the other planets, but quite complicated if you include them (and you must include them if you want accuracy [#]).
[#] e.g. sufficient accuracy to see the difference between NG and GR.
>  Also I want to calculate a Galaxy Rotation Curve. 
Let's not discuss this now, there's too much else on the table. (But this is VERY different from the solar system calculations.)
>  In both cases I want to see what is involved when I use GR. 
Using NG for the solar system is already quite complicated; AFAIK nobody has used GR for this, as that is far too complicated. What people actually do is use the postNewtonian (or postpostNetonian) approximation to GR. This is more complicated than using NG alone, but is tractable. Note, however, that programs to calculate the solar system at this level have been developed over many staffyears by experts; you have a long and arduous road ahead.... And a lot to learn....
>  what is the purpose of SR? 
It was a VERY important step on the road to GR. And since GR is so complicated to apply, SR remains quite useful in situations in which gravitation can be neglected.
Consider the LHC experiments. Each is in a cavern less than 100 meters large, and all the particles of interest travel with speed > 0.99 c relative to the cavern. So let's apply SR in the locally inertial frame that is at rest relative to the cavern at the instant of the crossing (the interaction that produces the particles of interest). Within 300 ns all the particles have left the cavern and can no longer be observed by the detector. During 300 ns that locally inertial frame falls 0.5 g t^2 = 4.4E12 meters. The detectors have resolutions on the order of a micron or more, so the error in assuming the detector is at rest in an inertial frame is FAR below the experimental resolution  SR can be used without problem. (A calculation for the rotation of the earth yields an error that's even smaller than this.)
>  IMO one important question to answer is what is the function of the speed of light (ie photons) in relation to the laws of nature... 
I suspect it has essentially no role at all in fundamental physical phenomena. That's because all such phenomena appear to be LOCAL (<< 1E6 meters), so the propagation of light is just irrelevant.
>  ... i.e. GR. 
Most physicists doubt very much that GR is a "law of nature". It seems MUCH more likely that it is merely an approximation to something more fundamental. But the jury is still out....
Tom Roberts
> 
Nicolaas Vroom wrote: 
> > 
Just some thoughts. IMO this synchronisation process is already rather complex. IMO the mountaintop should issue a light signal at regular intervals. You get than a string like 6, 8, 10, 12 and 14. 
Skip
>  What do you mean with "time to go from top to valley"? The time a signal takes to run from top to valley? In GR, this time can mean the proper time of the signal (what is zero in the case of a light signal) or the 
Skip
It is important to remember that my posting is a reply on the following posting by Tom Roberts:
>  Op woensdag 5 augustus 2015 21:38:22 UTC+2 schreef Tom Roberts: 
>>  On 8/4/15 8/4/15 7:48 AM, Nicolaas Vroom wrote: 
>> >  IMO to calculate the speed of light under such conditions is tricky. 
>> 
It's much worse than merely "tricky", it is AMBIGUOUS and therefore not well defined. Consider a simple oneway measurement of the speed of light from a mountaintop to the adjacent valley, using two (ideal) clocks, neglecting air. The clocks must be synchronized, so imagine you do that using a light ray. 
What I try to do is answer the question is the speed of light constant. To do that let me first define a simple experiment. The experiment consists of dropping a ball from the Tower of Pisa, which bounches back. The objective is to measure the time when the ball reaches its highest point. In order to measure this time I use a small ball which bounces between two horizontal plates. The total number of counts (bounces) is 10. Next I perform the same experiment but I use half the distance. The total number of counts is 7. That means for the first part the number of counts is 7 and for the second part 3. My reasoning the speed of the ball is not constant. Is this correct?
The second experiment is physical identical as above but instead of a ball I use a light ray which is reflected. To measure the time I also use a light ray between two mirrors. The results are totally different but suppose I get for the total count 2000 and for the first part 1001. That means for the second part 999. Is this feasible? My conclusion is the same: The speed of light is not constant. Is this correct?
> >  The question than remains: what is the purpose of SR? 
> 
Describing situation where gravity can be neglected. 
Interesting. My impression is that in all (?) experiments in the realm of SR gravity is involved. (moving clocks in airplane) That means (My impresion) you can describe each of these experiments also without SR and only solely with GR. or is this wrong reasoning?
Nicolaas Vroom
>  On 8/12/15 8/12/15 5:05 AM, Nicolaas Vroom wrote: 
> > 
The problem is what I want to do is to simulate the movements of the planets around the sun, specific the planet Mercury. 
> 
Using Newtonian gravitation (NG) this is simple if you ignore the other planets, but quite complicated if you include them (and you must include them if you want accuracy [#]). 
[[Mod. note  Note that as well as "all" the planets, you probably want lots of moons and asteroids, too.  jt]]
The problem is the perihelion shift of Mercury of 43 arc sec. You can also use NG as a bassis to solve that, but than you have to modify NG and take into account that gravity does act instantaneous.
> >  Also I want to calculate a Galaxy Rotation Curve. 
> 
Let's not discuss this now, there's too much else on the table. (But this is VERY different from the solar system calculations.) 
See for example: http://users.telenet.be/nicvroom/VB%20Gal%20Mond%20operation.htm The purpose of the Visual Basic "VB Gal MOND" is to simulate a Galaxy starting from the Galaxy Rotation Curve. That means first the mass distribution is calculated and than the Galaxy is simulated.
The purpose of the program is primarily to compare NG with MOND. What the program shows that with MOND there is no mass in the disc in that part where the rotation curve is flat. That you cannot use MOND to simulate our Solar system.
> >  In both cases I want to see what is involved when I use GR. 
> 
Using NG for the solar system is already quite complicated; 
>  AFAIK nobody has used GR for this, as that is far too complicated. 
>  What people actually do is use etc. 
[[Mod. note  What people actually do use is a very good approximation to GR called the Parameterized PostNewtonian (PPN) Formalism. This is basically a Taylorseries expansion of GR about the flat metric. This is described in detail in sections 3 and 4 of Clifford M. Will's article "The Confrontation between General Relativity and Experiment" (Living Reviews in Relativity, 2014, free online at http://relativity.livingreviews.org/Articles/lrr20144/fulltext.html
Another very good description, with lots of details on how the actual tests are done, is an oldbutverygood conference paper, Ronald W Hellings "Testing Relativity with Solar System Dynamics" p.365385 in... B Bertotti, F. de Felice, and A. Pascolini "General Relativity and Gravitation" [Invited Papers and Discussion Reports of the 10th International Conference on General Relativity and Gravitation, Padua (Italy), 38 July 1983] Reidel, Dordrecht (Holland), 1984 ISBN 9027718199  jt]]
> >  what is the purpose of SR? 
> 
It was a VERY important step on the road to GR. And since GR is so complicated to apply, SR remains quite useful in situations in which gravitation can be neglected. 
My question is specific in relation to the simulation of the solar system, a galaxy, the universe in total.
> >  IMO one important question to answer is what is the function of the speed of light (ie photons) in relation to the laws of nature... 
> 
I suspect it has essentially no role at all in fundamental physical phenomena. That's because all such phenomena appear to be LOCAL (<< 1E6 meters), so the propagation of light is just irrelevant. 
Again in relation to the simulation of the Solar system, a galaxy the Universe
A different document to study is this: http://users.telenet.be/nicvroom/galaxy%20simulation.htm
> >  ... i.e. GR. 
> 
Most physicists doubt very much that GR is a "law of nature". It seems MUCH more likely that it is merely an approximation to something more fundamental. But the jury is still out.... 
and what about SR, Newton's Law and MOND
>  Tom Roberts 
thanks.
Nicolaas Vroom
>  What I try to do is answer the question is the speed of light constant. 
This question is not precise enough. When talking about a speed in GR, you have to distinguish between the speed measured in a local inertial frame and the speed measured in a coordinate system. The description you provide below indicates that you refer to the speed measured in a coordinate system (for more details see below). For the speed of light, this indeed implies that it is not constant, unlike the speed of light measured in a local inertial frame that remains constant in GR.
>  To do that let me first define a simple experiment. The experiment consists of dropping a ball from the Tower of Pisa, which bounches back. The objective is to measure the time when the ball reaches its highest point. In order to measure this time I use a small ball which bounces between two horizontal plates. The total number of counts (bounces) is 10. Next I perform the same experiment but I use half the distance. The total number of counts is 7. That means for the first part the number of counts is 7 and for the second part 3. My reasoning the speed of the ball is not constant. 
Your descrption implies that you define a coordinate system, with the following properties:
(1) The top and the ground of the Tower have fixed spatial coordinates
(2) The elapsing coordinate time is proportional to the number of bounces of the bouncing ball between the plates.
(3) Time translation invariance applies: the coordinate time interval that the ball takes for the trip from top to ground is the same as the coordinate time interval the ball takes for the backtrip from ground to top.
The speed of the ball measured in that coordinate system is not constant, that is correct.
>  The second experiment is physical identical as above but instead of a ball I use a light ray which is reflected. To measure the time I also use a light ray between two mirrors. The results are totally different but suppose I get for the total count 2000 and for the first part 1001. That means for the second part 999. Is this feasible? My conclusion is the same: The speed of light is not constant. 
Measured with respect to the coordinate system that you apply here, which is the same coordinate system as in the ball version of the experiment, the speed of light is not constant, that is correct.
However, that speed of light is not "the speed of light". It is just the speed of light *in the coordinate system you have chosen*. In GR, the choice of the coordinate system is arbitrary, instead of the coordinate system that you applied above you could as well choose any other coordinate system, e.g. one in which the speed of light turns out to be constant for your experiment. Due to this, the speed of light in the currently chosen coordinate system is an arbitrary quantity in GR and therefore not very meaningful.
A rather meaningful indication of the speed of light is the indication with respect to a local inertial frame. That speed of light is always constant in GR. In your experiment, you can apply a local inertial frame at the top of the Towever, and you will find the speed of light constant. You can apply a different local inertial frame at the middle of the tower, and you will find the speed of light constant again. Finally, you can apply another local inertial frame at the bottom of the tower, and you will find the speed of light constant another time.
What is not possible, though, is to apply the same local inertial frame for the whole trip from top to bottom, since the corresponding spacetime region is not sufficiently limited.
>>>  The question than remains: what is the purpose of SR? 
>> 
Describing situation where gravity can be neglected. 
> 
Interesting. My impression is that in all (?) experiments in the realm of SR gravity is involved. (moving clocks in airplane) 
The HafeleKeating experiment to which you seem to be referring indeed did not test the effects of SR on their own, but rather the combined effects of SR and GR.
However, there have been different experiments where GR effects were not relevant. Take e.g. experiments in particle accelerators. Since all parts of an accelerator are at the same height with respect to the ground, differences in gravitational field are out of relevance. Or take muon experiments. The muons are changing in height, though, but the gravitational time dilation effects are neglectible compared to the SR time dilation due to the high speed of the muons.
>  Nicolaas Vroom wrote: 
> > 
What I try to do is answer the question is the speed of light constant. 
> 
This question is not precise enough. 
I think that my question is rather simple ? Is the speed of light (the speed of the photons) in the universe everywhere the same and if not what is the physical cause.
>  When talking about a speed in GR, you have to distinguish between the speed measured in a local inertial frame and the speed measured in a coordinate system. 
>  The description you provide below indicates that you refer to the speed measured in a coordinate system (for more details see below). For the speed of light, this indeed implies that it is not constant, unlike the speed of light measured in a local inertial frame that remains constant in GR. 
My suggestion is to define your experiment which demonstrates that the speed of light is constant. By preference you should not include any moving clock.
> >  My reasoning the speed of the ball is not constant. 
> 
skip
>  The speed of the ball measured in that coordinate system is not constant, that is correct. 
In fact you can also make the coordinate system much larger. You can easily include the earth in total.
> >  The second experiment is physical identical as above etc My conclusion is the same: The speed of light is not constant. 
> 
Measured with respect to the coordinate system that you apply here, which is the same coordinate system as in the ball version of the experiment, the speed of light is not constant, that is correct. 
It is something more: the speed of light increases when it travels towards the earth. However also in reverse sense: The speed of light decreases when the distance from the earth increases. (Within limits of the solar system)
>  instead etc. you could as well choose any other coordinate system, e.g. one in which the speed of light turns out to be constant for your experiment. 
My same suggestion: Supply me the details.
>  In your experiment, you can apply a local inertial frame at the top of the Towever, and you will find the speed of light constant. 
The same as above
>  You can apply a different local inertial frame at the middle of the tower, and you will find the speed of light constant again. 
IMO why should I do that it makes a simulation of the solar system of a galaxy terrible complicated (I think)
>  What is not possible, though, is to apply the same local inertial frame for the whole trip from top to bottom, since the corresponding spacetime region is not sufficiently limited. 
What is wrong in using one coordinate system for our whole galaxy?
[[Mod. note  The issue is that you can't use a single (global) *inertial* coordinate system for the whole trip  the whole message of GR is that no such coordinate system can exist, i.e., that no coordinate system can have the property of being globalinertial (i.e., flat) *and* cover a large region of a spacetime with significant gravitational effects.  jt]]
>  The HafeleKeating experiment to which you seem to be referring indeed did not test the effects of SR on their own, but rather the combined effects of SR and GR. 
But why not solely using GR for the whole experiment?
[[Mod. note  Since GR is a superset of SR, you *could* analyse the whole experiment in the framework of GR. However, some (though not all) of the effects in this experiment (= flying atomic clocks around the world) are already present in an SR model, and it's useful to analyses these effects from the perspective of SR.  jt]]
Nicolaas Vroom
>>>  What I try to do is answer the question is the speed of light constant. 
>> 
This question is not precise enough. 
> 
I think that my question is rather simple ? Is the speed of light (the speed of the photons) in the universe everywhere the same 
Within the framework of a theory in which the term "speed of light" has a clear, unique meaning (e.g. SR), your question might be simple. But in GR, the term "speed of light" does not have such a clear meaning. "Speed of light" can either mean the speed of light measured in a local inertial frame, or the speed of light measured in a coordinate system.
>  and if not what is the physical cause. 
What is in general not constant in GR is the speed of light in a coordinate system. However, this does not have a physical cause, since it is just a property of the chosen coordinate system. At best, one can ask for the physical cause why one cannot apply inertial frames like in SR, but is obliged to come along with more general coordinate systems. The physical cause for that is the curvature of spacetime: in a curved spacetime, inertial frames can only be constructed locally, not globally for the complete spacetime.
Take for illustration the surface of sphere. That is a curved twodimensional space. It's easy to seen that it's impossible to construct a Cartesian (x,y) coordinate system that covers the complete surface. A Cartesian coordinate system can only be constructed locally around a chosen point on the surface, in an environment that is small compared to the sphere's radius. The same applies for inertial frames in a curved spacetime.
>>  When talking about a speed in GR, you have to distinguish between the speed measured in a local inertial frame and the speed measured in a coordinate system. 
>  Ofcourse if you want to measure the speed of light you have to quantify the distance and time you use which implies a coordinate system. That is not what I have done. The speed is in counts of one counter. 
If we follow your description, the counts of the counter are nothing but a number that is proportional to the coordinate time of a coordinate system you apply. That means that you are using a coordinate system and measure speeds with respect to it.
>>  The description you provide below indicates that you refer to the speed measured in a coordinate system (for more details see below). For the speed of light, this indeed implies that it is not constant, unlike the speed of light measured in a local inertial frame that remains constant in GR. 
> 
My suggestion is to define your experiment which demonstrates that the speed of light is constant. 
Since the term "the speed of light" does not have a clear meaning in GR, this requirement is not wellformulated. Let's assume that your requirement was instead to define an experiment that demonstrates that the speed of light *in a local inertial frame* is constant.
This can e.g. be done by performing three experiments, one at the top of the tower, one at the middle, and one at the bottom. In each experiment, you measure the speed of light in the following way:
Put two clocks that are synchronized to two positions that are close to each other, where close means that the distance between both positions is much smaller than the height of the tower. Let a light ray run from the first clock to the second one. Not the clock time the first clock shows when the light ray starts, and the clock time the second clock shows when the light ray arrives. Divide the distance between the two clocks by the difference between the noted clock times.
The resulting quantity is the speed of light measured in a local inertial frame that is momentarily resting relative to the particular stage of the tower (top, middle, bottom). According to GR, that quantity is the same in all three experiments.
>>  The speed of the ball measured in that coordinate system is not constant, that is correct. 
> 
In fact you can also make the coordinate system much larger. You can easily include the earth in total. 
Different coordinate systems are not constructed by making a given coordinate system larger, but rather by attaching different coordinates to the same spacetime points.
Take the coordinate system that you defined in the description of your experiment. In that coordinate system, top and bottom of the tower have fixed spatial coordinates, i.e. the spatial coordinates are always the same for all values of the coordinate time. In a different coordinate system, the spatial coordinates of these two positions may be changing by time. Or they may be fixed, too, but time translation invariance does not apply, i.e. the time coordinate is different in that way that the trip from top to bottom takes a different coordinate time interval than the backtrip from bottom to top.
More in detail: the coordinate system that you are using can be easily identified with Schwarzschild coordinates. These coordinates are very useful to describe situations in the gravitational field of an ordinary celestial body, like a star or planet. However, they become impractical if you want to describe a black hole, since they have a coordinate singularity at the event horizon. Therefore, one has to apply alternative coordinate systems. Two examples are EddingtonFinkelstein coordinates and freefalling coordinates. In both, top and bottom of your tower have fixed spatial coordinates like in Schwarzschild coordinates, but time coordinates of events are different.
As you can read e.g. here:
http://casa.colorado.edu/~ajsh/schwp.html
the time coordinate t_ff of freefalling coordinates can by calculated from Schwarzschild coordinate time t_SS by
t_ff = t_SS + 2 r^(1/2) + ln(r^(1/2)  1)/(r^(1/2) + 1)
where r is the radial spatial coordinate, that both coordinate systems share. For the coordinate time t_EF of EddingtonFinkelstein coordinates, the formula is
t_EF = t_SS + lnr1
Let's use EddingtonFinkelstein coordinates for your ball experiment. Let the radial coordinate of the top of the tower be r = r_top, the radial coordinate of the bottom r = r_bottom. The Schwarzschild coordinate time when the ball starts to fall is t_SS = t_SS_1, the Schwarzschild coordinate time when the ball reaches the bottom is
t_SS = t_SS_2 = t_SS_1 + T
and the Schwarzschild coordinate time when the ball turns back to the top is
t_SS = t_SS_3 = t_SS_1 + 2T
where T is the Schwarzschild coordinate time interval the ball takes from top to bottom. So, the worldline of the ball passes through three spacetime points that have the following coordinates in Schwarzschild coordinates:
(t_SS_1, r_top), (t_SS_1 + T, r_bottom), (t_SS_1 + 2T, r_top)
Now, let's calculate the EddingtonFinkelstein coordinate times of the three events:
t_EF_1 = t_SS_1 + lnr_top + 1
t_EF_2 = t_SS_2 + lnr_bottom + 1 = t_SS_1 + T + lnr_bottom + 1
t_EF_3 = t_SS_3 + lnr_top + 1 = t_SS_1 + 2T + lnr_top + 1
Next, we calculate the coordinate time intervals. From the trip from top to bottom, the ball takes the EddingtonFinkelstein coordinate time interval
T_EF_12 = t_EF_2  t_EF_1 = T + lnr_bottom + 1  lnr_top + 1
For the backtrip from bottom to top:
T_EF_23 = t_EF_3  t_EF_2 = T + lnr_top + 1  lnr_bottom + 1
So, we see, the two coordinate time intervals are different in EddingtonFinkelstein coordinates, unlike in Schwarzschild coordinates where both intervals are equal, namely T. That means that there is no time translation invariance in EddingtonFinkelstein coordinates.
There is another coordinate system, that is also useful for black holes, KruskalSzekeres coordinates (often simply called Kruskal coordinates). In these coordinates, there is no timetranslation invariance, too, and in addition, the top and bottom of your tower do not have fixed spatial coordinates. However, the speed of light in these coordinates is constant, at least for radially propagating light rays.
One could now be temptated to argue that as long as we do not consider black holes, there is no need for EddingtonFinkelstein coordinates, freefalling coordinates or Kruskal coordinates, so that we come along with Schwarzschild coordinates, especially since Schwarzschild coordinates have the nice property of time translation invariance and that bodies that are obviously resting in a gravitational field, like the Tower of Pisa, have fixed spatial coordinates.
However, when considering the question whether the speed of light is constant in GR, we must take into account the full symmetries of GR. GR is not only about ordinary celestial bodies, but also about black holes, and in addition, not only about Schwarzschild solution (that describes the gravitational fields of both, ordinary celestial bodies and black holes), but about arbitrary spacetime metrics. Therefore, we must not restrict ourselves to consider Schwarzschild coordinates, and to imagine the speed of light in Schwarzschild coordinates as being specially meaningful.
GR is generally covariant, i.e. the chosen coordinate system is arbitrary, and thefore the speed of light in the actual coordinate system little meaningful, no matter how useful that coordinate system is in special cases.
>>>  The second experiment is physical identical as above etc My conclusion is the same: The speed of light is not constant. 
>> 
Measured with respect to the coordinate system that you apply here, which is the same coordinate system as in the ball version of the experiment, the speed of light is not constant, that is correct. 
> 
It is something more: the speed of light increases when it travels towards the earth. 
No. The sentence is not wellformulated, seen from the viewpoint of GR. The speed of light *in Schwarzschild coordinates* increases.
>>  instead etc. you could as well choose any other coordinate system, e.g. one in which the speed of light turns out to be constant for your experiment. 
> 
My same suggestion: Supply me the details. 
See above: KruskalSzekeres coordinates. Also see:
https://en.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres_coordinates
Take the diagram to the right, we the numbers I, II, III and IV in different colors. Imagine the top of the Tower having the hyperbola r=1.6 as wordline, the middle r=1.4 and the bottom r=1.2. Radial light ray follow diagonal lines in the diagram, i.e. their speed (in that coordinate system) is constant.
>>  You can apply a different local inertial frame at the middle of the tower, and you will find the speed of light constant again. 
> 
IMO why should I do that it makes a simulation of the solar system of a galaxy terrible complicated (I think) 
Your question to which I answered was not "How can I keep my simulation simple?". It was rather "Is the speed of light constand in GR?".
If you prefer an answer to the question "How can I keep my simulation simple?": just use Schwarzschild coordinates. Concerning the speed of light: that is not constant in these coordinates.
>>  What is not possible, though, is to apply the same local inertial frame for the whole trip from top to bottom, since the corresponding spacetime region is not sufficiently limited. 
> 
What is wrong in using one coordinate system for our whole galaxy? 
I did not say that there would be something wrong in using one coordinate system for our whole galaxy. What I said is that it is not possible to construct an inertial frame that covers a spacetime region that is not small compared to scales on which the spacetime curvature becomes relevant. To understand the reason just try to construct a Cartesian (x,y) coordinate system on a sphere's surface.
>>  The HafeleKeating experiment to which you seem to be referring indeed did not test the effects of SR on their own, but rather the combined effects of SR and GR. 
> 
But why not solely using GR for the whole experiment? 
One solely uses GR for the whole experiment. However, in GR, one can distinguish between effects that also exist in SR, and effects that are special to GR. The latter category, I called "GR effects", and the first category "SR effects".
>  Nicolaas Vroom wrote: 
> >>> 
What I try to do is answer the question is the speed of light constant. 
> >> 
This question is not precise enough. 
> > 
I think that my question is rather simple ? Is the speed of light (the speed of the photons) in the universe everywhere the same 
> 
Within the framework of a theory in which the term "speed of light" has a clear, unique meaning (e.g. SR), your question might be simple. But in GR, the term "speed of light" does not have such a clear meaning. "Speed of light" can either mean the speed of light measured in a local inertial frame, or the speed of light measured in a coordinate system. 
Can you give me an idea what is the difference between measuring something in a local inertial frame versus in a coordinate system? I my opinion in practice when you perform an experiment there exists not such a difference.
> >  and if not what is the physical cause. 
> 
What is in general not constant in GR is the speed of light in a coordinate system. However, this does not have a physical cause, since it is just a property of the chosen coordinate system. At best, one can ask for the physical cause why one cannot apply inertial frames like in SR, but is obliged to come along with more general coordinate systems. The physical cause for that is the curvature of spacetime: in a curved spacetime, inertial frames can only be constructed locally, not globally for the complete spacetime. 
This gives me the impression that you can not use GR to simulate a complete galaxy. Using Newton's Law this is difficult in practice because you have to know the initial positions of all objects at the same instance. In order to calculate the initial speed for each object you need at least two specific instances. It is not so difficult to simulate starting from an artificial configuration. See http://users.telenet.be/nicvroom/galaxy%20simulation.htm
> >>  When talking about a speed in GR, you have to distinguish between the speed measured in a local inertial frame and the speed measured in a coordinate system. 
> >  Ofcourse if you want to measure the speed of light you have to quantify the distance and time you use which implies a coordinate system. That is not what I have done. The speed is in counts of one counter. 
> 
If we follow your description, the counts of the counter are nothing but a number that is proportional to the coordinate time of a coordinate system you apply. That means that you are using a coordinate system and measure speeds with respect to it. 
I performed two experiments: One with a ball and one with light. Both are reflected. In both cases each experiment consists of two parts: full distance and half distance. In each case starting point is the same. In order to "measure" I use a counter, one using a ball and the other one using light. The result in both cases (my prediction) that the speed is not constant. In the case of a ball this is in accordance with Newton's Law. For light I assume the same.
>  Since the term "the speed of light" does not have a clear meaning in GR, this requirement is not wellformulated. Let's assume that your requirement was instead to define an experiment that demonstrates that the speed of light *in a local inertial frame* is constant. 
What I am discussing is the result of experiments. First "we" have to agree about the outcome of the experiment. The second step is to agree which theories predict or describe these experiments.
> 
This can e.g. be done by performing three experiments, one at the top of
the tower, one at the middle, and one at the bottom. In each experiment,
you measure the speed of light in the following way:
Put two clocks that are synchronized to two positions that are close to each other, where close means that the distance between both positions is much smaller than the height of the tower. Let a light ray run from the first clock to the second one. Not the clock time the first clock shows when the light ray starts, and the clock time the second clock shows when the light ray arrives. Divide the distance between the two clocks by the difference between the noted clock times. 
No this is not the way I propose. I try as simple as possible. In each experiment there is only one sort of clock used (counter), which is at rest.
>  Different coordinate systems are not constructed by making a given coordinate system larger, but rather by attaching different coordinates to the same spacetime points. 
IMO this makes everything very complex.
>  These coordinates are very useful to describe situations in the gravitational field of an ordinary celestial body, like a star or planet. However, they become impractical if you want to describe a black hole, since they have a coordinate singularity at the event horizon. 
In the simulations I have done you can insert at the center a BH. In our Galaxy we are lucky because "we" can observe induvidual stars which are rotating around the BH. This allows you to calculate the mass of the BH. However that is not the topic of this discussion.
>  Therefore, we must not restrict ourselves to consider Schwarzschild coordinates, and to imagine the speed of light in Schwarzschild coordinates as being specially meaningful. 
IMO opinion the speed of light is specific important in order to process measurement data ie positions and speeds. In order to predict future positions I doubt if the speed of light is important.
> >  It is something more: the speed of light increases when it travels towards the earth. 
> 
No. The sentence is not wellformulated, seen from the viewpoint of GR. The speed of light *in Schwarzschild coordinates* increases. 
The result of the experiment show in both cases that the number of counts in each half distance is different. To be more specific the number of counts in the second part is smaller than the first part. This means that the speed is different. This means that the speed in the second part is larger.
> 
See above: KruskalSzekeres coordinates. Also see:
https://en.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres_coordinates Take the diagram to the right, we the numbers I, II, III and IV in different colors. Imagine the top of the Tower having the hyperbola r=1.6 as wordline, the middle r=1.4 and the bottom r=1.2. Radial light ray follow diagonal lines in the diagram, i.e. their speed (in that coordinate system) is constant. 
In that article they discuss physical singularity. IMO singualrities only "exist" in mathematical sense.
The important thing is that in order to discuss or perform experiments related to the speed of light you should not use clocks which are affected by your experiment. As such I'am not measuring the speed of light quantitative, but only demonstrate that the speed is not constant.
See also paragraph 7.3 in the book Gravitation which discusses an experiment I try to perform a simpler experiment.
Albert Einstein's used thought experiments to "demonstrate" SR and GR (my impression) He used thought experiments to demonstrate or explain that the path of lightrays are bended around mass. IMO that is very tricky. Page 13 in the book Gravitation states: "In each case one is following a natural track through spacetime". That maybe true, but what does it mean? See also: http://users.telenet.be/nicvroom/ScientificAm%20September%202015%20Reality.htm
Nicolaas Vroom
Nicolaas Vroom wrote:
>>>>>  What I try to do is answer the question is the speed of light constant. 
>>>> 
This question is not precise enough. 
>>> 
I think that my question is rather simple ? Is the speed of light (the speed of the photons) in the universe everywhere the same 
>> 
Within the framework of a theory in which the term "speed of light" has a clear, unique meaning (e.g. SR), your question might be simple. But in GR, the term "speed of light" does not have such a clear meaning. "Speed of light" can either mean the speed of light measured in a local inertial frame, or the speed of light measured in a coordinate system. 
> 
Can you give me an idea what is the difference between measuring something in a local inertial frame versus in a coordinate system? I my opinion in practice when you perform an experiment there exists not such a difference. 
As far as the procedure is concerned, there is no difference. In both, local inertial frames and general coordinate systems, a speed measurement for some body can be performed by the following procedure:
 Take two points P and Q on the worldline of the body  Determine the coordinates xP^mu = (tP, xP^i), mu=0,1,2,3, i=1,2,3, of point P  Determine the coordinates xQ^mu = (tQ, xQ^i) of point Q  Divide the difference in spatial coordinates by the difference in time coordinate: v^i = (xQ^i  xP^i) / (tQ  tP)
What makes the difference is that the general coordinate system is a general coordinate system whereas the local inertial frame is a local inertial frame. The result in the general coordinate system is arbitrary, since the coordinate system itself is arbitrary. The result in the local inertial frame, however, is meaningful, because the local inertial frame is very special.
For a better understanding of this fact, consider a twodimensional space. Let's first assume the this space is flat, i.e. not curved, and has a Euklidian metric. In this space, you can construct various coordinate systems. However, there is a very special class of coordinate systems, the Cartesian coordinate systems. In such a Cartesian coordinate system, you have two coordinates (x,y), and the coordinate system has two crucial properties:
 x and y coordinate lines are perpendicular to each other everywhere
 x and y coordinate lines are straight everywhere
You can construct nonCartesian coordinate systems, that violate at least one of these properties. For example, you can construct an obliqueangled coordinate system. The coordinate lines are still straight then, but not perpendicular to each other. Or you can construct polar coordinates (r,phi). The coordinate lines are perpendicular to each other then, but the phi coordinate lines are not straight.
No let's assume that the twodimensional space is no longer flat, but is curved. One the first things you will found out is that it is no longer possible to construct a Cartesian coordinate system globally. You can try to construct a coordinate system with straight coordinate lines, but you will soon find out that the coordinate lines are not perpendicular to each other everywhere. Or you can try to construct a coordinate system with coordinate lines that are perpendicular everywhere, but the coordinate lines are not straight everywhere. Only locally, in a region small compared to the curvature radius of the space, a coordinate system can be construct that matches the properties of a Cartesian coordinate system in good approximation.
Now let's return to the fourdimensional spacetime of Relativity. In SR, where the spacetime is flat, things are similar to the flat twodimensional space discussed above. As you can construct global Cartesian coordinate systems (x,y) in flat twodimensional space, you can construct inertial frames (t,x,y,z) in flat spacetime. You can imagine inertial frames as generalization of Cartesian coordinate systems: all four coordinate lines, the three spatial ones and the time coordinate line, are straight, and all four coordinate lines are orthogonal to each other ("orthogonal" means something like "perpendicular", but is more general, in mathematics, one uses the term "perpendicular" only for special spaces).
As you can construct nonCartesian coordinate systems in flat twodimensional space, you can as well construct general coordinate systems in flat SR spacetime that are no inertial frames, e.g. coordinate systems in which the time coordinate line is not orthogonal to the three spatial coordinate lines. In such a coordinate system, the SR postulate of constant speed of light does NOT apply. Only in inertial frames, that postulate applies generally. Analogously, in flat twodimensional space, there are rules that apply in Cartesian coordinate systems only, not in general coordinate systems.
Finally, let's come to the curved spacetime of GR. As we cannot construct global Cartesian coordinate systems in curved twodimensional space, we cannot construct global inertial frames here. Trying to construct a global inertial frame would either result in nonorthogonal coordinate lines or in coordinate lines not being straight.
Take e.g. Schwarzschild coordinates (t,r,phi,theta) that are similar to the coordinates you used in your Pisa Tower thought experiment: the coordinate lines are orthogonal, but not straight. As far as the angle coordinates (phi,theta) are concerned, this is trivial, however, the same is true for time coordinate t and radial coordinate r: a body resting at fixed spatial coordinates, i.e. travelling on a time coordinat line, is not freefalling, implying that the body's wordline is not a geodesic. In turn, this means that the time coordinate line is no geodesic, too, and thefore not straight.
And as in SR, the postulate of constant speed of light applies in inertial frames only, but not in general coordinate systems, the analog is true in GR: the postulate of constant speed of light applies in local inertial frames only, not in general coordinate systems. So, it is even wrong to say the postulate of constant speed of light is less valid in GR than in SR. It is valid in GR as much as in SR: in SR, it applies in inertial frames only, and analogously, in GR, the postulate applies in local inertial frames only.
>>>  and if not what is the physical cause. 
>> 
What is in general not constant in GR is the speed of light in a coordinate system. However, this does not have a physical cause, since it is just a property of the chosen coordinate system. At best, one can ask for the physical cause why one cannot apply inertial frames like in SR, but is obliged to come along with more general coordinate systems. The physical cause for that is the curvature of spacetime: in a curved spacetime, inertial frames can only be constructed locally, not globally for the complete spacetime. 
> 
This gives me the impression that you can not use GR to simulate a complete galaxy. 
Why this? Do you maybe presume that one needs to use an inertial frame to simulate a galaxy? There is no reason why this should be true  one can use a general coordinate system as well.
>  Using Newton's Law this is difficult in practice because you have to know the initial positions of all objects at the same instance. 
The same is true in GR. It's even worse in GR: since the gravitational field has own dynamical degrees of freedom, you need to know the initial configuration of the gravitational field.
>>>>  When talking about a speed in GR, you have to distinguish between the speed measured in a local inertial frame and the speed measured in a coordinate system. 
>>>  Ofcourse if you want to measure the speed of light you have to quantify the distance and time you use which implies a coordinate system. That is not what I have done. The speed is in counts of one counter. 
>> 
If we follow your description, the counts of the counter are nothing but a number that is proportional to the coordinate time of a coordinate system you apply. That means that you are using a coordinate system and measure speeds with respect to it. 
> 
I performed two experiments: One with a ball and one with light. Both are reflected. In both cases each experiment consists of two parts: full distance and half distance. In each case starting point is the same. In order to "measure" I use a counter, one using a ball and the other one using light. The result in both cases (my prediction) that the speed is not constant. 
No, this is not the result. Primarily, the result is that there is a quantity with the dimension of a speed ([length]/[time]) that is not constant. To interpret this result as "the speed" not being constant, you at first would have to apply a theory that allows you for interpreting the measured quantity as "the speed".
Newtonian Gravity as well as a specialrelativistic theory of gravity (if there were any) would allow you for interpreting the quantity as the speed in an inertial frame, which can be imagined meaningfully as "the speed". GR, however, does not allow you for that. In GR, the quantity you measured can only be interpreted as the speed in a general coordinate system, which is an arbitrary and therfore not very meaningful quantity, since the choice of the coordinate system is arbitrary.
>>  Since the term "the speed of light" does not have a clear meaning in GR, this requirement is not wellformulated. Let's assume that your requirement was instead to define an experiment that demonstrates that the speed of light *in a local inertial frame* is constant. 
> 
What I am discussing is the result of experiments. First "we" have to agree about the outcome of the experiment. The second step is to agree which theories predict or describe these experiments. 
In your "first step", i.e. without referring to a theory like GR or Newtonian Gravity, all you know about the outcome of the experiment you described is that it is a quantity with the dimension of a speed ([length]/[time]) and that it is not constant. To find out whether and how far you can identify this quantity with a meaningful speed, you need to refer to a theory, i.a. proceed to your "second step".
>> 
This can e.g. be done by performing three experiments, one at the
top of the tower, one at the middle, and one at the bottom. In each
experiment, you measure the speed of light in the following way:
Put two clocks that are synchronized to two positions that are close to each other, where close means that the distance between both positions is much smaller than the height of the tower. Let a light ray run from the first clock to the second one. Not the clock time the first clock shows when the light ray starts, and the clock time the second clock shows when the light ray arrives. Divide the distance between the two clocks by the difference between the noted clock times. 
> 
No this is not the way I propose. 
You asked me for an experiment that demonstrates that the speed of light in a local inertial frame is constant. My description answers your question, no matter if it matches what you propose.
>>  Different coordinate systems are not constructed by making a given coordinate system larger, but rather by attaching different coordinates to the same spacetime points. 
> 
IMO this makes everything very complex. 
Maybe. But in GR, you are obliged to take into account that the particular coordinate system you are actually using is not the only one that can be used, what makes the results that you gain in this coordinate system arbitrary if they turn out to be coordinatedependent.
>>>  It is something more: the speed of light increases when it travels towards the earth. 
>> 
No. The sentence is not wellformulated, seen from the viewpoint of GR. The speed of light *in Schwarzschild coordinates* increases. 
