1 liam@ork.net  Speed of Gravity  maandag 3 september 2001 5:24  
2 dlzc@aol.com (formerly) 
Re: Speed of Gravity  maandag 3 september 2001 7:40  
3 Martin Hogbin 
Re: Speed of Gravity  maandag 3 september 2001 10:27  
4 Tom Van Flandern 
Re: Speed of Gravity  dinsdag 4 september 2001 19:07  
5 Martin Hogbin 
Re: Speed of Gravity  dinsdag 4 september 2001 20:41  
6 fred b mcgalliard 
Re: Speed of Gravity  dinsdag 4 september 2001 21:09  
7 Nemesis 
Re: Speed of Gravity  woensdag 5 september 2001 10:51  
8 Tom Van Flandern 
Re: Speed of Gravity  donderdag 6 september 2001 22:55  
9 Steve Carlip 
Re: Speed of Gravity  vrijdag 7 september 2001 1:57  
10 Nemesis 
Re: Speed of Gravity  vrijdag 7 september 2001 9:45  
11 Steve Carlip 
Re: Speed of Gravity  zaterdag 8 september 2001 3:42  
12 Nemesis 
Re: Speed of Gravity  zaterdag 8 september 2001 6:13  
13 Sam Wormley  Re: Speed of Gravity  zaterdag 8 september 2001 6:29  
14 G=EMC^2 Glazier 
Re: Speed of Gravity  zaterdag 8 september 2001 15:16  
15 tj Frazir 
Re: Speed of Gravity  zondag 9 september 2001 4:25  
16 Tom Van Flandern 
Re: Speed of Gravity  maandag 10 september 2001 19:41  
17 Nemesis 
Re: Speed of Gravity  dinsdag 11 september 2001 7:22  
18 Sam Wormley 
Re: Speed of Gravity  dinsdag 11 september 2001 7:39  
19 Sam Wormley 
Re: Speed of Gravity  dinsdag 11 september 2001 7:46  
20 Nemesis 
Re: Speed of Gravity  dinsdag 11 september 2001 8:51  
21 Charles Francis 
Re: Speed of Gravity  dinsdag 11 september 2001 9:34  
22 Charles Francis 
Re: Speed of Gravity  dinsdag 11 september 2001 9:41  
23 Charles Francis 
Re: Speed of Gravity  dinsdag 11 september 2001 10:05  
24 Nemesis 
Re: Speed of Gravity  dinsdag 11 september 2001 10:52  
25 Nemesis 
Re: Speed of Gravity  dinsdag 11 september 2001 11:01  
26 Charles Francis 
Re: Speed of Gravity  dinsdag 11 september 2001 13:27  
27 Charles Francis 
Re: Speed of Gravity  dinsdag 11 september 2001 13:44  
28 G=EMC^2 Glazier 
Re: Speed of Gravity  dinsdag 11 september 2001 14:47  
29 Steve Carlip 
Re: Speed of Gravity  woensdag 12 september 2001 1:04  
30 Steve Carlip 
Re: Speed of Gravity  woensdag 12 september 2001 22:10  
31 Charles Francis 
Re: Speed of Gravity  donderdag 13 september 2001 8:45  
32 Nemesis 
Re: Speed of Gravity  zaterdag 15 september 2001 7:33  
33 Charles Francis 
Re: Speed of Gravity  zaterdag 15 september 2001 8:42  
34 Nemesis 
Re: Speed of Gravity  zaterdag 15 september 2001 21:04  
35 Nicolaas Vroom 
Re: Speed of Gravity  zaterdag 15 september 2001 21:41  
36 Tom Van Flandern 
Re: Speed of Gravity  maandag 17 september 2001 5:08  
37 tj Frazir  Re: Speed of Gravity  maandag 17 september 2001 17:02  
38 Jim Carr  Re: Speed of Gravity  zondag 23 september 2001 5:17  
39 Steve Carlip  Re: Speed of Gravity  maandag 24 september 2001 1:33  
40 Aleksandr Timofeev  Re: Speed of Gravity  maandag 24 september 2001 15:28  
41 Steve Carlip  Re: Speed of Gravity  maandag 24 september 2001 19:20 
Where are we today on this?
First we read that it is speed of light, then not...
We are very consistently at c for propagation of changes in gravity, say due to sudden loss of mass.
Anything else is speculation. It is surprising that the Sun and Jupiter experience curvature centered exactly where they are located *now* and not offset by 2 hours.
> 
Where are we today on this?
First we read that it is speed of light, then not... 
Do you have a citation?
David A. Smith

Martin Hogbin
> 
Where are we today on this?
First we read that it is speed of light, then not... 
http://hepweb.rl.ac.uk/ppUK/PhysFAQ/grav_speed.html
Martin Hogbin
>  Where are we today on this [the speed of gravity]? First we read that it is speed of light, then not... 
That is because widespread confusion exists between changes in gravitational fields and gravitational radiation (also called "gravitational waves"). These are two different, essentially unrelated phenomena.
Gravitational radiation is an ultraweak "spacetime" disturbance that has never yet been directly detected in the solar system, although it apparently has been seen indirectly in distant binary pulsars. Analogous to the electromagnetic radiation (e.g., light) that is emitted when a charge is accelerated, gravitational radiation occurs when a mass is accelerated, as in supernova explosion or when binary pulsars orbit one another. Like any wave propagating through the "spacetime medium", gravitational radiation travels at the speed of light.
