- The postings 1-2 are a thread in sci.physics.research (9 Sept 04 and 1 Oct 04)

- The postings 1-8 are a thread in sci.physics

- The postings 9-14 are a thread in sci.astro.research and sci.physics.research

- The postings 15-21 are a thread in sci.astro and sci.physics

For an updated account about the problems explained in this dicussion read the following: 6 Questions "Our Galaxy and the movement of planet Mercury"

1 "Nicolaas Vroom" |
How important is SR for the precession of Mercury | vrijdag 15 oktober 2004 14:28 |

2 "Nicolaas Vroom" |
Re: How important is SR for the precession of Mercury | vrijdag 15 oktober 2004 14:30 |

3 "Nicolaas Vroom" |
Re: How important is SR for the precession of Mercury | vrijdag 15 oktober 2004 14:35 |

4 "Nicolaas Vroom" |
Re: How important is GR for the precession of Mercury | woensdag 27 oktober 2004 14:15 |

5 "Ken S. Tucker" |
Re: How important is GR for the precession of Mercury | donderdag 28 oktober 2004 11:31 |

6 "Nicolaas Vroom" |
Re: How important is GR for the precession of Mercury | maandag 1 november 2004 20:47 |

7 "Ken S. Tucker" |
Re: How important is GR for the precession of Mercury | dinsdag 2 november 2004 11:26 |

8 "Nicolaas Vroom" |
How important is GR for the precession of Mercury | woensdag 10 november 2004 13:15 |

9 "T. Essel" |
Re: How important is GR for the precession of Mercury | woensdag 17 november 2004 17:46 |

10 "greywolf42" |
Re: How important is GR for the precession of Mercury | vrijdag 19 november 2004 20:30 |

11 "Nicolaas Vroom" |
Re: How important is GR for the precession of Mercury | vrijdag 19 november 2004 20:31 |

12 "Nicolaas Vroom" |
Re: How important is GR for the precession of Mercury | donderdag 9 december 2004 9:02 |

13 "Nicolaas Vroom" |
Re: How important is GR for the precession of Mercury | zaterdag 25 december 2004 22:28 |

14 "Nicolaas Vroom" |
Re: How important is GR for the precession of Mercury | dinsdag 1 februari 2005 20:31 |

15 "greywolf42" |
How important is GR etc. (banned reply) | woensdag 17 november 2004 23:32 |

16 "Martin Hogbin" |
Re: How important is GR etc (banned reply) | donderdag 18 november 2004 0:49 |

17 "mountain man" |
Re: How important is GR etc (banned reply) | donderdag 18 november 2004 7:00 |

18 "Eric Gisse" |
Re: How important is GR etc (banned reply) | donderdag 18 november 2004 10:45 |

19 "greywolf42" |
Re: How important is GR etc (banned reply) | donderdag 18 november 2004 18:41 |

20 "Socks" |
Re: How important is GR etc (banned reply) | donderdag 18 november 2004 19:22 |

21 "mountain man" |
Re: How important is GR etc (banned reply) | zaterdag 20 november 2004 0:23 |

Starting point of this posting is chapter 15.3 "Advance of the perihelion of Mercury" the pages 195 to 198 in the book "Introducing Einstein's Relativity" by Ray d'Inverno.

IMO the whole purpose of this exercise is to calculate with a model the future positions of the planets (i.e. Mercury) solely based on past observations (positions) as acurate as possible.

In order to do this you need a 3D grid of measuring rods and clocks. The clocks are located at the cross sections of the rods and the clocks are all synchronised with a clock at the origin. In order to predict you need a model. One model can be eq. 15.25 which is the relativistic version of Binet's eq. and differs from Newton's by the presence of the last term.

Using this 3D grid and the clocks you can perform the past observations of the positions of the planets. This is important because eq. 15.25 contains constants. IMO the only correct way to calculate those constants (for example m) is to use eq. 15.25 based on past observations.

One parameter discussed is proper time tau. In the grid there are no moving clocks involved. On the other hand if you attach a clock onto Mercury and you synchronise this clock with the nearest clock from the grid, you will see that this moving clock constantly runs behind the nearest clock from the grid (based on its moving position) and that this difference is increasing (at variable rate).

I expect that in order to calculate proper time tau you can also use eq. 8.16 i.e. as a function of v and c. I expect that v is measured with the clocks from the 3D grid.

IN eq 15.22 a constant k is calculated by means of a factor dtau/dt (multiplied by 1-2m/r). I expect that k is only a constant because r is variable.

What amases me that in equation 15.25 the factor k has disappeared. Does this mean that the concept proper time is of less importance inorder to calculate the precession of Mercury ?

How do I compare the above with the following
sentence from
http://arxiv.org/PS_cache/gr-qc/pdf/0103/0103044.pdf
The Meaning of Einstein's Equation

Authors: John C. Baez, Emory F. Bunn

at page 3 of 19:
"Thus the concept of inertial frame, so important in SR
is banned from GR"

Nicolaas Vroom http://users.pandora.be/nicvroom/

"Nicolaas Vroom"

> |
In order to do this you need a 3D grid of measuring rods and clocks. The clocks are located at the cross sections of the rods and the clocks are all synchronised with a clock at the origin. |

One of the best url's to study such a grid is the following:
http://www.astro.utu.fi/EGal/elg/ELG3D.html
The two main questions are:

1. Is such a grid the right tool to study GR
(Finally in order to simulate the planet Mercury)

2. If yes: What is the metric (tensor) involved.

The "centre" of the grid shows the Milkway galaxy as a large yellow dot and 3 other major galaxies. Each of those galaxies is surrounded by a cloud of smaller galaxies in red.