> 
The result of the experiment show in both cases that the number of counts in each half distance is different. To be more specific the number of counts in the second part is smaller than the first part. This means that the speed is different. This means that the speed in the second part is larger. 
No, is does not mean that. It does not mean anything concerning any speed as long as you do not apply a special coordinate system with the three properties I alreay mentioned:
(1) The top and the ground of the Tower have fixed spatial coordinates
(2) The elapsing coordinate time is proportional to the number of bounces of the bouncing ball between the plates.
(3) Time translation invariance applies: the coordinate time interval that the ball takes for the trip from top to ground is the same as the coordinate time interval the ball takes for the backtrip from ground to top.
The speed *in this special coordinate system* is larger in the second part. But since this coordinate system is arbitrary, this result is arbitrary, too.
>> 
See above: KruskalSzekeres coordinates. Also see:
https://en.wikipedia.org/wiki/Kruskal%E2%80%93Szekeres_coordinates Take the diagram to the right, we the numbers I, II, III and IV in different colors. Imagine the top of the Tower having the hyperbola r=1.6 as wordline, the middle r=1.4 and the bottom r=1.2. Radial light ray follow diagonal lines in the diagram, i.e. their speed (in that coordinate system) is constant. 
> 
In that article they discuss physical singularity. IMO singualrities only "exist" in mathematical sense. 
That does not change in any way the fact that KruskalSzekeres coordinates are an example for what you asked me, namely an example for a coordinate system in which the speed of light turns out to be constant for your experiment.
Or did you intend to reject the concept of black holes because of their central singularities and therefore the usage of Kruskal coordinates that can be used to describe the interior of a black hole? Then you would reject GR at all, and then it wouldn't make sense for you to ask whether the speed of light is constant in GR.
>  The important thing is that in order to discuss or perform experiments related to the speed of light you should not use clocks which are affected by your experiment. As such I'am not measuring the speed of light quantitative, but only demonstrate that the speed is not constant. 
No, you do not demonstrate that. You demonstrate that the speed of light *in the special coordinate system you are using* is not constant. Seen from GR, this result is arbitrary, though, since your choice of coordinate system is arbitrary.
>  See also paragraph 7.3 in the book Gravitation which discusses an experiment I try to perform a simpler experiment. 
You mean figure 7.1B? In this figure, however, a special coordinate system was used, namely Schwarzschild coordinates, or at least a coordinate system in which the two observers have fixed spatial coordinates and time translation invariance applies. The variable speed of light to see in figure 7.1B is valid in that special coordinate system only.
>  Albert Einstein's used thought experiments to "demonstrate" SR and GR (my impression) He used thought experiments to demonstrate or explain that the path of lightrays are bended around mass. IMO that is very tricky. Page 13 in the book Gravitation states: "In each case one is following a natural track through spacetime". That maybe true, but what does it mean? 
That means that the worldline of a freefalling body is a geodesic in spacetime. Let a stone fall from your hand. The stone falls towards the ground and touches the ground after some seconds. The segment of the stone's wordline between your hand and the ground is a geodesic. Unlike your own worldline that is no geodesic since you are not free falling.
Thanks.
>  Nicolaas Vroom wrote: 
> > 
Can you give me an idea what is the difference between measuring something in a local inertial frame versus in a coordinate system? I my opinion in practice when you perform an experiment there exists not such a difference. 
> 
As far as the procedure is concerned, there is no difference. In both, local inertial frames and general coordinate systems, a speed measurement for some body can be performed by the following procedure:  Take two points P and Q on the worldline of the body 
And how do you do that in practice? The same for next sentences.
>  The result in the general coordinate system is arbitrary, since the coordinate system itself is arbitrary. 
>  The result in the local inertial frame, however, is meaningful, because the local inertial frame is very special. 
An coordinate system should be unambigeous. The same for people overhere as overthere. In a different galaxy.
>  For a better understanding of this fact, consider a twodimensional space. 
Skip.
>  As you can construct nonCartesian coordinate systems in flat twodimensional space 
Sorry I'm lost.
>  Take e.g. Schwarzschild coordinates (t,r,phi,theta) that are similar to the coordinates you used in your Pisa Tower thought experiment: the coordinate lines are orthogonal, but not straight. 
The Tower of Pisa experiment is not a thought experiment. It is a description of an actual experiment. It is something like: You put a camera at a large distance from the tower. You drop an apple from the tower. You take a picture with the camera each second. When you compare the pictures you will see that the speed of the apple is not constant but increases.
The problem with this experiment is that you need a clock.
In the experiment I propose there is no clock. In the experiment I use a bouncing ball and the clock becomes a counter which is also a bouncing ball. Using that scenenario and performing the experiment from two different hights, the result is that the speed of the ball is not constant.
In stead of a ball in principle I can also use a light signal. Of course to perform this experiment from the Tower of Pisa is not realistic. However what I expect that the result of the experiment is the same: that the speed of light is not constant. The question of course is if this conclusion is correct.
> 
As far as the angle
coordinates (phi,theta) are concerned, this is trivial, however, the
same is true for time coordinate t and radial coordinate r: a body
resting at fixed spatial coordinates, i.e. travelling on a time
coordinat line, is not freefalling, implying that the body's wordline
is not a geodesic. In turn, this means that the time coordinate line is
no geodesic, too, and thefore not straight.
And as in SR, the postulate of constant speed of light applies in inertial frames only, but not in general coordinate systems, the analog is true in GR: the postulate of constant speed of light applies in local inertial frames only, not in general coordinate systems. So, it is even wrong to say the postulate of constant speed of light is less valid in GR than in SR. It is valid in GR as much as in SR: in SR, it applies in inertial frames only, and analogously, in GR, the postulate applies in local inertial frames only. 
Do I really need of all this to answer my question?
> >  This gives me the impression that you can not use GR to simulate a complete galaxy. 
> 
Why this? Do you maybe presume that one needs to use an inertial frame to simulate a galaxy? There is no reason why this should be true  one can use a general coordinate system as well. 
See next.
> >  Using Newton's Law this is difficult in practice because you have to know the initial positions of all objects at the same instance. 
> 
The same is true in GR. It's even worse in GR: since the gravitational field has own dynamical degrees of freedom, you need to know the initial configuration of the gravitational field. 
That means you agree with my previous remark: GR is "tricky"
> >  I performed two experiments: One with a ball and one with light. Both are reflected. In both cases each experiment consists of two parts: full distance and half distance. In each case starting point is the same. In order to "measure" I use a counter, one using a ball and the other one using light. The result in both cases (my prediction) that the speed is not constant. 
> 
No, this is not the result. Primarily, the result is that there is a quantity with the dimension of a speed ([length]/[time]) that is not constant. To interpret this result as "the speed" not being constant, you at first would have to apply a theory that allows you for interpreting the measured quantity as "the speed". 
The first conclusion is that the number of counts to travel (fall) over the two identical distances (first part and second part) is not identical. This is "translated" that the speed is not constant and that there is acceleration involved.
>  Newtonian Gravity as well as a specialrelativistic theory of gravity (if there were any) would allow you for interpreting the quantity as the speed in an inertial frame, which can be imagined meaningfully as "the speed". GR, however, does not allow you for that. In GR, the quantity you measured can only be interpreted as the speed in a general coordinate system, which is an arbitrary and therfore not very meaningful quantity, since the choice of the coordinate system is arbitrary. 
The first question to answer if you agree with the outcome of the two experiments. The next question is if the outcome is in agreement with Newton's Law. The same for GR.
> >  The result of the experiment show in both cases that the number of counts in each half distance is different. To be more specific the number of counts in the second part is smaller than the first part. This means that the speed is different. This means that the speed in the second part is larger. 
> 
No, is does not mean that. It does not mean anything concerning any speed as long as you do not apply a special coordinate system with the three properties I alreay mentioned: (1) The top and the ground of the Tower have fixed spatial coordinates (2) The elapsing coordinate time is proportional to the number of bounces of the bouncing ball between the plates. (3) Time translation invariance applies: the coordinate time interval that the ball takes for the trip from top to ground is the same as the coordinate time interval the ball takes for the backtrip from ground to top. The speed *in this special coordinate system* is larger in the second part. But since this coordinate system is arbitrary, this result is arbitrary, too. 
I would agree with you if you call this a local experiment, in the sense that the speed of the ball in this local experiment is not constant. The same should than also be true for the speed of light.
But if you agree that the speed of light is not constant in this local experiment why should than this also not to be true in a much broader sense?
Why should the speed of light be physical constant if you transmit a light signal from the earth to the moon?
> >  Page 13 in the book Gravitation states: "In each case one is following a natural track through spacetime". That maybe true, but what does it mean? 
> 
That means that the worldline of a freefalling body is a geodesic in spacetime. 
Is that a natural track through spacetime?
GR is "tricky"
Nicolaas Vroom
>>>  Can you give me an idea what is the difference between measuring something in a local inertial frame versus in a coordinate system? I my opinion in practice when you perform an experiment there exists not such a difference. 
>> 
As far as the procedure is concerned, there is no difference. In both, local inertial frames and general coordinate systems, a speed measurement for some body can be performed by the following procedure:  Take two points P and Q on the worldline of the body 
> 
And how do you do that in practice? 
Attach two clocks to two different spatial positions with known spatial coordinates. Ensure that the two clocks are synchronous with the coordinate time. Note the displayed clock times at which the body passes each of the two clocks.
>>  The result in the general coordinate system is arbitrary, since the coordinate system itself is arbitrary. 
>  That means should not be used ? 
You can use it if you want, but you have to be aware that it is arbitrary.
>>  The result in the local inertial frame, however, is meaningful, because the local inertial frame is very special. 
> 
An coordinate system should be unambigeous. 
A coordinate system is unambigeous, or unique, in that sense that every spacetime point is assigned to a unique set of coordinates. A general coordinate system is not unambigeous, though, in that sense that the choice of the coordinate system is arbitrary, i.e. that one could choose a different coordinate system as well. An inertial frame (in Newtonian Mechanics or SR) is more unambigeous in this sense: if you choose an observer, e.g. yourself, then you already fix the inertial frame to be used.
>>  For a better understanding of this fact, consider a twodimensional space. 
>  Two dimensional SPACE does not exist. Sorry I'm lost. 
The twodimensional space was just to make the understanding easier. We can of course do all consideration in fourdimensional spacetime if you prefer that. It's just a little more complicated.
>>  Take e.g. Schwarzschild coordinates (t,r,phi,theta) that are similar to the coordinates you used in your Pisa Tower thought experiment: the coordinate lines are orthogonal, but not straight. 
> 
The Tower of Pisa experiment is not a thought experiment. It is a description of an actual experiment. It is something like: You put a camera at a large distance from the tower. You drop an apple from the tower. You take a picture with the camera each second. When you compare the pictures you will see that the speed of the apple is not constant but increases. 
No, I don't see that. And you don't see that, too. You may conclude that from what you see, but to draw this conclusion, you have to make some assumptions. Those assumptions contain the usage of a coordinate system, and that quantities measured with respect to this coordinate systems are in some way meaningful.
More in detail:
 Primarily, you have a collection of pictures. You then emumerate the
pictures (1,2,3,...).
 Then you assume that you can apply a coordinate system to a spacetime
region that contains the wordline of the apple, the worldlines of the
light signals that travel from the apple to the camera, and the wordline
of the camera itself.
 Then you assume that the coordinate time interval for a light signal
to travel from the apple to the camera is the same for all light
signals, so that you can identify the coordinate time interval between
two light signals reaching the camera with the interval between two
light signals emitted by the apple.
 Then you identify the number of each picture with the coordinate time
at which the particular light signal reached the camera.
 Then you identify the apple's position on the particular picture with
the spatial coordinates of the apple at the particular coordinate time
minus the coordinate time the light signal took from the apple to the
camera.
After doing this, you can draw the conclusion that the speed of the apple in the coordinate system you have chosen increases. Then you assume that this coordinate system is very special, so that you can interpret the speed of the apple in this coordinate system as "the" speed of the apple.
> 
The problem with this experiment is that you need a clock.
In the experiment I propose there is no clock. 
In the one experiment, the role of the clock is undertaken by the bouncing ball, in the other experiment, the role of the clock is undertaken by the enumeration of the picture photographed by the camera. I don't see a great difference. In both cases, you use a number (count of ball bounces, index of picture) as a replacement for the coordinate time.
>  Using that scenenario and performing the experiment from two different hights, the result is that the speed of the ball is not constant. 
No, the result is not that the speed of the ball is not constant. The result is that in the one case, the round trip of the ball takes more bounces than in the other case.
To draw any conclusions from this result that concern the speed of the ball, you again have to construct a coordinate system. Then you have the speed of the ball in the particular coordinate system. To interpret this speed as "the" speed of the ball, you again have to assume that this coordinate system is specially meaningful.
>  In stead of a ball in principle I can also use a light signal. Of course to perform this experiment from the Tower of Pisa is not realistic. However what I expect that the result of the experiment is the same: that the speed of light is not constant. The question of course is if this conclusion is correct. 
The answer is: no. The conclusion would be correct if the assumptions you make would be correct. In Newtonian Gravity, they would: the coordinate system you are using could be considered as an inertial frame (of an observer resting with respect to the Tower, or of the Tower itself). In GR, however, they do not: the coordinate system you are using for your conclusion is arbitrary there.
>> 
As far as the angle
coordinates (phi,theta) are concerned, this is trivial, however, the
same is true for time coordinate t and radial coordinate r: a body
resting at fixed spatial coordinates, i.e. travelling on a time
coordinat line, is not freefalling, implying that the body's wordline
is not a geodesic. In turn, this means that the time coordinate line is
no geodesic, too, and thefore not straight.
And as in SR, the postulate of constant speed of light applies in inertial frames only, but not in general coordinate systems, the analog is true in GR: the postulate of constant speed of light applies in local inertial frames only, not in general coordinate systems. So, it is even wrong to say the postulate of constant speed of light is less valid in GR than in SR. It is valid in GR as much as in SR: in SR, it applies in inertial frames only, and analogously, in GR, the postulate applies in local inertial frames only. 
> 
Do I really need of all this to answer my question? 
To answer your question whether the SR postulate of constant light speed applies in GR, yes.
>>>  This gives me the impression that you can not use GR to simulate a complete galaxy. 
>> 
Why this? Do you maybe presume that one needs to use an inertial frame to simulate a galaxy? There is no reason why this should be true  one can use a general coordinate system as well. 
> 
See next. 
>>> 
Using Newton's Law this is difficult in practice because you have to know the initial positions of all objects at the same instance. 
>> 
The same is true in GR. It's even worse in GR: since the gravitational field has own dynamical degrees of freedom, you need to know the initial configuration of the gravitational field. 
> 
That means you agree with my previous remark: GR is "tricky" 
Your previous remark was: "See next". And now, when I see next, you suggest me your previous remark again?
Or do you want to say that you cannot GR to simulate a galaxy because a simulation based on GR would be more complicated than one base on Newtonian Gravity? This, however, has little to do with inertial frames not being applicable in GR.
>>>  I performed two experiments: One with a ball and one with light. Both are reflected. In both cases each experiment consists of two parts: full distance and half distance. In each case starting point is the same. In order to "measure" I use a counter, one using a ball and the other one using light. The result in both cases (my prediction) that the speed is not constant. 
>> 
No, this is not the result. Primarily, the result is that there is a quantity with the dimension of a speed ([length]/[time]) that is not constant. To interpret this result as "the speed" not being constant, you at first would have to apply a theory that allows you for interpreting the measured quantity as "the speed". 
> 
The first conclusion is that the number of counts to travel (fall) over the two identical distances (first part and second part) is not identical. 
For this conclusion, you already need to apply a coordinate system that tells you that the spatial distances of the two parts are identical. This property of the two distances is coordinatedependent.
>  This is "translated" that the speed is not constant and that there is acceleration involved. 
For this translation, you need to apply a theory that tells you whether the coordinate system you are using is specially meaningful (e.g. an inertial frame) and therefore the speed in this coordinate system considerable as "the" speed.
>>  Newtonian Gravity as well as a specialrelativistic theory of gravity (if there were any) would allow you for interpreting the quantity as the speed in an inertial frame, which can be imagined meaningfully as "the speed". GR, however, does not allow you for that. In GR, the quantity you measured can only be interpreted as the speed in a general coordinate system, which is an arbitrary and therfore not very meaningful quantity, since the choice of the coordinate system is arbitrary. 
> 
The first question to answer if you agree with the outcome of the two experiments. 
No, I don't. What you call the outcome of the experiments is not the outcome of the experiments, but a conclusion from the outcome that is based on wrong assumptions.
>  The next question is if the outcome is in agreement with Newton's Law. The same for GR. 
To gain what you call the outcome of the experiments, but which is rather a conclusion from the outcome and not the outcome itself, you apply assumptions that are in contradiction to GR (namely that the coordinate system you are using would be specially meaningful). So, you already presume that GR is wrong. To ask whether results are in agreement with GR does not make sense any more then.  show quoted text  No, I do not call your experiment a local experiment, in that sense that this experiment would be local whereas an experiment that involves a broader spatial region that include Earth and Moon would not be local. Your experiment as well as a comparable experiment that involve Earth and Moon are not local, in that sense that they both involve spacetime regions that are not sufficiently limited to apply the concept of an inertial frame. A local experiment would be one that involves a spacetime region that is sufficiently limited, e.g. one that involves a small region around the top (or the bottom) of the Towor.
In other words: the postulate of constant speed of light does not apply in a spatially *broader* sense in GR, but in a spatially *narrower" sense, namely in that sense that the speed of light is constant in a local inertial frame. The region where a local inertial frame can be applied is not broader, it is narrower.
One could explain this quite easy using a twodimensional space, but since you reject such a consideration, you'll have to come along with the more complicated consideration of fourdimensional spacetime.
>>>  Page 13 in the book Gravitation states: "In each case one is following a natural track through spacetime". That maybe true, but what does it mean? 
>> 
That means that the worldline of a freefalling body is a geodesic in spacetime. 
> 
Is that a natural track through spacetime? 
Yes. Like moving in a straight line with constant speed is the natural track in a flat, uncurved spacetime.
Remember Newton's first law: a body remains in the state of rest or uniform motion unless it is enforced to change its state by acting forces. In a flat spacetime, this means that a forcefree body moves along a straight worldline. In a curved spacetime, it means that a forcefree body moves along a geodesic worldline.
Again: this could be very easiely illustrated in a twodimensional space, but you reject that.
> 
The Tower of Pisa experiment is not a thought experiment. It is a
description of an actual experiment.
It is something like:
You put a camera at a large distance from the tower.
You drop an apple from the tower.
You take a picture with the camera each second.
When you compare the pictures you will see that the speed of
the apple is not constant but increases.
The problem with this experiment is that you need a clock. In the experiment I propose there is no clock. In the experiment I use a bouncing ball and the clock becomes a counter which is also a bouncing ball. 
A remark to this experiment: the bouncing ball that is used as clock bounces do to gravitational effects. So, by definition, this experiment necessarily involves a spacetime region that is not sufficiently limited to apply SR. Therefore, an experiment of this kind cannot be performed within a local inertial frame. In other words: to perform measurements with respect to a local inertial frame (for which you asked me), this type of experiment is impractical.
>  The Tower of Pisa experiment is not a thought experiment. It is a description of an actual experiment. 
The difference between those two types of experiment are merely time, effort an money ;)
> 
It is something like:
You put a camera at a large distance from the tower.
You drop an apple from the tower.
You take a picture with the camera each second.
When you compare the pictures you will see that the speed of
the apple is not constant but increases.
The problem with this experiment is that you need a clock. In the experiment I propose there is no clock. In the experiment I use a bouncing ball and the clock becomes a counter which is also a bouncing ball. 
A 'clock' in the sense of a timemeasuring device is any device that allows to count welldefined time intervals. It is for convenience that usually these time intervalls are of identical length, i.e. the device counts the cycles of a periodic system like the oscillations between two electronic states of an atom or the swinging of a pendulum.
So your bouncing ball *is* a clock. A lousy one, but a clock nevertheless.
 Space  The final frontier
> 
Nicolaas Vroom 
> > 
The Tower of Pisa experiment is not a thought experiment. It is a description of an actual experiment. 
> 
The difference between those two types of experiment are merely time, effort an money ;) 
I think it is something more. See below.
> >  In the experiment I propose there is no clock. In the experiment I use a bouncing ball and the clock becomes a counter which is also a bouncing ball. 
> 
A 'clock' in the sense of a timemeasuring device is any device that allows to count welldefined time intervals. It is for convenience that usually these time intervalls are of identical length, i.e. the device counts the cycles of a periodic system like the oscillations between two electronic states of an atom or the swinging of a pendulum. So your bouncing ball *is* a clock. A lousy one, but a clock nevertheless. 
What I do is to compare the outcome of two identical physical experiments. In the first experiment I use two balls. Ball #1 bounces between two plates and services as an oscillator. Ball #2 bounces only once in two different cases. In case 1 the ball starts at the top, bounces at the bottom. The experiment finishes when the ball is back at its highest position. In case 2 the ball bounces back halfway between top and bottom. The object of the experiment is to count the number of bounces/counts of the oscillator. The results of the experiment show (as an example) that the number of counts when you drop ball #2 in case 1 is 17 and 10 in case 2 (first half) The strategy of the experiment is that the oscillator does not move! The first question is if you agree that the number of counts from inbetween to the bottom is 7? (second half) The second question is if you agree that the speed is increasing when the ball drops from top to inbetween to the bottom? Speed defined as distance divided by counts.
The whole purpose of this experiment to perform the same experiments but now not with balls but with two light signals. The oscillator in this case becomes light signal #1. Again also in this case the first question is if you agree that there is a difference in counts in the first half compared with the second half. The second question is if you agree that when the counts are different that the speed of light is not constant but has increased,
The whole idea behind each experiment is to use in each case only one physical concept. In the first experiment this is a falling ball #2 which is influenced by the gravitational field of the earth. In the second experiment this is a lightsignal #2 which is also supposed to be influenced by the gravitational field of the earth.
IMO this is identical from a physical point of view if you shoot a bullet horizontal or if you shine a lightsignal horizontal. Both the path of the bullet and of the lightsignal are bended.
To call each of the two oscillators ie ball #1 and light signal #1, a clock is only in the name. The issue is that both oscillators are physical processes and are influenced by the same physical phenomena as their counter parts.
To perform experiment #1 with the bouncing balls is rather simple The biggest problem that the bouncing should be perfect. This means the two distances (down and up) should be the same.
Experiment #2 is extremely difficult and IMO is much more like a thought experiment, but requires an honnest investigation. The experiment becomes more tricky when the movement of the earth around the Sun, and more global in our Galaxy is included. Still the two lightsignals behave the same. Experiment #2 is different from the Pound and Rebka experiment and from the concept of Gravitational redshift.
Nicolaas Vroom
>>  And as in SR, the postulate of constant speed of light applies in inertial frames only, but not in general coordinate systems, the analog is true in GR: the postulate of constant speed of light applies in local inertial frames only, not in general coordinate systems. So, it is even wrong to say the postulate of constant speed of light is less valid in GR than in SR. It is valid in GR as much as in SR: in SR, it applies in inertial frames only, and analogously, in GR, the postulate applies in local inertial frames only. 
> 
Do I really need of all this to answer my question? 
A remark: maybe you are not really interested in the question whether the SR postulate of constant speed of light applies in GR, but rather in the question whether you can consider the speed of light as being variable in the coordinate system you are using for a galaxy simulation? That is question is very much simpler, and very easy to answer: yes, you can do that.
>  Nicolaas Vroom wrote: 
> >> 
And as in SR, the postulate of constant speed of light applies in inertial frames only, but not in general coordinate systems, the analog is true in GR: the postulate of constant speed of light applies in local inertial frames only, not in general coordinate systems. So, it is even wrong to say the postulate of constant speed of light is less valid in GR than in SR. It is valid in GR as much as in SR: in SR, it applies in inertial frames only, and analogously, in GR, the postulate applies in local inertial frames only. 
> > 
Do I really need of all this to answer my question? 
> 
A remark: maybe you are not really interested in the question whether the SR postulate of constant speed of light applies in GR, but rather in the question whether you can consider the speed of light as being variable in the coordinate system you are using for a galaxy simulation? That is question is very much simpler, and very easy to answer: yes, you can do that. 
I would add that Einstein himself gave serious consideration to the consistency of the speed of light being relative not absolute. That is to say the speed of light is constant for a given frame of reference. The speed of light being constant to all frames of reference is not the same as saying the speed of light is constant in a absolute sense. If someone very close to a black hole and time dilated to the point that their voice is notably 1 octave lower do you trust their judgement when they tell they measure the speed of light to be c ? With a clock running at half speed I would not trust that voice in the dark. More likely the speed is 1/2 c but they measure it to be c with a clock that is ticking at 1/2 its normal rate.
[[Mod. note  Many of the questions you pose are (in their present form) insufficiently precise to be answered.
For example, "If someone very close to a black hole and time dilated to the point that their voice is notably 1 octave lower" doesn't specify (the spacetime worldline of) the observer who measures that time dialation. And simply saying "1 octave lower" leaves unanswered the question of "1 octave lower than what?". (The standard answer to this latter question is, "with respect to a recording of the nowclosetotheBH speaker, made when she was far from the BH, and coincident with and at rest with respect to the recorder". In other words, adiabatic clock transport, treating the speaker's vocal cords as a clock. Is this what you mean?)
And when that observer "measure[s] the speed of light", we need to know just how that measurement is made. For example, it might be a local measurement made in a freefalling local Lorenz frame... [n.b. "local" here means "small enough that we can approximate spacetime as flat within this region"] ... but then within that frame special relativity applies, and the answer of that measurement MUST be 299792458 m/s. So I guess you mean some other sort of measurement... which needs to be specified.  jt]]
>  I would add that Einstein himself gave serious consideration to the consistency of the speed of light being relative not absolute. That is to say the speed of light is constant for a given frame of reference. The speed of light being constant to all frames of reference is not the same as saying the speed of light is constant in a absolute sense. If someone very close to a black hole and time dilated to the point that their voice is notably 1 octave lower do you trust their judgement when they tell they measure the speed of light to be c ? With a clock running at half speed I would not trust that voice in the dark. More likely the speed is 1/2 c 
In GR, you have to distinguish between local inertial frames and general coordinate systems, like e.g. Schwarzschild coordinates in Schwarzschild solution. Considered in Schwarzschild coordinates, the clock of the observer near the black hole is running at half speed (compared to Schwarzschild coordinate time), and the speed of light is 1/2 c. However, choosing Schwarzschild coordinates is an arbitrary choice, one could as well choose EddingtonFinkelstein coordinates, freefalling coordinates or Kruskal coordinates. In each of those coordinate systems, you'll gather different results for the clock running speed and for the speed of light. Therefore, the speed of light measured with respect to a general coordinate system is arbitrary, and due to that, little meaningful.
The only meaningful speed measurements in GR are those that are performed with respect to a local inertial frame. According to GR, the observer near the black hole will measure c for the speed of light, and since he performed his measurement with respect to a local inertial frame, one can trust his result.
Good point. I made the measurement leaving earth with a calibrated 1 meter stick and an atomic clock. I reported to you from near a black hole that the speed of light is c as I measure it with my 1 meter stick and atomic clock. The gravitational time dilation from this location near a black hole caused my atomic clock to run at 1/2 its normal speed compared with earth. When talking to you on my intergalactic cell phone you noted my voice was one octave lower than normal suggesting my clock has been compromised running at only 1/2 its normal rate caused by gravitational time dilation. With these conditions I put the question to you on earth. Is the speed of light in my location near a black hole , c or 1/2 c ? Keep in mind I should have said 2 c not c if the speed of light is absolute with a time dilated clock but I do not want to bias your thoughts. In your mind in the broader sense is the consistency of the speed of light absolute or relative in the big picture. It is all relative so you may use the earth as the as an arbitrary reference point to make this judgement and assume idea conditions of the earth not changing.
>  Good point. I made the measurement leaving earth with a calibrated 1 meter stick and an atomic clock. I reported to you from near a black hole that the speed of light is c as I measure it with my 1 meter stick and atomic clock. The gravitational time dilation from this location near a black hole caused my atomic clock to run at 1/2 its normal speed compared with earth. When talking to you on my intergalactic cell phone you noted my voice was one octave lower than normal suggesting my clock has been compromised running at only 1/2 its normal rate caused by gravitational time dilation. 
That I noted your voice one octave lower is primarily due to the gravitational redshift which the electromagnetic waves emitted by your cell phone undergo on their towards me.
To conclude that this gravitational redshift is caused by gravitational time dilation, you need to apply Schwarzschild coordinates, in which we both have fixes spatial positions (wordlines with r = const, where r is the Schwarzschild radial coordinate) and time translation invariance applies, so that the waves emitted by your cell phone propagate on wordlines that are equivalent, except a coordinate time shift.
However, instead of Schwarzschild coordinates, we can as well apply a coordinate system with a time coordinate tau that relates to Schwazschild coordinates by
tau = (1  rs/r) t
so that
d(tau) = (1  rs/r) dt  rs t dr / r^2
On our worldlines, r = const applies so that dr = 0, resulting in
d(tau) = (1  rs/r) dt
In this coordinate system, there is no gravitational time dilation. Of course, we again observe the gravitational redhift, since it is coordinateindependent, but in this coordinate system, we do not conclude that is is caused by gravitational time dilation, but rather by differences in propagation of subsequently emitted waves: the later a wave is emitted from your cell phone, the longer is the coordinate time interval the wave takes to reach me (there is no timetranslation invariance like in Schwarzschild coordinates).
Or let use apply Kruskal coordinates. Then our is result is that we both are moving (our worldlines are hyperbolas in a Kruskal spacetime diagram), and that the gravitational redshift is mainly due to our different movements.
So, we see: the gravitational redshift is coordinateindependent, but its relation to a gravitational time dilation depends on the applied coordinate system.
Due to the general covariance of GR, all three mentioned coordinate systems are in the same way valid, there is none of them more valid than the other ones. Therefore, the result you gather in Schwarzschild coordinates, namely that the gravitational redshift is caused by a gravitational time dilation only, is arbitrary and therefore little meaningful.
The only coordinate systems in GR that are valid in a greater measure are the local inertial frames, and in those, there is neither a gravitational time dilation nor a gravitational redshift, since they are limited to spacetime regions that too small to recognize gravitational effects.
To get a better impression of different coordinate systems for Scharzschild geometry, have a look on the spacetime diagrams on this page:
http://casa.colorado.edu/~ajsh/schwp.html
>  With these conditions I put the question to you on earth. Is the speed of light in my location near a black hole , c or 1/2 c ? 
By this formulation, the question is ambigous, since you do not indicate whether you refer to a local inertial frame or to a general coordinate system.
As we have seen above, you obviously refer to Schwarzschild coordinate, and in those, the speed of light indeed is c / 2 in you location. But since Schwarzschild coordinates are arbitrary, this result is little meaningful. The most meaningful indication of the speed of light is with respect to your local inertial frame.
>  Keep in mind I should have said 2 c not c if the speed of light is absolute with a time dilated clock but I do not want to bias your thoughts. In your mind in the broader sense is the consistency of the speed of light absolute or relative in the big picture. It is all relative 
Sad to say, I do not really understand what you try to say here. Assumed, you wanted to claim that the speed of light is not absolute in GR, but rather relative: in GR, the speed of light is always the same in local inertial frames, namely c, whereas in general coordinate systems (Schwarzschild, EddingtonFinkelstein, Kruskal...), it may vary, like it becomes c / 2 near a black hole in Schwarzschild coordinates. The situation is already similar in SR, though: the invariance of the speed of light applies in inertial frames only there, not in e.g. accelerated frames of reference.
>  so you may use the earth as the as an arbitrary reference point to make this judgement 
When saying "reference point", you obviously refer to the SR concept of a frame of reference. However, this concept is not applicable in GR, except in its SR limit, i.e. in spacetime regions suffiently limited.
In SR, when you choose an observer, you automatically declare a frame of reference, that provides a method to compare any clock in the universe to the observer's clock. In GR, however, things are different. By choosing an observer far away from a black hole, you do NOT declare a frame of reference, and you do NOT have a distinct method to compare clocks near the black hole to the observer's clock.
You may, if you want, choose Schwarzschild coordinates, yielding the result, that a clock at radial coordinate r runs by factor sqrt(1  rs/r) slower than the clock of the far away observer, e.g. by factor 1/2 for r = 4/3 rs. But as well, you can choose a different coordinate system, yielding a different ratio for the running speeds of the same two clocks, e.g. the coordinate system with coordinate time tau from above, in which both, the clock near the black hole and the clock of the far aways observer, run at the same speed.
So, by choosing the far away observer as "reference point", you do not fix the clock near the black hole to run with half speed. You need to choose to apply Schwarzschild coordinates in addition. And that choice is arbitrary.
>  So, by choosing the far away observer as "reference point", you do not fix the clock near the black hole to run with half speed. You need to choose to apply Schwarzschild coordinates in addition. And that choice is arbitrary. 
Really now! If the experiment were actually performed, there would be only ONE result. This "arbitrariness" makes no sense and sounds like obfuscation to me.
Gary
>  John Heath wrote: 
> > 
Good point. I made the measurement leaving earth with a calibrated 1 meter stick and an atomic clock. I reported to you from near a black hole that the speed of light is c as I measure it with my 1 meter stick and atomic clock. The gravitational time dilation from this location near a black hole caused my atomic clock to run at 1/2 its normal speed compared with earth. When talking to you on my intergalactic cell phone you noted my voice was one octave lower than normal suggesting my clock has been compromised running at only 1/2 its normal rate caused by gravitational time dilation. 
> 
That I noted your voice one octave lower is primarily due to the gravitational redshift which the electromagnetic waves emitted by your cell phone undergo on their towards me. To conclude that this gravitational redshift is caused by gravitational time dilation, you need to apply Schwarzschild coordinates, in which we both have fixes spatial positions (wordlines with r = const, where r is the Schwarzschild radial coordinate) and time translation invariance applies, so that the waves emitted by your cell phone propagate on wordlines that are equivalent, except a coordinate time shift. However, instead of Schwarzschild coordinates, we can as well apply a coordinate system with a time coordinate tau that relates to Schwazschild coordinates by tau = (1  rs/r) t so that d(tau) = (1  rs/r) dt  rs t dr / r^2 On our worldlines, r = const applies so that dr = 0, resulting in d(tau) = (1  rs/r) dt In this coordinate system, there is no gravitational time dilation. Of course, we again observe the gravitational redhift, since it is coordinateindependent, but in this coordinate system, we do not conclude that is is caused by gravitational time dilation, but rather by differences in propagation of subsequently emitted waves: the later a wave is emitted from your cell phone, the longer is the coordinate time interval the wave takes to reach me (there is no timetranslation invariance like in Schwarzschild coordinates). Or let use apply Kruskal coordinates. Then our is result is that we both are moving (our worldlines are hyperbolas in a Kruskal spacetime diagram), and that the gravitational redshift is mainly due to our different movements. So, we see: the gravitational redshift is coordinateindependent, but its relation to a gravitational time dilation depends on the applied coordinate system. Due to the general covariance of GR, all three mentioned coordinate systems are in the same way valid, there is none of them more valid than the other ones. Therefore, the result you gather in Schwarzschild coordinates, namely that the gravitational redshift is caused by a gravitational time dilation only, is arbitrary and therefore little meaningful. The only coordinate systems in GR that are valid in a greater measure are the local inertial frames, and in those, there is neither a gravitational time dilation nor a gravitational redshift, since they are limited to spacetime regions that too small to recognize gravitational effects. To get a better impression of different coordinate systems for Scharzschild geometry, have a look on the spacetime diagrams on this page: 
> > 
With these conditions I put the question to you on earth. Is the speed of light in my location near a black hole , c or 1/2 c ? 
> 
By this formulation, the question is ambigous, since you do not indicate whether you refer to a local inertial frame or to a general coordinate system. As we have seen above, you obviously refer to Schwarzschild coordinate, and in those, the speed of light indeed is c / 2 in you location. But since Schwarzschild coordinates are arbitrary, this result is little meaningful. The most meaningful indication of the speed of light is with respect to your local inertial frame. 
> > 
Keep in mind I should have said 2 c not c if the speed of light is absolute with a time dilated clock but I do not want to bias your thoughts. In your mind in the broader sense is the consistency of the speed of light absolute or relative in the big picture. It is all relative 
> 
Sad to say, I do not really understand what you try to say here. Assumed, you wanted to claim that the speed of light is not absolute in GR, but rather relative: in GR, the speed of light is always the same in local inertial frames, namely c, whereas in general coordinate systems (Schwarzschild, EddingtonFinkelstein, Kruskal...), it may vary, like it becomes c / 2 near a black hole in Schwarzschild coordinates. The situation is already similar in SR, though: the invariance of the speed of light applies in inertial frames only there, not in e.g. accelerated frames of reference. 
> > 
so you may use the earth as the as an arbitrary reference point to make this judgement 
> 
When saying "reference point", you obviously refer to the SR concept of a frame of reference. However, this concept is not applicable in GR, except in its SR limit, i.e. in spacetime regions suffiently limited. In SR, when you choose an observer, you automatically declare a frame of reference, that provides a method to compare any clock in the universe to the observer's clock. In GR, however, things are different. By choosing an observer far away from a black hole, you do NOT declare a frame of reference, and you do NOT have a distinct method to compare clocks near the black hole to the observer's clock. You may, if you want, choose Schwarzschild coordinates, yielding the result, that a clock at radial coordinate r runs by factor sqrt(1  rs/r) slower than the clock of the far away observer, e.g. by factor 1/2 for r 4/3 rs. But as well, you can choose a different coordinate system, yielding a different ratio for the running speeds of the same two clocks, e.g. the coordinate system with coordinate time tau from above, in which both, the clock near the black hole and the clock of the far aways observer, run at the same speed. So, by choosing the far away observer as "reference point", you do not fix the clock near the black hole to run with half speed. You need to choose to apply Schwarzschild coordinates in addition. And that choice is arbitrary. 
Nice link , I bookmarked it. And thanks for taking the time for a long response. I can see I have failed to set the conditions of the test in a clear way. Perhaps I should state the condition instead of creating the condition . I will state the conditions.
A] Alice is on earth with a 1 meter stick and a atomic clock to measure the speed of light.
B] Bob is gravity time dilated 50 percent. His clock is ticking at 1/2 its rate relative to Alice's clock.
C] There is no Doppler effect or SR effects. Assume ideal conditions of no movement between Alice and Bob.
If Bob measures the speed of light to be 2c then we can assume that the speed of light is absolute at c and it is his slow clock that is causing him to think it is 2c. If Bob measures the speed of light to be c then we can assume the speed of light will always measure c and is not absolute but relative to the observer. This would require the speed of light to be variable in the larger picture to guarantee that all observers measure the speed of light to be c. It should be noted that Alice on earth is the observer. If Bob is the observer then Alice should say the measured speed of light is 1/2 c caused by her fast clock relative to Bob if light speed is absolute. If light speed is relative then Alice will measure it to be c and therefore speed of light is variable in the larger picture , god's view.
The Schwarzschild model requires a more complicated setup of a copper wire link between Alice and Bob to demonstrate causality concerns with multiple time lines. For this reason I have set it aside for now in the interest of clarity of thought. I would enjoy going there but for now it will confuse the issue at hand with too many variables on the table.
To return to the burning question. In your mind is the speed of light absolute or variable. It is a given light will always measure c but is it constant in the larger picture of god looking down at Alice and Bob from a great distance?
[[Mod. note  Once again, many of these questions are insufficiently precise to have welldefined answers.
For example, you write "If Bob measures the speed of light to be 2c". But any (correct) *local* measurement [i.e., a measurement made entirely within a (freelyfalling) local inertial reference frame] of the speed of light gives c (independendent of the details of how the measurement is made). So your description must refer to some sort of *nonlocal* measurement. You need to specificy precisely how that measurement is made.
 jt]]
>>  So, by choosing the far away observer as "reference point", you do not fix the clock near the black hole to run with half speed. You need to choose to apply Schwarzschild coordinates in addition. And that choice is arbitrary. 
Gary Harnagel
>
Really now! If the experiment were actually performed, there would be
only ONE result. This "arbitrariness" makes no sense and sounds like
obfuscation to me.
The problem is that you (Gary harnagel) haven't specified the experiment in sufficient detail. There are many possible experiments which would be consistent with your description, and (in general) these experiments will give different answers.
For example, here are four possible experiments consisten with your description: (a) The faraway observer is a rest with respect to the black hole (BH). She drops a clock into the BH; that clock sends out a sequence of radiowave "ticks" at uniform time intervals as measured by the falling clock; each "tick" also encodes the falling clock's current position (areal radial coordinate) with respect to the BH. The faraway observer measures the arrival frequency of the radiowave "ticks" as a function of the encoded position. (b) Same thing as (a), but change "areal radial coordinate" to "isotropic radial coordinate". (c) The faraway observer is a rest with respect to the BH. She releases a clock which is just like the clock in (a), but is also equipped with a rocket engine. The rocketengineclock is programmed to fly down to a specific position (areal radial coordinate) with respect to the BH, hold itself at that position for a while, then fly to a new position (areal radial coordinate) with respect to the BH, hold itself at that position for a while, then fly to another position, etc etc. The faraway observer measures the arrival frequency of the radiowave "ticks" at each rocketengineclock position, as a function of the encoded radius. (d) Same thing as (c), but change "areal radial coordinate" to "tortise radial coordinate". [there are many other possibilities as well]
As I suggested above, experiments (a), (b), (c), and (d) will (in general) give four different answers to the question "at what rate do the clockneartheBH ticks arrive at the farfromtheBH clock when the clockneartheBH is at the position r=3M?". You haven't specified which of these is the experiment which you're asking about, and nature doesn't single out any of these as "the natural or obvious way to do this experiment".
The fact that there are these multiple possibilities, all of them equally physically meaningful and all of them plausible operational definitions of "the gravitational redshift at a distance r=3M from the BH", is a consequence of the arbitrariness which Gregor Scholten was referring to.

 "Jonathan Thornburg [remove animal to reply]"
> 
Nice link , I bookmarked it. And thanks for taking the time for a
long response. I can see I have failed to set the conditions of the
test in a clear way. Perhaps I should state the condition instead
of creating the condition . I will state the conditions.
A] Alice is on earth with a 1 meter stick and a atomic clock to measure the speed of light. B] Bob is gravity time dilated 50 percent. His clock is ticking at 1/2 its rate relative to Alice's clock. 
According to GR, this statement is ambigous. You missed indicating what coordinate system you applied to compare Bob's clock to Alice's clock.
In SR, you would be finished by just stating "relative to Alice's clock" because that would define a frame of reference. In GR, however, you are not finished, you in addition need to indicate what coordinate system you are applying.
Let's assume you are applying Schwarzschild coordinates.
> 
C] There is no Doppler effect or SR effects. Assume ideal conditions
of no movement between Alice and Bob.
If Bob measures the speed of light to be 2c then we can assume that the speed of light is absolute at c and it is his slow clock that is causing him to think it is 2c. If Bob measures the speed of light to be c then we can assume the speed of light will always measure c and is not absolute but relative to the observer. 
According to GR, this is another ambigous statement. When talking about Bob measuring a speed, you have to indicate with respect to what coordinate systems he is performing his measurement.
Let's assume he measures the speed of light to a local inertial frame. If he then measures the speed of light to be 2c, he has falsified GR and we can immediately skip this discussion about statements of GR. If he, instead, measures to speed of light to be c, we can assume that GR remains applicable, and that with respect to Schwarzschild coordinates, the speed of light at Bob's position is c/2.
What we cannot assume then, though, is that the speed of light would be relative to the observer. Because being relative to an observer is a concept from SR that implies that choosing an observer defines a frame of reference. In GR, there is no concept of frames of reference  except in SR limit  and therefore no concept of being relative to an observer.
>  This would require the speed of light to be variable in the larger picture to guarantee that all observers measure the speed of light to be c. 
Assumed, you mean Schwarzschild coordinates when saying "in the larger picture", you are right. This "larger picture", however, is arbitrary, since one could as well apply different coordinates that yield a different running speed ratio between Bob's clock and Alice's clock than 1/2.
>  It should be noted that Alice on earth is the observer. If Bob is the observer then Alice should say the measured speed of light is 1/2 c caused by her fast clock relative to Bob if light speed is absolute. 
In GR, it does not make sense to say that Bob is "the" observer or that Alice is "the" observer. Defining someone as "the" observer makes sense in SR only, where one can apply the concept of a frame of reference. In SR, one could assign a frame of reference to Alice and one to Bob, and by choosing one of both frames, one would choose either Alice or Bob as "the" observer. In GR, however, there's no frame of reference. One can consider each of both, Alice and Bob, as "an" observer, but none of them as "the" observer.
>  If light speed is relative 
When talking about "relative" or "absolute", you seem to SR's concept of relative and absolute: relative means "depending on the frame of reference" and absolute means "not depending on the frame of reference". In GR, this concept is obsolete, since there's no frame of reference.
>  To return to the burning question. In your mind is the speed of light absolute or variable. It is a given light will always measure c but is it constant in the larger picture of god looking down at Alice and Bob from a great distance? 
In my mind, your question is based on assumptions that aren't valid in GR. When asking for being absolute or relative/variable, you seem to refer to SR concepts that are obsolete in GR. Therefore, your question cannot be answered meaningfully.
>>  So, by choosing the far away observer as "reference point", you do not fix the clock near the black hole to run with half speed. You need to choose to apply Schwarzschild coordinates in addition. And that choice is arbitrary. 
> 
Really now! If the experiment were actually performed, there would be only ONE result. 
This one result, however, would be a result for gravitational redshift, not for gravitational time dilation. You CAN, if you want, apply Schwarzschild coordinates, and based on that, interpret the result as caused by gravitational time dilation. This interpretation, however, is arbitrary, since applying Schwarzschild coordinates is arbitrary.
Or you can modifiy the experiment's prescription by explicitly specifying that Schwarzschild coordinates are to be applied and that observed redshift is to be interpreted as time dilation with respect to Schwarzschild coordinates. This, however, would make the experiment's prescription arbitrary, since one could as well define a prescription specifying the application of a different coordinate system.
>>  Really now! If the experiment were actually performed, there would be only ONE result. This "arbitrariness" makes no sense and sounds like obfuscation to me. 
> 
The problem is that you (Gary harnagel) haven't specified the experiment in sufficient detail. There are many possible experiments which would be consistent with your description, and (in general) these experiments will give different answers. For example, here are four possible experiments consisten with your description: (a) The faraway observer is a rest with respect to the black hole (BH). 
This specification, however, isn't sufficiently detailed, too. "At rest with respect to the blach hole" does not have a disctinct meaning in GR, since there is no such thing like a frame of reference of the black hole. To specify the observer as being resting, you need to specify a coordinate system with respect to which the observer is resting. If you want, you can take Schwarzschild coordinates, like John and Gary obviously do.
>  She drops a clock into the BH; that clock sends out a sequence of radiowave "ticks" at uniform time intervals as measured by the falling clock; each "tick" also encodes the falling clock's current position (areal radial coordinate) with respect to the BH. The faraway observer measures the arrival frequency of the radiowave "ticks" as a function of the encoded position. (b) Same thing as (a), but change "areal radial coordinate" to "isotropic radial coordinate". (c) The faraway observer is a rest with respect to the BH. She releases a clock which is just like the clock in (a), but is also equipped with a rocket engine. The rocketengineclock is programmed to fly down to a specific position (areal radial coordinate) with respect to the BH, hold itself at that position for a while 
As far as John specified the experiment, thise case (c) is presumed, with "holding itself at that position" meaning holding at a fixed Schwarzschild radial coordinate r = const.
What makes the experiment's outcome for gravitational time dilation arbitrary is NOT that there also the cases (a), (b) and (d), but rather that choosing Schwarzschild coordinates for conclusions about the apperaring time dilation is arbitrary.
>  As I suggested above, experiments (a), (b), (c), and (d) will (in general) give four different answers to the question "at what rate do the clockneartheBH ticks arrive at the farfromtheBH clock when the clockneartheBH is at the position r=3M?". 
No, they will give many more different answers, since for each of them, one can apply different coordinate systems. Only for the gravitational redshift, they yield only four different results.
>  You haven't specified which of these is the experiment which you're asking about 
But John had done this before.
[[Mod. note  I agree with all of Gregor Scholten's points. Mea culpa for trying to post about GR when tired and in a rush. :)  jt]]
>  On Thursday, December 10, 2015 at 11:12:56 PM UTC5, Gregor Scholten wrote: 
[]
>  To return to the burning question. In your mind is the speed of light absolute or variable. It is a given light will always measure c but is it constant in the larger picture of god looking down at Alice and Bob from a great distance? 
I would argue that there are two reasonably consistent ways of describing 'what's actually going on'. One is the GR model, in which spacetime is curved, and light (and other energy) travels along those curves at c everywhere. The other is a model in which gravity is a kind of force that causes light (and other energy) to bend and slow. In this way of describing things, light slows down in gravitational fields, and the background spacetime is considered flat just as in your 'god's eye' view.
When I say 'what's actually going on' I mean descriptions that connect or could possibly connect with deeper or separated areas of physics. Descriptions that are not necessarily great for solving specific problems, but better for understanding fundamentals. Each of these descriptions naturally suggests a particular type of coordinate system, but neither is really 'about' coordinate systems.
So, does light *really* slow down or not? Pick one of the above, and you have chosen the answer you prefer. No further measurement required, as we already understand the implications quite well. These two descriptions are the ones we can reasonably offer at present when the question of "what really happens" is asked. (Maybe there are 'deeper' options, but in the current context there are only these two.)
However, much of physics involves discussions of particular physical situations which in the context of gravity tend to involve various carefully selected curved coordinate systems. Because even if the 'gravity as force' model is the best fundamental description, its effects are often most easily described in terms of geometry. Anyway, all these ad hoc coordinate systems are essentially arbitrary as Gregor was saying  or more precisely, they are chosen to fit a particular problem. For example, Schwarzschild coordinates are useful in describing the gravitational field surrounding a star or a black hole.
Hope that is some help.
 Gerry Quinn
 This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus
> 
Gary Harnagel wrote: 
I understand that choosing an experiment where r is constant for Bob leaves out how that condition can be maintained. Specifying that phi and theta are also constant, all wrt a distant observer, means that either Bob is standing on a surface or he is in a rocket. Specifying that the derivative of phi or theta is constant means that he maintains r = constant by orbital motion. Different experimental conditions. But it appears to me that either case can be addressed using Schwarzschild coordinates. One may get different results for the two cases, but the results must agree regardless of the coordinate system used.
Also, there seems to be some conflation about gravitational red shift versus time dilation. Just use an atomic clock to measure the difference in time. Then the change in the wavelength of the carrier is irrelevant.
Gary
>  I like Jonathon's explanation that choosing different coordinate types means choosing a different experiment 
Jonathan did not bring up such an explanation. Jonathan described different experiment, though, but those experiments are not defined by different choices of coordinates. As I pointed out in my reply to Jonathan, the experiments were are talking about here are of (c) type. And as I pointed out, one can choose different coordinate types for experiment (c).
>  to which you allude in your last paragraph. The problem is that by calling out different coordinate systems, the shift to a different experiment isn't made explicit, and this is VERY confusing to neophytes like me. 
This depends on the experiment's prescription. If the prescrition defines that the experiment just measures the gravitational redshift, then the result is just a gravitational redshift, not a gravitational time dilation. Conclusions that the resulting redshift may be caused by gravitational time dilation are not part of the experiment then, and an eventually concluded time dilation is not part of the result then. Choosing different coordinates does not change the experiment then.
If, on the other hand, the experiment's prescription explicitly specifies that Schwarzschild coordinates are to be used, and that gravitational redshift is to be interpreted as gravitational time dilation, then choosing different coordinates changes the experiment, since it changes its prescription.
>  I understand that choosing an experiment where r is constant for Bob leaves out how that condition can be maintained. Specifying that phi and theta are also constant, all wrt a distant observer, means that either Bob is standing on a surface or he is in a rocket. Specifying that the derivative of phi or theta is constant means that he maintains r = constant by orbital motion. Different experimental conditions. 
These are out of interest, though, since John's experiment definition specified that both, the far distant observer and the observer near the black hole, are resting with respect to Schwarzschild coordinates, i.e. for both apply r = const, theta = const and phi = const.
>  But it appears to me that either case can be addressed using Schwarzschild coordinates. 
Of course. But as well, each case can be addressed different coordinates. And due to that, using Schwarzschild coordinates is arbitrary.
>  One may get different results for the two cases, but the results must agree regardless of the coordinate system used. 
That depends on the experiment's prescription, as explained above. A prescription that defines the experiment as measuring a coordinateindependent quantity, like the gravitational redshift, then the result is coordinateindependent. If, however, the prescription defines the experiment as measuring a coordinatedependent quantity, like gravitational time dilation, and specifies a coordinate system to measure that quantity, like Schwarzschild coordinates, the result may be different for different coordinate systems.
>  Also, there seems to be some conflation about gravitational red shift versus time dilation. Just use an atomic clock to measure the difference in time. Then the change in the wavelength of the carrier is irrelevant. 
However, one single atomic clock cannot be used to measure a gravitational time dilation. You need at least two of them, and they must the spatially separated. To measure the gravitational time dilation in Schwarzschild coordinates, one could e.h. the following experiment:
Attach two clocks to two different spatial positions, the first at r = r1, the second at r = r2 > r1. For both clocks apply theta = const and phi = const. Now let the first clock emit a light signal to the second one. Note the proper time tau2_1 displayed by the second clock when the light signals arrives it. After some proper time interval Delta tau1 on the first clock, e.g. 1 second, let this clock emit another light signal to the second clock. Note again ther proper time tau2_2 the second clocks displays when this second signals arrives.
You will find out that the proper time interval on the second clock,
Delta tau_2 = tau2_2  tau2_1
is different from the proper interval Delta tau1 on the first clock, namely that Delta tau2 is longer: Delta tau_2 > Delta tau1. Since the propagation of both light signals is equivalent in Schwarzschild coordinate due to time translation invariance, you will conclude that this difference in the proper time interval is caused by gravitational time dilation.
This result, however, is coordinatedependent. Instead of Schwarzschild coordinates (t, r, theta, phi), you could instead use a coordinate system (T, R, Theta, Phi), that transforms from Schwarzschild coordinates by
T = (1  rs/r) t R = r Theta = theta Phi = phi
Applying these coordinates, wou will NOT conclude that the difference in proper time interval is due to gravitational time dilation, but rather by different propagation of the two light signals (there is no time translation invariance in these coordinates): the second signal took a longer coordinate time interval to reach the second clock.
You can define different experiments than this one to measure the gravitational time dilation, but as long as the two uses clocks always remain in their fixed different spatial positions, you will be obliged to use some kind of signals travelling between them to perform the experiment, and this makes necessary to take the propagation of these signals into account.
Alternatively, you can use clocks that are initially close together and encounter again finally. Then you do not need signals. You can assume, the both clocks start at r = r2, and that the first clocks moves from r2 to r1 then, stays at r1 for a long proper time interval, and then return to r2 finally. When the first clocks returns to r2, you can compare the different elapsed proper time intervals of the to clocks.
However, also in this experiment, conclusions from the result that concern gravitational time dilation are coordinatedependent again: in Schwarzschild coordinates, you will conclude that during the most elapsed coordinate time, the first clocks stayed at r = r1, and that the time intervals the clock took to transit from r2 to r1 and from r1 to r2 again were neglectably short, so that the difference in elapsed proper time obviously came from the time when the fist clock stayed at r1.
Applying the coordinate (T, R, Theta, Phi) I described above, on the other hand, your conclusions are completely different: the difference in elapsed proper time comes from the phases where the clock was travelling from r2 to r1, and back from r1 to r2, not from the phase where it stayed at r1.
Now, one could be temptated to claim that Schwarzschild coordinates are more valid than the coordinates (T, R, Theta, Phi) since in Schwarzschild coordinates, time translation invariance applies, making these coordinates specially meaningful. As far as the Schwarzschild solution is considered on its own, one could indeed think that this argumentation would be valid.
However, in any solutions of the field equations of GR, one always has to keep in mind the full symmetries of GR, and these include general covariance which implies that coordinate systems without time translation invariance are as good as coordinate systems with time translation invariance. Keep in mind that there are solutions of field equations where you cannot construct coordinate systems with translation invariance at all, e.g. cosmological solutions that describe an expanding universe. Therefore, GR cannot ascribe a special validity to time translation invariant coordinate systems, and this remains valid even for solution where such coordinate systems can be concstructed.
The only special coordinate systems in GR are the local inertial frames, since they can be constructed in any arbitrary solution of the field equations.
[...]
>  I can see I have failed to set the conditions of the test in a clear way. Perhaps I should state the condition instead of creating the condition . I will state the conditions. 
Others have given good answers to this, but let me try to say it in slightly different words. I'll avoid referring to coordinate systems, since strictly speaking, no physical result should depend on a choice of coordinate system  the problem is that unless you're very careful, different coordinates push you toward different hidden assumptions. (Conversely, hidden assumptions about things like simultaneity can often be converted to statements about choices of coordinates.)
There's a slogan that all misunderstandings about relativity come from a failure to appreciate the relativity of simultaneity. This is an exaggeration, of course, but there's some truth to it. It's very easy to forget that there's no single "right" way to compare clocks or meter sticks at different locations, and that different choices can lead to different conclusions.
In particular:
>  A] Alice is on earth with a 1 meter stick and a atomic clock to measure the speed of light. 
Here, you're implicitly assuming that the two "meter sticks" are the same length. How do you determine that?
>  B] Bob is gravity time dilated 50 percent. His clock is ticking at 1/2 its rate relative to Alice's clock. 
How can you tell? For this to mean something, you need a method to compare clocks at two different locations. Different choices give different results.
>  C] There is no Doppler effect or SR effects. Assume ideal conditions of no movement between Alice and Bob. 
How do you tell? To say that Alice and Bob are at rest relative to each other, you need a way to compare their velocities. How do you do that? One way would be to look for Doppler shift, but how would you propose to disentangle that from gravitational red shift?
Consider the first question, the length of Alice's and Bob's meter sticks. It may be tempting to say that if Alice and Bob start with identical meter sticks at the same place and then move apart, their meter sticks stay the same. But would you say that about their clocks as well? If so, then if Bob and Alice started with identical atomic clocks, Bob's clock is still measuring time at the same rate as Alice's not "ticking at half its rate."
Or are you saying you want the length of a meter stick to remain constant when its location changes, but the speed of a clock to change? You *can* make such a choice  actually in infinitely many ways  but you have to specify a precise method.
Another way to compare the meter sticks would be to have Alice and Bob each time a pulse of light as it moves from one end of a stick to the other. If it takes about 3.336 nanoseconds, then each stick is one meter long. This is a nice, consistent method, and it's pretty much the "standard" choice. But of course with this definition, the speed of light is automatically the same for both Alice and Bob.
[...]
>  To return to the burning question. In your mind is the speed of light absolute or variable. It is a given light will always measure c but is it constant in the larger picture of god looking down at Alice and Bob from a great distance? 
It depends on how god is synchronizing clocks and determining lengths. Te key lesson of relativity is that there is no "right" answer, no choice that is a "god'seye view."
Steve Carlip
I wish to convey the simultaneity of time to a class using the classic train and lightening strikes. A hand goes up in the back of the class wanting to know if it is a steam powered train or a diesel powered train. How do I respond? Jumping out the window to just end it all is one option.
>  Jonathan Thornburg wrote: 
>>  (a) The faraway observer is a rest with respect to the black hole (BH). 
> 
This specification, however, isn't sufficiently detailed, too. "At rest with respect to the blach hole" does not have a disctinct meaning in GR, 
But when does "at rest" have a meaning, then? Being at rest w.r.t. empty space has no meaning, so at least we need one particle in it and how is a black hole different from a particle? (OK, it's mass might be of a different scale, but what is essentially different?)
 Jos
[[Mod. note  In the context of general relativity: For an asymptoticallyflat spacetime (this includes Schwarzschild and Kerr black holes) we can define a notion of the total 4momentum of the spacetime, as measured far from the BH (either at spatial infinity or at future null infinity). This then lets us define "at rest" (choose a farfromtheBH observer, then Lorentzboost her until she measures no spatial component to the total 4momentum).  jt]]
>  In article <0fc9baa217e64b72a050fbc3f9988580@googlegroups.com>, heath...@gmail.com says... 
> >  On Thursday, December 10, 2015 at 11:12:56 PM UTC5, Gregor Scholten wrote: 
> 
[] 
> > 
To return to the burning question. In your mind is the speed of light absolute or variable. It is a given light will always measure c but is it constant in the larger picture of god looking down at Alice and Bob from a great distance? 
> 
I would argue that there are two reasonably consistent ways of describing 'what's actually going on'. One is the GR model, in which spacetime is curved, and light (and other energy) travels along those curves at c everywhere. The other is a model in which gravity is a kind of force that causes light (and other energy) to bend and slow. In this way of describing things, light slows down in gravitational fields, and the background spacetime is considered flat just as in your 'god's eye' view. When I say 'what's actually going on' I mean descriptions that connect or could possibly connect with deeper or separated areas of physics. Descriptions that are not necessarily great for solving specific problems, but better for understanding fundamentals. Each of these descriptions naturally suggests a particular type of coordinate system, but neither is really 'about' coordinate systems. So, does light *really* slow down or not? Pick one of the above, and you have chosen the answer you prefer. No further measurement required, as we already understand the implications quite well. These two descriptions are the ones we can reasonably offer at present when the question of "what really happens" is asked. (Maybe there are 'deeper' options, but in the current context there are only these two.) However, much of physics involves discussions of particular physical situations which in the context of gravity tend to involve various carefully selected curved coordinate systems. Because even if the 'gravity as force' model is the best fundamental description, its effects are often most easily described in terms of geometry. Anyway, all these ad hoc coordinate systems are essentially arbitrary as Gregor was saying  or more precisely, they are chosen to fit a particular problem. For example, Schwarzschild coordinates are useful in describing the gravitational field surrounding a star or a black hole. Hope that is some help.  Gerry Quinn  This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus 
[[Mod. note  Please limit your text to fit within 80 columns, preferably around 70, so that readers don't have to scroll horizontally to read each line. I have manually reformatted this article, making an educated guess at paragraph breaks.  jt]]
Well said. If memory serves your last post was the same in that you understood the point being made the first time. If I were smart I would leave at that on a high note but it is not in my nature:<). I would like to demonstrate from a philosophical position that gravitational red shift could be in violation of causality provided ideal conditions of Doppler and SR effects are set aside. The way to do this is to state ahead of time that there is no movement between A and B therefore there can not be a Doppler or SR effect. Now that the clutter of too many variables on the table has cleared we have only gravitation time dilation and gravitational red shift of B atomic clock observed by A that is not time dilated. The exact amount of time dilation is not relevant other than being consistent so I leave it to the read to assume then set ideal condition for it to be so. If Schwarzschild coordinates are useful then a toss of dice could set the exact time dilation and then reverse construct the Schwarzschild coordinates. I am kidding of course :<). Clock B may have missing ticks without violating causality as it is time dilated therefore justified to have missing ticks as observed by A. However if gravitational red shift were in any way effect the B clock rate as observed by A then there is a violation to causality. Where are the missing ticks? There is no longer a Doppler effect to continuously hide them in space. Where did they go? From this I conclude that gravitational red shift is simply the observation of gravity time dilation.
There in is the rub. From energy conservation laws the frequency of a photon must go down caused by G red shift. From a causality position the frequency can not go down as it violates causality. Where are you going to hide the missing tick . Only gravity time dilation is allowed to have missing ticks not gravitational red shift as it is only a carrier of information. I do not have an answer for this.
On 12/11/15 12/11/15  6:00 AM, Gary Harnagel wrote:
>  Really now! If the experiment were actually performed, there would be only ONE result. This "arbitrariness" makes no sense and sounds like obfuscation to me. 
If one specifies the experiment sufficiently well, then GR predicts a single result. For a basic redshift measurement of an electromagnetic signal, a sufficient specification consists of: 1) the metric of spacetime at all events of interest 2) the position and 4velocity of the emitter when the signal is emitted 3) the position and 4velocity of the detector when the signal is detected 4) the path of the EM signal between emission and detection 5) the proper period of the emitted EM signal; it must be very much smaller than any other timescale in the problem
Without all that, one cannot calculate the redshift. But with all that one can calculate the redshift in a coordinateindependent way:
A) Form the displacement 4vector between two successive wavecrests of the emitted wave. This is necessarily parallel to the emitter's 4velocity, with norm (5). B) Parallel propagate that displacement 4vector along the signal path to the detector. C) Compute the dot product of the result of (B) with the detector's 4velocity. This is the measured period of the detected wave.
Note this algorithm is quite general and works in any manifold of GR (including Minkowski spacetime of SR, and nonstatic/nonstationary manifolds). It depends on the metric at the emission event, everywhere along the signal path, and at the detection event.
Note also it does not distinguish among "gravitational time dilation", "gravitational redshift", "redshift due to relative velocity", and "Doppler shift"  all it does is give you the predicted numerical result; what label one chooses to apply does not really matter.
Tom Roberts
>  However if gravitational red shift were in any way effect the B clock rate as observed by A then there is a violation to causality. Where are the missing ticks? 
Instead of Schwarzschild coordinates, you can e.g. choose coordinates in which time translation invariance does not apply. In such coordinates, the light signals propagating from clock B to clock A may propagate differently: the later a signal is emitted by clock B, the more coordinate time takes it to reach clock A. Due to the symmetry of GR, such a coordinate is as valid as Schwarzschild coordinates are.
I made two spacetime diagrams that illustrate this:
http://fs5.directupload.net/images/151215/ny7cjhue.png
The left diagram is based on Schwarzschild coordinates. Since time translation invariance applies there, the light signals from clock B to A are equivalent, except the second one being shifted by some coordinate time interval. The right diagram is in coordinates without time translation invariance. The second light signal takes longer (i.e. a longer coordinate time interval) to reach clock A.
>  There is no longer a Doppler effect to continuously hide them in space. 
But differences in light propagation due to time translation invariance not applying.
>  Where did they go? From this I conclude that gravitational red shift is simply the observation of gravity time dilation. 
Your conclusion is based on the presumption that a coordinate system in which time translation invariance applies is more valid than a coordinate system in which there is no time translation invariance. According to GR, this presumption must be considered as wrong.
Although Schwarzschild solution has special properties that may temptate one to make this wrong presumption, one has to keep in mind that the full symmetry of GR, i.e. general covariance, applies in any solution of the field equations, even in those with special properties.
>  There in is the rub. From energy conservation laws the frequency of a photon must go down caused by G red shift. From a causality position the frequency can not go down as it violates causality. Where are you going to hide the missing tick . 
To a coordinate system without time translation invariance. According to the symmetries of GR, such a coordinate system is as valid as one with time translation invariance like Schwarzschild coordinates.
>  Only gravity time dilation is allowed to have missing ticks not gravitational red shift as it is only a carrier of information. 
Once again: this conclusion is based on the presumption that time translation invariance is obliged to apply. This presumption is wrong in GR.
>  I do not have an answer for this. 
You are wrong, you have one, since I indicated it to you several times: instead of Schwarzschild coordinates, you can as well apply coordinates in which time translation invariance does not apply.
>>>  (a) The faraway observer is a rest with respect to the black hole (BH). 
>> 
This specification, however, isn't sufficiently detailed, too. "At rest with respect to the blach hole" does not have a disctinct meaning in GR, 
> 
But when does "at rest" have a meaning, then? Being at rest w.r.t. empty space has no meaning, so at least we need one particle in it and how is a black hole different from a particle? 
In GR, a particle is even not sufficient to define being at rest, since unlike in SR, the particle does not define a frame of reference. So, in addition to a particle, you need a coordinate system.
In SR, a particle would be sufficient, but not in GR.
More in detail: an inertial frame, like it is constructable in SR, is like a fourdimensional Cartesian coordinate systems: the coordinate lines of it four coordinates (t,x,y,z) are straight lines and orthogonal to each other. In the flat spacetime of SR, such an inertial frame can be defined in a distinct way by choosing a uniformly moving particle: the wordline of that particle is a straight line, and all the t coordinate lines of the inertial frame are parallel to the particle's worldline, while the spatial coordinate lines are orthogonal to the so defined t coordinate lines. In the curved spacetime of GR, however, there is no such procedure to define an inertial frame or any other type of coordinate system from just choosing a particle. You won't be able to construct a coordinate system where all coordinate lines are straight (i.e. geodesic) everywhere and at the same time orthogonal to each other everywhere.
Take e.g. Schwarzschild coordinates, those are orthogonal, but their coordinate lines are not straight (proof: a particle with a worldline on which r = const, theta = const, phi = const applies, i.e. with a wordline that matches a t coordinate line, is not freefalling, so the wordline is not goedesic, and by this, the t coordinate line is not geodesic, too). Therefore, choosing Schwarzschild coordinates is arbitrary. Instead, one could as well choose coordinates where the coordinate lines are geodesic, but not orthogonal to each other. In those coordinates, being at rest will probably have a different meaning than in Schwarzschild coordinates (e.g. a free falling particle might have a wordline that matches a t coordinate line, implying it is at rest in these coordinates, whereas it is surely not at rest in Schwarzschild coordinates.).
>  (OK, it's mass might be of a different scale, but what is essentially different?) 
Different to a particle in the flat spacetime of SR? The spacetime curvature generated by the black hole that destroys to applicability of frames of reference.
>  John Heath wrote: 
> > 
However if gravitational red shift were in any way effect the B clock rate as observed by A then there is a violation to causality. Where are the missing ticks? 
> 
Instead of Schwarzschild coordinates, you can e.g. choose coordinates in which time translation invariance does not apply. In such coordinates, the light signals propagating from clock B to clock A may propagate differently: the later a signal is emitted by clock B, the more coordinate time takes it to reach clock A. Due to the symmetry of GR, such a coordinate is as valid as Schwarzschild coordinates are. I made two spacetime diagrams that illustrate this: http://fs5.directupload.net/images/151215/ny7cjhue.png The left diagram is based on Schwarzschild coordinates. Since time translation invariance applies there, the light signals from clock B to A are equivalent, except the second one being shifted by some coordinate time interval. The right diagram is in coordinates without time translation invariance. The second light signal takes longer (i.e. a longer coordinate time interval) to reach clock A. 
> > 
There is no longer a Doppler effect to continuously hide them in space. 
> 
But differences in light propagation due to time translation invariance not applying. 
> > 
Where did they go? From this I conclude that gravitational red shift is simply the observation of gravity time dilation. 
> 
Your conclusion is based on the presumption that a coordinate system in which time translation invariance applies is more valid than a coordinate system in which there is no time translation invariance. According to GR, this presumption must be considered as wrong. Although Schwarzschild solution has special properties that may temptate one to make this wrong presumption, one has to keep in mind that the full symmetry of GR, i.e. general covariance, applies in any solution of the field equations, even in those with special properties. 
> > 
There in is the rub. From energy conservation laws the frequency of a photon must go down caused by G red shift. From a causality position the frequency can not go down as it violates causality. Where are you going to hide the missing tick . 
> 
To a coordinate system without time translation invariance. According to the symmetries of GR, such a coordinate system is as valid as one with time translation invariance like Schwarzschild coordinates. 
> > 
Only gravity time dilation is allowed to have missing ticks not gravitational red shift as it is only a carrier of information. 
> 
Once again: this conclusion is based on the presumption that time translation invariance is obliged to apply. This presumption is wrong in GR. 
> > 
I do not have an answer for this. 
> 
You are wrong, you have one, since I indicated it to you several times: instead of Schwarzschild coordinates, you can as well apply coordinates in which time translation invariance does not apply. 
I appreciate the effort you are making to get your point across and I would add Tom as well for taking the time to make the counter argument as clear as possible. I know from experience that it takes a good hour if not more to word it just right , for myself anyways , so I appreciate the time taken to conveying these thoughts. l hear you.
Founding principles of physics are not to be played with. Energy conservation , momentum conservation , causality. This is our candle of light to navigate this wonderful subject of physics. These principles can not be set aside if it is inconvenient. On another note one can have 1 variable on the table and be okay. You can have 2 variables on the table and still be okay provided one is willing to pace the floor a few nights to sort out all the possible alternatives. If there are 3 variables on the table it is unlikely anything productive can come out as there are just too many roads to explore. If there are 4 variables on the table forget it as it not going to happen. Maybe a computer but not the human mind with a clock rate of 25 Hz at best.
I have made what I consider a valid argument from a philosophical position that gravitational red shift can not change rate of ticks , amount of time dilation , without being in conflict with causality within the limitations of no SR effects and no Doppler effects. The only two variables are gravitational time dilation and gravitational red shift. If new variables are introduce such as this coordinate system vs that then we have 3 or 4 variables on the table to consider. This is beyond human capacity and will lead to nothing more than dogs barking at the moon into the wee hours. Surely we are better than dogs barking at the moon into the wee hours. Please restrict your self to gravitational time dilation and gravitational red shift only to proceed in a productive way.
For clarification a photon leaving earth must be reduced in frequency to satisfy energy concentration laws. If the frequency of the photon is reduced within a medium , medium between earth and space , there will be a violation to causality.
To understand why think of a rigid hollow rod between A and B with information of atomic clock ticks being conveyed by a laser in the middle of the rigid rod. With the rigid rod there can not be Doppler effects. With this in place make sure the rod is not rotating relative to the stars so that there can not be a SR effects within that local area. This leavers us with only 2 variables of G time dilation and G red shift between A and B. I do not think it is possible for G red shift to change time dilation without being in violation of causality. However if photon energy therefore frequency is not adjusted for G red shift then energy conservation will be violated. Either way it is dead end road. Where is the compromise for both causality and energy conservation to be satisfied under these conditions?
Always good to describe a problems two ways to best communicate a thought. B sends a sample of 1000 pules to A from his atomic clock to test for time dilation caused by G time dilation. There is not a violation to causality here. However for G red shift to change measurements of time dilation it must change 1000 pulses to 999 or 1001 pulses which is a clear violation to causality. Keep in mind G red shift is information on a laser beam of light that can not go back in time to change the atomic clock as it is just a wave of information of 1000 pulses. There is no Doppler effect to hide pulses. Only G time dilation can change atomic tick rates. G red shift does not have the means to effect clock rate other than delayed in time but it will still be 1000 pulses only at a rate consistent with the rate pulses are leaving B. If not there will be too many or not enough pulses in the information channel which will be unmanageable over a period of time if 1000 pulses is changed to 1 10^10 pulses. Where can one hide these pulses in a G red shift as it is just a medium that conveys information from A to B.
[[Mod. note  Energy and momentum conservation are nice principles, but they're very tricky in a curved spacetime. Notably, it's very hard to even *define* the total energy/momentum in some finite volume: You can (fairly) easily define the energy/momentum in an infinitesimal volume, but in a generic curved spacetime there's no unique way to add up (volumeintegrate) the contributions from all the different infinitesimal regions.  jt]]
>  On Sunday, December 13, 2015 at 1:19:20 AM UTC5, Gerry Quinn wrote: 
[]  show quoted text  I'm not precisely clear as to your exact thought experiment, but it seems to me that you can start by looking at things through 'god's eye' coordinates, a.k.a. coordinates natural to an observer in a low gravitational far from the system of interest. In these flat spacetime coordinates, light slows and bends in gravitational fields. But so long as you consider only regions outside event horizons, you can describe any physical system in a way that is consistent with any system of GR curved coordinates.