However the same grid can be used as a part of our Milkyway galaxy. The Yellow dot in the centre is than the Sun surrounded by local stars.

At an even smaller scale the centre is still the Sun surrounded by planets.

What ever the scale at the crossing points of the
grids there are clocks (and a light), all synchronised.
When you look at clocks on the grid, all clocks show
exactly the same time.

However that is not what you see when you are
at the center of the grid.

When you are at the center of the grid and when there
are no masses involved and when you look along the
line x=0 all clocks at different distances show a different
time (as a function of distance and c).
In fact you only see the first clock (light).

When the whole grid only contains one object (one mass) the object moves in a perfect straight line through the grid.

Suppose this object crosses the line x=0 very close to the clock which shows 6.00 (Suppose all the clocks show ONE hour difference) Suppose the clock at the center shows 12.00. The question is what will be observed by an observer at the center ? The observer will not see the clocks at 11.00, 10.00, 9.00 8.00 7.00 and 6.00 but the observer will be able to see the clocks (light from the clocks) at 5.00 and earlier because light from those clocks is bended by the (moving) mass. (This only for a small period of time)

However, and this is important, you do not have to include this light bending in order to describe the movent of your moving object. (i.e. all the objects)

Suppose the center of the grid shows the Sun and there
is only one planet (the Earth)
Suppose the Earth crosses the line x=0 twice
at x= x0 and x= -x0. Suppose there are two clocks
fixed at the grid and there is one moving clock.
Suppose you synchronise your moving clock with
the clock at x=x0.

What will happen that your moving clock will run
behind the two fixed clocks after one revolution
and that this discrepancy will increase after each
revolution.
However, again, you do not have to include this behavior
(slow down) of the moving clock to include in order to
describe the movent of your moving object. (and objects)

But you must take it into account when you convert earth based observations into grid based "observations" and vice versa. The same with light bending. This becomes more complex when the sun itself is moving in your grid, but the concept is the same.

The final question to answer is what is the metric of the grid.

What is the proper time in the grid ?

> | Nicolaas Vroom http://users.pandora.be/nicvroom/ |

"Nicolaas Vroom"

> |
"Nicolaas Vroom" |

> > |
In order to do this you need a 3D grid of measuring rods and clocks. The clocks are located at the cross sections of the rods and the clocks are all synchronised with a clock at the origin. |

> |
One of the best url's to study such a grid is the following: http://www.astro.utu.fi/EGal/elg/ELG3D.html |

In this grid all the objects have grid positions based on
grid coordinates.
We measure (observe) each of those are (Earth based)
positions.
As I explained in my previous posting in order to use the
grid you have to convert your (Earth based) observations
in grid coordinates by taking into account the following
two concepts:

Time dilation and light bending.

Using the positions in grid coordinates and using a set of rules you can now predict future grid positions.

If you want to test those predicted grid positons with actual observed (earth based) positions you have to convert the grid coordinates in Earth based coordinates taking into account the following two concepts (inverse form): Time dilation and light bending.

> | The final question to answer is what is the metric of the grid. |

The question is which laws apply to describe the movement of the objects using the grid coordinates.

IMO there is no time dilation (there are no moving clocks) and no light bending involved (light bending has to do with observations but light does not influence the movement)

There is length contraction involved, however I do not know if that influences the movement of the objects. (My guess is no)

As a first approximation you can use Newton's Law in order to describe the movement of the objects in the grid.

One of the most important question to answer is what is the function of the speed of light within the grid. (As explained above in order to covert earth based to grid based coordinates c is important)

IMO the most important parameter to describe the movement more accurate (beside Newton's law and the calculated mass parameter m for each object ) is the speed of gravity propagation parameter cg

> > | Nicolaas Vroom http://users.pandora.be/nicvroom/ |

As a result of this discussion I received the following by private e-mail:

"it is not clear what the point is that you are trying to make."

The point I try to make is very simple if you change SR into GR.

What I did in a simple wording is remove "the noise of observations" in order to transform real observations into positions in a reference frame consisting of rods and synchronised clocks. I did this by using the laws of SR.

My question is how do you describe the movements of the
objects in this reference frame ?
By using SR ?

By using GR ?

Do you need everything (all the complexity) described in the book
a) Introducing Einstein's Relativity ?

b) GRAVITATION ?

Do you need the c the speed of light ?

Or should that be c the speed of electro-magnetic radiation ?

What about cg the speed of gravitation ?

(When you are finished you have to "add" the noise of observations, in order to transform the calculated positions into real observations.)

I have doubts If you need all that is described in the two above mentioned books and that you can do this in a much simpler way. IMO the most important parameter is cg, i.e. you have to mimic the behaviour of the gravitons, for what ever this is worth.

Anyone responds ?

Nicolaas Vroom http://users.pandora.be/nicvroom/

"Nicolaas Vroom"
Anyone responds ?
Nicolaas Vroom
http://users.pandora.be/nicvroom/

>
IMO the most important parameter is cg,
i.e. you have to mimic the behaviour of the gravitons,
for what ever this is worth.

It's always difficult to determine which specific physical thing causes GR effects. The easiest way to get to the precession is to take the derivative of the energy

E = 1/sqrt(1-2GM/rc^2) of a unit mass

dE/dr ~ -(GM/r^2)*(1+3GM/rc^2) = force

That is from E = mc^2/sqrt(g_00).