There is no causality violation in either description. If B moves in close to a black hole for a while and comes back again, he will have aged less than A, according to either formulation. But there are no 'missing ticks'. In the flat spacetime formulation, that's because light and time slowed down where he was. In the curved spacetime formulation, light and time go at the same speed everywhere, but spacetime is distorted. So when he meets up again with A, he finds less time passed on the route he took. And when they meet, the number of ticks observed by both parties will be identical.
Remember, in relativity it's very important to talk only about local measurements  so you can't safely add the ticks until A and B meet, nor can you claim that there is no relative movement. In the flat spacetime formulation, that's still technically the case if we are talking about relative movement and invoking special relativity, but where there is no relative movement [and no acceleration  this doesn't apply in a rotating system!] we can assert the fact without tripping ourselves up. In the discussion of the general relativistic formulation of this thought experiment, we can't really do that. You can't claim a paradox in a theory based on nonmeasureable entities that aren't considered meaningful in that theory.
Also, note that energy conservation applies in asymptotically flat spacetimes in GR, but is not necessarily applicable when only part of such a spacetime is considered.
 Gerry Quinn
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[[Mod. note  Your description doesn't tell me how to define your "god's eye" (GE) coordinates.
Let's be specific. What's your operational definition of GE coordinates for Schwarzschild spacetime, and why should we believe that these are unique (i.e., that they're the *only* coordinates "natural to an observer in a low gravitational far from the system of interest")?
And, how do we know that the GE coordinates cover all "interesting" regions of spacetime. For example, can you prove that GE coordinates don't have any coordinate singularities outside the event horizon?  jt]]
> 
For clarification a photon leaving earth must be reduced in frequency
to satisfy energy concentration laws. If the frequency of the photon
is reduced within a medium , medium between earth and space , there
will be a violation to causality.
To understand why think of a rigid hollow rod between A and B with information of atomic clock ticks being conveyed by a laser in the middle of the rigid rod. With the rigid rod there can not be Doppler effects. 
You have to keep in mind, though, that according to Relativity, there is no such thing like an ideal rigid rod. Any real rod is deformable. Imagine a rod consisting of atoms. The atoms are bound together by interatomic forces. With the rod exposed to a gravitational field, the position of each atom is determined by an equilibrium of the gravitational forces (the rod and its atoms are not freefalling, so each atom experiences a gravitational force) and the interatomic forces from the other atoms.
Now consider things in Schwarzschild coordinates. The gravitational field is static there (in the sense that the derivatives to coordinate time vanish), so the equilibrium positions of the atoms of the rod are static, too, making the rod not stretching or shrinking.
But now consider things in e.g. Kruskal coordinates. With passing Kruskal coordinate time v, a rod with two ends for which r = const applies each is shrinking more and more. This is in full compliance with the rod atoms' positions being determined by equilibrium between gravitational force and interatomic forces: the gravitational field is not static in Kruskal coordinates, but rather changing by coordinate time v. So, the equilibrium positions of the rod atoms are changing, too, making the rod being shrinking.
Therefore, your argument that there cannot be a Doppler effect  or let's say: a redshift due to movement  is wrong.
In principle, this rod examples shows what I said in a parallel post in this thread, namely that in a curved spacetime, there is no distinct procedure to construct a frame of reference. With the assumption of a rigid rod, one could be temptated to claim that such a rod should provide such a procedure: namely that the wordlines of the rod atoms might define the t coordinate lines of a frame of reference. But this is wrong: there is no reason why a rod had to be rigid, and therefore no reasong to prefer coordinate systems in which both ends of the rod are resting.
>  Always good to describe a problems two ways to best communicate a thought. B sends a sample of 1000 pules to A from his atomic clock to test for time dilation caused by G time dilation. There is not a violation to causality here. However for G red shift to change measurements of time dilation it must change 1000 pulses to 999 or 1001 pulses which is a clear violation to causality. 
You are again making the wrong assumption that time translation invariance had to apply. In Schwarzschild coordinates, time translation invariance applies, making all 1000 pulses take the same coordinate time interval to propagate from B to A. So that redshift only can be explained by different ratios of the proper times of the two clocks to coordinate time.
However, in GR, there is no reason why not to apply coordinates without time translation invariance. Take again the following coordinates:
T = sqrt(1  rs/r) t R = r Theta = theta Phi = phi
You will see that the second pulse from B to A takes a little more coordinate time T to propagate than the first pulse, the third pulse takes again a little more coordinate time than the second one, and so on. Let Delta T_B denote the coordinate time interval it takes to emit all 1000 pulses from clock B. And let Delta T_A denote the coordinate time interval it takes to receive all 1000 pulses at clock A. Then the relation is
Delta T_A = 1.001 * Delta T_B
So, in a coordinate time interval of length Delta T_B, clock A receives only 999 pulses, not 1000. The 1000th pulse comes a little later.
A further analysis shows up that when we consider pulses propagating in the opposite direction, namely inwards from clock A to clock B, the propagation time interval of those pulses becomes shorter and shorter, and after a finite coordinate time T, it hits zero. In other words: the radial coordinate R becomes timelike. This simply means that the coordinates (T, R, Theta, Phi) have a coordinate singularity in future direction, outside the black hole. This implies that their range of validity (their "map") is even more limited than the one of Schwarzschild coordinates (which is limited to r > rs). But within this range, the coordinates (T, R, Theta, Phi) are  according to GR  as good as any other coordinate system.
>  Keep in mind G red shift is information on a laser beam of light that can not go back in time to change the atomic clock as it is just a wave of information of 1000 pulses. There is no Doppler effect to hide pulses. 
But there is a lack of time translation invariance (in the coordinates (T, R, Theta, Phi)) that allows the 1000 pulses to stretch, from Delta T_B to
Delta T_A = 1.001 * Delta T_B
> 
.... [[Mod. note  Your description doesn't tell me how to define your "god's eye" (GE) coordinates. Let's be specific. What's your operational definition of GE coordinates for Schwarzschild spacetime, 
Wouldn't that be r = infinity?
>  and why should we believe that these are unique (i.e., that they're the *only* coordinates "natural to an observer in a low gravitational far from the system of interest")? 
There should be an infinite number of coordinates that are at r < infinity but still large enough to be insignificantly different from r = infinity by our measurement techniques.
>  And, how do we know that the GE coordinates cover all "interesting" regions of spacetime. 
But the GE coordinates are essentially where WE are, and we're in peril if we aren't there.
>  For example, can you prove that GE coordinates don't have any coordinate singularities outside the event horizon?  jt]] 
What about a circular orbit at r = 1.5*r_schw?
Gary
On 12/18/15 12/18/15 1:14 AM, Gerry Quinn wrote:
>  [...] it seems to me that you can start by looking at things through 'god's eye' coordinates, a.k.a. coordinates natural to an observer in a low gravitational far from the system of interest. In these flat spacetime coordinates, light slows and bends in gravitational fields. But so long as you consider only regions outside event horizons, you can describe any physical system in a way that is consistent with any system of GR curved coordinates. 
This is just plain not true. You cannot apply such "flat coordinates" to any manifold of GR containing mass or energy, as such manifolds are not flat. Remember "flat" is a property of the metric, not the coordinates, and the metric is a tensor (field) and therefore independent of coordinates.
What you seem to be thinking of is a completely different formulation of gravity as a spin2 field on a flat manifold. This is a MUCH bigger difference than mere selection of coordinates as you say. This model can account for many properties of GR, but in particular it can be compared to GR only in regions in which gravitation is weak (so you can put the manifolds of the two models into 1to1 correspondence with negligible error, and thus compare them). This comparison fails wherever gravity is not weak, and that can happen well outside any event horizons.
>  There is no causality violation in either description. 
This depends IN DETAIL on what one means by "causality". The casual notion of "this caused that" is both hopelessly naive and completely useless. So what do you mean?
In relativity, causality is the property that at any given event in the manifold, the fields depend only their values at events within the past lightcone of the event in question. How they depend is an aspect of the specific fields being discussed, and their properties and interactions.
>  If B moves in close to a black hole for a while and comes back again, he will have aged less than A, according to either formulation. But there are no 'missing ticks'. In the flat spacetime formulation, that's because light and time slowed down where he was. 
It OUGHT to be obvious that mere coordinate choice cannot possibly do that  it requires a physical process to make "light and time [be] slowed down".
>  In the curved spacetime formulation, light and time go at the same speed everywhere, but spacetime is distorted. So when he meets up again with A, he finds less time passed on the route he took. 
Note that in neither model are there any "missing ticks". In GR the integrated proper time (= tick count) over the two paths is different; in the other model B's clock physically ticked slower for much of his path. But nobody could possibly notice that some ticks were "missing".
>  And when they meet, the number of ticks observed by both parties will be identical. 
I think you meant to say that A and B can have different tick counts (elapsed proper times) when they meet, but the two models agree on what those counts are.
>  Remember, in relativity it's very important to talk only about local measurements 
Hmmm. One can discuss nonlocal "measurements" as long as one specifies how they are performed with sufficient clarity and precision. Of course the actual act of measurement takes place at a single event and is thus inherently "local", so by "nonlocal measurement" one really means combining measurements performed at different events.
>  so you can't safely add the ticks until A and B meet, 
I think you mean "count the ticks on clocks A and B, ending when they meet". One can certainly compare the clock readings of two clocks, but then, one must specify HOW they are compared; this is simple when the clocks are colocated, but when they aren't this would be a "nonlocal measurement" that must be specified in more detail. Note this applies to both the beginning and the end of the interval over which they are to be compared.
>  [... further discussion which I cannot decipher at all] 
>  Also, note that energy conservation applies in asymptotically flat spacetimes in GR, but is not necessarily applicable when only part of such a spacetime is considered. 
Energy conservation in GR is subtle and complicated. But if you follow your own dictum above, "talk only about local measurements", then it is easy: energy and momentum are locally conserved at every event in the manifold.
>  [[Mod. note  Your description doesn't tell me how to define your "god's eye" (GE) coordinates. Let's be specific. What's your operational definition of GE coordinates for Schwarzschild spacetime, [...] 
He intends the "GE" coordinates to be "flat", which simply is not possible in Schw. spacetime.
Tom Roberts
>  But now consider things in e.g. Kruskal coordinates. With passing Kruskal coordinate time v, a rod with two ends for which r = const applies each is shrinking more and more. This is in full compliance with the rod atoms' positions being determined by equilibrium between gravitational force and interatomic forces: the gravitational field is not static in Kruskal coordinates, but rather changing by coordinate time v. So, the equilibrium positions of the rod atoms are changing, too, making the rod being shrinking. 
Another remark: considering the Schwarzschild solution in Kruskal coordinate is similar to considering a uniformly accelerating rocket in SR. Instead of Kruskal coordinates (u,v), there are the coordinates of the inertial frame (X,T) where the rocket is initially resting in, and instead of the Schwarzschild coordinates (r,t), there the socalled Rindler coordinates (x,t) that can be imagined as defining the accelerated frame of reference of the rocket:
https://en.wikipedia.org/wiki/Rindler_coordinates#Relation_to_Cartesian_chart
The front and back of the rocket can be thought as having constant spatial Rindler coordinate x (e.g. x = 1 for the front and x = 0.6 for the back). Now, when the rocket accelerates more and more, the front and back of the rocket come closer and closer together seen from the inertial frame (X,T), due to Lorentz contraction.
In the inertial frame (X,T), this Lorentz contraction can also be interpreted as being caused by the interatomic forces of the rocket's material: assumed, the forces are of electromagnetic nature, it follows that they can be described by LineardWiechert potentials, resulting in electric fields being Lorentzcontracted due to the movement of the electric charges in the rocket atoms (seen from the inertial frame (X,T)). Those Lorentzcontracted electric fields can be thought as causing the rocket atoms to be Lorentzcontracted, and finally, the rocket itself.
Returning to Kruskal coordinates in Schwarzschild coordinates, we can conclude that your "rigid" rod, which is of constant length in Schwarzschild coordinates, is contracted by an analogous mechanism: it's not only the gravitational field that causes the atoms' equilibriums positions to evolve in a way that the rod is contracted, there are also the interatomic forces behaving in a way that yields a contraction effect on the rod (in Kruskal coordinates).
> 
[[Mod. note  I have manually rewrapped overlong lines.  jt]]
On 12/18/15 12/18/15 1:14 AM, Gerry Quinn wrote: 
> >  [...] it seems to me that you can start by looking at things through 'god's eye' coordinates, a.k.a. coordinates natural to an observer in a low gravitational far from the system of interest. In these flat spacetime coordinates, light slows and bends in gravitational fields. But so long as you consider only regions outside event horizons, you can describe any physical system in a way that is consistent with any system of GR curved coordinates. 
> 
This is just plain not true. You cannot apply such "flat coordinates" to any manifold of GR containing mass or energy, as such manifolds are not flat. Remember "flat" is a property of the metric, not the coordinates, and the metric is a tensor (field) and therefore independent of coordinates. What you seem to be thinking of is a completely different formulation of gravity as a spin2 field on a flat manifold. This is a MUCH bigger difference than mere selection of coordinates as you say. 
And indeed I indicated clearly that this was what I meant two posts upstream. It should be obvious here in any case, since I state in the above paragraph that in this model light slows and bends in gravitational fields. Only one viable class of models exist in which the gravitational force has such effects.
>  This model can account for many properties of GR, but in particular it can be compared to GR only in regions in which gravitation is weak (so you can put the manifolds of the two models into 1to1 correspondence with negligible error, and thus compare them). This comparison fails wherever gravity is not weak, and that can happen well outside any event horizons. 
Completely untrue. It models GR in strong fields too (or why do you think anyone would bother with it?). What you are missing, perhaps, is that the graviton field acts on gravitons as well as photons (it acts on all energy, as I noted more than once in the thread). Due to this self coupling, the end result is exactly the same math we get from the geometric model, but without any need for a fundamental concept of spacetime curvature.
Now it is true that the matchup is not absolutely perfect. To make the graviton theory match GR perfectly everywhere would require a perfectly fundamental spin2 field, but only an effective field (lowenergy) can be made consistent with quantum theory. It should also be obvious that a model with a flat background isn't going to be able to be made consistent with GR anywhere the latter predicts nonsimple topologies. This means that at some point the theories must diverge significantly, but that most likely requires a very strong field indeed. (In this context, "lowenergy" means up to 10^30 K or more!)
The debate is not rendered less contentious by the fact that at the Schwarzshield radius, one model sees strong fields, and the other does not!
[What seems strange to me, given GR's problems with singularities etc., is how long it has taken for this imperfect matchup to be begun to be seen as a feature, not a bug...]
Regarding the rest, I think if you read previous posts in the thread for context, and do not instantly assume that I am making jejune errors such as thinking that coordinate choices have physical effects, you won't have any difficulty understanding the points I was making.  show quoted text 
> 
[[Mod. note  Your description doesn't tell me how to define your "god's eye" (GE) coordinates. Let's be specific. What's your operational definition of GE coordinates for Schwarzschild spacetime, and why should we believe that these are unique (i.e., that they're the *only* coordinates "natural to an observer in a low gravitational far from the system of interest")? 
The techniques used to choose them would be the same as those used by astronomers on Earth to underpin Coordinated Universal Time. Basically, observation and correlation of various distant objects that display periodic behaviour. Of course, there's a real possibility that the entire measured region could be in a huge gravitational well, but in any case we would still have a better approximation to the 'ultimate' universal time than would someone in a microcosm of our space in which we observe the presence of a gravitational field.
Nothing in this discussion requires very strong or even strong fields. Except for the drama associated with numerically large red shifts, everything under debate could be analysed in an Earthbased laboratory, with experimenter A remaining on the ground floor while experimenter B makes a daring excursion to the basement.
As regards uniqueness aside from the obvious arbitrary choice of origin and velocity, I am not clear what it would mean for two observers in communication in an asymptotically flat region of space to disagree. It would be as if Martian astronomers were unable to make their observations of Halley's comet consistent with those of Earthlings. It would break numerous laws of physics.
>  And, how do we know that the GE coordinates cover all "interesting" regions of spacetime. For example, can you prove that GE coordinates don't have any coordinate singularities outside the event horizon?  jt]] 
They don't have any coordinate singularities *anywhere*. They are just universal background Minkowski spacetime. Gravity is treated as just another force that does what it does, bending and slowing light (and all known energy). It must be assumed that GR breaks down inside black holes  and when it does, highenergy clocks of some kind will in principle be available. (Though it might not be possible to make measurements inside one and convey them out in any reasonable external timeframe. It is enough that time can be measured in principle.)
Again, this is not really germane. When I said there were two reasonably consistent models, I did not intend to ignite a debate about which one is better, or more consistent. Both will stand up well enough in regard to the issues raised by the OP.
 Gerry Quinn
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[[Mod. note  It's impossible to set up "universal background Minkowski" coordinates in a curved spacetime: *any* coordinates you set up are going to fail to have some of the key properties of coordinates in Minkowski spacetime, namely that all the components of the Reimann tensor (computed in those coordinates) vanish.
Also, If you set up coordinates far from a black hole, and use ingoing light rays to extend those coordinates inwards, the ingoing rays will often cross (forming coordinate caustics where the coordinates are singular) long before reaching the black hole. In fact, the coordinates will often cross when they're still in the weakfield region.
This problem is wellknown to people trying to use such "ingoing null" coordinates to do numerical calculations in general relativity. The usual solution is to start with coordinates chosen near to the black hole, and extend those *outwards* via light rays  that works and doesn't produce caustics.  jt]]
> 
In article 
> > 
[[Mod. note  Your description doesn't tell me how to define your "god's eye" (GE) coordinates. Let's be specific. What's your operational definition of GE coordinates for Schwarzschild spacetime, and why should we believe that these are unique (i.e., that they're the *only* coordinates "natural to an observer in a low gravitational far from the system of interest")? 
> 
The techniques used to choose them would be the same as those used by astronomers on Earth to underpin Coordinated Universal Time. Basically, observation and correlation of various distant objects that display periodic behaviour. Of course, there's a real possibility that the entire measured region could be in a huge gravitational well, but in any case we would still have a better approximation to the 'ultimate' universal time than would someone in a microcosm of our space in which we observe the presence of a gravitational field. 
[]
> 
[[Mod. note 
It's impossible to set up "universal background Minkowski" coordinates
in a curved spacetime: *any* coordinates you set up are going to fail
to have some of the key properties of coordinates in Minkowski spacetime,
namely that all the components of the Reimann tensor (computed in those
coordinates) vanish.
Also, If you set up coordinates far from a black hole, and use ingoing light rays to extend those coordinates inwards, the ingoing rays will often cross (forming coordinate caustics where the coordinates are singular) long before reaching the black hole. In fact, the coordinates will often cross when they're still in the weakfield region. 
It can't be impossible because we do it all the time. The space in the solar system is curved, and we still use flat coordinates for most purposes.
Why are you talking about extending coordinates using light rays? Where there is a gravitational field, light rays have bent trajectories in flat coordinates, and obviously cannot be used to extend them. Light rays can only be used directly for extending coordinates in the GR model, in which spacetime is curved. We're not talking about that, except to see how it compares now and again.
Let's put the extreme case. We have a big laboratory containing a black hole. We'll pretend that the lab is big enough that we can come to some reasonable agreement that the walls are X, Y and Z metres long. And we'll assume a plane of simultaneity based on the inertial frame of the lab. Now what I mean by flat coordinates is that every point in the lab, including points inside the black hole, can be assigned a coordinate (x,y,z,t) such that (0..x..X, 0..y..Y, 0..z..Z), and t = current lab clock time.
Now obviously light rays won't be much use to extend such coordinates; we certainly can't use them to probe the black hole. But I'm asserting that we can nevertheless model the syatem in terms of such coordinates. At a given point (x,y,z,t) inside the black hole, there is *something*  probably very hot stringy stuff. There's no conversion of spsce into time or anything like that to be considered. I assume the GR black hole interior solutions are irrelevant because according to this hypothesis GR must break down completely around the Schwarzschield radius.
If you don't like the above, replace the black hole by a small neutron star. Does that change anything? You *still* can't get light rays into the interior, regardless of whether you describe it in Minkowski or Schwarzschild coordinates, so why does it matter from a practical perspective whether the coordinates correspond to the paths of light rays?
What about replacing the neutron star by an ordinary rock? You can't tell me we don't use such coordinates every day!
In short, I'm using radically flat coordinates, in which you can say "one inch inside the Schwarzschild radius" just as easily and unambiguously as you can say "one inch inside this concrete wall". Since I'm talking about coordinates, a human invention, I'm making no specific claims about physics, although the *usefulness* of different coordinate concepts does obviously depend somewhat on physics.
Of course, you may argue that the coordinates are useful for discussing wall interiors because they are a reasonable approximation to the true geometry, but useless for black hole interiors, because the true geometry is different. But then it is *you* who are asserting without proof that sofar unobserved physics must correspond to your coordinate system!
>  This problem is wellknown to people trying to use such "ingoing null" coordinates to do numerical calculations in general relativity. The usual solution is to start with coordinates chosen near to the black hole, and extend those *outwards* via light rays  that works and doesn't produce caustics. 
I don't doubt that they have very good reasons for doing as they do, but the coordinates they are using are not the same as those I was talking about.  show quoted text 
>  I have made what I consider a valid argument from a philosophical position that gravitational red shift can not change rate of ticks , amount of time dilation , without being in conflict with causality within the limitations of no SR effects and no Doppler effects. The only two variables are gravitational time dilation and gravitational red shift. 
A(nother) problem with this argument is the use of the phrase "gravitational red shift" as if it were unique. Let's suppose we specify a pair of observers A and B, with A close to a black hole and B far away, and have A send out timetagged oncepersecond radio pulses. If B receives A's oncepersecond pulses at a rate of one pulse per 2 seconds, I think you're arguing that (we should defined) the gravitational redshift from A to B is (to be) a factor of 2.
The problem is, what if B receives each pulse more than once... and the different arrival times are associated with different arrival rates?
For example, consider the following scenario (times in hh:mm:ss):
at Bclockreading 15:15:00, B receives A's 12:00:00 pulse
at Bclockreading 15:15:02, B receives A's 12:00:01 pulse
at Bclockreading 15:15:04, B receives A's 12:00:02 pulse
at Bclockreading 15:15:06, B receives A's 12:00:03 pulse
but B is a patient observer, and keeps listening. A bit later, ...
at Bclockreading 19:38:00, B receives A's 12:00:00 pulse again
at Bclockreading 19:38:05, B receives A's 12:00:01 pulse again
at Bclockreading 19:38:10, B receives A's 12:00:02 pulse again
at Bclockreading 19:38:15, B receives A's 12:00:03 pulse again
and still later, ...
at Bclockreading 23:12:00, B receives A's 12:00:00 pulse again
from directiononthesky #1
at Bclockreading 23:12:11, B receives A's 12:00:01 pulse again
from directiononthesky #1
at Bclockreading 23:12:22, B receives A's 12:00:02 pulse again
from directiononthesky #1
at Bclockreading 23:12:33, B receives A's 12:00:03 pulse again
from directiononthesky #1
while at the same time, ...
at Bclockreading 23:12:00, B receives A's 12:00:00 pulse again
from directiononthesky #2
at Bclockreading 23:12:07, B receives A's 12:00:01 pulse again
from directiononthesky #2
at Bclockreading 23:12:14, B receives A's 12:00:02 pulse again
from directiononthesky #2
at Bclockreading 23:12:21, B receives A's 12:00:03 pulse again
from directiononthesky #2
at Bclockreading 23:12:28, B receives A's 12:00:04 pulse again
from directiononthesky #2
What would you say is the gravitational redshift from A to B?
(If this scenario seems implausible, consider that there can be multiple propagation paths from A to B, e.g., going clockwise vs counterclockwise around a spinning black hole. In general each path will have its own timedelay.)
As noted by another poster earlier in this thread, to uniquely define gravitational redshift requires specifying not a pair of *observers*, but rather a pair of *events* AND a propagation path between them.
This means that "gravitational redshift" is NOT an attribute of a position or event.  show quoted text 
>  It can't be impossible because we do it all the time. The space in the solar system is curved, and we still use flat coordinates for most purposes. 
We use them for most engineering purposes, with accuracy tolerances which are loose enough that we can ignore the curvedspacetime effects. But if we want high accuracy, we can't ignore those effects, and we can't use GE coordintes (or even *define* coordinates with the GE properties).
> 
Why are you talking about extending coordinates using light rays? Where
there is a gravitational field, light rays have bent trajectories in
flat coordinates, and obviously cannot be used to extend them. Light
rays can only be used directly for extending coordinates in the GR
model, in which spacetime is curved. We're not talking about that,
except to see how it compares now and again.
Let's put the extreme case. We have a big laboratory containing a black hole. We'll pretend that the lab is big enough that we can come to some reasonable agreement that the walls are X, Y and Z metres long. And we'll assume a plane of simultaneity based on the inertial frame of the lab. Now what I mean by flat coordinates is that every point in the lab, including points inside the black hole, can be assigned a coordinate (x,y,z,t) such that (0..x..X, 0..y..Y, 0..z..Z), and t = current lab clock time. Now obviously light rays won't be much use to extend such coordinates; we certainly can't use them to probe the black hole. But I'm asserting that we can nevertheless model the syatem in terms of such coordinates. At a given point (x,y,z,t) inside the black hole, [[...]] 
The problem is, how do we measure (operationally define) that (x,y,z,t)?
In fact, let's consider the simpler "model problem" of determining (operationally defining) a "sample point"'s (x,y) given that z=0 and t is known. [This simplifies the exposition, but doesn't change the underlying issues.]
To further simplify things, let's consider the simplerstill case where instead of a BH in the middle of our lab, there's just a nonBH massive object there. For example, our "lab" might be some part of solar system, with a single massive body (the Sun) surrounded by (what we can for present purposes approximate as) empty space.
There are plenty of ways to measure (operationallydefine) our sample point's (x,y), but your desire to not use light rays (or, I presume, other propagating electromagnetic signals) rules out some of them.
For example:
(a) We could place meter sticks across the lab floor and throughout the lab's volume. Since we don't want to use light rays (to sight along the meter sticks to lay them in "straight" lines), we'll lay the meter sticks out in a (rigid) triangular lattice, using Euclidian geometry to figure out the (x,y) of the nearest vertex in the lattice to the sample point. By using a finer lattice (e.g., use 10cmsticks instead of metersticks) this approximation can be made arbitrarily good.
But (how) do we know that it's possible to fill the lab with a triangular lattice of meter sticks? That is, what (do we do) if the 6 meter sticks which are supposed to meet at a lattice point, don't meet? Which meter stick(s) do we cut short or lengthen to make them all meet, and how do we define that lattice point's (x,y)? Any choice we make would be arbitrary, causing this procedure to fail as a "universal" operational definition of GE coordinates.
(b) We could first prepare a long reel of strong cable with length markings, then stretch two lengths of cable from the sample point to two corresponding suspension points along the lab walls (separated by a known distance), measure the cable lengths, and use Euclidian geometry to figure out (x,y).
Since we don't want to sight along the cables to make sure they're "straight", we can just stretch them tight (i.e., among all possible cable paths, choose the one(s) with minimum length).
But what do we do if our results for (x,y) depend on which pair of suspension points we choose? Equivalently, if we try to use 3 or more cables for redundancy, what do we do if there's no consistent solution for (x,y)? In this case this procedure also fails as an operational definition of GE coordinates.
(c) Same as (b), but imagine the cable ends freely *falling* from the lab walls into the sample point. (Let's suppose we use the lab's plane of simultaneity to make the length measurements at precisely the same time that the cable ends cross the sample point.)
What will we do (i.e., how should we define GE coordinates) if this method gives a different (x,y) from method (b)?
(d) We could set up a pair of theodolites along the lab walls, separated by a known baseline ("known" in terms of the labwall coordinates), measure the apparent angular position of the sample point as seen from each theodolite, and (again) use Euclidean geometry to figure out (x,y). But this method is ruled out  it uses propagating light (the theodolites are observing *light* from the sample point).
If we did try to use this method, what would we do (how would we define the GE coordinates) if the resulting (x,y) turned out to depend on where along the lab walls we put the pair of theodolites? Equivalently, if we tried to use 3 or more theodolites for redundancy, would we do if there were no consistent solution for (x,y)?
(e) We could set up two radar sets along the lab walls, put a radar reflector at the sample point, time how long it takes for radar echos to bounce back from the reflector to the transmitters, and again use Euclidean geometry to figure out (x,y).
But this has the same sort of problems as (d): it uses propagating radio signals. If we did try to use this method, what would we do if we got differing results depending on where along the lab walls we put the pair of theodolites? Equivalently, what would we do if we tried to use 3 or more radar sets for redundancy, and failed to find a consistent solution for (x,y)?
If our lab satisfies the axioms of Euclidean geometry, then the "what if" situations I've outline above won't happen, all the above procedures will give the *same* (x,y), and any of them are a reasonable operational definition of (x,y).
But the central message of GR is that in the real world in which we live, our lab (a.k.a. the solar system) does *not* satisfy the axioms of Euclidean geometry, i.e., those "what if" situations *do* actually arise in practice.
In other words, GR asserts that the meter sticks of our lattice will *not* meet at the vertex where they were supposed to meet, that there is *not* an (x,y) consistent with the suspensioncable lengths when we have a redundant set of suspension points, that (a) and (b) will in general give different (x,y), etc etc.
If we put our lab walls near the Earth's orbit, the inconsistencies will be on the order of a centimeter near the Sun's surface. This is small enough that for many purposes we can do as you suggested:
>  solar system is curved, and we still use flat coordinates for most purposes. 
In other words, there's no consistent way to define your GE coordinates close to a massive body.
>  If you don't like the above, replace the black hole by a small neutron star. Does that change anything? [[...]] 
In terms of the above argument, no.
>  Of course, you may argue that the coordinates are useful for discussing wall interiors because they are a reasonable approximation to the true geometry, but useless for black hole interiors, because the true geometry is different. But then it is *you* who are asserting without proof that sofar unobserved physics must correspond to your coordinate system! 
In astrophysics our standards of proof often depend on inferences about objects of which we have only limited observations. It would be really nice to (say) be able to go look at the nucleus of M87 from the other side, but we don't have the technology to do that (nor would the results be available in either of our lifetimes). :(
You seem to be arguing that GR is valid outside a BH [where we have a great deal of experimental evidence, from things like observations of planetary and spacecraft orbits in the solar system  see (e.g.) http://www.livingreviews.org/lrr20144/ http://www.livingreviews.org/lrr20107/ http://www.livingreviews.org/lrr20031/ for some beautifullywritten reviews, and section 6 of http://www.livingreviews.org/lrr20089 for some tests involving neutron stars] but breaks down inside a BH. Perhaps the burden of proof should be on you to propose a selfconsistent theory of gravitation which agrees with all known observations (including the presense of "things" which are very massive, and accrete matter without showing any luminosity from that matter hitting a surface), but which has "nicer" properties inside BHs?
ciao,  show quoted text 
> 
Gerry Quinn 
> >  It can't be impossible because we do it all the time. The space in the solar system is curved, and we still use flat coordinates for most purposes. 
> 
We use them for most engineering purposes, with accuracy tolerances which are loose enough that we can ignore the curvedspacetime effects. But if we want high accuracy, we can't ignore those effects, and we can't use GE coordintes (or even *define* coordinates with the GE properties). 
Why not? So long as the topology is the same, changing coordinates is just changing the numbers we assign to any point in spacetime.
> 
The problem is, how do we measure (operationally define) that (x,y,z,t)?
In fact, let's consider the simpler "model problem" of determining (operationally defining) a "sample point"'s (x,y) given that z=0 and t is known. [This simplifies the exposition, but doesn't change the underlying issues.] To further simplify things, let's consider the simplerstill case where instead of a BH in the middle of our lab, there's just a nonBH massive object there. For example, our "lab" might be some part of solar system, with a single massive body (the Sun) surrounded by (what we can for present purposes approximate as) empty space. There are plenty of ways to measure (operationallydefine) our sample point's (x,y), but your desire to not use light rays (or, I presume, other propagating electromagnetic signals) rules out some of them. 
There's no rule against using them  we can't do much without using the electromagnetic force! What I cannot assume is that light rays travel in straight lines where there is a gravitational field present  I must take the effects of gravity into account. Once I have detected and measured the strength and shape of the field, I can estimate its bending and slowing effects on light, and correct my light ray measurements accordingly. At worst I might have to do a series of iterations to reduce the error below any desired limit. But really, there's nothing unusual, difficult or complex about this  it is a process similar to many that are used all the time in all areas of science.
Or if you are happy that coordinates can be measured using Schwarzschild coordinates, you could just do that in any fashion you prefer, and transform them to the coordinates of an observer in asymptotically flat spacetime.
[Snip ingenious but unnecessary attempts at making measurements without the use of light or any knowledge of the effects of gravity  the last part being the more problematic. We are not obliged to develop a theory of gravity simultaneously with our making of measurements!]
> 
If our lab satisfies the axioms of Euclidean geometry, then the
"what if" situations I've outline above won't happen, all the above
procedures will give the *same* (x,y), and any of them are a reasonable
operational definition of (x,y).
But the central message of GR is that in the real world in which we live, our lab (a.k.a. the solar system) does *not* satisfy the axioms of Euclidean geometry, i.e., those "what if" situations *do* actually arise in practice. In other words, GR asserts that the meter sticks of our lattice will *not* meet at the vertex where they were supposed to meet, that there is *not* an (x,y) consistent with the suspensioncable lengths when we have a redundant set of suspension points, that (a) and (b) will in general give different (x,y), etc etc. 
Not a problem  it is no more difficult in principle to assume that the meter sticks change in length etc. depending on the gravitational potential than to assume that spacetime is curved under the same conditions.
> >  Of course, you may argue that the coordinates are useful for discussing wall interiors because they are a reasonable approximation to the true geometry, but useless for black hole interiors, because the true geometry is different. But then it is *you* who are asserting without proof that sofar unobserved physics must correspond to your coordinate system! 
> 
In astrophysics our standards of proof often depend on inferences about objects of which we have only limited observations. It would be really nice to (say) be able to go look at the nucleus of M87 from the other side, but we don't have the technology to do that (nor would the results be available in either of our lifetimes). :( 
Inference is okay for GR coordinates, but not for alternatives?
>  You seem to be arguing that GR is valid outside a BH [where we have a great deal of experimental evidence, from things like observations of planetary and spacecraft orbits in the solar system  see (e.g.) http://www.livingreviews.org/lrr20144/ http://www.livingreviews.org/lrr20107/ http://www.livingreviews.org/lrr20031/ for some beautifullywritten reviews, and section 6 of http://www.livingreviews.org/lrr20089 for some tests involving neutron stars] but breaks down inside a BH. Perhaps the burden of proof should be on you to propose a selfconsistent theory of gravitation which agrees with all known observations (including the presense of "things" which are very massive, and accrete matter without showing any luminosity from that matter hitting a surface), but which has "nicer" properties inside BHs? 
We do have such a theory, which as far as I can see is *more* consistent that GR  e.g. it doesn't have pathology such as singularities. It is the theory of a spin2 effective field on a flat background.
Under all but the strongest fields, its differences from GR are negligible  it can be assumed that the energy needed to probe the breakdown of the effective field is at least 10^30 K, and probably more.
Near to and inside the Schwarzschild radius of a black hole, the effective field will break down, and the physics will diverge from GR. We can assume that matter reaching this region  at least in a well established black hole  will encounter extremely high temperatures and will break down (adding fuel to the 'fire'). Hawking radiation is nothing more than gravitationally redshifted thermal radiation from this 'firewall'. (That's why it drains mass from the black hole, and gets hotter as the black hole shrinks  no questionable 'heuristics' needed to explain it! And of course it's obvious that the information content of infalling matter will come out eventually, instead of falling into some mysterious singularity and *still* somehow finding a way into the Hawking radiation...)
I should note that the last paragraph is my own interpretation of what physicists working on this model believe  if anyone knows better I am sure we would all love to be informed!  show quoted text 
> >  I have made what I consider a valid argument from a philosophical position that gravitational red shift can not change rate of ticks , amount of time dilation , without being in conflict with causality within the limitations of no SR effects and no Doppler effects. The only two variables are gravitational time dilation and gravitational red shift. 
> 
A(nother) problem with this argument is the use of the phrase "gravitational red shift" as if it were unique. Let's suppose we specify a pair of observers A and B, with A close to a black hole and B far away, and have A send out timetagged oncepersecond radio pulses. If B receives A's oncepersecond pulses at a rate of one pulse per 2 seconds, I think you're arguing that (we should defined) the gravitational redshift from A to B is (to be) a factor of 2. The problem is, what if B receives each pulse more than once... and the different arrival times are associated with different arrival rates? 
> 
What would you say is the gravitational redshift from A to B? (If this scenario seems implausible, consider that there can be multiple propagation paths from A to B, e.g., going clockwise vs counterclockwise around a spinning black hole. In general each path will have its own timedelay.) As noted by another poster earlier in this thread, to uniquely define gravitational redshift requires specifying not a pair of *observers*, but rather a pair of *events* AND a propagation path between them. This means that "gravitational redshift" is NOT an attribute of a position or event.

 "Jonathan Thornburg [remove animal to reply]" 
You are over thinking the problem. There is a rigid rod between A and B . The rigid rod is hollow to provide a means for a laser light within the hollow rigid rod to communicate clock pulses. This hopefully eliminates all possible options to avoid a conflict with causality. I would have a marked preference for saying "assume ideal conditions" and leave it at that. However if the ideal condition need to be spelled out then so be it. Please do not rotate the system leading to SR effects.
With all this in place there is gravitational time dilation , 1/2 to B. This is fine and will not violate causality when A receives clock pulses from B at 1/2 their normal rate. However we are obligated to add gravitational red shift time dilation according to the equivalence principle by an imperative Doppler effect that is inherent in the equivalence principle. If there is a rigid rod between A and B how can a Doppler effect be accommodated without violating causality? Gravitational time dilated B is sending 1/2 rate pulses. Once B sends 1/2 pulses how can A hear 1/3 the pulses to accommodate gravitational red shift in addition to gravitational time dilation. How can one hide pulses inside a rigid hollow rod without violating causality.
The only way I see out of this is to say use gravitational time dilation or gravitational red shift but not both. In short gravitational time dilation and gravitational red shift are the same and therefore should not be added together as this would be redundant leading to a violation of causality. Somewhat like adding simultaneity of time to length contraction in special relativity leading to a double gamma. A mistake I have noticed more than once.
John Heath
>
You are over thinking the problem. There is a rigid rod between A
and B . The rigid rod is hollow to provide a means for a laser light
within the hollow rigid rod to communicate clock pulses.
I'll assume that you meant that the rigid rod should be "straight", i.e., [this is my operational definition of "straight"] that with a suitable alignment of the laser, the laser light does NOT touch the inside walls of the rod.
My question is, why should there be only ONE such rod between A and B?
Or more precisely, what if we can place (say) TWO such rods (both rigid
and "straight" by the definition I just gave) between A and B... and
the redshift of the light arriving at B from A through rod #1 differs
from the redshift of the light arriving at B from A through rod #2.
[For example, the two rods might pass on either side
of a massive body (say a star, galaxy, or black hole)
which is acting as a gravitational lens. And that
massive body might be spinning.]
How then should we define "the gravitational redshift from A to B"?
My argument is that such a situation shows that we can't (uniquely) define such a quantity: gravitational redshift is (in general) *not* an attribute of a pair of observers, but rather of a pair of *events* *and* a particular (light) propagation path between them.
>  Please do not rotate the system leading to SR effects. 
Hmm. If A is close to a spinning black hole and B is far away, it's a bit tricky to define what you mean by "do not rotate the system". But we can certainly say that the observer who is far from the black hole isn't rotating with respect to a (local) inertial reference frame.

 "Jonathan Thornburg [remove animal to reply]"
> 
In article 
>> 
Gerry Quinn 
>>>  It can't be impossible because we do it all the time. The space in the solar system is curved, and we still use flat coordinates for most purposes. 
The curvature of spacetime near the earth is quite small: only about a part per million (i.e. the trajectories of the moon and other satellites deviate from straight lines by about 1 part per million).
What do I mean by "a part per million from a straight line", when these objects obviously follow geodesic paths? I mean that in earthfixed coordinates their path is a helix with radius about a million times smaller than the length of its period (coordinates with c=1).
>>  We use them for most engineering purposes, with accuracy tolerances which are loose enough that we can ignore the curvedspacetime effects. But if we want high accuracy, we can't ignore those effects, and we can't use GE coordintes (or even *define* coordinates with the GE properties). 
> 
Why not? So long as the topology is the same, changing coordinates is just changing the numbers we assign to any point in spacetime. 
It is in general not possible to apply your GE coordinates to a curved manifold, regardless of topology. They can only be applied to a "small" region, where "small" is defined by the error acceptable to your application.
For instance, in 2 dimensions, it is not possible to cover the sphere with ANY coordinate system, much less the 2d analog of your GE coordinates. Indeed, on the surface of the earth, the errors inherent in using GE coordinates are quite noticeable for regions only a few miles in size (in Chicago, wherever surveyor's regions meet along a main street, all the cross streets are offset by 2030 feet).
>  it is no more difficult in principle to assume that the meter sticks change in length etc. depending on the gravitational potential than to assume that spacetime is curved under the same conditions. 
I doubt this very much. Elsewhere I have posted the algorithm for computing the redshift of an EM signal. Given a curved metric of spacetime, it is straightforward (albeit tedious) to do the calculation. I doubt you could do it at all by assuming that rulers change length and clocks change tick rates.
In particular, how could you ever determine or verify that spacetime is flat (as you assume), when rulers and clocks cannot be trusted?
Indeed, if I construct a 3d latticework of 1meter rods, and they don't meet up at the corners, it seems simplest to take this as an indication that space is curved, not that rods constructed to be 1 meter long are not.
It seems to me that you are taking an "armchair" attitude here, and have never actually tried to apply your GE coordinates and varying rulers and clocks to the Schwarzschild manifold of GR. I think that if you try, you will find it MUCH more difficult than you imagine  Chicago streets seem to me to be a strong indication of that: imagine trying to survey what was back then a trackless wilderness, using rulers that vary in length....
>  [...] pathology such as singularities. 
Singularities are not really "pathological". They merely represent places where the theory breaks down (does not apply). EVERY theory has limits to its domain; GR is one of the few that can compute at least some of those limitations (most theories are mute on the subject of where/when they don't apply; usually one must go outside the theory to determine this).
For instance, in 3d Euclidean space we don't reject cylindrical and spherical coordinates merely because they have singularities  rather, we simply don't apply them there. Ditto for the curvature singularities of GR.
Tom Roberts
Imagine flat creatures living on the surface of a sphere, unaware of a third dimension. They might hypothesise that their space is curved. Or they might hypothesise that it is embedded in a higher dimensional space, and some force causes their meter sticks to bend to conform to a sphere. If they believed in the latter, they could still define a two parameter coordinate system (e.g. latitude and longitude), and there is no reason why they could not convert such coordinates to 3D coordinates, make calculations, convert them back again, and build roads with perfect accuracy.
Or they might use the same coordinates as their friends who believe in curved space when it is convenient, but point out that their system is just as accurate in principle, and that the inconvenience of using it is not a relevant argument when it comes to debating what underlies the physics of their world.
> >  it is no more difficult in principle to assume that the meter sticks change in length etc. depending on the gravitational potential than to assume that spacetime is curved under the same conditions. 
> 
I doubt this very much. Elsewhere I have posted the algorithm for computing the redshift of an EM signal. Given a curved metric of spacetime, it is straightforward (albeit tedious) to do the calculation. I doubt you could do it at all by assuming that rulers change length and clocks change tick rates. In particular, how could you ever determine or verify that spacetime is flat (as you assume), when rulers and clocks cannot be trusted? Indeed, if I construct a 3d latticework of 1meter rods, and they don't meet up at the corners, it seems simplest to take this as an indication that space is curved, not that rods constructed to be 1 meter long are not. It seems to me that you are taking an "armchair" attitude here, and have never actually tried to apply your GE coordinates and varying rulers and clocks to the Schwarzschild manifold of GR. I think that if you try, you will find it MUCH more difficult than you imagine  Chicago streets seem to me to be a strong indication of that: imagine trying to survey what was back then a trackless wilderness, using rulers that vary in length.... 
An armchair attitude is appropriate, given that we are discussing theory, not the taking of measurements. The curved space enthusiasts on my planet of flat creatures could make the same arguments that you have made. And yet, if they live in our universe, those arguments are wrong. There really IS a force bending their meter sticks. (Or if it is geometry, it is at least geometry at one remove  the geometry of general relativity as it applies to our world is not relevant to their current scientific concerns.)
As for verification that spacetime is flat, the only sure way I know at present is to jump into a very large black hole, and find out whether you get incinerated near the Schwarzschild radius, or progress further only to be spaghettified at some point inside. Failing that, we can only argue on the basis of what is consistent, including what is consistent with the rest of physics such as quantum theory and thermodynamics. In my view, the geometric theory of gravity cannot easily be made consistent with these.
> >  [...] pathology such as singularities. 
> 
Singularities are not really "pathological". They merely represent places where the theory breaks down (does not apply). EVERY theory has limits to its domain; GR is one of the few that can compute at least some of those limitations (most theories are mute on the subject of where/when they don't apply; usually one must go outside the theory to determine this). For instance, in 3d Euclidean space we don't reject cylindrical and spherical coordinates merely because they have singularities  rather, we simply don't apply them there. Ditto for the curvature singularities of GR. 
I don't disagree that singularities are not necessarily more than an indication of where a theory breaks down. However I strongly disagree with the second part. It seems to me that GR is actually a theory which has allowed singularities to be wished away. I believe the Schwarzschild singularity is actually the breakdown point of GR  and if we accept this, we do not have any particularly fundamental problems about black holes in terms of thermodynamics etc. But the geometric theory has allowed the Schwarzschild singularity to be defined away as a coordinate singularity, and solutions continued inward from it. The end result, though, is an intractable central singularity that makes no sense whatsoever in terms of thermodynamics, or physics in general. This should be taken as a sign that the interpretation of the Schwarzschild singularity as a coordinate singularity is incorrect, and that conditions there are such that the symmetries of GR, which allow the extension to interior solutions, no longer apply.
"But how can that be", you ask? "GR predicts that conditions at the Schwarzschild radius of a large black hole are nothing special. So obviously GR cannot break down there. Your alternative hypotheses are unimaginable!"
And therein lies the problem. Internal consistency is not truth, and powerful theories of symmetry cannot imagine their symmetries broken.
I think "going outside the theory" is something that proponents of the geometric view of gravity should practice more!  show quoted text 
> 
I wrote:
 A(nother) problem with this argument is the use of the phrase
 "gravitational red shift" as if it were unique. Let's suppose we
 specify a pair of observers A and B, with A close to a black hole and
 B far away, and have A send out timetagged oncepersecond radio
 pulses. If B receives A's oncepersecond pulses at a rate of one
 pulse per 2 seconds, I think you're arguing that (we should defined)
 the gravitational redshift from A to B is (to be) a factor of 2.

 The problem is, what if B receives each pulse more than once... and
 the different arrival times are associated with different arrival rates?
[[...]]
 What would you say is the gravitational redshift from A to B?

 (If this scenario seems implausible, consider that there can be
 multiple propagation paths from A to B, e.g., going clockwise vs
 counterclockwise around a spinning black hole. In general each path
 will have its own timedelay.)



 As noted by another poster earlier in this thread, to uniquely define
 gravitational redshift requires specifying not a pair of *observers*,
 but rather a pair of *events* AND a propagation path between them.

 This means that "gravitational redshift" is NOT an attribute of a
 position or event.
John Heath 
> >  You are over thinking the problem. There is a rigid rod between A and B . The rigid rod is hollow to provide a means for a laser light within the hollow rigid rod to communicate clock pulses. 
> 
I'll assume that you meant that the rigid rod should be "straight", i.e., [this is my operational definition of "straight"] that with a suitable alignment of the laser, the laser light does NOT touch the inside walls of the rod. My question is, why should there be only ONE such rod between A and B? Or more precisely, what if we can place (say) TWO such rods (both rigid and "straight" by the definition I just gave) between A and B... and the redshift of the light arriving at B from A through rod #1 differs from the redshift of the light arriving at B from A through rod #2. [For example, the two rods might pass on either side of a massive body (say a star, galaxy, or black hole) which is acting as a gravitational lens. And that massive body might be spinning.] How then should we define "the gravitational redshift from A to B"? My argument is that such a situation shows that we can't (uniquely) define such a quantity: gravitational redshift is (in general) *not* an attribute of a pair of observers, but rather of a pair of *events* *and* a particular (light) propagation path between them. 
> > 
Please do not rotate the system leading to SR effects. 
> 
Hmm. If A is close to a spinning black hole and B is far away, it's a bit tricky to define what you mean by "do not rotate the system". But we can certainly say that the observer who is far from the black hole isn't rotating with respect to a (local) inertial reference frame.

 "Jonathan Thornburg [remove animal to reply]" 
Dr Thornburg please allow my words to trap you in a corner. If you resist a delicate point of a possible violation to causality when adding gravitational red shift to gravitational time dilation could be lost. You need to be trapped in the same corner as I am to stand in my shoes to see a possible violation to causality. With this in mind allow my words to trap in a corner willingly without resistance.
A is time dilated sending 10 pulses per second. B receives 9 pulses per second as B is not time dilated. We are fine as causality is not violated as gravitational time dilation justifies this. However when we are required to add gravitational red shift to gravitational time dilation a problem pops up with causality. B must now hear 8 pulses per second not 9. Where can 1 pulse per second be hiding if the distance between A and B is fixed. A is sending 10 pulses per second , 9 pulses per second according to Bs clock , but B is hearing 8 pulses per when grt5avitational red shift is added to gravitational time dilation. How can this happen without violating causality?
> 
In article 
>>  On 1/1/16 1/1/16  8:45 AM, Gerry Quinn wrote: 
>  I believe the Schwarzschild singularity is actually the breakdown point of GR 
Why do you think anything breaks down if particles simply keep following a nice continuous trajectory when thy cross the Schwarzschild radius? (And waves likewise.) There is nothing special happening to anything at that radius (nor at a 10% smaller radius).
Do you have anything to offer as an indication of "break down" except for the accidental choice of some coordinate function?
>   and if we accept this, we do not have any particularly fundamental problems about black holes in terms of thermodynamics etc. 
And why *would* we have such problems if we define the "breakdown" at a 10% smaller radius? So again, what do you have to offer as special behavior of physics near the Schwarzschild radius?
>  But the geometric theory has allowed the Schwarzschild singularity to be defined away as a coordinate singularity, and solutions continued inward from it. 
But the coordinate theory *also* allows you to take slightly (or radically) different coordinates for which the coordinate functions are defined further inwards. It is exactly a shortcoming of your cherished coordinates that they break down at all kind of arbitrary points where nothing strange happens to the laws of physics at all.
And whether you "believe" that GR breaks down is uninteresting if you fail to mention any indication that the laws of physics change at that point (i.e. they should start to differ from GR).
...
>  The end result, though, is an intractable central singularity that makes no sense whatsoever in terms of thermodynamics, 
So then why don't you call a spade a spade and say that *there* is the point where GR breaks down? And if you don't want to, why do you bring up this fact? It actually weakens your case! Your post tells us that: 1) Inside the Schwarzschild radius GR is still consistent. 2) Things become intractable at a central singularity 3) But according to you GR breaks down not at 2) but at 1)
You are not just forgetting to give arguments for your claim, it seems more like you give counterarguments!
 Jos
>  On 1/12/2016 11:56 PM, Gerry Quinn wrote: 
>  .. 
> >  I believe the Schwarzschild singularity is actually the breakdown point of GR 
> 
Why do you think anything breaks down if particles simply keep following a nice continuous trajectory when thy cross the Schwarzschild radius? (And waves likewise.) There is nothing special happening to anything at that radius (nor at a 10% smaller radius). Do you have anything to offer as an indication of "break down" except for the accidental choice of some coordinate function? 
Obviously I don't believe they keep following such a trajectory.
"There is nothing special happening to anything..." I believe I pointed out the circularity of that argument in the post you are responding to. If GR breaks down at the Schwarzschild radius, then GR's prediction that nothing special is happening there doesn't mean very much.
The choice of coordinates is nothing to do with the breakdown, except insofar as GR allows coordinate choices that in its own terms allow patching of interior solutions (which in my view are spurious, corresponding to no physical reality) to external ones.
I don't believe in any special behaviour of physics anywhere. I think gravity can be described  like the other forces  in terms of a field on a flat background (albeit an effective field, which cannot be fundamental). At the Schwarzschild radius, this becomes topologically incompatible with the geometric theory of gravity, so one of them (at least) must be wrong.
I suppose in a sense I'm saying that both are wrong, as the effective field must itself break down here. The effective field acts like geometric gravity. But unlike geometric gravity, it has a way to fail gracefully, as highenergy underlying processes become observable.
As to the actual mechanics of how such forces might become observable, there are several angles. We can say that ordinary 'lowenergy' clocks become time dilated to the point of stopping, so only highenergy clocks remain. We can argue that the intense gravitational time dilation means that the absorption of Hawking radiation by distant observers corresponds to highenergy events at the Schwarzschild radius. And we can argue that decay processes catalysed by highenergy interactions eventually 'start a fire' so to speak, which brings the Schwarzschild region up to a temperature where we'd expect the breakdown of the effective field theory anyway (the socalled 'firewall').
[]
> >  The end result, though, is an intractable central singularity that makes no sense whatsoever in terms of thermodynamics, 
> 
So then why don't you call a spade a spade and say that *there* is the point where GR breaks down? And if you don't want to, why do you bring up this fact? It actually weakens your case! Your post tells us that: 1) Inside the Schwarzschild radius GR is still consistent. 2) Things become intractable at a central singularity 3) But according to you GR breaks down not at 2) but at 1) You are not just forgetting to give arguments for your claim, it seems more like you give counterarguments! 
You are misundertanding my argument. I am saying that the central singularity that arises if the equations of geometric gravity are extended into the black hole interior is a monstrosity that doesn't make sense even as the breakdown point of a theory. What sort of new physics can you imagine that will take the place of general relativity there? If we did not have quantum mechanics, we might imagine that matter is somehow crushed out of existence entirely, leaving only its gravitational field as a kind of ghost. But if we hope to be compatible with quantum theory, even this in untenable.
So we must have made a mistake  the breakdown point must have been earlier. And there is only one other distinctive place where it could be  the Schwarzschild radius, which must not have been a mere coordinate singularity after all...
(As to whether the patching of interior to exterior solutions is really consistent, to be honest I'm not certain that it is, but I don't think either side would have their views affected by argument on the subject.)  show quoted text 
>  In article <56959110$0$23771$e4fe...@news.xs4all.nl>, jos.ber...@xs4all.nl says... 
>>  On 1/12/2016 11:56 PM, Gerry Quinn wrote: 
> 
>> 
.. 
>>>  I believe the Schwarzschild singularity is actually the breakdown point of GR 
>> 
Why do you think anything breaks down if particles simply keep following a nice continuous trajectory when thy cross the Schwarzschild radius? (And waves likewise.) There is nothing special happening to anything at that radius (nor at a 10% smaller radius). Do you have anything to offer as an indication of "break down" except for the accidental choice of some coordinate function? 
> 
Obviously I don't believe they keep following such a trajectory. 
Again you talk about your "belief". It is not interesting. Your homework is: 1) Give observational proof. 2) Explain how you remove the inconsitencies. About the second point: how can GR breakdown if there is nothing indicating where the Schwarzschild radius is? It cannot be the curvature of space, because at the Schwarzschild radius of a large black hole that is completely different from a small one. Also the presence of other gravitating objects would create asymmetry. You really would not *believe* that for a black hole binary GR breaks down exactly in two spherical regions around each of them without the slightest influence of the other, or do you?
...
>  "There is nothing special happening to anything..." I believe I pointed out the circularity of that argument in the post you are responding to. If GR breaks down at the Schwarzschild radius, then GR's prediction that nothing special is happening there doesn't mean very much. 
GR isn't needed for that prediction. Also without GR (or *even more so* without GR) there is no criterion possible that gives you the position of the Schwarzschild radius based on the physical situation of the point where you believe it to be. There is not a specific value of any physical quantity that can serve to position it.
You write that you *believe* that something special is happening at certain boundaries in space but in fact you are fooling yourself because you evade any definition of what those special boundaries are.
>  The choice of coordinates is nothing to do with the breakdown, 
Of course not. But you also fail to give us anything else that could have something to do with it. Therefore there cannot be a breakdown.
>  I don't believe in any special behaviour of physics anywhere. 
Your *believe* is extremely flexible. You just argued against "There is nothing special happening to anything" being used by others, but now you seem to believe exactly that yourself.
>  I think gravity can be described  like the other forces  in terms of a field on a flat background (albeit an effective field, which cannot be fundamental). At the Schwarzschild radius, this becomes topologically incompatible with the geometric theory of gravity, so one of them (at least) must be wrong. 
But you "don't believe in any special behaviour of physics anywhere" so your choice will be that the field on the flat background would be wrong and GR correct.
>  I suppose in a sense I'm saying that both are wrong, as the effective field must itself break down here. 
Why? It is on a flat background, you say! So it doesn't have any problem.
>  The effective field acts like geometric gravity. But unlike geometric gravity, it has a way to fail gracefully, as highenergy underlying processes become observable. 
But there are no high energy processes activated if you approach the Schwarzschild radius. NB: there also is no large gavitational force field if it is a large black hole (the larger it is, the *weaker* its gravitational field at the Schwarzschild radius.)
>  As to the actual mechanics of how such forces might become observable, 
Yes, the mechanism is what you leave out. In everything you wrote until now.
>  there are several angles. We can say that ordinary 'lowenergy' clocks become time dilated to the point of stopping, so only highenergy clocks remain. 
Those are all meaningless words, especially since you denounce GR. Write down a welldefined theory for what you want to say and perhaps we can discuss it further.
...
>>>  The end result, though, is an intractable central singularity that makes no sense whatsoever in terms of thermodynamics, 
>> 
So then why don't you call a spade a spade and say that *there* is the point where GR breaks down? And if you don't want to, why do you bring up this fact? It actually weakens your case! Your post tells us that: 1) Inside the Schwarzschild radius GR is still consistent. 2) Things become intractable at a central singularity 3) But according to you GR breaks down not at 2) but at 1) You are not just forgetting to give arguments for your claim, it seems more like you give counterarguments! 
> 
You are misundertanding my argument. I am saying that the central singularity that arises if the equations of geometric gravity are extended into the black hole interior is a monstrosity that doesn't make sense even as the breakdown point of a theory. 
Here your words are *not even meaningless* I would say. If the singularity doesn't make sense in an existing theory then by the accepted meaning of these words this is synonymous to the theory breaking down.
You are now descending into the rather pointless game of stripping words of there ordinary meaning!
>  What sort of new physics can you imagine that will take the place of general relativity there? If we did not have quantum mechanics, we might imagine that matter is somehow crushed out of existence entirely, leaving only its gravitational field as a kind of ghost. But if we hope to be compatible with quantum theory, even this in untenable. 
On the contrary, things that are classically a singular point, could become manageable in quantum theory. Even in other theories, there might be some region where the theory changes gradually. This could be just outside the classical point of singularity, but far inside the Schwarzschild radius.
>  So we must have made a mistake  the breakdown point must have been earlier. 
So that could be just outside the classical point of singularity, but still far inside the Schwarzschild radius.
>  And there is only one other distinctive place where it could be  the Schwarzschild radius, 
That is not distinctive at all! You failed miserably until now to define what distinguishes the Schwarzschild radius from any other point in space.
 Jos
> 
On 1/15/2016 8:51 AM, Gerry Quinn wrote: 
> >  .... So we must have made a mistake  the breakdown point must have been earlier. 
> 
So that could be just outside the classical point of singularity, but still far inside the Schwarzschild radius. 
> > 
And there is only one other distinctive place where it could be  the Schwarzschild radius, 
> 
That is not distinctive at all! You failed miserably until now to define what distinguishes the Schwarzschild radius from any other point in space.  Jos 
Work by Samir Mathur and others suggest that the Schwarzschild radius points (or just outside them) have structure:
https://www.quantamagazine.org/20150623fuzzballsblackholefirewalls/
http://arxiv.org/pdf/1207.3123.pdf
Very interesting stuff.
Gary
>>> 
Why do you think anything breaks down if particles simply keep following a nice continuous trajectory when thy cross the Schwarzschild radius? (And waves likewise.) There is nothing special happening to anything at that radius (nor at a 10% smaller radius). 
The coordinate "r" in the Schwarzschild solution is essentially the radial distance from the center of the (uncollapsed) spherical mass WHEN r is sufficiently large, and "t" is the time coordinate when r is greater than 1. But for r < 1, r becomes the time coordinate, and t becomes one of the three spatial coordinates. So when r is 10% smaller that 1, it is NOT a "radius", it is a time. And r = 0 is NOT the "center" of the blackhole.
I'm one of the few people who believe that the r < 1 solution to the quadratic equation obtained in the Schwarzschild derivation is just a spurious mathematical result, with no physical significance in our universe. The "center" of the blackhole is at r = 1, and there is nothing "inside" of that ... there IS no "inside" of that.
I realize I'm a member of a tiny minority holding this view, but I'm in very good company: some years ago (after I had arrived at my view), I found out that Dirac had the same view. Made my day!
 https://sites.google.com/site/cadoequation/cadoreferenceframe
"Accelerated Observers in Special Relativity", PHYSICS ESSAYS, December 1999, p629.
All you ever need to know about the twin "paradox".
>  [...] a possible violation to causality when adding gravitational red shift to gravitational time dilation [...] 
You attempt to make a distinction without a difference.
"Gravitational redshift" and "gravitational time dilation" are the same phenomenon, and nobody in their right mind would "add" them.
See my earlier post on how to compute them  one uses exactly the same algorithm for both, which is why I say they are the same phenomenon. You just apply different words as labels to a single phenomenon. The physics, of course, is completely independent of your labels.
Tom Roberts
>  On Sunday, January 17, 2016 at 3:16:31 AM UTC7, Jos Bergervoet wrote: 
>>  On 1/15/2016 8:51 AM, Gerry Quinn wrote: 
>>>  .... So we must have made a mistake  the breakdown point must have been earlier. 
>> 
So that could be just outside the classical point of singularity, but still far inside the Schwarzschild radius. 
>>> 
And there is only one other distinctive place where it could be  the Schwarzschild radius, 
>> 
That is not distinctive at all! You failed miserably until now to define what distinguishes the Schwarzschild radius from any other point in space. 
> 
Work by Samir Mathur and others suggest that the Schwarzschild radius points (or just outside them) have structure: https://www.quantamagazine.org/20150623fuzzballsblackholefirewalls/ 
They want the "firewall" to be located at some "horizon" (p. 13, "Conclusions") but they write that is is: "not determined by any local feature but by a global property." They even admit that: (p. 14) "..we pass through Rindler horizons all the time and do not burn up or experience obvious new physics."
So then the burden is on the authors to show that there can be a consistent definition of where we will, and where we *will not* see this new physics happening.
It must in particular be applicable to combined Rindler Schwarzschild situations for multiple black holes and masses with all kind of accelerations. And it must explain *why* this should happen despite the absence of "any local feature" (a fact that they admit.)
Their answer, "We believe that this is due to an essential difference.." (p. 14) is not accompanied by any explanation. It doesn't look much better than the "we believe" arguments that people in this thread are making.
 Jos
>  On 1/17/16 3:16 AM, Jos Bergervoet wrote: 
>>>> 
Why do you think anything breaks down if particles simply keep following a nice continuous trajectory when thy cross the Schwarzschild radius? (And waves likewise.) There is nothing special happening to anything at that radius (nor at a 10% smaller radius). 
> 
The coordinate "r" in the Schwarzschild solution is essentially the radial distance from the center of the (uncollapsed) spherical mass WHEN r is sufficiently large, and "t" is the time coordinate when r is greater than 1. But for r < 1, r becomes the time coordinate, and t becomes one of the three spatial coordinates. 
Those are the coordinate functions used in that case. So how does that prove that anything strange is the matter with space? You mention only a peculiarity of your chosen coordinates. So I could elaborate:
"There is nothing special happening to anything at the Schwarzschild radius, nor at a 10% smaller r in those coordinates, nor in the region going further inwards (which is another direction than decreasing r)."
A region "further in" should be in the direction following the spacelike coordinate that goes further in. You can draw a curve going in spacelike direction regardless of the coordinates you have chosen.
So where do you see anything that blocks you from drawing the curve further inwards?
..
>  I'm one of the few people who believe that the r < 1 solution to the quadratic equation obtained in the Schwarzschild derivation is just a spurious mathematical result, 
Why would it matter what the coordinates do? You do not answer the question what would be preventing us from constructing a spacelike curve inwards.
 Jos
>  I'm one of the few people who believe that the r < 1 solution to the quadratic equation obtained in the Schwarzschild derivation is just a spurious mathematical result, with no physical significance in our universe. 
You seem to not understand the difference between coordinates and the geometry or physics  neither geometry nor physics can depend on the coordinates used. Your statements are inextricably bound to the usual Schwarzschild coordinates, and simply do not apply to the manifold itself. The physics and geometry are in the manifold, not the coordinates.
Technically the Schw. solution clearly has no relevance to the universe we inhabit (the world we inhabit is nowhere close to being static and spherically symmetric). But it is not unreasonable to expect that solution to approximate certain regions of our universe  indeed we observe that it does apply to our solar system outside the solar surface. I see no reason to think this would not apply to isolated objects smaller than their Schw. radius  certainly GR remains valid for such objects (within the approximation of applying GR to just a region of the universe). Indeed there are many objects observed that are consistent with being black holes, and for which no alternative description has been found.
>  The "center" of the blackhole is at r = 1, and there is nothing "inside" of that ... there IS no "inside" of that. 
This is just not so. The manifold extends inside the horizon, and the physics and geometry are in the manifold. Yes, the coordinates you use do not extend inside, but that does not AND CAN NOT affect the manifold, the physics, or the geometry.
>  I realize I'm a member of a tiny minority holding this view, but I'm in very good company: some years ago (after I had arrived at my view), I found out that Dirac had the same view. Made my day! 
I'll bet that was an opinion that he formed long before the complete geometry was known.
Tom Roberts
Thank you.
On 1/12/16 1/12/16 4:56 PM, Gerry Quinn wrote:
> 
In article 
>> 
It is in general not possible to apply your GE coordinates to a curved manifold,
regardless of topology. They can only be applied to a "small" region, where
"small" is defined by the error acceptable to your application.
For instance, in 2 dimensions, it is not possible to cover the sphere with ANY coordinate system, much less the 2d analog of your GE coordinates. Indeed, on the surface of the earth, the errors inherent in using GE coordinates are quite noticeable for regions only a few miles in size (in Chicago, wherever surveyor's regions meet along a main street, all the cross streets are offset by 2030 feet). 
> 
Those errors arise from using them incorrectly. 
No. The surveyors correctly applied Euclidean geometry. The errors arise from the MISMATCH between their assumption of Euclidean geometry and the actual curved geometry of the surface of the earth.
Your "GE coordinates" will have the same problem.
>  You are assuming, just as Jonathan did, that I think that orthogonal straight lines, measured according to your operational definition (which in the case of your Chicago example presumably means great circles) must under all conditions form a rectilinear grid. I do not say that. 
If you don't say that, at least locally and at every point, then you don't understand what a manifold is. A manifold is BY DEFINITION locally equivalent to a Euclidean space. And in Euclidean space orthogonal straight lines do form a rectangular grid.
>  Imagine flat creatures living on the surface of a sphere, unaware of a third dimension. They might hypothesise that their space is curved. Or they might hypothesise that it is embedded in a higher dimensional space, and some force causes their meter sticks to bend to conform to a sphere. If they believed in the latter, they could still define a two parameter coordinate system (e.g. latitude and longitude), and there is no reason why they could not convert such coordinates to 3D coordinates, make calculations, convert them back again, and build roads with perfect accuracy. 
Sure. But those coordinates are not your "GE coordinates", because latitude and longitude do NOT yield geodesics. If they try to use geodesics ("straight lines"), they will find inconsistencies and problems in sufficiently large regions.
>>  It seems to me that you are taking an "armchair" attitude here, and have never actually tried to apply your GE coordinates and varying rulers and clocks to the Schwarzschild manifold of GR. [...] 
> 
An armchair attitude is appropriate, given that we are discussing theory, not the taking of measurements. 
I meant "armchair" not in the sense of thinking mathematically, but in the sense of NOT applying mathematics. Because you haven't tried to apply your "GE coordinates" on Schw. spacetime. You ASSERT it is "no more difficult in principle", but you have not actually TRIED. I strongly suspect your assertion is false, and it would be MUCH more difficult to use your approach.
>  As for verification that spacetime is flat, the only sure way I know at present is to jump into a very large black hole, and find out whether you get incinerated near the Schwarzschild radius, or progress further only to be spaghettified at some point inside. 
You are mixing metaphors  that is not at all "flat".
The issue of whether GR fails at the Schwarzschild radius of a Schw. black hole has been resolved for many decades: GR is valid at the horizon and inside it until the singularity at the "center" is approached.
Whether there exist such objects in the world we inhabit is a completely different issue. As is the issue of whether other physics applies (e.g. some asyetunknown quantum theory).
>  Failing that, we can only argue on the basis of what is consistent, including what is consistent with the rest of physics such as quantum theory and thermodynamics. In my view, the geometric theory of gravity cannot easily be made consistent with these. 
Yes, consistency of GR and QM is a major current topic.
>  It seems to me that GR is actually a theory which has allowed singularities to be wished away. I believe the Schwarzschild singularity is actually the breakdown point of GR 
You are wrong on both points. GR is _KNOWN_ to be well behaved at the horizon of a Schw. black hole. There is no "wishing away of singularities, BECAUSE THERE IS NO SINGULARITY THERE.
It may be that other physics becomes important at or near the horizon, rendering GR only an approximation, or even invalid. But GR itself does not "breakdown" there at all.
>  But the geometric theory has allowed the Schwarzschild singularity to be defined away as a coordinate singularity, and solutions continued inward from it. 
This is not "defined away", it is rather the correction of an old mistake. I repeat: THERE IS NO SINGULARITY THERE. It's just that historically people made a poor choice of coordinates that made them THINK there was a singularity there, WHEN THERE WASN'T.
>  The end result, though, is an intractable central singularity that makes no sense whatsoever in terms of thermodynamics, or physics in general. 
Hmmmm. Other theories of physics may indeed need to be modified to be consistent with GR, or GR may need to be modified to be consistent with them. At present, nobody has done so. This is a major area of research.
>  This should be taken as a sign that the interpretation of the Schwarzschild singularity as a coordinate singularity is incorrect, and that conditions there are such that the symmetries of GR, which allow the extension to interior solutions, no longer apply. 
I see no reason to expect that.
Remember that "all physics is local" [Einstein and others]. Locally, the horizon is no different from any other point in the manifold. There is no possible local experiment or measurement that can identify the horizon.
> 
"But how can that be", you ask? "GR predicts that conditions at the
Schwarzschild radius of a large black hole are nothing special. So
obviously GR cannot break down there. Your alternative hypotheses are
unimaginable!"
And therein lies the problem. Internal consistency is not truth, and powerful theories of symmetry cannot imagine their symmetries broken. I think "going outside the theory" is something that proponents of the geometric view of gravity should practice more! 
I think you greatly overstate the case. I think not enough is known about how GR relates to other theories of physics, and until more is known about that this will have to remain unresolved.
Tom Roberts
>  On 1/17/16 1/17/16 3:12 PM, Mike Fontenot wrote: 
>> 
I realize I'm a member of a tiny minority holding this view, but I'm in very good company: some years ago (after I had arrived at my view), I found out that Dirac had the same view. Made my day! 
> 
I'll bet that was an opinion that he formed long before the complete geometry was known. 
I THINK the paper in which Dirac stated those conclusions was published around 1965 or so. And as I recall, it was the moderator of the sci.physics.foundations newsgroup who told me about Dirac's conclusions (after I had expressed my conclusions on that newsgroup, and acknowledged that I knew I was in a tiny minority with that opinion), and he gave me an online link to that paper. I've got that link (and perhaps a printout of the paper) around here somewhere, but I don't know where ... it's probably been about 10 years since I found out about it.  show quoted text 
> 
...
In the book "Subtle is the Lord..." by Abraham Pais at page 140
and 141 we read: The two postulates: 1. The laws of physics take the same form in all inertial frames. 2. In any given inertial system the velocity of light c is the same whether the light be emitted by a body at rest or by a body in uniform motion. ... 
Hi Nicolaas!
Einstein's two postulates aren't enough on their own to uniquely define the physics of special relativity. We also seem to need a third, "geometrical", postulate, the assumption that spacetime is and remains "flat" and that the presence or introduction of stationary or moving matter doesn't affect the propagation of light, or the resulting lightbeam geometry.
The physics of how relativelymoving bodies interact in real life is //never// conducted in totally empty space (because the space under consideration has to contain the bodies!), so our third postulate should probably be that the "mathematical" lightbeam geometry derived by SR for empty space is still correct in the presence of physicallyreal moving masses and observers.
If we don't apply this third postulate, we can imagine a different physics that still obeys the principle of relativity and the law of local lightspeed constancy, without being the 1905 theory.
For instance, we could take Fresnel's early C19th idea of local lightdragging as the basis of a relativistic draggedlight model, eliminate the "aether" terminology and restate it as a geometrical theory where the dragging is a gravitoelectromagnetic effect, use GEM to regulate local lightspeeds and use W.K. Clifford's late C19th concept of "all physics as curvature" to reject the idea of movingbody physics having a valid flatspacetime solution. We'd then have a different theory of relativity that'd seem to agree with the physical evidence available in 1905, but which wouldn't be Einstein's special theory.
Physicists in 1905 may have believed that two postulates were sufficient to make SR inevitable, but we now have a broader and more sophisticated conceptual vocabulary, which opens up other possibilities. This means that defining SR's position within "theoryspace" and distinguishing it from its neighbours requires more parameters.
Eric Baird https://www.researchgate.net/profile/Eric_Baird
Tom Roberts 5 Mar On 2/28/16 2/28/16 2:39 AM, erkd...@gmail.com wrote:
>  Einstein's two postulates aren't enough on their own to uniquely define the physics of special relativity. We also seem to need a third, "geometrical", postulate, the assumption that spacetime is and remains "flat" and that the presence or introduction of stationary or moving matter doesn't affect the propagation of light, or the resulting lightbeam geometry. 
Much of this is subsumed in the definition of "inertial frame", which Einstein phrased in 1905 as "a system of coordinates in which the equations of Newtonian mechanics hold good". A modern definition is more complicated, but is absolutely required to derive the equations of SR.