Regards Ken S. Tucker

"Ken S. Tucker"

> |
"Nicolaas Vroom" |

> | ... |

> > |
IMO the most important parameter is cg,
i.e. you have to mimic the behaviour of the gravitons,
for what ever this is worth.
Anyone responds ? Nicolaas Vroom http://users.pandora.be/nicvroom/ |

> |
It's always difficult to determine which specific physical thing causes GR effects. The easiest way to get to the precession is to take the derivative of the energy E = 1/sqrt(1-2GM/rc^2) of a unit mass dE/dr ~ -(GM/r^2)*(1+3GM/rc^2) = force That is from E = mc^2/sqrt(g_00). |

That is maybe finally what I'am looking for,
but first at for all what I want to know is what
are the laws that are valid within the reference frame
i.e. within the frame from which I have removed
all observer dependent influences i.e. light bending
and moving clocks.

(The first approximation can be Newton's law,
but that is not the total picture)
Within this reference frame you should consider all
objects as "invisible" dark objects i.e. objects whose
behaviour is not influenced by the speed of light
(Assuming that my understanding is correct)
As such I do not "understand" the c^2 parameter in your
equation.
Or is this c the same as cg i.e. the speed of gravitation ?

Nicolaas Vroom http://users.pandora.be/nicvroom/

"Nicolaas Vroom"
Anyone responds ?
Nicolaas Vroom
http://users.pandora.be/nicvroom/
It's always difficult to determine which specific
physical thing causes GR effects.
The easiest way to get to the precession is
to take the derivative of the energy
E = 1/sqrt(1-2GM/rc^2) of a unit mass
dE/dr ~ -(GM/r^2)*(1+3GM/rc^2) = force
That is from E = mc^2/sqrt(g_00).

>
"Ken S. Tucker"

> >
"Nicolaas Vroom"

>
news:

> >
...

> > >
IMO the most important parameter is cg,
i.e. you have to mimic the behaviour of the gravitons,
for what ever this is worth.

> >

> |
That is maybe finally what I'am looking for,
but first at for all what I want to know is what
are the laws that are valid within the reference frame
i.e. within the frame from which I have removed
all observer dependent influences i.e. light bending
and moving clocks. (The first approximation can be Newton's law, but that is not the total picture) Within this reference frame you should consider all objects as "invisible" dark objects i.e. objects whose behaviour is not influenced by the speed of light (Assuming that my understanding is correct) As such I do not "understand" the c^2 parameter in your equation. |

"c" is the usual constant speed of light.

> | Or is this c the same as cg i.e. the speed of gravitation ? |

I think the "speed of gravity" = g_00

> |
Nicolaas Vroom http://users.pandora.be/nicvroom/ |

Ken

In the newsgroup sci.physics.relativity I started a posting with the subject title. The purpose was how do you simulate the movement of the planets, specific the movement of Mercury.

Not many people responded to my messages and as such I try in this newsgroup, maybe with a better result.

The approach I take is slightly different as maybe expected and
that maybe explains the low responds.

Starting point is to convert human observations into a frame
which complies to SR.

This frame consists of a 3D grid of rods with synchronised clocks
at all cross sections.

This frame in 2D looks very much like a computer screen, each
pixel can be the position of one clock which all show the same
time. In reality this means you only need one clock.

This frame does not show what a user observes. If you place an Observer somewhere "all" the clocks that he (she) sees show a different time, the further away the more retarded.

As part of the conversion from observations into the frame
I also take light bending into account.
My question is what are the rules that describe the behaviour
of the stars and planets within this frame.
It is not (If you want to be very accurate) Newton's Law because
Newton's Law assumes that all forces act instantaneous.

It is not SR.

But is it GR. And if it GR how does it "looks". Can this not be
simpler as described in books like GRAVITATION ?

The mayor problem is what is the function of c in this frame.
In fact what I have done as part of the conversion I have removed
the human part, what is left over is a dark universe independent
of human influences (almost).

In a sense you should close your eyes and ask the question:
which are the rules that describe the behaviour of the stars ?
What is the physical explanation for this behaviour ?

If the answer is gravitons than the speed of gravity cg has
to be included.

The question is what is the value of cg ? identical to c ?
and how do you prove this.
My understanding is that gravitons "move" in perfect straight
lines and are not bended.
This has been proved during solar eclipses.

For a 3D picture of the galaxies see: http://www.astro.utu.fi/EGal/elg/ELG3D.html

Nicolaas Vroom

http://users.pandora.be/nicvroom/

On Wed, 10 Nov 2004, Nicolaas Vroom asked (in s.a.r.)

> | In the newsgroup sci.physics.relativity I started a posting with the subject title. The purpose |

question?

> |
was how do you simulate the movement of the planets, specific the
movement of Mercury.
Not many people responded to my messages and as such I try in this newsgroup, maybe with a better result. The approach I take is slightly different as maybe expected and that maybe explains the low responds. |

You have asked very similar questions before in various forums including s.a.r. and s.p.r., and on several previous occasions, I have gone to great lengths to help you understand what gtr says about the extraNewtonian precession of Mercury (and why gtr is such a satisfactory theory for purposes of explaining this and a multitude of other observational/experimental evidence). Unfortunately, results have been unsatisfactory. But for the benefit of lurkers who may have similar questions, I'll just restate a few general and oft-repeated observations.