One also needs the "hidden postulates" Einstein described in a 1907 paper: a) clocks and rulers have no memory, b) space is homogeneous and isotropic, and c) time is homogeneous. Plus one he didn't mention: d) light follows a null geodesic in the spacetime geometry. Note (b) and (c) are part of the definition of inertial frames, and (d) can be derived from that and the second postulate.
Note also that it is the instantaneous tick rate of a clock that has no memory, not the counter or indicated time (which is clearly a type of memory).
>  The physics of how relativelymoving bodies interact in real life is //never// conducted in totally empty space (because the space under consideration has to contain the bodies!), so our third postulate should probably be that the "mathematical" lightbeam geometry derived by SR for empty space is still correct in the presence of physicallyreal moving masses and observers. 
Physics is never exact. All that is required is that other effects are small enough to be neglected. Here on earth that is so (see below).
>  If we don't apply this third postulate, we can imagine a different physics that still obeys the principle of relativity and the law of local lightspeed constancy, without being the 1905 theory. 
But the key theoretical characteristic of SR is Lorentz invariance; local lightspeed constancy is required for that, but is itself not very important, theoretically. Without your "third postulate" (or equivalent) you don't have Lorentz invariance, and arrive at an essentially useless theory (examples of other useless theories below).
>  For instance, we could take Fresnel's early C19th idea of local lightdragging as the basis of a relativistic draggedlight model, eliminate the "aether" terminology and restate it as a geometrical theory where the dragging is a gravitoelectromagnetic effect, use GEM to regulate local lightspeeds and use W.K. Clifford's late C19th concept of "all physics as curvature" to reject the idea of movingbody physics having a valid flatspacetime solution. We'd then have a different theory of relativity that'd seem to agree with the physical evidence available in 1905, but which wouldn't be Einstein's special theory. 
I don't think that any of this leads anywhere useful, for the simple reason that here on earth spacetime curvature is quite small (on the order of 1 partpermillion). Of course some experiments are sensitive enough to detect that, but the great majority are not.
This is easy to compute: in coordinates fixed to the earth, the moon follows a helical path with radius 1.3 lightsec and period 27.3 lightdays. That helix differs from a straight line by about 0.5 ppm. Somewhat larger values apply to falling rocks near the surface.
>  Physicists in 1905 may have believed that two postulates were sufficient to make SR inevitable, but we now have a broader and more sophisticated conceptual vocabulary, which opens up other possibilities. This means that defining SR's position within "theoryspace" and distinguishing it from its neighbours requires more parameters. 
Hmmmm. I don't think those "neighbors" are useful at all.
You did not mention the infinite set of aether theories which are experimentally indistinguishable from SR. These are theories in which the roundtrip vacuum speed of light is isotropically c in every inertial frame, but the onesay speed of light differs from c; how it differs distinguishes these theories from one another. This set includes Lorentz Ether Theory (LET), the Tangherlini transforms, and an infinite number of even less well known theories. Except for SR, none of them are useful theoretically, as they do not obey Lorentz invariance.
These are discussed by Zhang, were he calls them "Edwards frames". Zhang, _Special_Relativity_and_its_Experimental_Foundations_.
Tom Roberts
>  On 2/28/16 2/28/16 2:39 AM, Eric Baird wrote: 
> >  Einstein's two postulates aren't enough on their own to uniquely define the physics of special relativity. We also seem to need a third, "geometrical", postulate, the assumption that spacetime is and remains "flat" and that the presence or introduction of stationary or moving matter doesn't affect the propagation of light, or the resulting lightbeam geometry. 
> 
Much of this is subsumed in the definition of "inertial frame", which Einstein phrased in 1905 as "a system of coordinates in which the equations of Newtonian mechanics hold good". A modern definition is more complicated, but is absolutely required to derive the equations of SR. 
Yes, the two standard postulates, plus the concept of the "inertial frame" gives special relativity. The "frame" approach assumes that the global lightspeed across a region is the same as the local lightspeed measured anywhere within it, providing SR's required third postulate of flat spacetime.
If we don't make this additional assumption, then there is at least one other way of implementing the principle of relativity for inertial physics. Globally flat geometry plus the principle of relativity gives SR, but a //locally//constant c pus the principle of relativity seems to lead //either// to special relativity or to a relativistic acoustic metric.
> 
One also needs the "hidden postulates" Einstein described in a 1907
paper: a) clocks and rulers have no memory, b) space is homogeneous and
isotropic, and c) time is homogeneous. Plus one he didn't mention: d)
light follows a null geodesic in the spacetime geometry. Note (b) and
(c) are part of the definition of inertial frames, and (d) can be
derived from that and the second postulate.
Note also that it is the instantaneous tick rate of a clock that has no memory, not the counter or indicated time (which is clearly a type of memory). 
> > 
The physics of how relativelymoving bodies interact in real life is //never// conducted in totally empty space (because the space under consideration has to contain the bodies!), so our third postulate should probably be that the "mathematical" lightbeam geometry derived by SR for empty space is still correct in the presence of physicallyreal moving masses and observers. 
> 
Physics is never exact. All that is required is that other effects are small enough to be neglected. Here on earth that is so (see below). 
Mmm ... according to Einstein's description of the effects that appear under GR, rotational motion and forcibly accelerated motion both create significant deviations from flat spacetime. The calculated magnitude of those effects for circling bodies was the same as the magnitude of SR effects, leading to the assumption that we could describe the time dilation of a circling clock either as an SR time dilation effect due to speed, or as a gravitational time dilation effect due to the apparent radial ("Machian") gravitational field due to rotation. It was assumed that if a central observer didn't rotate with the centrifuge then they could blame the effect on relative motion and SR, but if they rotated with the centrifuge, so that there was no relative motion between the two, they could explain exactly the same result by blaming spacetime curvature.
In 1960, those two arguments were found to be in apparent conflict, because if we allowed the gravitational calculation, the associated intrinsic curvature would be present for both the rotating and the nonrotating observers. This suggested that the gravitational interpretation had priority and that the SR interpretation wasn't fundamental, but was providing a sort of rough "flat approximation" of effects that were intrinsically curvedspacetime phenomena.
In late 1960 the community apparently decided that losing SR wasn't acceptable, and standardised on the "SR" explanation rather than the "curvaturebased" one.
If we'd taken the other path and given the GPoR priority over SR, then we'd have lost special relativity and would have had to implement a curvedspacetime replacement, with curvature effects being fundamental not only to relative acceleration and relative rotation, but also to relative velocity.
Nowadays (post1960), we "know" that gravitational/ distortional effects don't play a part in everyday physics because we "know" that SR is correct and that the GPoR isn't to be taken too seriously. Where the GPoR and SR generate similar predictions for an effect, we say that the SR version is correct and the GPoR version is wrong, and that the success of the SR explanation means that there's nothing left for the GPoR to explain, and therefore no measurable effect due to acceleration (see: "SR clock hypothesis").
But this "knowledge" is based on interpretation rather than raw phenomenology. We believe it because we grew up in a society where SR was the norm.
If in 1960 the community had decided to take the other "fork in the road" and had decided to support the GPoR rather than SR, we'd now be saying with similar certainty that that we "know" that distortional effects are strong in rotation and and acceleration, that we "know" that particle lifetimes in accelerator storage rings support the GPoR rather than SR, and that we "know" that SR isn't correct core theory.
Until we have better reasons for selecting one or other of these two interpretations, I don't think that we can safely say that we "know" that curvature effects are vanishingly weak and too small to worry about in Earthbased physics. I think that people are certainly entitled to argue in favour of that position, but I don't think that the issue has yet been settled.
> >  If we don't apply this third postulate, we can imagine a different physics that still obeys the principle of relativity and the law of local lightspeed constancy, without being the 1905 theory. 
> 
But the key theoretical characteristic of SR is Lorentz invariance; local lightspeed constancy is required for that, but is itself not very important, theoretically. Without your "third postulate" (or equivalent) you don't have Lorentz invariance, and arrive at an essentially useless theory ... 
IMO, The current concept of Lorentz invariance hasn't yet been shown to be essential to relativity theory.
The principle of relativity seems to require that there be a "Lorentzlike" factor involved, expressable as the ratio [1  vv/cc]^x, where the exponent has a value in the range 0.5 to 1 ... but it doesn't tell us what that exponent's value ought to be.
* If we assume that the existence and motion of particles has zero effect on the lightbeam geometry of a region, we can set x=0.5 and get the unique flatspacetime solution of special relativity. * If we assume that the recoverable kinetic energy of a system is expressed as a physical spacetime distortion between moving bodies, then we need a value of x that's greater than 0.5, but no greater than 1. * If we require the theory to also produce the classical counterpart of Hawking radiation (for compatibility with QM), we seem to require x to be equal to one.
Assuming flat spacetime gives a straightforward way of immediately ruling out all possibilities apart from x=0.5 ... which is certainly convenient ... , but that doesn't necessarily mean that x=0.5 is the right answer.
>  ... (examples of other useless theories below). 
> > 
For instance, we could take Fresnel's early C19th idea of local lightdragging as the basis of a relativistic draggedlight model, eliminate the "aether" terminology and restate it as a geometrical theory where the dragging is a gravitoelectromagnetic effect, use GEM to regulate local lightspeeds and use W.K. Clifford's late C19th concept of "all physics as curvature" to reject the idea of movingbody physics having a valid flatspacetime solution. We'd then have a different theory of relativity that'd seem to agree with the physical evidence available in 1905, but which wouldn't be Einstein's special theory. 
> 
I don't think that any of this leads anywhere useful, for the simple reason that here on earth spacetime curvature is quite small (on the order of 1 partpermillion). Of course some experiments are sensitive enough to detect that, but the great majority are not. This is easy to compute: in coordinates fixed to the earth, the moon follows a helical path with radius 1.3 lightsec and period 27.3 lightdays. That helix differs from a straight line by about 0.5 ppm. Somewhat larger values apply to falling rocks near the surface. 
I think you've just produced an excellent argument for why it can be dangerous to artificially set the strength of "puny" effects to zero. If we tried to construct a theory of gravity, and said that the moon's deviation from a straight line was only about 0.5ppm, and that the deviation was too small to be taken seriously, and should be set to zero ... and we then based a gravitational theory on the assumption that it //was// zero ... we would be liable to get a very bad theory.
It's often the job of theoretical physics to fixate on effects that are so small as to be undetectable or nearlyundetectable, but which should (or might) exist, and to calculate the consequences, not just of the effects themselves, but of the design changes that we make to theories to accommodate those imperceptiblysmall effects.
It's the job of theoretical physics to try to be ahead of the experimental data. If we're operating in a region where the theoretical inputs and outputs are all well within the range that can be easily measured and verified, then we're probably not doing theoretical physics but engineering.
> >  Physicists in 1905 may have believed that two postulates were sufficient to make SR inevitable, but we now have a broader and more sophisticated conceptual vocabulary, which opens up other possibilities. This means that defining SR's position within "theoryspace" and distinguishing it from its neighbours requires more parameters. 
> 
Hmmmm. I don't think those "neighbors" are useful at all. 
Knowing which set of Lorentzlike equations is the correct one impacts on some interesting issues, ranging from horizon physics, to the problem of how to reconcile GR with QM, to whether or not we can ever build a warp drive.
SR's "near neighbours" where the Lorentzlike difference is small are probably not all that interesting (except as a proofs of concept), but the solution at the farthest end of the range from SR (x=1 rather than 0.5), with nominal relationships that are redder and shorter than SR's by one complete extra Lorentz factor, is IMO rather intriguing.
If future experiments turn out to confirm that this "redder" solution is more accurate than the SR version, then modifying GR to accept the revised equations would seem to solve the black hole information paradox. That would be a useful thing.
> 
You did not mention the infinite set of aether theories which are
experimentally indistinguishable from SR. These are theories in which
the roundtrip vacuum speed of light is isotropically c in every
inertial frame, but the onesay speed of light differs from c; how it
differs distinguishes these theories from one another. This set includes
Lorentz Ether Theory (LET), the Tangherlini transforms, and an infinite
number of even less well known theories. Except for SR, none of them are
useful theoretically, as they do not obey Lorentz invariance.
These are discussed by Zhang, were he calls them "Edwards frames". Zhang, _Special_Relativity_and_its_Experimental_Foundations_. 
You're right, I'm less interested in theories that are completely identical to SR, or completely experimentally indistinguishable from SR, and which don't obviously lead to any new physics.
The switch from a flat SR approach to a relativistic acoustic metric isn't in that category, though  it'd seem to reinstate the GPoR as a proper principle, it'd seem to fix most or all of the outstanding problems with GR including the incompatibility with QM, it'd lead to GR being extendable down to the realm of particle physics, it'd change the way that we think about gravitational horizons, and it'd allow experimental verification (or disproof) using labscale physics.
I had a look though as much of the relevant parts of that Zhang book as I could using Google Books preview, but I didn't see anything that seemed to me to be in this league.
BTW, in the Zhang book, the term "SR test theory" seems to be used to mean "a theory to be compared against SR", whereas in all the papers I've seen, it usually means "the principles and procedures of how we should go about comparing SR against other theories".
I've always used this second definition  if you're more familiar with the first, from Zhang's book, then some of my older posts may seem rather confusing.
Eric
>  Op zaterdag 2 mei 2015 20:50:53 UTC+2 schreef Tom Roberts: (in thread "rigid rotating dics") 
>  In the book "Subtle is the Lord..." by Abraham Pais at page 140 and 141 we read: The two postulates: 1. The laws of physics take the same form in all inertial frames. 2. In any given inertial system the velocity of light c is the same whether the light be emitted by a body at rest or by a body in uniform motion. 
Aren't there at least three or four postulates to begin with? Or, isn't there at least two or three postulates entangled just in #1 above?
Something like:
0. Motion is not manybody, multiplestate or multiplefieldfield related but arises only due to universe being composed of space and time describable in terms as inertial frames. 2. The laws of physics take the same form in all inertial frames (described in terms of increments, and increments orf increments of the assumed space and time). 3. In any given inertial system the velocity of light c is the same whether the light be emitted by a body at rest or by a body in uniform motion.
Ralph
Eric,
In order to unravel what you mean with GPoR (General Principle of Relativity) I found this link (Search "Eric Baird GPoR")
https://books.google.be/books?id=bU4xUMuJlukC&pg=PA50&lpg=PA50&dq=Eric+Baird+GPoR&source=bl&ots=GXCAWjTrA&sig=xHChQLpBXsNqHywrRxf6FyQMVw&hl=nl&sa=X&ved=0ahUKEwjR3dr5vNfMAhWqDMAKHUpyAJYQ6AEIMTAC#v=onepage&q=Eric%20Baird%20GPoR&f=false
Op dinsdag 10 mei 2016 12:07:07 UTC+2 schreef Eric Baird:
> 
Yes, the two standard postulates, plus the concept of the "inertial frame" gives special relativity. The "frame" approach assumes that the global lightspeed across a region is the same as the local lightspeed measured anywhere within it, providing SR's required third postulate of flat spacetime. 
What is the purpose of Science? IMO (very rough definition): Based on the present (a small period) to predict the future and the past. That means what will happen in the future and what has happened in the past. What is the purpose of the medical Science? The same. The subjects are humans, but is only relevant for a small period in total. The internal structure is considered.
What is the purpose of Newton's Law? The same but for single objects. The time frame is long. The internal structure of the objects is "not" considered. What is the purpose of GR GPoR? The same as Newton's Law but more accurate. What is the purpose of SR? IMO: ? This reply seems negative, but I think that is the question you try to answer.
>  In 1960, those two arguments were found to be in apparent conflict, because if we allowed the gravitational calculation, the associated intrinsic curvature would be present for both the rotating and the nonrotating observers. This suggested that the gravitational interpretation had priority and that the SR interpretation wasn't fundamental, but was providing a sort of rough "flat approximation" of effects that were intrinsically curvedspacetime phenomena. 
This text raises the following question: How important are observers related to the study of science? IMO generally speaking zero. For medicine this is 100%. The laws of "nature" are independent of humans. What is important are the concepts of speed and acceleration. What is also important that you first start from a fixed reference coordination system. When that leads to contradiction you can try something else. When you start from a fixed frame all observers fixed to the frame are the same and there are no moving clocks involved. It is like placing the Sun in the center of the solar system and not the earth.
>  In late 1960 the community apparently decided that losing SR wasn't acceptable, and standardised on the "SR" explanation rather than the "curvaturebased" one. 
This swings the pendulum into the SR camp.
>  If we'd taken the other path and given the GPoR priority over SR, then we'd have lost special relativity and would have had to implement a curvedspacetime replacement, with curvature effects being fundamental not only to relative acceleration and relative rotation, but also to relative velocity. 
Again this raises the question: What is the practical importance of SR?
>  Nowadays (post1960), we "know" that gravitational/ distortional effects don't play a part in everyday physics because we "know" that SR is correct and that the GPoR isn't to be taken too seriously. Where the GPoR and SR generate similar predictions for an effect, we say that the SR version is correct and the GPoR version is wrong, and that the success of the SR explanation means that there's nothing left for the GPoR to explain, and therefore no measurable effect due to acceleration (see: "SR clock hypothesis"). 
Which particular physical processes do you have in mind? IMO accelerations are always involved in any physical process.
>  But this "knowledge" is based on interpretation rather than raw phenomenology. We believe it because we grew up in a society where SR was the norm. 
I do not agree with this. My "background" is more that SR is "simple" and GR is "complex"
>  If in 1960 the community had decided to take the other "fork in the road" and had decided to support the GPoR rather than SR, we'd now be saying with similar certainty that that we "know" that distortional effects are strong in rotation and and acceleration, that we "know" that particle lifetimes in accelerator storage rings support the GPoR rather than SR, and that we "know" that SR isn't correct core theory. 
IMO the limited implication of SR is much more that it "only" handles physical concepts like v/c along straight lines. To calculate the particle lifetimes of different reactions (after the collisions?) in LHC, using GR, I expect is extremely difficult. Can you give me a glue how this is done?
snip
>  You're right, I'm less interested in theories that are completely identical to SR, or completely experimentally indistinguishable from SR, and which don't obviously lead to any new physics. 
New physics is a misnomer. The point is how accurate can you do science using an existing theory. If "your" predictions don't match observations and a different theory is more accurate than either "you" have to modify "your" theory or switch to the other camp.
An interesting document to read is this: http://arxiv.org/pdf/physics/0207109.pdf?origin=publication_detail It gives an idea how difficult SR is.
[[Mod. note  The official arxiv url for this (excellent) paper is http://arxiv.org/abs/physics/0207109  jt]]
Nicolaas Vroom
>  On Saturday, 5 March 2016 15:12:33 UTC, Tom Roberts wrote: 
>> >  On 2/28/16 2/28/16 2:39 AM, Eric Baird wrote: 
>  If we'd taken the other path and given the GPoR priority over SR, then we'd have lost special relativity 
Why is that? If SR worked as well as the other approach you simply would have had the luxury to keep both of them!
>  and would have had to implement a curvedspacetime replacement, with 
Why the latter? Constant velocity can never transform flat coordinates to a nonflat situation. So you would not have had to implement that (nor even have been able to do so, in fact).
 Jos
Dne 16/05/2016 v 05:02 Nicolaas Vroom napsal(a):
> 
This text raises the following question: How important are observers related to the study of science? IMO generally speaking zero. For medicine this is 100%. The laws of "nature" are independent of humans. What is important are the concepts of speed and acceleration. What is also important that you first start from a fixed reference coordination system. When that leads to contradiction you can try something else. When you start from a fixed frame all observers fixed to the frame are the same and there are no moving clocks involved. It is like placing the Sun in the center of the solar system and not the earth. 
As experimental information and feedback in science is get from ( generalized ) observers, the statement their importance is zero is .... ... interesting.
The consequence would be physics can be reduced to the theoretical physics and no examination is needed.
 Poutnik ( The Pilgrim, Der Wanderer ) Knowledge makes great men humble, but small men arrogant.
>  Op dinsdag 10 mei 2016 12:07:07 UTC+2 schreef Eric Baird: 
> > 
Yes, the two standard postulates, plus the concept of the "inertial frame" gives special relativity. The "frame" approach assumes that the global lightspeed across a region is the same as the local lightspeed measured anywhere within it, providing SR's required third postulate of flat spacetime. 
Again I would like to comment on this text but in a more general(?) way.
Consider the following experiment. At point A you have a lightsource and a photon detector. At point B a distance x away, there is a mirror. With the lightsource you emit a flash at A which is reflected with the mirror at B and detected with the photon detector at A. All this sounds reasonable. Next you place a second mirror at C. The distance AB = BC = x You also place a mirror at A. At A in stead of one flash you simultaneous emit two flashes. The first flash goes from A to B back to A (reflection) to B and back to A. The second flash goes from A to C (reflection) and back to A.
Question: Are the two flashes finally arriving at A simultaneous? IMO because the distance is identical 4*(AB) = 2*(AC) they will arrive simultaneous. But there is more: you can move this setup in any direction horizontal and the answer will be the same. Ofcourse such an experiment in reality is extremely difficult and the accuracy not very reliable.
Next we perform the same experiment but now in vertical direction.
Point A is at the top and point C at the bottom.
There are two possible outcomes in principle:
1) The two final flashes arrive simultaneous.
2) The two final flashes do not arrive simultaneous.
The one which goes via the bottom first.
When the result is (1) the speed of light is constant and you can
describe the experiment using SR.
When the result is (2) the speed of light is not constant and you must
describe the experiment using GR. (GPoR)
Any comments?
Nicolaas Vroom
Dne 20/05/2016 v 04:43 Poutnik napsal(a):
> 
[[Mod. note  1. I apologise for the delay in processing this article, which arrived at my moderation inbox on monday 20160516. 2. It's very important to distinguish between the following different meanings of the word "observer":  an inertial reference frame in the context of special relativity  a *macroscopic* observer in the context of quantum mechanics ("an observation collapses the wave function")  a worldline in general relativity  a coordinate system in general relativity  jt]] 
>> 
> 
As experimental information and feedback in science
is get from ( generalized ) observers,
the statement their importance is zero is .... 
> 
Consider the following experiment.
At point A you have a lightsource and a photon detector.
At point B a distance x away, there is a mirror.
With the lightsource you emit a flash at A which is reflected with the
mirror at B and detected with the photon detector at A. All this sounds reasonable. Next you place a second mirror at C. The distance AB = BC = x You also place a mirror at A. At A in stead of one flash you simultaneous emit two flashes. The first flash goes from A to B back to A (reflection) to B and back to A. The second flash goes from A to C (reflection) and back to A. Question: Are the two flashes finally arriving at A simultaneous? 
Your description is incomplete, as you did not specify the distance A to C.
If I suppose that the distance AC is twice AB, then your description is still incomplete; if I further suppose that all components are at rest in an inertial frame in a region in which gravitation is negligible, then the two flashes arrive at A simultaneously. [These further suppositions permit me to apply SR in a simple and obvious manner.]
>  IMO because the distance is identical 4*(AB) = 2*(AC) they will arrive simultaneous. 
Your description did not say this, but it is my first supposition in the second paragraph above. Apparently you are assuming (but did not say) that A, B, and C are lined up along a straight line, with B midway between A and C. How the two flashes are kept separate and follow their specified paths is not mentioned, but this is a detail we can ignore.
>  But there is more: you can move this setup in any direction horizontal and the answer will be the same. 
Perhaps. If the further suppositions above are valid this is true for any meaning of "horizontal", but if they do not hold this might not, either.
>  Ofcourse such an experiment in reality is extremely difficult and the accuracy not very reliable. 
Let's keep this a gedanken.
>  Next we perform the same experiment but now in vertical direction. 
If the further suppositions above are valid, then "vertical" has no real meaning and is the same as "horizontal".
So I assume this means you don't want to make my further suppositions above, and want to consider gravity to be important. This opens a very large can of worms as one must apply GR.... As a simple example, there is now no definite meaning to "distance AB", and you must specify how it is to be measured (i.e. along which spacelike geodesic; this is directly related to choosing a time coordinate...). Remember that above I had to suppose all components were at rest in some inertial frame, which resolves this ambiguity for SR, but not for GR with nonnegligible gravity.
To proceed, let me make these further assumptions (which I suspect are
what you have in mind); remember this is a gedanken:
* the experiment is performed on the surface of the earth
* the earth is a perfect sphere with its usual mass
* all other massive objects are ignored, as is the atmosphere
* all components are supported against gravity, on the surface
* horizontal means a constant altitude from the surface
* vertical means along a radius from the center of the earth
* the metric is static (follows from the above assumptions)
* the time coordinate is the timelike Killing vector
* all distance measurements are made along spacelike geodesics
orthogonal to the time coordinate
* All components are very close together compared to the radius
of the earth. In particular, within the apparatus the difference
between an initially horizontal spacelike geodesic and an
initially horizontal null geodesic is negligible (note that
neither is the "horizontal distance", but this assumption also
makes the difference to that be negligible).
Explanation of this last: if two points have identical altitudes, the (constanttime) spacelike geodesic along which the distance between them is measured does not have that altitude everywhere between them, and there is no such thing as a "horizontal plane"; this assumption makes the effect of that be negligible within the apparatus and permits me to use a horizontal plane there.
[These deal with the major worms; I'll ignore any others.]
First let me consider a simpler physical situation: A still has a pulsed light source and detector; there are mirrors at D and E which are always a distance x from A, but their positions (orientations wrt A) can vary; A can always send a pulse to both D and E and detect the two reflected pulses (i.e. the mirrors are always adjusted to make this so, as is the detector orientation).
If A, D, and E are all in a horizontal plane, then the pulses arrive at A simultaneously. If they are not in a horizontal plane, then the pulses in general do NOT arrive simultaneously at A (for certain specific situations they can, such as DAE forming a vertical "V").
Consider AD horizontal, and AE vertical, with E above A. Remember the distance AD = AE, and both distances are measured simultaneously in the above coordinates. The pulse A>E>A will arrive before the pulse A>D>A. If E is vertically below A, then A>E>A will arrive after A>D>A.
For your physical situation with A, B, and C along a straight line with B midway between A and C, and the light traverses AB four times and AC twice: if the line is horizontal the pulses arrive simultaneously; if AC is vertically upward, A>C>A arrives before A>B>A>B>A; if AC is vertically downward, A>C>A arrives after A>B>A>B>A.
Note all these nonsimultaneous arrivals come far too close together to actually measure in a real experiment with x less than a km or so. So this must remain a gedanken unless possibly an interferometer setup can be invented; the basic problem is comparing horizontal and vertical distances to the required accuracy without using light (use light and the result is foreordained).
> 
There are two possible outcomes in principle: 1) The two final flashes arrive simultaneous. 2) The two final flashes do not arrive simultaneous. When the result is (1) the speed of light is constant and you can describe the experiment using SR. 
Not necessarily (see below).
>  When the result is (2) the speed of light is not constant and you must describe the experiment using GR. 
If gravitation is not negligible, you cannot use SR and must use GR. Even if you happen to luck out and the flashes arrive simultaneously.
Tom Roberts
>  On 5/20/16 5/20/16 7:16 AM, Nicolaas Vroom wrote: 
> >  Consider the following experiment. At point A you have a lightsource and a photon detector. At point B a distance x away, there is a mirror. With the lightsource you emit a flash at A which is reflected with the mirror at B and detected with the photon detector at A. All this sounds reasonable. Next you place a second mirror at C. The distance AB = BC = x You also place a mirror at A. 
I have to apoligize. I should have drawn a sketch
' ABC 'Light Mirror Mirror' E0> ' < From A to B to A to B ' > ' E1< ' E0> ' E2< from A to C to A
> > 
At A in stead of one flash you simultaneous emit two flashes.
The first flash goes from A to B back to A to B and back to A.
The second flash goes from A to C (reflection) and back to A.
Question: Are the two flashes finally arriving at A simultaneous? 
> 
Your description is incomplete, as you did not specify the distance A to C. 
All is in horizontal plane on surface of the earth
The two original lightflashes are at E0.
Via B the second detection at A is at E1
Via C the first detection at A is at E2
The question is are E1 and E2 simultaneous.
>  If I suppose that the distance AC is twice AB, then your description is still incomplete; if I further suppose that all components are at rest in an inertial frame in a region in which gravitation is negligible, then the two flashes arrive at A simultaneously. [These further suppositions permit me to apply SR in a simple and obvious manner.] 
I agree with you in the horizontal setup
> 
> > 
IMO because the distance is identical 4*(AB) = 2*(AC) they will arrive simultaneous. 
> 
Your description did not say this, but it is my first supposition in the second paragraph above. Apparently you are assuming (but did not say) that A, B, and C are lined up along a straight line, with B midway between A and C. How the two flashes are kept separate and follow their specified paths is not mentioned, but this is a detail we can ignore. 
I agree.
> >  But there is more: you can move this setup in any direction horizontal and the answer will be the same. 
> 
Perhaps. If the further suppositions above are valid this is true for any meaning of "horizontal", but if they do not hold this might not, either. 
I agree
> >  Next we perform the same experiment but now in vertical direction. 
> 
If the further suppositions above are valid, then "vertical" has no real meaning and is the same as "horizontal". 
No that's not I have in mind. The idea is that the whole set up is in a vertical direction and that the light signal first travels towards the center of the earth.
> 
So I assume this means you don't want to make my further suppositions
above, and want to consider gravity to be important. This opens a very
large can of worms as one must apply GR.... As a simple example, there
is now no definite meaning to "distance AB", and you must specify how
it is to be measured (i.e. along which spacelike geodesic; this is
directly related to choosing a time coordinate...). Remember that above
I had to suppose all components were at rest in some inertial frame,
which resolves this ambiguity for SR, but not for GR with nonnegligible
gravity.
To proceed, let me make these further assumptions (which I suspect are what you have in mind); remember this is a gedanken: 
Sorry SNIP
I like all the technical subtleties you bring into this discussion but I do not know if they are necessary.
> 
Explanation of this last: if two points have identical
altitudes, the (constanttime) spacelike geodesic along
which the distance between them is measured does not have
that altitude everywhere between them, and there is no
such thing as a "horizontal plane"; this assumption makes
the effect of that be negligible within the apparatus
and permits me to use a horizontal plane there.
First let me consider a simpler physical situation: A still has a pulsed light source and detector; there are mirrors at D and E which are always a distance x from A, but their positions (orientations wrt A) can vary; A can always send a pulse to both D and E and detect the two reflected pulses (i.e. the mirrors are always adjusted to make this so, as is the detector orientation). If A, D, and E are all in a horizontal plane, then the pulses arrive at A simultaneously. 
> 
If they are not in a horizontal plane, then the pulses
in general do NOT arrive simultaneously at A (for certain specific
situations they can, such as DAE forming a vertical "V").
Consider AD horizontal, and AE vertical, with E above A. Remember the distance AD = AE, and both distances are measured simultaneously in the above coordinates. 
>  The pulse A>E>A will arrive before the pulse A>D>A. 
>  If E is vertically below A, then A>E>A will arrive after A>D>A. 
In this case gravity has to be considered. Tricky IMO this example is much more complex than I have in mind.
>  For your physical situation with A, B, and C along a straight line with B midway between A and C, and the light traverses AB four times and AC twice: if the line is horizontal the pulses arrive simultaneously; if AC is vertically upward, A>C>A arrives before A>B>A>B>A; 
>  if AC is vertically downward, A>C>A arrives after A>B>A>B>A. 
The issue is that when you perform such an experiment gravity is involved
and SR is not sufficient.
The center idea is that incase of AB 4 times the same path (length) is
considered. In the case of AC this is also the situation.
However (downward) the difference is that in the case of AB
two times a path AB is considered and in the case of AC two times the path
BC is considered.
AB is rougly speaking high above the surface and BC low above the surface.
The issue is if this has any relation with the speed of light.
When the speed increases going from top to bottom this will mean that
light via C arrives earlier than light via B (at A)
When the speed decreases going from top to bottom this will mean that
light via C arrives later than light via B (at A)
>  Note all these nonsimultaneous arrivals come far too close together to actually measure in a real experiment with x less than a km or so. So this must remain a gedanken unless possibly an interferometer setup can be invented; the basic problem is comparing horizontal and vertical distances to the required accuracy without using light (use light and the result is foreordained). 
I fully agree with you. Such an experiment is in practice very difficult to perform. The whole issue is that, no clock is involved. However that is not totally true. The signal ABABA services as a clock for the signal ACA.
> > 
There are two possible outcomes in principle: 1) The two final flashes arrive simultaneous. 2) The two final flashes do not arrive simultaneous. When the result is (1) the speed of light is constant and you can describe the experiment using SR. 
> 
Not necessarily (see below). 
> > 
When the result is (2) the speed of light is not constant and you must describe the experiment using GR. 
> 
If gravitation is not negligible, you cannot use SR and must use GR. Even if you happen to luck out and the flashes arrive simultaneously. 
Exactly. You have to use GR for the vertical set up. That is what I have in mind to challenge that the speed of light is constant.
However there is more it places the importance of GR above SR. And you can ask yourself the question how important is the third postulate proposed by Eric Baird.
>  Tom Roberts 
Nicolaas Vroom
>  Op zondag 22 mei 2016 09:47:44 UTC+2 schreef Tom Roberts: 
>>  [...] 
' ABC ' Light Mirror Mirror
All is in horizontal plane on surface of the earth
And we agree that light A>B>A>B>A arrives at A simultaneously with light A>C>A. (Distance AB = distance BC.)
>>>  Next we perform the same experiment but now in vertical direction. 
>  The idea is that the whole set up is in a vertical direction and that the light signal first travels towards the center of the earth. [...] In this case gravity has to be considered. Tricky 
Not terribly tricky.
The trick is keeping FIRMLY IN MIND what one means by "speed". Remember that in GR the LOCAL speed of light in vacuum is always c when measured in a locally inertial frame. Remember also that the size of such a locally inertial frame depends on the measurement accuracy with which one can make the relevant measurements.
From that we can immediately conclude if the distance AC is "small" enough, and if the apparatus is in freefall, the two light pulses above will arrive simultaneously at A, regardless of the orientation of the apparatus. (This basically means that the measurement resolution is insufficient to observe the difference in their arrival times.)
But you want to keep the apparatus at rest on earth's surface, and you want to use essentially infinite accuracy. So the apparatus is not at rest in a locally inertial frame. All is not lost, and we can make some conclusions (see below).
>>  if AC is vertically downward, A>C>A arrives after A>B>A>B>A. 
> 
Both AC and AB are downward. This is the situation I have in mind.
The issue is that when you perform such an experiment gravity is involved and SR is not sufficient. 
Yes. But very general things are known about GR. For this conclusion I simply applied the analysis of the Shapiro time delay  BC is below AB, and thus from the perspective of an observer at A, light traversing BC is delayed more than light traversing AB. Hence I can make this conclusion without performing a detailed calculation.
But I would NOT claim "light travels slower BC than AB". That would be a PUN on "speed", because we normally reserve that word for measurements in locally inertial frames. And also because we did not measure it.
Interesting observation: as in QM, in GR it is usually not possible to discuss quantities which were not measured. Here the delays of pulses are measured (compared) and I can make definitive statements about them; but their speed is NOT measured, and I cannot make definite statements. It is remarkable that the two major revolutions in physics of the 20th century, quantum mechanics and relativity, share this emphasis on measurements. But the reasons for this similarity are QUITE different: in QM it is because such quantities have no definite value, while in GR it happens because such statements invariably involve a choice of coordinates, and such choices are arbitrary (coordinatedependent quantities need not reflect the underlying physical processes as they also involve aspects of the coordinate choice).
Why are measurements so "special" in GR?  because they are necessarily independent of coordinates. That is, every measurement projects the quantity being measured onto the measuring instrument. As you were taught in kindergarten, the ruler must be aligned with the object to measure its length (the ruler projects onto itself, and if not aligned the projection will not be the desired result); this is inherently a very general aspect of measuring instruments.
>  You have to use GR for the vertical set up. That is what I have in mind to challenge that the speed of light is constant. 
Hmmmm. As I said above: keep FIRMLY IN MIND what you mean by "speed". When you try to say "the speed of light is not constant" you are using a PUN on "speed". The vacuum speed of light measured in a locally inertial frame is c, everywhere and everywhen. But if you choose to divide a distance by a flight time and call the result "speed", even when the measurements are not in a locally inertial frame, then OF COURSE you can obtain a result not equal to c. Indeed GR predicts this (c.f the Shapiro time delay  if you insist on calling the result "speed" then of course it is not equal to c; that's why it is termed a DELAY and not a "reduction in speed").
>  However there is more it places the importance of GR above SR. 
Yes, of course. The only reasons SR is still taught are a) because it is the local limit of GR, and b) is ENORMOUSLY less difficult to apply [#].
Moreover, most ordinary measurements are made in a locally inertial frame in which SR can be applied with negligible error. This includes every aspect of our daily lives, every elementary particle experiment, and almost all optical experiments performed on a table.
[#] Remember the details I gave earlier in this thread, for the horizontal situation where the light path does not correspond to a spacelike geodesic between endpoints AC  so what does "distance" mean when attempting to apply the definition of speed? No matter what you do, you will have to CHOOSE coordinates (or at least a foliation of spacetime into space and time), and the result will depend on your choice.
>  And you can ask yourself the question how important is the third postulate proposed by Eric Baird. 
He proposed adding "flat spacetime"  that is inherent in applying SR and presuming it to be exact. But as the local limit of GR it can be a very useful and accurate approximation in many physical situations of interest.
Tom Roberts
>  On 5/24/16 5/24/16 3:04 PM, Nicolaas Vroom wrote: 
Sorry I have to skip this part.
> >>  if AC is vertically downward, A>C>A arrives after A>B>A>B>A. 