1. Prerequisites for discussion of this topic include some elements of perturbation theory itself. This is an important body of concepts/techniques in applied mathematics which applies to equations in general. Once you acquire this background, you can see that similar techniques are used in several places in standard textbooks on gtr:

(a) locating horizons (in some parameterized family of solutions, such as the Schwarzschild family, which is parameterized by a parameter m which can be interpreted as the mass of the gravitating object) sometimes involves studying the location of positive real roots of univariate polynomials, and then it is helpful to know what happens to the roots as we let a parameter (e.g. m) get small,

(b) in studying geodesics in (semi)-Riemannian manifolds (as in the problem at hand!), perturbation analysis of approximate solutions of a suitable ODE (in this case, the Einstein-Binet equation) can be very helpful,

(c) metric perturbations of Lorentzian spacetimes are useful in studying say a Schwarzschild hole perturbed by incoming radiation.

2. In addition, of course, perturbation theory is needed to follow classical work (predating gtr!) within Newtonian gravitation. Here too, exact solutions for multibody systems such as our Solar System are hard to come by, so one attempts to find approximate solutions modeling a situation "close" to a situation for which we have an exact solution (e.g. Keplerian motion). This is how one tries to study analytically the effect of the motion of Jupiter on the motions of the other planets, etc., within the context of Newtonian gravity. This is needed in the problem at hand because the theoretical problem confronting Einstein in 1916 was not to explain the precession of Mercury in its orbit around the Sun, but rather to explain a small residual remaining after a perturbation theory analysis of a model in Newtonian gravity had explained all but a small part of the observed motion.

3. A solid background in "mathematical methods", and other prerequisites for manifold theory and elementary modern differential geometry are needed for both gtr and Newtonian gravitation. Knowledge of Maxwell's theory of EM is also very helpful in many places, e.g. for supplying analogous concepts to compare and contrast with gtr. A typical case in point: I am about to mention "multipole moments", a concept which is best studied in Newtonian gravitation, then Maxwell's theory of EM, then weak-field gtr.

4. Notice that in Newtonian gravitation, the field equation (Laplace's equation) is linear; nonetheless, as I said, exact solutions suitable for modeling our Solar System are unavailable. This is why the nineteenth century mathematical physicists turned to perturbation analysis. In gtr, we have the additional complication that the full field equation (the EFE) is nonlinear, but this plays no role here because we can get away with studying solutions to a linearized version of the EFE.

5. AE's analysis of the extraNewtonian precession of Mercury uses linearized gtr. (Indeed, his original paper slightly precedes Schwarzschild's discovery of the first exact solution of the full field equations.) This is a key point because you can superimpose solutions in a linear theory. This explains why Einstein was justified in -isolating- the extra-Newtonian precession, the part which was observed but could not be explained by Newtonian theory. This extra-Newtonian precession is quite small compared to the actual precession, which is mostly attributable to the perturbing influence of Jupiter's motion. Note that AE studied a single test particle (modeling Mercury) in an almost elliptical orbit about a weak-field Schwarzschild object (modeling the Sun), which is what I mean by saying he "isolated the extraNewtonian precession". This procedure only makes sense because of what I have just said!

6. If you lack the assumed background in differential geometry, you will probably find it very difficult to separate out physical/geometric phenomena from mere coordinate artifacts. E.g. if you follow my advice and compare AE's method in exact Schwarzschild with its weak field limit (of course you should get the same result!), presumably working with polar spherical type local coordinate charts, you might get confused by the various "radii". See the "coordinate tutorial" on Baez's "Relativity on the World Wide Web" for some help on this kind of issue. This falls under the heading of textbook authors assuming suitable "mathematical maturity". Similarly, beginners might get confused by the question of justifying interpretation of parameters as "mass" or whatever. This falls under the heading of textbook authors assuming sufficient prior experience with simpler theories.

7. "ExtraNewtonian" deserves a small caveat because of an issue which was raised in some "early modern" gtr textbooks (but which has since largely been laid to rest): if the Sun had a slightly different shape from the simplest possibility, it might acquire multipole moments sufficient to alter some predictions from a suitable Newtonian model. Unfortunately, it is notoriously difficult to make direct observations of the shape of the Sun! So we study the motion of the planets, etc., and try to deduce what we can from these; basically, it turns out that the results are consistent with the simplest possible shape, even though this is difficult to confirm by direct observation. This might seem circular, but here is one quick way to see that such indirect reasoning need not be unjustifiable: note that the effects of a nonzero quadrupole moment scale quite differently from the extraNewtonian precession from linearized gtr which was found by AE. This is most easily studied by deriving the precession of a test particle in almost elliptical orbit around a static axisymmetric object with a finite number of nonzero multipole moments (all in weak-field gtr). I have carried out this exercise in great detail on previous occasions and discussed the implications of the results for the question of whether possible undiscovered solar oblateness could explain the observed motions of various systems such as our solar system.

8. Perturbation analysis in Newtonian gravitation or gtr is usually preferable to numerical simulation where possible, precisely because perturbation analysis is very good at giving analytical results in a situation which is "close" to a much simpler and well-understood situation. Typically we get information about how various effects "scale" with small values of perturbation parameters. This kind of result is easy to interpret and almost always gives valuable physical insight, whereas it can be very difficult to extract similar insight from numerical simulations. However, if you insist on doing numerical simulation, as I gather is the case, you need to be aware of a multitude of pitfalls which can lead to -wildly misleading results- if you are not careful, even in Newtonian gravitation.

9. If you want to conveniently compare predictions for the extraNewtonian precession from various competing classical relativistic field theories of gravitation, there is a highly developed formalism for doing this: PPN and its derivatives. One important result from PPN is that in various precise senses, gtr is the simplest such theory, which makes it even more striking that gtr explains -all- current observational/experimental evidence (at least, all the evidence everyone agrees is solid). Some competing theories yield the same weak-field extraNewtonian precession formula as gtr, but presumably we are not interested in a theory which explains one more thing than Newton did, but fails to explain say the observed "Shapiro time delay" effect! This is analogous to the point I made above, at a lower level of structure, where assuming a suitable amount of solar oblateness (too small to directly observe) we could perhaps after all explain the motion of Mercury within Newtonian gravitation--- but then we'd have a problem with the motion of Venus, and so on.

10. To set up something like PPN, you need to begin by defining some class of theories. Inevitably, this involves making -some- assumptions, possibly including "hidden" assumptions. If later on you with to remove one of them (e.g. possibly different speeds of gravitational and EM radiation), you should probably begin by setting up a more general "theory of intertheory comparison", starting with a more general class of theories.

OK, 'nuff said.

Suggested reading:

See a very recent post in s.p.r. where I suggested some good places to begin studying perturbation theory in the sense of applied mathematics. See also the gtr problem book by Press et al. for a problem on solar oblateness versus Einstein's precession formula; compare their solution in the back to the one I gave in the above mentioned posts to s.p.r. a few years ago. Note that they directly compare a result from Newtonian theory to one from weak-field gtr, without comment. Again, this is entirely justified, but only because weak-field gtr is a linear field theory! As I said, in my solution I worked entirely in weak-field gtr to obtain both results, which may help some students understand that there is no "funny business" going on here. For numerical simulations, again the textbook by Richards is a good place to start on trying to understand "stability" in general. Then one can consult specialized textbooks on numerical methods for more about careful numerical integration of differential equations. For PPN, see a survey paper by Clifford Will on the ArXiV.

"T. Essel" (hiding somewhere in cyberspace)

"T. Essel"

> | On Wed, 10 Nov 2004, Nicolaas Vroom asked (in s.a.r.) |

> > |
In the newsgroup sci.physics.relativity I started a posting with the subject title. The purpose was how do you simulate the movement of the planets, specific the movement of Mercury. Not many people responded to my messages and as such I try in this newsgroup, maybe with a better result. The approach I take is slightly different as maybe expected and that maybe explains the low responds. |

> |
You have asked very similar questions before in various forums including s.a.r. and s.p.r., and on several previous occasions, I have gone to great lengths to help you understand what gtr says about the extraNewtonian precession of Mercury (and why gtr is such a satisfactory theory for purposes of explaining this and a multitude of other observational/experimental evidence). |

It would be polite to provide a link to said statements. A google search of your posts shows no matches against "Nicolaas Vroom". In fact, there is only one post against your name (to Bill Kavanah), that contains the word "mercury" or the phrase "perturbation theory": http://www.google.com/groups?selm=cmq3is%24a2m%241%40lfa222122.richmond.edu And in this post, you again make unreferenced statements that you've "posted on this (perturbation theory) very extensively before."

> | Unfortunately, results have been unsatisfactory. |

For whom?

> | But for the benefit of lurkers who may have similar questions, I'll just restate a few general and oft-repeated observations. |

Mere repetition is not a hallmark of either veracity or correctness.

> | 1. Prerequisites for discussion of this topic include some elements of perturbation theory itself. This is an important body of concepts/techniques in applied mathematics which applies to equations in general. Once you acquire this background, you can see that similar techniques are used in several places in standard textbooks on gtr: |

This is true, but irrelevant to the question asked. Which was not about how to manipulate the details of perturbation theory, but about the physical calculation of the NNPA of Mercury.

{snip a bit of irrelevant detail}

> | 2. In addition, of course, perturbation theory is needed to follow classical work (predating gtr!) within Newtonian gravitation. Here too, exact solutions for multibody systems such as our Solar System are hard to come by, so one attempts to find approximate solutions modeling a situation "close" to a situation for which we have an exact solution (e.g. Keplerian motion). This is how one tries to study analytically the effect of the motion of Jupiter on the motions of the other planets, etc., within the context of Newtonian gravity. This is needed in the problem at hand because the theoretical problem confronting Einstein in 1916 was not to explain the precession of Mercury in its orbit around the Sun, but rather to explain a small residual remaining after a perturbation theory analysis of a model in Newtonian gravity had explained all but a small part of the observed motion. |

On the contrary. The explicit, stated purpose of Einstein was to obtain Newcomb's published value (43" per century*) for the NNPA of Mercury. Einstein's primary theoretical effort (the Entwurf version of 1913) only resulted in a value of about 17" per century. Einstein considered this a "problem", and fiddled with things until he could reproduce Newcomb's value. Einstein's partner (Grossmann) on the other hand, remeasured the NNPA of Mercury ... and got 18 to 28" per century**.

*In order to get this value, Newcomb assumed that Mercury's eccentricity varied during each orbit (his value was for an ephemerides, not an attempt to prove physical theory). Einstein's value does not include variations in Mercury's eccentricity.

** Using non-varying eccentricity.

> | 3. A solid background in "mathematical methods", and other prerequisites for manifold theory and elementary modern differential geometry are needed for both gtr and Newtonian gravitation. Knowledge of Maxwell's theory of EM is also very helpful in many places, e.g. for supplying analogous concepts to compare and contrast with gtr. A typical case in point: I am about to mention "multipole moments", a concept which is best studied in Newtonian gravitation, then Maxwell's theory of EM, then weak-field gtr. |

And totally irrelevant to the question asked.