> > 
Both AC and AB are downward. This is the situation I have in mind.
The issue is that when you perform such an experiment gravity is involved and SR is not sufficient. 
> 
Yes. But very general things are known about GR. For this conclusion I simply applied the analysis of the Shapiro time delay  BC is below AB, and thus from the perspective of an observer at A, light traversing BC is delayed more than light traversing AB. Hence I can make this conclusion without performing a detailed calculation. 
In order to refresh my mind about the Spapiro effect I have studied paragraph 15.6 (page 204) from the book 1:"Introducing Einstein's Relativity" by Ray d'Inverno and page 1106 etc of the book 2:"Gravitation."
Consider dropping a ball A from the top of a tower with height h. The
ball is reflected completely without any friction. T1 is the moment when
the ball A is back at the top Consider dropping a second ball B
simultaneous with A from the top, however this ball is reflected at
height h/2. When ball B is back at the top the ball is immediate dropped
again. T2 is the moment when ball B is back at the top for the second
time. Question is T1=T2 or T1
But that is not what I want. I'am interested in the behavior of a light signal with goes "undisturbed" straight towards to the (center of) the earth. For example starting half way between the Moon and the Earth.
The initial speed can be "c". The first question is will this speed increase or decrease or decrease when the photons travel towards the earth.
>  But I would NOT claim "light travels slower BC than AB". That would be a PUN on "speed", because we normally reserve that word for measurements in locally inertial frames. And also because we did not measure it. 
I'am not that "strict". If you compare two light signals, which both travel over the same distance and the first arrives before the second than the speed of the first is higher than the second without any indication what the actual speed is.
>  Interesting observation: as in QM, in GR it is usually not possible to discuss quantities which were not measured. Here the delays of pulses are measured (compared) and I can make definitive statements about them; but their speed is NOT measured, and I cannot make definite statements. 
I agree with this, but I do not think this is particular related to GR. IMO there is a hugh difference for the laws that are relevent at macro niveau versus micro niveau. You "can not" use GR to predict earthquakes.
>  It is remarkable that the two major revolutions in physics of the 20th century, quantum mechanics and relativity, share this emphasis on measurements. But the reasons for this similarity are QUITE different: in QM it is because such quantities have no definite value, while in GR it happens because such statements invariably involve a choice of coordinates, and such choices are arbitrary 
This whole discussion is very tricky. Suppose you want to simulate a whole galaxy. To do that you have to measure the position of the stars involved over a series of intervals. In order to do that you need one coordinate system. When the positions are known the next step is to calculate the masses of the stars in the galaxy, using a certain model. However in order to measure the position of a single star light signals are involved which have to be corrected because the signals are bended by masses of stars inbetween this single star and the measuring instrument. In fact you have to take the behaviour of photons (QM?) into account if you want to do this very accurate.
>  Why are measurements so "special" in GR?  because they are necessarily independent of coordinates. That is, every measurement projects the quantity being measured onto the measuring instrument. As you were taught in kindergarten, the ruler must be aligned with the object to measure its length (the ruler projects onto itself, and if not aligned the projection will not be the desired result); this is inherently a very general aspect of measuring instruments. 
For me a much more important issue is the relation of a measurement versus a calculation. Went you want to know the order of the runners in a maraton this is a (direct) measurement. The first one arriving runs the fastest. When you want to know the speed of each runner this is a calculation because it depents on two measurements.
>  The vacuum speed of light measured in a locally inertial frame is c, everywhere and everywhen. IMO this is a calculation. When you declare c 
>  But if you choose to divide a distance by a flight time and call the result "speed", even when the measurements are not in a locally inertial frame, then OF COURSE you can obtain a result not equal to c. Indeed GR predicts this (c.f the Shapiro time delay  if you insist on calling the result "speed" then of course it is not equal to c; that's why it is termed a DELAY and not a "reduction in speed"). 
When you study Fig 15.13 book 1 the shortest distance is called D. In fig 40.3 book 2 this is the distance slightly larger than b. For me the important question is the speed of light constant from transmitter to reflector? Is the speed the highest at the shortest distance near the Sun? To answer that question IMO you have to divide the path in for example 10 smaller parts with the same length and investigate each. In the experiment I propose I try to answer that same question very close to the earth by comparing two signals without the aid of a clock and "no" mathematics.
Thanks Tom.
Nicolaas Vroom
Is the speed the highest at the shortest distance near the
>  Sun? To answer that question IMO you have to divide the path in for example 10 smaller parts with the same length and investigate each. In the experiment I propose I try to answer that same question very close to the earth by comparing two signals without the aid of a clock and "no" mathematics. 
Suppose there was self aware matter that could answer these questions? I put it to you that we are self aware matter and if it does not seem to be logical from our shoes then all efforts should be made to make sense of it. Myself having lucked out as being self aware matter for a brief period of time can say the consistency of the speed of light is only true for measurements the observer not reality in the larger picture. Your only obligation to fulfill the postulate of SR is to measure the speed of light to be c. This is not the same as saying the speed of light is constant at c. If one lived in a hot air balloon it is never a windy day and one could conclude that the speed of sound is constant at 1000 feet per second. If we are a product of a vacuum we would be under the same illusion that the speed of light is constant. However a hot air balloon Einstein would never be noted as a hero in physics as every hot air balloon person would be is aware that temperature effects time. A hot air person , cloud in the sky , will know intuitively to leave earlier to arrive on time on a cold day. Temperature effects time. What seems obvious to a cloud in the sky could lead to misunderstanding to us as solids so we celebrate Einstein as a hero in physics. A vacuum sets time for us in the same way the temperature effects time for a cloud in the sky. Both the cloud gas and ourselves solids think the speed of sound for clouds and the speed of light is constant by measurements made in both cases. In both cases we are wrong for the same reasons. There is no way the speed of light is c near a black hole as this would violate the postulate the laws physics are the same for all Frames of reference. The speed of light only measures c for the same reason the speed of sound always measure 1000 feet per second for a hot air balloon.
> 
> > 
Nicolaas Vroom wrote: Is the speed the highest at the shortest distance near the Sun? To answer that question IMO you have to divide the path in for example 10 smaller parts with the same length and investigate each. In the experiment I propose I try to answer that same question very close to the earth by comparing two signals without the aid of a clock and "no" mathematics. 
> 
Suppose there was self aware matter that could answer these questions? I put it to you that we are self aware matter and if it does not seem to be logical from our shoes then all efforts should be made to make sense of it. 
The concept of "self aware matter" is out side the physical reality which makes any discussion immediate tricky.
>  Your only obligation to fulfill the postulate of SR is to measure the speed of light to be c. This is not the same as saying the speed of light is constant at c. 
The current topic in the discussion is the speed of light. What I try to answer is the question: is this speed always the same or is this speed variable. Specific I want to find out "if" and "what" the influence of matter or gravity is. The influence of vacuum should also be considered. What I presently do not want to discuss is the actual (average?) value of the speed of light. In order to study the behaviour of photons, I propose an experiment (using light, a tower and mirrors). See previous postings. The current discussion is to predict the outcome of this experiment. My understanding is that the speed will increase when the photons approach the earth. In fact when you send a light signal from the sun towards the earth, first the speed will decrease and than increase.
The problem with this whole discussion is that it belongs more in the newsgroup :Sci.physics.foundations. However at this moment this is impossible, because the newsgroup is temporary "out of order".
When you study: https://en.wikipedia.org/wiki/Speed_of_light you can read: "the metre was redefined in the SI Units as the distance travelled by light in vacuum in 1/299792458 of a second." The problem with this defintion is when the speed is not constant the length of a metre also changes.
What is important as part of this discussion: what is the definition of a vacuum. Accordingly to: https://en.wikipedia.org/wiki/Vacuum : "Vacuum is space void of matter" But that does not exist in outerspace. In fact the whole universe is filled with photons, which makes any definition based on vacuum misleading(?)
A different reason, why the issue is important, is the program "VB light" See: http://users.telenet.be/nicvroom/VB%20Light%20operation.htm In this program light rays around matter are simulated, specific to study: "The bending of light around matter". What this simulation shows (based on Newton's Law) that the speed of light (photons) is not constant.
Nicolaas Vroom.
>  When you study: https://en.wikipedia.org/wiki/Speed_of_light you can read: "the metre was redefined in the SI Units as the distance travelled by light in vacuum in 1/299792458 of a second." The problem with this defintion is when the speed is not constant the length of a metre also changes. 
If the speed of light is not constant, there would be many other worries besides problems with the definition of the metre!
>  What is important as part of this discussion: what is the definition of a vacuum. Accordingly to: https://en.wikipedia.org/wiki/Vacuum : "Vacuum is space void of matter" But that does not exist in outerspace. In fact the whole universe is filled with photons, which makes any definition based on vacuum misleading(?) 
No; you can always discuss the limit of a true vacuum.
>  A different reason, why the issue is important, is the program "VB light" See: http://users.telenet.be/nicvroom/VB%20Light%20operation.htm In this program light rays around matter are simulated, specific to study: "The bending of light around matter". What this simulation shows (based on Newton's Law) that the speed of light (photons) is not constant. 
You can't expect to learn anything based on Newton's laws. We know that they are wrong. Yes, they are good approximations in some limits, but you have to know what those are before you can safely use Newton's laws.
The point is that any LOCAL measurement of the speed of light always gives the same value.
> 
In article <04c3fc4122cb43aab59484fb25c038ae@googlegroups.com>,
Nicolaas Vroom 
>> 
When you study: https://en.wikipedia.org/wiki/Speed_of_light you can read: "the metre was redefined in the SI Units as the distance travelled by light in vacuum in 1/299792458 of a second." The problem with this defintion is when the speed is not constant the length of a metre also changes. 
> 
If the speed of light is not constant, there would be many other worries besides problems with the definition of the metre! 
Very few, actually. The speed of light is both a *concept* (let's call it c0=1 for simplicity) and a measured quantity 'c' (though via the SI the latter has to be done indirectly).
The *experimentally* established mass of the photon is smaller than 10^18 eV [1]  everything below that is simply terra incognita. It could be that the photon had a mass of, say 4*10^21 eV. That would lead to not only to a speed of light different from c0 but also a *frequency dependent* speed of light.
Not a problem there, obviously, as this might actually be the case for all that we know.
Now, the *concept* of a finite speed limit in the Universe is fully independent of any actual physical realisation or, indeed, experimental proof.
If it turned out that 'real' light is not quite the 'conceptual light' and that the photon has a mass, very few actual things would change. So few, that with all our rather well developed measurement devices we are currently not able to measure the effects of a massive photon, provided the mass is smaller than said 10^18 eV.
[1] Interestingly enough, the mass of the graviton (or in absence of a quantum theory of gravity, the dispersion of gravitational waves) is known better than that  m_g < 1.2e22 eV. Still, we call it 'speed of light' and not 'speed of gravity', because the for the ART, it is the *concept* that matters, not so much the actual speed.  Space  The final frontier
>>>  by light in vacuum in 1/299792458 of a second." The problem with this defintion is when the speed is not constant the length of a metre also changes. 
>> 
If the speed of light is not constant, there would be many other worries besides problems with the definition of the metre! 
> 
Very few, actually. The speed of light is both a *concept* (let's call it c0=1 for simplicity) and a measured quantity 'c' (though via the SI the latter has to be done indirectly). 
What I meant was that a nonconstant speed of light, finite rest mass of the photon, etc, would imply some sort of new physics. The metre is defined by the speed of light, and relies on the second, which is defined in terms of a specific wavelength of light. One could specify that the metre should also use this wavelength.
> 
Now, the *concept* of a finite speed limit in the Universe is fully
independent of any actual physical realisation or, indeed, experimental
proof.
If it turned out that 'real' light is not quite the 'conceptual light' and that the photon has a mass, very few actual things would change. So few, that with all our rather well developed measurement devices we are currently not able to measure the effects of a massive photon, provided the mass is smaller than said 10^18 eV. 
Right. Practical consequences would be almost none. It would mean a lot conceptually, though.
> 
In article <04c3fc4122cb43aab59484fb25c038ae@googlegroups.com>,
Nicolaas Vroom 
>>  ... 
>  ... 
>>  What is important as part of this discussion: what is the definition of a vacuum. Accordingly to: https://en.wikipedia.org/wiki/Vacuum : "Vacuum is space void of matter" 
A Wikipedia definition is not necessarily scientifically accurate, unless it is an exact copy or translation of a definition agreed by the relevant international body.
>  The point is that any LOCAL measurement of the speed of light always gives the same value. 
Any purely LOCAL errorfree measurement of the speed of light in empty flat space nowadays will give a result of 299792458 m/s, by tautology.
Any apparent discrepancy in an errorfree imperfectly local measurement must result from the local area used being not flat. Nonempty space cannot be flat, although nonflatness is generally only a minor consequence of nonemptiness.
 (c) John Stockton, Surrey, UK. ¬@merlyn.demon.co.uk Turnpike v6.05 MIME. Merlyn Web Site < >  FAQish topics, acronyms, & links.
> 
In article <04c3fc4122cb43aab59484fb25c038ae@googlegroups.com>,
Nicolaas Vroom 
> > 
When you study: https://en.wikipedia.org/wiki/Speed_of_light you can read: "the metre was redefined in the SI Units as the distance travelled by light in vacuum in 1/299792458 of a second." The problem with this defintion is when the speed is not constant the length of a metre also changes. 
> 
If the speed of light is not constant, there would be many other worries besides problems with the definition of the metre! 
What is physical wrong with the idea that the speed of light (radiation) is not always the same? (can vary). The same with any particle? The opposite would be amazing. Why should the speed be constant
As I said before this whole discussion belongs more in the newsgroup: sci.physics.foundations. When consider the above definition of a metre you must also define what a second is and such a second must also be a physical constant process. We know by experiment that that is also difficult to establish. A whole different physical issue the speed of gravition. It is physical possible that this speed is much more "fixed" (stable?) than the speed of light. In principle such a speed (if constant) is a better starting point to define a metre. (But is has its own problems)
> > 
What is important as part of this discussion: what is the definition
of a vacuum. Accordingly to: https://en.wikipedia.org/wiki/Vacuum :
"Vacuum is space void of matter" But that does not exist in outerspace. In fact the whole universe is filled with photons, which makes any definition based on vacuum misleading(?) 
> 
No; you can always discuss the limit of a true vacuum. 
The point is when you use the concept "vacuum" in a defintion than the concept vacuum should also clearly be defined. I doubt it is. A different issue is than also always when you consider the speed of light in any discussion it should be in a vacuum. The point is when the physical state between the Sun and the earth is not a vacuum than you cannot use the definition in order to measure distance. (Of course for most applications you can)
> >  A different reason, why the issue is important, is the program "VB light" See: http://users.telenet.be/nicvroom/VB%20Light%20operation.htm In this program light rays around matter are simulated, specific to study: "The bending of light around matter". What this simulation shows (based on Newton's Law) that the speed of light (photons) is not constant. 
> 
You can't expect to learn anything based on Newton's laws. We know that they are wrong. Yes, they are good approximations in some limits, but you have to know what those are before you can safely use Newton's laws. 
I agree quantitatif that you are right. The point I want to make is that using Newton's Law you can see that the speed is not always the same, which raises an issue to be discussed.
>  The point is that any LOCAL measurement of the speed of light always gives the same value. 
As I stated before it is primarily not my strategy to calculate the speed of light. What I want to challenge is the idea that this speed is not always the same. To do that I use one observer, two light sources, a tower, and two mirrors at different heights. The question is what is the outcome of the two experiments.
Nicolaas Vroom.
>  My understanding is that the speed will increase when the photons approach the earth. In fact when you send a light signal from the sun towards the earth, first the speed will decrease and than increase. 
You mean, you want to consider the combined gravitational field of Sun and Earth. The first thing you have to note then is that there is no known exact solution of GR field equations for a gravitational field with more than one centre of gravity. For one single centre of gravity, there is Schwarzschild solution, but for two or more centres of gravity, there is no exact solution known. And due to nonlinearity of GR, you cannot simply construct such as solution by combining two Schwarzschild solutions.
However, you could argue that an eventual solution for two centres of gravity, like Sun and Earth, should in some way look similar to a combination of two Schwarzschild solutions, at least in that way that one should be able to find a coordinate system in which the speed of light, measured with respect to that coordinate systems, shows the behaviour you described.
>  The problem with this whole discussion is that it belongs more in the newsgroup :Sci.physics.foundations. However at this moment this is impossible, because the newsgroup is temporary "out of order". 
Assumed, in spf would someone reply to you who has good knowledge in GR, his answer might probably be similar to the answers you got here. So, it wouldn't make any difference.
>  When you study: https://en.wikipedia.org/wiki/Speed_of_light you can read: "the metre was redefined in the SI Units as the distance travelled by light in vacuum in 1/299792458 of a second." The problem with this defintion is when the speed is not constant the length of a metre also changes. 
As far as the variability of the speed of light due to gravitational effects is concerned, the metre definition is not touched in any way: to define the metre, one uses the speed of light measured with respect in a local inertial frame, which is applied in a small spacetime region limited enough to neglect gravitational effects and to apply the SRlimit of GR.
As far as an eventual variability of the speed of light is concerned that might occur even in a local inertial frame due to an eventual failure of GR and SR, the "problem" you described is not different from the "problem" any other metre definition would cause, and the definition of the unit of any other quantity causes. As you can read here:
https://en.wikipedia.org/wiki/History_of_the_metre#International_prototype_metre
one used the international prototype metre to define the metre from 1889 until 1960. At that time, the "problem" you describe was that changes in the length of the prototype metre resultet in changes in the length of the metre. They were even well aware of this fact: they knew that the length of the prototype metre had an uncertainty of about 0.1 micrometers, causing a relative uncertainty of 10^7. But this was a much better precision than former definition for the metre or other length unit could achieve. And as you can read here:
https://en.wikipedia.org/wiki/History_of_the_metre#Krypton_standard
from 1960 until 1983, the metre was defined as 1650763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton 86 atom. This caused again a "problem" as you describe it: changes in the wavelength of the radiation of krypton atoms resulted in changes in the length of the metre. At that time, it was well known that wavelength of the radiation of krypton atoms it not constant: like any other spectal line, the spectral line of the 2p10 to 5d5 transition of krypton 86 atoms has a nonzero line width, making the wavelength fluctuate. This fluctuation of the wavelength caused a relative uncertainty in the metre definition of 10^8. But this was by one order better than the relative uncertainty yielded by the former metre definition by the prototype metre.
So, what we can see is that the aim of unit definitions is to achieve a precision that is as high as possible. The krypton standard yielded a relative uncertainty of 10^8, what is a better precision than the relativ uncertainty of 10^7 that was formerly achieved using the prototype metre. And the today's metre definition:
https://en.wikipedia.org/wiki/History_of_the_metre#Speed_of_light_standard
yields an even better precision, the relative uncertainty is only 10^10.
So, if we assumed that the speed of light might vary, even in situations where the SR limit of GR should be applicable, because GR and SR break down, the consequence would be, that the relative uncertainty of the metre definition is higher that assumed so far. Assumed, it turned out that the uncertainty exceeds 10^8, they would skip the speed of light standard and e.g. return to the krypton standard.
>  What is important as part of this discussion: what is the definition of a vacuum. Accordingly to: https://en.wikipedia.org/wiki/Vacuum : "Vacuum is space void of matter" But that does not exist in outerspace. 
A very general procedure in physics is to use idealizations and approximations. One could e.g. reason that in a real vacuum (as is can be created in a laboratory), the speed of light is in good approximation equal to the speed of light in an ideal vacuum.
This isn't in any way special to relativistic physics. Take e.g. Newton formula F=m*a. Rigorously, this formula applies in ideal inertial frames only. However, there are to ideal inertial frames, because there is no observer that is ideally forcefree. There are only observer who can be thought as being forcefree in good approximation.
But even that is not really necessary. One could as well argue that there should be a speed of light, let's call it c0, that would be the speed of light in a hypothetical perfect vacuum. Then one could postulate that this speed c0 is always the same, in all inertial frames, and conclude that SR effects occur at velocities near this speed. Frome the fact that we observe SR effects near the real speed of light that we can factually measure in a real vacuum, let's call it c', we then can conclude that both speeds, c0 and c', are very close to each other.
>  A different reason, why the issue is important, is the program "VB light" See: http://users.telenet.be/nicvroom/VB%20Light%20operation.htm In this program light rays around matter are simulated, specific to study: "The bending of light around matter". What this simulation shows (based on Newton's Law) that the speed of light (photons) is not constant. 
It shows that in Newtonian Gravity, the speed of light is variable. Or more precisely: in Newtonian Gravity amended by some assumptions on how light is influenced by gravity. However, since Newtonian Gravity is known to be wrong, except in nonrelativistic regime, this result shows little about reality. At best, is *suggests* that also in a relativistic theory of gravity, i.e. in GR, the speed of light should be variable in some way.
And indeed, in GR, the speed of light turns out to be variable in some way. Namely in that way, that the speed of light measured with respect to a general coordinate system is variable. But not the speed of light measured with respect to a local inertial frame.
>  Nicolaas Vroom wrote: 
> > 
My understanding is that the speed will increase when the photons approach the earth. In fact when you send a light signal from the sun towards the earth, first the speed will decrease and than increase. 
> 
You mean, you want to consider the combined gravitational field of Sun and Earth. The first thing you have to note then is that there is no known exact solution of GR field equations for a gravitational field with more than one centre of gravity. For one single centre of gravity, there is Schwarzschild solution, but for two or more centres of gravity, there is no exact solution known. 
This IMO raises an issue when you want to study the merging of two black holes using GR.
>  However, you could argue that an eventual solution for two centres of gravity, like Sun and Earth, should in some way look similar to a combination of two Schwarzschild solutions, at least in that way that one should be able to find a coordinate system in which the speed of light, measured with respect to that coordinate systems, shows the behaviour you described. 
As such we both agree.
> >  When you study: https://en.wikipedia.org/wiki/Speed_of_light you can read: "the metre was redefined in the SI Units as the distance travelled by light in vacuum in 1/299792458 of a second." The problem with this defintion is when the speed is not constant the length of a metre also changes. 
> 
As far as the variability of the speed of light due to gravitational effects is concerned, the metre definition is not touched in any way: to define the metre, one uses the speed of light measured with respect in a local inertial frame, which is applied in a small spacetime region limited enough to neglect gravitational effects and to apply the SRlimit of GR. 
I agree with you, however this becomes an issue when light years are considered.
Sorry, I skipped a lot of your text but it is very worthwhile reading.
>  But even that is not really necessary. One could as well argue that there should be a speed of light, let's call it c0, that would be the speed of light in a hypothetical perfect vacuum. Then one could postulate that this speed c0 is always the same, in all inertial frames, and conclude that SR effects occur at velocities near this speed. From the fact that we observe SR effects near the real speed of light that we can factually measure in a real vacuum, let's call it c', we then can conclude that both speeds, c0 and c', are very close to each other. 
I fully agree with you. The problem is more or less that in SR we start from the idea that the speed of light is constant (and in all directions the same) and equal to c. In reality this picture is much more complex.
> >  A different reason, why the issue is important, is the program "VB light" See: http://users.telenet.be/nicvroom/VB%20Light%20operation.htm In this program light rays around matter are simulated, specific to study: "The bending of light around matter". What this simulation shows (based on Newton's Law) that the speed of light (photons) is not constant. 
> 
It shows that in Newtonian Gravity, the speed of light is variable. Or more precisely: in Newtonian Gravity amended by some assumptions on how light is influenced by gravity. However, since Newtonian Gravity is known to be wrong, except in nonrelativistic regime, this result shows little about reality. At best, is *suggests* that also in a relativistic theory of gravity, i.e. in GR, the speed of light should be variable in some way. 
I fully agree. Specific I like the subtleties in your comments.
>  And indeed, in GR, the speed of light turns out to be variable in some way. Namely in that way, that the speed of light measured with respect to a general coordinate system is variable. But not the speed of light measured with respect to a local inertial frame. 
I doubt how important the last is. What is the point when local implies a very small region, while in general what we want is to study the evolution of the universe.
Nicolaas Vroom.
>>>  When you study: https://en.wikipedia.org/wiki/Speed_of_light you can read: "the metre was redefined in the SI Units as the distance travelled by light in vacuum in 1/299792458 of a second." The problem with this defintion is when the speed is not constant the length of a metre also changes. 
>> 
If the speed of light is not constant, there would be many other worries besides problems with the definition of the metre! 
> 
What is physical wrong with the idea that the speed of light (radiation) is not always the same? (can vary). The same with any particle? The opposite would be amazing. Why should the speed be constant 
According to all our obversations, the speed of light is constant in situations where the SRlimit of GR is applicable, i.e. where gravitational effects can be neglected. So, obviously, it would be physically wrong to say that the speed of light would vary in those situations.
Or did you want to ask for a theoretical explaination for the constancy of the speed of light? Within the framework of Relativity (no matter if SR or GR), the constancy of the speed of light is a fundamental postulate, i.e. it is considered as a fundamental property of nature. So, it cannot be explained (in the sense that it could be derived from a more fundamental principle).
This, however, is no lack of Relativity: every imaginable physical theory is based on fundamental assumptions that are not explained themselves. Take e.g. Newtonian Mechanics: there, the fundamental assumptations are that the three Newtonian axioms apply and that simultaneity is absolute (or in other world: Galilei invariance applies). Newtonians Mechanics does not explain why the three axioms apply or why simultaneity is absolute, it consider both as fundamental properties.
Relativity instead makes the fundamental assumption that the speed of light is constant and Lorentz invariance applies (globally in SR and locally in GR). Before SR was founded it 1905, there was Lorentzian Ether Theory (LET) that "explained" the constancy of the speed of light by the ether influencing yardsticks and clocks when moving relative to the ether. However, this wasn't a real explaination: this mechanism was more complex than the assumption that the speed of light is constant, and therefore did not match the requirement that explainations have to be simple.
>  As I said before this whole discussion belongs more in the newsgroup: sci.physics.foundations. When consider the above definition of a metre you must also define what a second is 
This is done:
https://en.wikipedia.org/wiki/Second#Based_on_caesium_microwave_atomic_clock
A second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium133 atom.
>  and such a second must also be a physical constant process. We know by experiment that that is also difficult to establish. 
What makes you think so?
>  A whole different physical issue the speed of gravition. It is physical possible that this speed is much more "fixed" (stable?) than the speed of light. In principle such a speed (if constant) is a better starting point to define a metre. 
But it would be much more difficult to measure this speed.
>>>  What is important as part of this discussion: what is the definition of a vacuum. Accordingly to: https://en.wikipedia.org/wiki/Vacuum : "Vacuum is space void of matter" But that does not exist in outerspace. In fact the whole universe is filled with photons, which makes any definition based on vacuum misleading(?) 
>> 
No; you can always discuss the limit of a true vacuum. 
> 
The point is when you use the concept "vacuum" in a defintion than the concept vacuum should also clearly be defined. I doubt it is. 
Remember, unit definitions are a matter of certainty. The speed of light in a hypothetical perfect vacuum may be a little different from the speed of light in a vacuum that can be created in a laboratory or that exists in outer space. But that difference is probably very small, much smaller than the known uncertainty in the metre definition of 10^10 relatively. So, this does not affect the certainty of the metre definition.
>  A different issue is than also always when you consider the speed of light in any discussion it should be in a vacuum. The point is when the physical state between the Sun and the earth is not a vacuum than you cannot use the definition in order to measure distance. 
You're wrong, you can, because the resulting contribution to the uncertainty of the metre definition is neglectable.
>  (Of course for most applications you can) 
Indeed. An this is why your argument is wrong.
>>  The point is that any LOCAL measurement of the speed of light always gives the same value. 
> 
As I stated before it is primarily not my strategy to calculate the speed of light. What I want to challenge is the idea that this speed is not always the same. To do that I use one observer, two light sources, a tower, and two mirrors at different heights. 
In other words: you consider a nonlocal setup. And since it is wellknown that the speed of light is not constant in such a setup and that this is in full agreement with GR (which claims that in a gravitational field, the speed of light is constant only locally), you do not challenge anything by this. Or at least no idea that is part of today's physics.
>>>  My understanding is that the speed will increase when the photons approach the earth. In fact when you send a light signal from the sun towards the earth, first the speed will decrease and than increase. 
>> 
You mean, you want to consider the combined gravitational field of Sun and Earth. The first thing you have to note then is that there is no known exact solution of GR field equations for a gravitational field with more than one centre of gravity. For one single centre of gravity, there is Schwarzschild solution, but for two or more centres of gravity, there is no exact solution known. 
> 
This IMO raises an issue when you want to study the merging of two black holes using GR. 
This can be done only numerically, not analytically. Of course, you could apply the same numerical methods for the SunEarth system.
>>>  When you study: https://en.wikipedia.org/wiki/Speed_of_light you can read: "the metre was redefined in the SI Units as the distance travelled by light in vacuum in 1/299792458 of a second." The problem with this defintion is when the speed is not constant the length of a metre also changes. 
>> 
As far as the variability of the speed of light due to gravitational effects is concerned, the metre definition is not touched in any way: to define the metre, one uses the speed of light measured with respect in a local inertial frame, which is applied in a small spacetime region limited enough to neglect gravitational effects and to apply the SRlimit of GR. 
> 
I agree with you, however this becomes an issue when light years are considered. 
To consider great spatial distances, you just consider a sequence of a high number of small yardsticks, each small enough to apply the SRlimit locally.
>>  But even that is not really necessary. One could as well argue that there should be a speed of light, let's call it c0, that would be the speed of light in a hypothetical perfect vacuum. Then one could postulate that this speed c0 is always the same, in all inertial frames, and conclude that SR effects occur at velocities near this speed. From the fact that we observe SR effects near the real speed of light that we can factually measure in a real vacuum, let's call it c', we then can conclude that both speeds, c0 and c', are very close to each other. 
> 
I fully agree with you. The problem is more or less that in SR we start from the idea that the speed of light is constant (and in all directions the same) and equal to c. 
There is no reason not to apply the described procedure: we just assume as c0 as the quantity for which the property to be always constant applies.
>>  And indeed, in GR, the speed of light turns out to be variable in some way. Namely in that way, that the speed of light measured with respect to a general coordinate system is variable. But not the speed of light measured with respect to a local inertial frame. 
> 
I doubt how important the last is. What is the point when local implies a very small region, while in general what we want is to study the evolution of the universe. 
If you restrict yourself to study the evolution of the universe, that point is not very relevant, that's correct. GR, however, is not only about the evolution of the universe.
>  According to all our obversations, the speed of light is constant in situations where the SRlimit of GR is applicable, i.e. where gravitational effects can be neglected. So, obviously, it would be physically wrong to say that the speed of light would vary in those situations. 
Yes.
>  Or did you want to ask for a theoretical explaination for the constancy of the speed of light? Within the framework of Relativity (no matter if SR or GR), the constancy of the speed of light is a fundamental postulate, i.e. it is considered as a fundamental property of nature. So, it cannot be explained (in the sense that it could be derived from a more fundamental principle). 
I disagree. In 1905 Einstein did indeed assume something close to this [#]. But
TODAY we have no need to do so. The equations of SR can be derived from:
a) the Principle of Relativity
b) the definition of inertial frames (referenced in the PoR)
c) any experimental result that distinguishes SR from Newtonian physics,
such as: kilometerlong pion beams exist
In this approach, the constancy of the speed of light is not at all assumed, and
is due to an underlying symmetry of the world we inhabit. This approach has the
advantage of separating the geometry (SR) from electrodynamics, which is HIGHLY
desirable pedagogically.
[#] Of course he actually postulated that "Any ray of light moves with the determined velocity c, whether the ray be emitted by a stationary or by a moving body." But when combined with the PoR this directly yields what you said.
>>  As I stated before it is primarily not my strategy to calculate the speed of light. What I want to challenge is the idea that this speed is not always the same. To do that I use one observer, two light sources, a tower, and two mirrors at different heights. 
> 
In other words: you consider a nonlocal setup. And since it is wellknown that the speed of light is not constant in such a setup and that this is in full agreement with GR (which claims that in a gravitational field, the speed of light is constant only locally), you do not challenge anything by this. Or at least no idea that is part of today's physics. 
Yes, assuming the measurement accuracy is sufficiently good to distinguish the result from c  that's not possible using current technology and any existing tower. Boreholes are considerably "taller", but they are not straight enough (not to mention the difficulty of lowering a vacuum pipe several km long into one). I cannot even devise an experiment to compare a horizontal and vertical path in an interferometer to sufficient accuracy, due to the impossibility of measuring distances accurately enough without using light, and the inevitable strains in a "rigid" rod rotated between horizontal and vertical.
Tom Roberts
>  On 7/10/16 7/10/16 5:53 AM, Gregor Scholten wrote: 
Nicolaas Vroom wrote:
> >>  As I stated before it is primarily not my strategy to calculate the speed of light. What I want to challenge is the idea that this speed is not always the same. To do that I use one observer, two light sources, a tower, and two mirrors at different heights. 
> > 
In other words: you consider a nonlocal setup. 
> >  And since it is wellknown that the speed of light is not constant in such a setup and that this is in full agreement with GR (which claims that in a gravitational field, the speed of light is constant only locally), you do not challenge anything by this. Or at least no idea that is part of today's physics. 
A whole different issue is, that I do not understand why GR claims that the speed is constant locally when any practical application (for example the forward movement of Mercury) is a global configuration?
>  Yes, assuming the measurement accuracy is sufficiently good to distinguish the result from c  that's not possible using current technology and any existing tower. Boreholes are considerably "taller", but they are not straight enough (not to mention the difficulty of lowering a vacuum pipe several km long into one). 
>  I cannot even devise an experiment to compare a horizontal and vertical path in an interferometer to sufficient accuracy, due to the impossibility of measuring distances accurately enough without using light, and the inevitable strains in a "rigid" rod rotated between horizontal and vertical. 
The experiment I propose does not have a horizontal component. The idea is to send a (two) light signals straight down. The reflection is upwards.
Nicolaas Vroom
>>  Or did you want to ask for a theoretical explaination for the constancy of the speed of light? Within the framework of Relativity (no matter if SR or GR), the constancy of the speed of light is a fundamental postulate, i.e. it is considered as a fundamental property of nature. So, it cannot be explained (in the sense that it could be derived from a more fundamental principle). 
> 
I disagree. In 1905 Einstein did indeed assume something close to this [#]. But
TODAY we have no need to do so. The equations of SR can be derived from: 
Does that mean that you want to replace the postulate of the speed of light being constant by the postulate that kilomerlong pion beams exist? That wouldn't be very straightforward: such a posulate would be much more special than the postulate of the speed of light being constant and therefore doesn't match the requirement that postulates have to be as general as possible.
Or do you want to say that we do not need any postulate at all any more because we have experimental facts? That would be completely wrong, due to the general structure of physical theories: a theory has to postulate fundamental statements, and those statements or the statements that can be derived from them have to be in agreement with the observations.
And BTW: the existence of kilometerlong pion beams could be as well explained by pions travelling 100 times faster than the light. A funny thing: when I first read about the long distance that pions travel before decaying many years ago, I thought this should be a proof for superluminal pions. It was only years later that I realized that this should rather be a proof for time dilation ;)
>  In this approach, the constancy of the speed of light is not at all assumed, and is due to an underlying symmetry of the world we inhabit. This approach has the advantage of separating the geometry (SR) from electrodynamics 
No, it does not have that advantage because the same is already true for the postulate that the speed of light is constant: what we call the "speed of light" is not a property of electrodynamics, but a general quantity. It's only due to historical reasons that the name of that quantity contains the name of an electrodynamic phenomenon (light).
>  Tom Roberts wrote: 
>>  The equations of SR can be derived from: a) the Principle of Relativity b) the definition of inertial frames (referenced in the PoR) c) any experimental result that distinguishes SR from Newtonian physics, such as: kilometerlong pion beams exist 
> 
Does that mean that you want to replace the postulate of the speed of light being constant by the postulate that kilomerlong pion beams exist? That wouldn't be very straightforward: such a posulate would be much more special than the postulate of the speed of light being constant and therefore doesn't match the requirement that postulates have to be as general as possible. 
One does not need (c) to be a postulate. (a) and (b) alone determine just three
potential theories, distinguished by their symmetry groups:
* the Galilei group
* the Euclid group (in 4d space+time)
* the Poincare' group
The first two are solidly refuted by literally zillions of experiments and
observations; the third is essentially SR.
The postulate "the speed of light is constant" brings in a whole lot of "baggage" you did not mention. In essence it brings in all of classical electrodynamics (c.f. the title of Einstein's 1905 paper).
>  Or do you want to say that we do not need any postulate at all any more because we have experimental facts? That would be completely wrong, due to the general structure of physical theories: a theory has to postulate fundamental statements, and those statements or the statements that can be derived from them have to be in agreement with the observations. 
See above. This approach does that. It's just that the postulates (a) and (b) do not determine a unique theory  as usual, one needs experiments to determine which theories are valid....
Tom Roberts
>  On 7/10/16 7/10/16 5:53 AM, Gregor Scholten wrote: 
> >  According to all our obversations, the speed of light is constant in situations where the SRlimit of GR is applicable, i.e. where gravitational effects can be neglected. So, obviously, it would be physically wrong to say that the speed of light would vary in those situations. 
> 
Yes. 
My interpretation of this is that both of you agree that the speed of light is constant in situations where SR applies and not where GR applies. My understanding is that when GR applies gravitational effects can not be neglected. Which raises the question if both of you agree that when GR applies the speed of light is not constant.
This question is of practical importance for almost all experiments because in reality always gravitational effects are involved, specific if you want to discuss the movement of physical objects.