> | 4. Notice that in Newtonian gravitation, the field equation (Laplace's equation) is linear; nonetheless, as I said, exact solutions suitable for modeling our Solar System are unavailable. This is why the nineteenth century mathematical physicists turned to perturbation analysis. In gtr, we have the additional complication that the full field equation (the EFE) is nonlinear, but this plays no role here because we can get away with studying solutions to a linearized version of the EFE. |

Which is simply the Newtonian equation, with an added speed-of-gravity parameter (equal to the speed of light). One doesn't need "GR" for this one. Paul Gerber did this 17 years before Einstein's GR.

> | 5. AE's analysis of the extraNewtonian precession of Mercury uses linearized gtr. (Indeed, his original paper slightly precedes Schwarzschild's discovery of the first exact solution of the full field equations.) This is a key point because you can superimpose solutions in a linear theory. This explains why Einstein was justified in -isolating- the extra-Newtonian precession, the part which was observed but could not be explained by Newtonian theory. This extra-Newtonian precession is quite small compared to the actual precession, which is mostly attributable to the perturbing influence of Jupiter's motion. Note that AE studied a single test particle (modeling Mercury) in an almost elliptical orbit about a weak-field Schwarzschild object (modeling the Sun), which is what I mean by saying he "isolated the extraNewtonian precession". This procedure only makes sense because of what I have just said! |

It makes sense simply because a finite propagation speed leads to precession. Whereas assuming an infinite speed avoids precession in a 1/r^2 force equation.

> | 6. If you lack the assumed background in differential geometry, you will probably find it very difficult to separate out physical/geometric phenomena from mere coordinate artifacts. |

Actually, it is simple to separate out physical phenomena that apply to the NNPA. Simply look at the equation that results either from GR, the Einstein/Grossmann "Entwurf" GR, or from any other theory with finite gravity speed:

K pi^3 delta theta = ------------------------------- (v_g)^2 a (1 - e^2)

Whether using Gerber or GR, there are only three parameters needed to determine perihelion shift: semimajor axis of the planet's orbit (a), eccentricity of the planet's orbit (e), and the speed of propagation of gravity. (v_g = c in GR) http://www.google.com/groups?selm=vr2941i226t8a5%40corp.supernews.com

For GR or Gerber's Newtonian, the constant, K is equal to 24. For Entwurf GR, or standard delayed-Newtonian the constant, K, is equal to 8.

Your details on the mechanics of how to make the calculation only covers how the value of the constant, K, is determined. Which is not trivial, certainly. But it doesn't address the question that was asked.

{snip more irrelevant detail}

> | 7. "ExtraNewtonian" deserves a small caveat because of an issue which was raised in some "early modern" gtr textbooks (but which has since largely been laid to rest): if the Sun had a slightly different shape from the simplest possibility, it might acquire multipole moments sufficient to alter some predictions from a suitable Newtonian model. Unfortunately, it is notoriously difficult to make direct observations of the shape of the Sun! |

It is straightforward, and has been done many times over the years. Unfortunately for GR, the directly-measured shape of the Sun is slightly oblate ... which gives rise to between 5 to 15 seconds of arc of the "43" unaccounted NNPA (depending on who does the measuring).

> | So we study the motion of the planets, etc., and try to deduce what we can from these; basically, it turns out that the results are consistent with the simplest possible shape, |

This is simply called ignoring the problem.

> | even though this is difficult to confirm by direct observation. This might seem circular, |

It is. Thanks for at least being honest. :)

> | but here is one quick way to see that such indirect reasoning need not be unjustifiable: note that the effects of a nonzero quadrupole moment scale quite differently from the extraNewtonian precession from linearized gtr which was found by AE. This is most easily studied by deriving the precession of a test particle in almost elliptical orbit around a static axisymmetric object with a finite number of nonzero multipole moments (all in weak-field gtr). I have carried out this exercise in great detail on previous occasions and discussed the implications of the results for the question of whether possible undiscovered solar oblateness could explain the observed motions of various systems such as our solar system. |

However, such gedanken exercises still don't give us any information on the real solar system.

{snip repetition 8, 9, and 10 of irrelevant detail}

--
greywolf42

ubi dubium ibi libertas

{remove planet for e-mail}

"T. Essel"

> | On Wed, 10 Nov 2004, Nicolaas Vroom asked (in s.a.r.) |

> > |
In the newsgroup sci.physics.relativity I started a posting with the subject title. The purpose |

> |
question? |

> > |
was how do you simulate the movement of the planets, specific the movement of Mercury. |

> |
You have asked very similar questions before in various forums including s.a.r. and s.p.r., and on several previous occasions, I have gone to great lengths to help you understand what gtr says about the extraNewtonian precession of Mercury (and why gtr is such a satisfactory theory for purposes of explaining this and a multitude of other observational/experimental evidence). |

I'am not aware of those discussions with you but anyway thanks for all the detailed information regarding perturbation theory.

> |
Unfortunately, results have been
unsatisfactory. But for the benefit of lurkers who may have similar
questions, I'll just restate a few general and oft-repeated observations.
1. Prerequisites for discussion of this topic include some elements of perturbation theory itself. |

In order to get some idea about about perturbation theory and astronomy I studied the following document: " Large-Scale Structure of the Universe and Cosmological Perturbation Theory" http://xxx.lanl.gov/abs/astro-ph/?0112551

My previous experience with perturbation theory was related to process control.

Maybe perturbation theory is the final tool that I need in order to solve the equations that describe the movements of the stars and planets (in a very acurate way ?) but first I need an answer on a couple of questions:

1) Does it make sense to transform human based observations into
grid based positions ?

2) Does it make sense to remove light bending as part of those
transformations ?

3) If those transformations make sense i.e. have an advantage above
other methods then:

4) What is the function of c within this grid or frame ?

5) What is the function of cg within this frame ?

6) Do I have to consider SR within this frame ?

7) Do I need the full complexity of GR to describe the movement
of the stars (and planets) ?

IMO the answer on that question is NO because there are no moving clocks involved.

Nicolaas Vroom

http://user.pandora.be/nicvroom/

> |
Suggested reading:
See a very recent post in s.p.r. where I suggested some good places to begin studying perturbation theory in the sense of applied mathematics. See also the gtr problem book by Press et al. for a problem on solar oblateness versus Einstein's precession formula; compare their solution in the back to the one I gave in the above mentioned posts to s.p.r. a few years ago. Note that they directly compare a result from Newtonian theory to one from weak-field gtr, without comment. Again, this is entirely justified, but only because weak-field gtr is a linear field theory! As I said, in my solution I worked entirely in weak-field gtr to obtain both results, which may help some students understand that there is no "funny business" going on here. For numerical simulations, again the textbook by Richards is a good place to start on trying to understand "stability" in general. Then one can consult specialized textbooks on numerical methods for more about careful numerical integration of differential equations. For PPN, see a survey paper by Clifford Will on the ArXiV. "T. Essel" (hiding somewhere in cyberspace) |

"Nicolaas Vroom"

SNIP

> |
but first I need an answer
on a couple of questions:
1) Does it make sense to transform human based observations into
grid based positions ? |

Not much responds to those questions. Still I consider them very important and I think a must if you want to simulate (predict) the positions of the stars and planets.

One additional questions bothers me tremendously:
Within this grid is there any bending of space-time involved ?

I expect if you want to visual observe the stars and planets
the answer is Yes.

But that is not the total issue.
The question is: if there is some form of space-time bending
involved within this frame(grid) does this bending have any
influence on the behaviour of the stars and planets ?
(And how ?)

Nicolaas Vroom

http://users.pandora.be/nicvroom/

If you want to simulate the movement of galaxies
stars or planets then one very important
question to answer is what is "timewise" the basis
of your simulation.

IMO there are two possibilities.
In both cases you start by selecting a reference point
(or origin) and a time t0 (or a now)

The first possibility is based on what you see.
That means you place yourself at the origin and you
observe the positions of the planets. Those positions
are the starting point of your simulation.

The second possibility is identical as the first, but the
starting position of the simulation is not the observed
position but the predicted position at the time t0 (now)

That means if a certain star is 1 light min away, you do not take the observed position, but the predicted position 1 min in the future from the observed position.

IMO this is the correct way to do your simulation because you are comparing more apples with apples.

The next question to answer is what should be
the origin of your simulation.

IMO the Sun is better than the Earth,
and even better is the centre of our Galaxy (than the Sun).
The reason is that a clock at the centre of Our Galaxy
is more stable as one at the Sun (or Earth)

The next question to answer is how should you
observe the positions of the stars.

IMO you should use a grid of synchronised clocks,
all at equal nearest distance, with one clock at your
origin.
If you place yourself at the origin than you will see
that all clocks at the same distance will run the same
timeperiod delta t behind.
For example a clock at 1 light minute will run 1 minute
behind.

The next, and most important, question to answer is what are the rules that describe the movement of the stars (or objects) assuming you have selected the second possibility.

Hopes this helps in the discussion.

For a 3D picture of the galaxies and to study
the grid See:
http://www.astro.utu.fi/EGal/elg/ELG3D.html

No 8 is the Milky Way Galaxy
No 32 is the Andromeda Galaxy
It is not clear if this 3D picture represents
possibility 1 or 2.

Nicolaas Vroom

http://users.pandora.be/nicvroom/

This responds is partly written as a reply of the thread: "non-GR theories of Gravity" initiated by Phillip Helbig.

"Nicolaas Vroom"

> | If you want to simulate the movement of galaxies |

> |
IMO there are two possibilities.
In both cases you start by selecting a reference point
(or origin) and a time t0 (or a now)
The first possibility is based on what you see. That means you place yourself at the origin and you observe the positions of the planets. Those positions are the starting point of your simulation. The second possibility is identical as the first, but the starting position of the simulation is not the observed position but the predicted position at the time t0 (now) |

This second possibilty is the prefered strategy but things are not that simple.

In order to calculate the predicted positions at time t0 you need a model.

One model can be Newton's Law.

The most important parameter of Newton's Law are
the masses of all the objects included in your simulation.
In order to calculate those masses you need as many
as possible observations of all your objects.
You need a set of estimated values for all your masses
and a set of initial positions (*) for your simulation.
With those two sets of information and with Newton's law
you can calculate the observed positions at the time
of those observations.
And you can calculate an overall error factor.

Next you can do the same for a different set of estimated values for all your masses and you can again calculate an overall error factor.

And again.

The set of estimated masses with the smallest overall error factor is the best.

(*) Your simulation starts with a set of initial positions
all at the same moment. Very often that set is not available
because most probably all you observations are
at a different moment. That means you have to calculate
those initial positions with the masses based on your
best estimate.

This makes this whole exercise very complex.

A different model can be MOND.

MOND stands for (Milgrom's?) Modified Newton Dynamics.
As the name explains MOND is based on Newton's Law
slightly modified with at least one additional parameter.
If you want to use MOND you have to estimate this parameter
and a set of masses for all the objects included.
Again you have to calculate an overall error factor
and the smallest overall error factor gives the best estimates.

MOND is a better theory than Newton's Law if the final overall error factor using MOND is the smallest of the two.