On Tuesday, 19 July 2016 01:13:50 UTC+2, Gregor Scholten wrote:
>  Tom Roberts wrote: 
> >> 
Or did you want to ask for a theoretical explaination for the constancy of the speed of light? Within the framework of Relativity (no matter if SR or GR), the constancy of the speed of light is a fundamental postulate, i.e. it is considered as a fundamental property of nature. So, it cannot be explained (in the sense that it could be derived from a more fundamental principle). 
> > 
I disagree. In 1905 Einstein did indeed assume something close to this [#].
But TODAY we have no need to do so. The equations of SR can be derived from: 
What type of experiment do you have in mind? Can you give a link where this is explained?
>  Does that mean that you want to replace the postulate of the speed of light being constant by the postulate that kilomerlong pion beams exist? 
This discussion is difficult to follow. My first impression is that they have "nothing" in common. Light is used to measure distance. Pion beams are used for ? Maybe see: https://en.wikipedia.org/wiki/Pion
>  That wouldn't be very straightforward: such a posulate would be much more special than the postulate of the speed of light being constant and therefore doesn't match the requirement that postulates have to be as general as possible. 
Skip
>  And BTW: the existence of kilometerlong pion beams could be as well explained by pions travelling 100 times faster than the light. 
Also this requires more detail (for most readers?)
>  A funny thing: when I first read about the long distance that pions travel before decaying many years ago, I thought this should be a proof for superluminal pions. It was only years later that I realized that this should rather be a proof for time dilation ;) 
I try to understand, but I do not.
Any way for me the most important question is why the claim that the speed of light is constant. A whole diferent issue the definition of what is a lightyear. The distance is: 9460730472580800 metres (exactly) See: https://en.wikipedia.org/wiki/Lightyear But that does not mean that the speed of light is always the same when the distance between two objects is 1 lightyear (For a pulse which travels that distance)
Nicolaas Vroom
>  On Wednesday, 13 July 2016 05:44:07 UTC+2, Tom Roberts wrote: 
>>  On 7/10/16 7/10/16 5:53 AM, Gregor Scholten wrote: 
>  Nicolaas Vroom wrote: 
>>>>  As I stated before it is primarily not my strategy to calculate the speed of light. What I want to challenge is the idea that this speed is not always the same. To do that I use one observer, two light sources, a tower, and two mirrors at different heights. 
>>> 
In other words: you consider a nonlocal setup. 
>  Why do you call this a nonlocal setup ? 
In GR a local region is one in which the curvature of spacetime can be neglected. The size of such a region depends directly on one's measurement resolution. Note that if the curvature can be neglected for a given resolution, then the vacuum speed of light will be equal to c within that resolution.
Your experiment explicitly requires a measurement resolution that can distinguish the measured value from c. So you must use a region that is not local.
>  What is the difference with a local setup ? 
In a local region the resolution is insufficiently good to distinguish the vacuum speed of light from c. So your experiment would be hopeless/useless.
>  My prediction of the outcome is that the two reflections do not arrive simultaneous. My question to the readers is if they agree with this. 
[Your experiment has two vertical light paths of length L and 2L, with mirrors such that one light ray goes downupdownup over L, and the other goes downup over 2L. The two rays start together.]
Nobody disputes that they will not arrive simultaneously, when measured with infinite precision. But in practice, on earth with current technology, it is not possible to achieve the requisite resolution for any practical paths (towers or boreholes).
I have considered very similar potential experiments. The limit is not in measuring time differences between light rays, the difficulty is in measuring the path lengths to the required accuracy without using light.
>  If my prediction is correct than my interpretation is that the speed of light is not always the same. 
Sure. Over NONLOCAL paths the vacuum speed of light need not be c. But one must be careful to define PRECISELY what one means by "speed" [#].
>  A whole different issue is, that I do not understand why GR claims that the speed is constant locally when any practical application (for example the forward movement of Mercury) is a global configuration? 
The postulate is that in the local limit SR applies  that is essential in deriving the field equation of GR. Yes, most applications of GR are probing the effects of gravity, so they involve nonlocal regions. Elementary calculations show that over nonlocal paths, the vacuum speed of light can differ from c (sometimes by a lot)  one MUST be careful to define PRECISELY what one means by "speed" [#].
[#] Here there be dragons.
Tom Roberts
>  My interpretation of this is that both of you agree that the speed of light is constant in situations where SR applies and not where GR applies. My understanding is that when GR applies gravitational effects can not be neglected. Which raises the question if both of you agree that when GR applies the speed of light is not constant. 
The speed of light, when measured locally, is constant. With gravitation, one can interpret the speed as being constant and space being stretched, or the speed slowing down. It doesn't matter how you think about it as long as you get the correct result.
>  This question is of practical importance for almost all experiments because in reality always gravitational effects are involved, specific if you want to discuss the movement of physical objects. 
The difference is negligible in practice, though.
>  A whole diferent issue the definition of what is a lightyear. The distance is: 9460730472580800 metres (exactly) See: https://en.wikipedia.org/wiki/Lightyear 
This is just the speed of light, which is defined exactly, times the length of a year, which is also defined exactly.
>  But that does not mean that the speed of light is always the same when the distance between two objects is 1 lightyear (For a pulse which travels that distance) 
Noone claims that it is. But, again, in practice the difference is negligible.
>  On 7/18/16 7/18/16 11:44 AM, Nicolaas Vroom wrote: 
> >  On Wednesday, 13 July 2016 05:44:07 UTC+2, Tom Roberts wrote: 
> >>  On 7/10/16 7/10/16 5:53 AM, Gregor Scholten wrote: 
> >  Nicolaas Vroom wrote: 
> >>>  In other words: you consider a nonlocal setup. 
> >  Why do you call this a nonlocal setup ? 
> 
In GR a local region is one in which the curvature of spacetime can be neglected. The size of such a region depends directly on one's measurement resolution. Note that if the curvature can be neglected for a given resolution, then the vacuum speed of light will be equal to c within that resolution. 
Okay, I agree
>  Your experiment explicitly requires a measurement resolution that can distinguish the measured value from c. So you must use a region that is not local. 
Okay, I agree
>  From a principle point it only makes sense to discuss this situation. 
In Scientific American August 2016 page 25 we read: "As a paricle moves into the void, etc, it slows down like a ball rolling up a hill; once it starts to move out of the void toward the dense area it accelerates etc. CMB photons behave similary, although they do not change speed (the speed of light is always constant)" Do you agree with the final remark?
> >  My prediction of the outcome is that the two reflections do not arrive simultaneous. My question to the readers is if they agree with this. 
> 
[Your experiment has two vertical light paths of length L and 2L, with mirrors such that one light ray goes downupdownup over L, and the other goes downup over 2L. The two rays start together.] Nobody disputes that they will not arrive simultaneously, when measured with infinite precision. But in practice, on earth with current technology, it is not possible to achieve the requisite resolution for any practical paths (towers or boreholes). 
I fully agree that "you" cannot perform such an experiment in practice. The discussion is only in principle. My intention is primarily not to calculate the speed of light.
>  I have considered very similar potential experiments. The limit is not in measuring time differences between light rays, the difficulty is in measuring the path lengths to the required accuracy without using light. 
I like such discussions because you "try to go to the limits".
> >  If my prediction is correct than my interpretation is that the speed of light is not always the same. 
> 
Sure. Over NONLOCAL paths the vacuum speed of light need not be c. But one must be careful to define PRECISELY what one means by "speed" 
I fully agree. That is why I try to define experiments, which are as simple as possible. (The same with length contraction and Schr=C3=B6dinger's Cat)
Thanks
Nicolaas Vroom
> 
Nicolaas Vroom 
> > 
My interpretation of this is that both of you agree that the speed of light is constant in situations where SR applies and not where GR applies. My understanding is that when GR applies gravitational effects can not be neglected. Which raises the question if both of you agree that when GR applies the speed of light is not constant. 
> 
The speed of light, when measured locally, is constant. 
It is possible that when you measure the speed of light (here on earth) you always get the same value. What I propose is an experiment and I ask the readers if they agree with me about the outcome of the experiment. In my opinion what the outcome of the experiment shows is that the speed of light is not always the same. The cause is gravitation. That means if you perform an experiment and no gravitation is involved it is possible that the speed of light is always the same.
>  With gravitation, one can interpret the speed as being constant and space being stretched, or the speed slowing down. It doesn't matter how you think about it as long as you get the correct result. 
The experiment is such that the distances involved are the same. To claim that the distances are changed when the results of the test shows that the speeds are diferent is "tricky"
> >  This question is of practical importance for almost all experiments because in reality always gravitational effects are involved, specific if you want to discuss the movement of physical objects. 
> 
The difference is negligible in practice, though. 
I agree that in many cases the differences are negligible, but that is not the issue.
> >  A whole diferent issue the definition of what is a lightyear. The distance is: 9460730472580800 metres (exactly) See: https://en.wikipedia.org/wiki/Lightyear 
> 
This is just the speed of light, which is defined exactly, times the length of a year, which is also defined exactly. 
I agree that the distances is mathematically defined exactly, but that does not mean in practice that it is that simple, specific when gravitation is involved.
> >  But that does not mean that the speed of light is always the same when the distance between two objects is 1 lightyear (For a pulse which travels that distance) 
> 
Noone claims that it is. But, again, in practice the difference is negligible. 
I fully agree with you.
Thanks
Nicolaas Vroom
> 
Nicolaas Vroom 
>>  A whole diferent issue the definition of what is a lightyear. The distance is: 9460730472580800 metres (exactly) See: https://en.wikipedia.org/wiki/Lightyear 
> 
This is just the speed of light, which is defined exactly, times the length of a year, which is also defined exactly. 
One should perhaps add that the year is a Julian Year of 365.25 days; those days contain 24*60*60 SI seconds and no leap seconds.
 (c) John Stockton, Surrey, UK. ?merlyn.demon.co.uk Turnpike v6.05 MIME.  show quoted text 
>>>>  As I stated before it is primarily not my strategy to calculate the speed of light. What I want to challenge is the idea that this speed is not always the same. To do that I use one observer, two light sources, a tower, and two mirrors at different heights. 
>>> 
In other words: you consider a nonlocal setup. 
>  Why do you call this a nonlocal setup ? What is the difference with a local setup ? 
A local setup is one that covers a spacetime region that is sufficiently limited to neglect the curvature of spacetime. In your experiment, you place two mirrors at different heights, with the difference in height being big enough to detect gravitational effects, i.e. effects caused by curvature of spacetime. So, obviously, the two mirrors cover a spacetime region that is not sufficiently limited.
>  A whole different issue is, that I do not understand why GR claims that the speed is constant locally when any practical application (for example the forward movement of Mercury) is a global configuration? 
One can reason this by two arguments:
1) An important property of GR is that in the limit of weak gravitational fields, it becomes equivalent to SR. And since GR describes gravity as curvature of spacetime, this limit is equivalent to the limit of small spacetime regions, because in the limit of small spacetime regions, the curvature becomes neglectable, like in the limit of weak gravitational fields. So, in the limit of small spacetime regions, GR must become equivalent to SR, too.
2) GR is based on the equivalence principle according to which a freefalling observer in a gravitational field is equivalent to a uniformly moving observer in a spacetime without gravity. So, it must be possible to describe a freefalling observer in a gravitational field by the terms of SR in some way. GR implements this requirement by being locally equivalent to SR.
>>  Yes, assuming the measurement accuracy is sufficiently good to distinguish the result from c  that's not possible using current technology and any existing tower. Boreholes are considerably "taller", but they are not straight enough (not to mention the difficulty of lowering a vacuum pipe several km long into one). 
>  I agree with the opinion that the experiment can not be performed accurately in practice using light signals. 
And this fact makes your experiment being a thought experiment. And a core property of a thought experiment is that you cannot ascertain its outcome without referring to a theory.
>  Nicolaas Vroom wrote: 
> >>>> 
As I stated before it is primarily not my strategy to calculate the speed of light. What I want to challenge is the idea that this speed is not always the same. To do that I use one observer, two light sources, a tower, and two mirrors at different heights. 
> >>> 
In other words: you consider a nonlocal setup. 
> >  Why do you call this a nonlocal setup ? What is the difference with a local setup ? 
> 
A local setup is one that covers a spacetime region that is sufficiently limited to neglect the curvature of spacetime. In your experiment, you place two mirrors at different heights, with the difference in height being big enough to detect gravitational effects, i.e. effects caused by curvature of spacetime. So, obviously, the two mirrors cover a spacetime region that is not sufficiently limited. 
IMO the difference is very arbitrary.
When gravitational effects are considered, distance and light
are a nonlocal effect.
As such light bending around a star (or any object) is nonlocal issue.
When gravitational effects are not considered distance and light
are a local issue. In such a scenario it makes sense to declare
the speed of light a constant.
> >>  Yes, assuming the measurement accuracy is sufficiently good to distinguish the result from c  that's not possible using current technology and any existing tower. Boreholes are considerably "taller", but they are not straight enough (not to mention the difficulty of lowering a vacuum pipe several km long into one). 
> >  I agree with the opinion that the experiment can not be performed accurately in practice using light signals. 
> 
And this fact makes your experiment being a thought experiment. And a core property of a thought experiment is that you cannot ascertain its outcome without referring to a theory. 
I agree that you can call this a thought experiment, but that does not
mean that we can not discuss what the outcome of this experiment could be.
The issue is that discussions about the speed of light in one direction
are very difficult. The same with experiments that are related with
the speed of light in one direction.
For more info: https://en.wikipedia.org/wiki/Oneway_speed_of_light
What this means that one way speed of light experiments are IMO also
thought experiments.
Anyway what I try to do is not to measure the speed of light, but only to try to answer the question if the speed of light going from object A to B is constant all the way down.
Nicolaas Vroom.
>>>  Why do you call this a nonlocal setup ? What is the difference with a local setup ? 
>> 
A local setup is one that covers a spacetime region that is sufficiently limited to neglect the curvature of spacetime. In your experiment, you place two mirrors at different heights, with the difference in height being big enough to detect gravitational effects, i.e. effects caused by curvature of spacetime. So, obviously, the two mirrors cover a spacetime region that is not sufficiently limited. 
> 
IMO the difference is very arbitrary. When gravitational effects are considered, distance and light are a nonlocal effect. As such light bending around a star (or any object) is nonlocal issue. When gravitational effects are not considered distance and light are a local issue. In such a scenario it makes sense to declare the speed of light a constant. 
It is not a matter of considering or non considering gravitational effects, but of considering spacetime regions sufficiently limited or not sufficiently limited to neglect gravitational effects. In a spacetime region that is sufficiently limited, you can, if you want, consider gravitational effects. However, this consideration yields the result that those effects are neglectable. It's like considering the electric field inside a charged conducting body: you will see the field being zero everyhwere inside the body.
In turn, you can consider a spacetime region that is not sufficiently limited to neglect gravitational effects, and skip considering gravitational effects. As long as you do not consider the behaviour of light as a gravitational effect itself, you can consider the speed of light in that region, and find out that it is variable, without considering gravitational effects.
What is indeed in some way arbitrary is the threshold for considering a spacetime region as sufficiently limited or as not sufficiently limited. One could e.g. claim that gravitational effects are neglectable when the deviation from Minkowski metric is < 10^10, or one could as well claim that gravitational effects are neglectable when the deviation is < 10^15. However, this is a general issue for limits, and in no way special to the SR limit of GR.
In fact, it is a matter of measurement precision: if your measurement setup is precise enough to detect a deviation of 10^10, then the threshold is lower than 10^10.
>>>>  Yes, assuming the measurement accuracy is sufficiently good to distinguish the result from c  that's not possible using current technology and any existing tower. Boreholes are considerably "taller", but they are not straight enough (not to mention the difficulty of lowering a vacuum pipe several km long into one). 
>>>  I agree with the opinion that the experiment can not be performed accurately in practice using light signals. 
>> 
And this fact makes your experiment being a thought experiment. And a core property of a thought experiment is that you cannot ascertain its outcome without referring to a theory. 
> 
I agree that you can call this a thought experiment, but that does not mean that we can not discuss what the outcome of this experiment could be. 
But we cannot discuss that without referring to a theory that predicts some outcome.
>  Am 15.08.2016 um 09:28 schrieb Nicolaas Vroom: 
> >>>  I agree with the opinion that the experiment can not be performed accurately in practice using light signals. 
> >> 
And this fact makes your experiment being a thought experiment. And a core property of a thought experiment is that you cannot ascertain its outcome without referring to a theory. 
For a description of the experiment see: http://users.telenet.be/nicvroom/wik_Lorentz_ether_theory.htm#ref1
> >  I agree that you can call this a thought experiment, but that does not mean that we can not discuss what the outcome of this experiment could be. 
> 
But we cannot discuss that without referring to a theory that predicts some outcome. 
The theory is called gravity.
In the newsgroup sci,astro In the post: "Link between dark matter and baryonic matter"
On Tuesday, 25 October 2016 20:30:27 UTC+2, Steve Willner wrote:
> 
Standard physics says photons have momentum and energy but zero rest mass. Photons react to gravity and (in principle, but I don't think it has been measured) create gravity, but neither of those properties requires rest mass. 
That is also my opinion. And if that is the case the speed of light cannot be called constant.
Nicolaas Vroom.
>  And if that is the case the speed of light cannot be called constant. 
The statement "the [vacuum] speed of light is constant" is NOT universally applicable. However when measured in a LOCALLY INERTIAL FRAME, the vacuum speed of light is constant, and equal to c (here "local" means "over a distance small enough that the effects of gravitation are too small to measure").
Yes, if you measure the vacuum speed of light over a distance long enough that gravity is not negligible, you can obtain a value different from c. Ditto if you use some noninertial "frame". There is no question whatsoever that General Relativity predicts this, and that experiments confirm it (c.f. the Shapiro time delay). I remark that in such cases one must be VERY careful to specify precisely what one means by "speed" (here there be dragons).
You keep bringing up an overly simplistic statement that comes from SPECIAL relativity over a century ago. We have learned A LOT since then, including the fact that the vacuum speed of light is not always c. But for most physical situations of interest the difference between the actual speed and c is too small to measure.
Stated differently: Special Relativity is not valid when gravitation is important. This OUGHT to be obvious.
Tom Roberts
> 
You keep bringing up an overly simplistic statement that comes from SPECIAL
relativity over a century ago. We have learned A LOT since then,
including the
fact that the vacuum speed of light is not always c. But for most physical
situations of interest the difference between the actual speed and c is too
small to measure.
Stated differently: Special Relativity is not valid when gravitation is important. This OUGHT to be obvious. 
I can only agree with you: that this should be obvious.
I doubt however if my statement or reasoning is overly simplistic.
In fact I have two questions:
1) What is the speed of light?
To define the speed of light as a constant and equal to 299792458 m/sec is
okay for normal applications, but is not a complete answer on this question.
I'am well aware that the specific conditions (vacuum) and how the speed
is measured, should be mentioned.
2) Is the speed of light constant?
I mean by that going from A to B any where in the universe is the speed
always the same. This question is simpler as question 1.
My interpretation of the comments above is that the speed of light
is not always c when gravitation is important.
I'am even willingly to conclude that the speed of light is not constant
when gravitation is involved.
When I study https://en.wikipedia.org/wiki/Speed_of_light IMO they only mention that: the speed of light in vacuum (=c) is a physical constant.
Should this document not be updated to reflect the opinion that the (vacuum) speed of light is not always c, specific when gravitation is important?
Nicolaas Vroom
> > 
You keep bringing up an overly simplistic statement that comes from SPECIAL
relativity over a century ago. We have learned A LOT since then,
including the
fact that the vacuum speed of light is not always c. But for most physical
situations of interest the difference between the actual speed and c is too
small to measure.
Stated differently: Special Relativity is not valid when gravitation is important. This OUGHT to be obvious. 
> 
I can only agree with you: that this should be obvious. I doubt however if my statement or reasoning is overly simplistic. In fact I have two questions: 1) What is the speed of light? 
299792458 m/sec. Details see below.
>  To define the speed of light as a constant and equal to 299792458 m/sec is okay for normal applications, but is not a complete answer on this question. 
Right.
>  I'am well aware that the specific conditions (vacuum) and how the speed is measured, should be mentioned. 
Right.
>  2) Is the speed of light constant? 
It is constant in vacuum when measured locally. No serious person has ever claimed anything else.
>  I mean by that going from A to B any where in the universe is the speed always the same. This question is simpler as question 1. 
No, it is much more complex. The answer is: no, it is not.
>  My interpretation of the comments above is that the speed of light is not always c when gravitation is important. 
Right. Or when there is no vacuum.
>  I'am even willingly to conclude that the speed of light is not constant when gravitation is involved. 
It's not a question whether you are willing; it is a fact.
> 
When I study https://en.wikipedia.org/wiki/Speed_of_light IMO they only
mention that: the speed of light in vacuum (=c) is a physical constant.
Should this document not be updated to reflect the opinion that the (vacuum) speed of light is not always c, specific when gravitation is important? 
Not everything in Wikipedia is correct.
There are three ways to think of this:
One can think of the constancy of the speed of light (when measured locally in vacuum) as a POSTULATE. Since this leads to no contradictions with observations, it seems to be true.
One can measure the speed of light locally in a vacuum. The answer is always the same.
Something of a red herring: Because of the two statements above, the meter is now defined as the length travelled by light in a specific time, so today, by definition, the speed of light is constant. But this is not a tautology, since it is merely a convenient and practical definition which follows from the two statements above.
It's not worth thinking about this anymore until you understand all three of these statements. And after that, you won't have a need to think about this anymore.
1/c^2 d^2/t^2 = d^2/d(c t)^2
This means that the constant is universal but can be meaured locally only in a space time area of some wavelengths and frequancy beats.
For a general geometry of space time with a metric G tensor the wave equation is
1/sqrt(det G) (d/dct , d/x ) sqrt(det G) G(t,x)^1 (d/ct, d/dx) f(t,x) =0
wich means that waves emanating from a point are filling space time by a complicated process of mode decomposition at the sender and composition somewhere else and later by the receptor.
Compare: An universal speed of a bunch of signals moving by packages from one computer through the knots and cables in the internet to a distant receptor computer is a completely senseless notion.

Roland Franzius
>> 
You keep bringing up an overly simplistic statement that comes from
SPECIAL relativity over a century ago. We have learned A LOT since
then, including the
fact that the vacuum speed of light is not always c. But for most
physical situations of interest the difference between the actual
speed and c is too small to measure.
Stated differently: Special Relativity is not valid when gravitation is important. This OUGHT to be obvious. 
> 
I can only agree with you: that this should be obvious. I doubt however if my statement or reasoning is overly simplistic. In fact I have two questions: 1) What is the speed of light? 
The speed v of a body is defined in that way that within a time interval Delta_t, the body crosses a spatial distance Delta_x = v * Delta_t. The speed of light is the application of this concept for light.
>  To define the speed of light as a constant and equal to 299792458 m/sec is okay for normal applications 
No, surely not. Even to make the statement that the speed of light is constant meaningful, a different definition is required.
>  but is not a complete answer on this question. 
Better say: it wouldn't be any answer at all.
> 
2) Is the speed of light constant?
I mean by that going from A to B any where in the universe is the
speed always the same. This question is simpler as question 1.
My interpretation of the comments above is that the speed of light is not always c when gravitation is important. 
That is correct. According to GR, the speed of light is locally constant, i.e. measured be a freefalling observer within the application range of his local inertial frame. On scales where gravity becomes important and the concept of an inertial frames breaks down, the speed of light is variable in general.
>  I'am even willingly to conclude that the speed of light is not constant when gravitation is involved. 
In what way is this statement different from the previous one?
>  When I study https://en.wikipedia.org/wiki/Speed_of_light IMO they only mention that: the speed of light in vacuum (=c) is a physical constant. 
They refer to the local speed of light.
>  Should this document not be updated to reflect the opinion that the (vacuum) speed of light is not always c, specific when gravitation is important? 
Feel free to add a section "The speed of light in General Relativity".
> 
Nicolaas Vroom 
>>> 
You keep bringing up an overly simplistic statement that comes from SPECIAL relativity over a century ago. We have learned A LOT since then, including the fact that the vacuum speed of light is not always c. But for most physical situations of interest the difference between the actual speed and c is too small to measure. Stated differently: Special Relativity is not valid when gravitation is important. This OUGHT to be obvious. 
>> 
I can only agree with you: that this should be obvious. I doubt however if my statement or reasoning is overly simplistic. In fact I have two questions: 1) What is the speed of light? 
> 
The speed v of a body is defined in that way that within a time interval Delta_t, the body crosses a spatial distance Delta_x = v * Delta_t. The speed of light is the application of this concept for light. 
But the essential part of it is to define what is moving, as there is defined several light speeds for light waves, like phase, group and energy propagation speed.
The phase and group speed can be higher than c.
Light beam propagation speed can be lower than c even for vacuum, if the beam has a special spatial structure and nonzero orbital angular momentum.
For energies where photons can be tracked then vacuum speed c as energy propagation speed can be observed.
 Poutnik ( The Pilgrim, Der Wanderer )
A wise man guards words he says, as they say about him more, than he says about the subject.
>  On Monday, 29 August 2016 22:46:05 UTC+2, Gregor Scholten wrote: 
>>  Am 15.08.2016 um 09:28 schrieb Nicolaas Vroom: 
> 
>> >>> 
I agree with the opinion that the experiment can not be performed accurately in practice using light signals. 
>> >> 
And this fact makes your experiment being a thought experiment. And a core property of a thought experiment is that you cannot ascertain its outcome without referring to a theory. 
> 
For a description of the experiment see: http://users.telenet.be/nicvroom/wik_Lorentz_ether_theory.htm#ref1 
That is nothing but yet another repition of the description you already brought up here numerous times here. BTW: ASCII art is really old schooled today, maybe you should try some graphics format. OpenOffice Draw is a nice program to draw diagrams with lines.
> 
>> > 
I agree that you can call this a thought experiment, but that does not mean that we can not discuss what the outcome of this experiment could be. 
>> 
But we cannot discuss that without referring to a theory that predicts some outcome. 
> 
The theory is called gravity. 
There is no such theory. There are theories that describe gravity, like Newtonian Gravity or General Relativity, making statements in what exact way gravity acts on the movements of bodies or on the propagation of light rays, but gravity on its own, i.e. the bare concept that there is a general mutual attraction of bodies, does not make up a theory.
> 
In the newsgroup sci,astro
In the post: "Link between dark matter and baryonic matter"
On Tuesday, 25 October 2016 20:30:27 UTC+2, Steve Willner wrote: 
>> 
Standard physics says photons have momentum and energy but zero rest mass. Photons react to gravity and (in principle, but I don't think it has been measured) create gravity, but neither of those properties requires rest mass. 
> 
That is also my opinion. And if that is the case the speed of light cannot be called constant. 
Why not?
If we follow General Relativity, we know that the speed of light is not constant except on local scales, but this has little to do with the fact that reacting to gravity and being a source of gravity does not require rest mass.
So, we know that the speed of light is not constant on scales where gravity is relevant, but not for the reason you claimed.
> 
In article 
> > > 
You keep bringing up an overly simplistic statement that comes from SPECIAL relativity over a century ago. We have learned A LOT since then, including the fact that the vacuum speed of light is not always c. But for most physical situations of interest the difference between the actual speed and c is too small to measure. Stated differently: Special Relativity is not valid when gravitation is important. This OUGHT to be obvious. 
> > 
I can only agree with you: that this should be obvious. I doubt however if my statement or reasoning is overly simplistic. In fact I have two questions: 1) What is the speed of light? 
> 
299792458 m/sec. Details see below. 
> > 
To define the speed of light as a constant and equal to 299792458 m/sec is okay for normal applications, but is not a complete answer on this question. 
> 
Right. 
> > 
I'am well aware that the specific conditions (vacuum) and how the speed is measured, should be mentioned. 
> 
Right. 
> > 
2) Is the speed of light constant? 
> 
It is constant in vacuum when measured locally. No serious person has ever claimed anything else. 
> > 
I mean by that, going from A to B anywhere in the universe, is the speed always the same. This question is simpler as question 1. 
> 
No, it is much more complex. 
When we agree that the speed of light is not constant it is extremely difficult to measure that in practice. I think the only way to demonstrate this is mathematically by means of a model. I have used Newton's Law. See http://users.telenet.be/nicvroom/VB%20Light%20operation.htm
>  The answer is: no, it is not. 
> > 
My interpretation of the comments above is that the speed of light is not always c when gravitation is important. 
> 
Right. Or when there is no vacuum. 
> > 
I'am even willingly to conclude that the speed of light is not constant when gravitation is involved. 
> 
It's not a question whether you are willing; it is a fact. 
> > 
When I study https://en.wikipedia.org/wiki/Speed_of_light IMO they only mention that: the speed of light in vacuum (=c) is a physical constant. Should this document not be updated to reflect the opinion that the (vacuum) speed of light is not always c, specific when gravitation is important? 
> 
Not everything in Wikipedia is correct. 
The Wikipedia document starts with a picture which shows the distance between the Sun and the Earth to indicate a lightray which goes from the Sun towards the Earth. The interesting part is when the lightray approaches the earth the speed is almost constant. Going the other way when the lightray aproaches the Sun this is different. The speed increases.
However I also have a whole different question: Why is it that people very often say: the speed of light c=1 I can understand that for some applications this seems handy. But in general IMO you have to use this "equation" with care.
Nicolaas Vroom
>>> 
I can only agree with you: that this should be obvious.
I doubt however if my statement or reasoning is overly simplistic.
In fact I have two questions: 1) What is the speed of light? 
>> 
The speed v of a body is defined in that way that within a time interval Delta_t, the body crosses a spatial distance Delta_x = v * Delta_t. The speed of light is the application of this concept for light. 
> 
But the essential part of it is to define what is moving, as there is defined several light speeds for light waves, like phase, group and energy propagation speed. 
All those speeds have in common that the described speed definition can be applied. And in vacuum, all those speeds are equal.
>  The phase and group speed can be higher than c. 
Not in vacuum.
>  Light beam propagation speed can be lower than c even for vacuum, if the beam has a special spatial structure and nonzero orbital angular momentum. 
Really? Can you bring up some resource about this?
And even if that is true: when claiming that the speed of light is constant in vacuum, one usually refers to plane waves.
> 
Poutnik 
>> 
But the essential part of it is to define what is moving, as there is defined several light speeds for light waves, like phase, group and energy propagation speed. 
> 
All those speeds have in common that the described speed definition can be applied. And in vacuum, all those speeds are equal. 
For monochromatic plain wave.
> 
>> 
The phase and group speed can be higher than c. 
> 
Not in vacuum. 
I have not said in vacuum.
> 
>> 
Light beam propagation speed can be lower than c even for vacuum, if the beam has a special spatial structure and nonzero orbital angular momentum. 
> 
Really? Can you bring up some resource about this? And even if that is true: when claiming that the speed of light is constant in vacuum, one usually refers to plane waves. 
And exactly this is claimed by those resurces. That c should be referred to plane wave propagation.
Said simplified, as I got it, the light is slowed by propagation in spirale instead of a line.
http://www.iflscience.com/physics/physicistsslowdownlightvacuumtwistingit/
http://www.sciencealert.com/physicistshavefoundawaytoslowlightdownbytwistingit
[[Mod. note  These articles describe the slowerthanc group velocity of certain *finitesized* light beams in a vacuum. The classical statement "The speed of light is always 299792458 m/s" refers to plane waves of *infinite* extent in a vacuum, so there's no contradiction with relativity here (nor do the researchers claim any such contradiction).
I also note that the scientific paper in question
Bareza & Hermosa
"Subluminal group velocity and dispersion of Laguerre Gauss beams
in free space"
http://dx.doi.org/10.1038/srep26842
http://www.nature.com/articles/srep26842
is (remarkably for a paper in a Naturegroup journal) openaccess!
 jt]]
 show quoted text 
>  Dne 18/11/2016 v 02:41 Gregor Scholten napsal(a): 
>> 
Poutnik 
>>> 
But the essential part of it is to define what is moving, as there is defined several light speeds for light waves, like phase, group and energy propagation speed. 
>> 
All those speeds have in common that the described speed definition can be applied. And in vacuum, all those speeds are equal. 
> 
For monochromatic plain wave. 
You must be joking. Is it a wave or not? You cant have them both. You mean EM which not propagate spherically or not diverges?
>>>  The phase and group speed can be higher than c. 
>> 
Not in vacuum. 
> 
I have not said in vacuum. 
Where then. Of course that can be both in vacuum. Or is something you both misunderstood completely.
> 
Nicolaas Vroom 
> > 
2) Is the speed of light constant? I mean by that going from A to B any where in the universe is the speed always the same. This question is simpler as question 1. My interpretation of the comments above is that the speed of light is not always c when gravitation is important. 
> 
That is correct. According to GR, the speed of light is locally constant, i.e. measured be a freefalling observer within the application range of his local inertial frame. On scales where gravity becomes important and the concept of an inertial frames breaks down, the speed of light is variable in general. 
What does this specific say if you want to simulate the planets around the sun or a small collections of star. Is there a freefalling observer? Is there a local inertial frame.? IMO in both cases you should take one star as the center of your coordinate system.
[[Mod. note  Let's think about Newtonian gravity for a moment. Suppose my "small collection of stars" is a binary star where the two stars have equal masses M1 = M2 = M. And for simplicity, let's have the two stars in circular orbits about each other. (I'm neglecting tidalfriction effects that could cause the stars to gradually spiral in or out.) Then if I choose Cartesian inertial xyz coordinates centered on the centerofmass point midway between the two stars, the stars are located at
' x1(t) = + R * cos(omega*t) x2(t) =  R * cos(omega*t) ' y1(t) = + R * sin(omega*t) y2(t) =  R * sin(omega*t) ' z1(t) = 0 z2(t) = 0Now think about doing a GR analysis of this same system? (Why) is it suddenly a good idea to attach my coordinates to one of the stars?  jt]]
> >  Should this document not be updated to reflect the opinion that the (vacuum) speed of light is not always c, specific when gravitation is important? 
> 
Feel free to add a section "The speed of light in General Relativity". 
I think if any we should first investigate this document: http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLigh/speed_of_light.html I have started a new discussion for this document.
Nicolaas Vroom
[[Mod. note  The correct url is http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html ]]  jt]]
>> > 
2) Is the speed of light constant?
I mean by that going from A to B any where in the universe is the
speed always the same. This question is simpler as question 1.
My interpretation of the comments above is that the speed of light is not always c when gravitation is important. 
>> 
That is correct. According to GR, the speed of light is locally constant, i.e. measured be a freefalling observer within the application range of his local inertial frame. On scales where gravity becomes important and the concept of an inertial frames breaks down, the speed of light is variable in general. 
> 
What does this specific say if you want to simulate the planets around the sun or a small collections of star. Is there a freefalling observer? 
Yes. E.g. an observer that is comoving with one of the planets.
>  Is there a local inertial frame.? 
Yes. The local inertial frame of the upper observer that is comoving with one of the planets. However, that local inertial frame is not appropriate for being used in a simulation of the planet system since it is only applicable in the local environment of the particular planet. For the simulation, you should rather use a general coordinate system, like you describe it on your own below:
>  IMO in both cases you should take one star as the center of your coordinate system. 
Indeed. With respect to that coordinate system, the speed of light is not constant according to GR.
> 
What does this specific say if you want to simulate the planets
around the sun or a small collections of star.
Is there a freefalling observer?
Is there a local inertial frame.?
IMO in both cases you should take one star as the center of your
coordinate system.
[[Mod. note  Let's think about Newtonian gravity for a moment. Suppose my "small collection of stars" is a binary star where the two stars have equal masses M1 = M2 = M. And for simplicity, let's have the two stars in circular orbits about each other. (I'm neglecting tidalfriction effects that could cause the stars to gradually spiral in or out.) Then if I choose Cartesian inertial xyz coordinates centered on the centerofmass point midway between the two stars, the stars are located at 
' x1(t) = + R * cos(omega*t) x2(t) =  R * cos(omega*t) ' y1(t) = + R * sin(omega*t) y2(t) =  R * sin(omega*t) ' z1(t) = 0 z2(t) = 0
>  Now think about doing a GR analysis of this same system? (Why) is it suddenly a good idea to attach my coordinates to one of the stars?  jt]] 
This is a tricky and too simple exercise. In fact you describe object 1 with a sequence of observations: (x10,y10), (x11,y11), (x12,y12), (x13,y13) with x12 meaning x1(2*deltat) = + R * cos(omega*2*deltat) That means you describe it as an exact circle. For object 2 exactly the same logic applies. You can only do that mathematically using Newton's Law, because Newton's acts instantaneous. (Infact when I do a simulation of the solar system using Newton's Law I do the same, contrary what I have written above)
In reality I have never done a serious GR analysis for such a system. What I have done in order to improve my simulations I use a modification of Newton's Law which includes the speed of gravity and retarded positions. Which such a modification you can simulate the 43 arc sec and calculate the speed of gravity by trial and error.
In relation to GR I only have implemented the equations which describe the movements of the planet Mercury. See: http://users.telenet.be/nicvroom/VB%20Mercury%20numerical.htm The issue that this exercise gives already many problems and is too simple. It includes one object which has a mass and the other one is massless. In your exercise atleast both objects have a mass.
When I do a simulation using the speed of gravity cg equal to c the two objects will spiral outwards. When cg is larger they will become more stable. This a simulation is in conflict which a simulation using GR and masses comparable to the Sun i.e. masses like 50*m0. In such cases the masses should spiral inwards and collide. As in the case of LIGO.
What this means in order to simulate the above observations using Newton's Law and the speed of gravity I have in some way or another to make mass a variable i.e. smaller as a function of t. In the case of GR I also have to make the mass variable, but larger.
I expect this is not the answer you have in mind.
Thanks
Nicolaas Vroom
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