In principle you can also use a different model.

For example you can use Newton's Law modified with a parameter which takes into account that Newton's Law does not act instantaneous. Again you have to calculate an overall error factor and the story repeats it self.

See also my postings in the thread Re: Perihelion of Mercury with classical mechanics ? in sci.astro

(It should be mentioned that each of those 3 theories gives different mass estimates)

For example you can use GR

Hopes this helps.

> | Nicolaas Vroom http://users.pandora.be/nicvroom/ |

The following post was banned from the sci.astro.research newsgroup ... without notice, and in violation of the newsgroup charter (as is usual for s.a.r).

Not only are substantive responses blocked, but the moderators (T. Essel) dual-posted a triple reply to s.p.r. and s.a.r, that was simply boilerplate cheerleading for GR. Without responding to the question posted by Nicholaas, of course.

"greywolf42"
{snip}
As part of the conversion from observations into the frame
I also take light bending into account.
This is one of the areas that are not often discussed by Relativists. It is
a tricky arena, because there have been major "problems" within GR in the
past (and still some minor ones remain).
It is not SR.
But is it GR. And if it GR how does it "looks". Can this not be
simpler as described in books like GRAVITATION ?
MTW is not a good way to learn GR. It's a decent way to expand your
knowledge in specific areas, once you have the basics down.
The mayor problem is what is the function of c in this frame.
It is the speed of gravity. In GR, Einstein assumed that the speed of
gravity was equal to the speed of light, "c". It is not an unreasonable
assumption.
In fact what I have done as part of the conversion I have removed
the human part, what is left over is a dark universe independent
of human influences (almost).
In Einstein's GR, yes.
and how do you prove this.
The first method is simply to assume that it is true. This is the approach
taken by most Relativists, and all GR texts that I've seen. The second
method is to measure the non-Newtonian apside advance of orbiting bodies.
(Usually called the NNPA of Mercury.) The advance is a direct function of
the speed of gravity.
My understanding is that gravitons "move" in perfect straight
lines and are not bended.
Gravitons are not allowed within GR.
This has been proved during solar eclipses.
Actually, no. The data that NASA gathered in 1999 has not yet been released
to the public.

>
"Nicolaas Vroom"

> >

>

> >

My question is what are the rules that describe the behaviour
of the stars and planets within this frame.

It is not (If you want to be very accurate) Newton's Law because
Newton's Law assumes that all forces act instantaneous.

>

> >

>

> >

>

> >

In a sense you should close your eyes and ask the question:
which are the rules that describe the behaviour of the stars ?
What is the physical explanation for this behaviour ?

If the answer is gravitons than the speed of gravity cg has
to be included.

The question is what is the value of cg ? identical to c ?

>

> >

>

> >

>

> >

>

--
greywolf42

ubi dubium ibi libertas

{remove planet for e-mail}

"greywolf42"

> |
The following post was banned from the sci.astro.research newsgroup ...
without notice, and in violation of the newsgroup charter (as is usual for
s.a.r).
Not only are substantive responses blocked, but the moderators (T. Essel) dual-posted a triple reply to s.p.r. and s.a.r, that was simply boilerplate cheerleading for GR. Without responding to the question posted by Nicholaas, of course. |

It is pity we cannot do the same here.

Martin Hogbin

"Martin Hogbin"

> |
"greywolf42" |

>> |
The following post was banned from the sci.astro.research newsgroup ...
without notice, and in violation of the newsgroup charter (as is usual
for
s.a.r).
Not only are substantive responses blocked, but the moderators (T. Essel) dual-posted a triple reply to s.p.r. and s.a.r, that was simply boilerplate cheerleading for GR. Without responding to the question posted by Nicholaas, of course. |

> |
It is pity we cannot do the same here. |

How much does "modern science" know?

How much does "modern science" not know?

Pete Brown

Falls Creek

Oz

**Van:** "Eric Gisse"

**Onderwerp:** Re: How important is GR inorder to calc the precession of Mercury (banned reply)

**Datum:** donderdag 18 november 2004 10:45

"greywolf42"

[snip]

Their newsgroup, their rules.

Its too bad (not really) that you don't like it, but I fail to see why you would think a) any of us side for you regarding your plight and b) that we would do anything about it and c) that posting in here about your plight will do anything.

"Eric Gisse"

> |
"greywolf42" |

> |
[snip] Their newsgroup, their rules. |

I have no problem with their rules. I just enjoy jerking the chain of people who claim to have rules, then break them whenever it suits their personal prejudices.

> | Its too bad (not really) that you don't like it, but I fail to see why you would think a) any of us side for you regarding your plight |

I don't have a "plight."

> | and b) that we would do anything about it |

You don't have to do anything.

> | and c) that posting in here about your plight will do anything. |

Posting here serves my purpose. It allows the response to exist for the person who asked the question. And it shows the hypocritical actions of the moderators.

--
greywolf42

ubi dubium ibi libertas

{remove planet for e-mail}

"mountain man"

>
How much does "modern science" know?

More than cranks and toilers.

> | How much does "modern science" not know? |

Less than cranks and toilers. Socks

"Socks"

> |
"mountain man" |

>> | How much does "modern science" know? |

> |
More than cranks and toilers. |

>> | How much does "modern science" not know? |

> |
Less than cranks and toilers. |

Modern science is unable to make any form of self-referential statement due to the situation that it is founded (and vigorously promulgated) on a collection of theories that are fundamentally unrelated to one another.

Pete Brown

Falls Creek

Oz
www.mountainman.com.au

Created: 15 November 2004

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