Changes in gravitational fields are major effects in the solar system, where the planets all perturb one another. Sensitive gravimeters can easily "see" the gravitational field of a person walking around a laboratory (but are not thereby seeing gravitational waves). Six experiments are sensitive to the speed of changes in gravitational fields, and have set a lower limit to that speed that is orders of magnitude faster than light. No experiment in existence has ever measured a speed as slow as c, the speed of light. Indeed, computer experiments show that, if gravitational field changes are updated as slowly as the speed of light, dynamical systems become unstable and fly apart because angular momentum is not conserved.
For more information about the six experiments sensitive to the speed of changes in gravitational fields, see "The speed of gravity  What the experiments say", Phys.Lett.A, v. 250, #13, pp. 111 (1998/12/21); also available on the web at http://metaresearch.org , "cosmology" tab, "gravity" subtab.
For more information on the distinction between gravitational waves and changes in gravitational fields, and on other consequences of gravitational fields propagating faster than light, see "The speed of gravity  Repeal of the speed limit" at the same web site location.
and David A. Smith
>  We are very consistently at c for propagation of changes in gravity, say due to sudden loss of mass. 
This, as you see from the preceding descriptions, is a statement about the speed of gravitational radiation, which is probably not what was meant by the question about the "speed of gravity".
>  Anything else is speculation. It is surprising that the Sun and Jupiter experience curvature centered exactly where they are located *now* and not offset by 2 hours. 
It might be speculative to guess what the speed of gravity actually is, but it is a firm result of all existing experiments that it cannot be as slow as lightspeed. This statement about the curvature of the SunJupiter binary pair is correct, and is only "surprising" if one were expecting changes in gravitational fields to suffer the same retardation that light fields experience. They do not.
As for the supposed causality violations of ftl propagation, those arise only in special relativity (SR). But it is now widely recognized that the mathematically equivalent Lorentzian Relativity (LR) has no such difficulties because, in it, "time dilation" is really "clock slowing". Speed produces no effects on time itself, so travel backwards in time does not occur.
and Martin Hogbin
>  Have a look at the FAQ: 
However, the current FAQ was written before the first paper cited above was published, and makes the same confusion between gravitational waves and changes in gravitational fields described above. Until the FAQ is updated to reflect the current state of the ongoing debate about this, it will merely add to the widespread confusion. Tom
Tom Van Flandern  Washington, DC  see our web site on replacement astronomy research at http://metaresearch.org

Martin Hogbin
"Tom Van Flandern"
> 
John Smith 
> > 
Where are we today on this [the speed of gravity]? First we read that it is speed of light, then not... 
> 
That is because widespread confusion exists between changes in gravitational fields and gravitational radiation (also called "gravitational waves"). These are two different, essentially unrelated phenomena. 
Tom has a unique point of view on this subject.
Martin Hogbin
"Tom Van Flandern"
> 
John Smith 
> > 
Where are we today on this [the speed of gravity]? First we read that it is speed of light, then not... 
> 
That is because widespread confusion exists between changes in gravitational fields and gravitational radiation 
Tom. Thanks for the interesting reference. It is worth a read and a few minutes thought. However, I should point out that as far as I can come in a quick noon time read, this may be little more than a heavy handed modeling of the situation. Good for college students to test their teath on, but not of much value otherwise. Whatever gravity is, it is not as simple to deal with as EM fields. The fact that you can't shield it suggests that the change is not mediated by radiation in the same way an EM field change is. A good clue is probably provided by analysing the problem your web site presents, but I am way not convinced that this shows gravity propagates faster than C. In fact, if we could show this in a more rigid study, it would not just overthrow all our existing physics, it would demand a lot of stuff that is shockingly absent. I suggest taking two steps, not one. Consider what the universe must look like if gravity has an infinite top speed. How would this work if we send gravity wave info a light day to a space ship pushing 3/4C, and then send it back. How does this look if we are the ones moving and the ship and gravity sources are stationary in the ships view? Every way I look at this I come to the conclusion that the two "frames" physics can't have exactly the same form and constants for this to be true, but the form and constants we get do not seem to be so frame dependant?
In article <9n31op$arc$1@bob.news.rcn.net>, "Tom Van Flandern"
> 
John Smith 
> 
>> 
Anything else is speculation. It is surprising that the Sun and Jupiter experience curvature centered exactly where they are located *now* and not offset by 2 hours. 
> 
It might be speculative to guess what the speed of gravity actually is, but it is a firm result of all existing experiments that it cannot be as slow as lightspeed. This statement about the curvature of the SunJupiter binary pair is correct, and is only "surprising" if one were expecting changes in gravitational fields to suffer the same retardation that light fields experience. They do not. 
This is interesting. I would like to make a few comments and ask some questions:
Newton and Signal Delay
If gravitational changes occur much faster than light speed, then Newtonian gravity is more or less correct since it assumes that changes are instantaneous. However, since Newton and the physicists of his day did not know the speed of light, they probably assumed that the observed positions of the various planets and the moon were their actual positions at the time of observation. In other words they did not compensate for the signal delay which can be many seconds to several minutes. Does anyone know if the delayed signal measurements were within the margin of error that would be expected in those days?
Physics Curriculum
According to the essay on your site, you were taught at Yale that the correct astronomical answers are obtained only if gravitational changes induced by the movements of the sun and the planets are assumed to be felt instantly by all bodies. I find this amazing since all relativists insist that changes in gravity propagates at c. Is this still being taught the same way in physics classes around the world?
Action at a Distance
You quote Newton thus: "That one body may act upon another at a distance through a vacuum, without the mediation of any thing else, by and through which their action and force may be conveyed from one to the other, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it."
You also write in the introduction: "Indeed, far from upsetting much of current physics, the main changes induced by this new perspective are beneficial to areas where physics has been struggling, such as explaining experimental evidence for nonlocality in quantum physics..."
I am not sure how instant gravity would explain nonlocality since they are both types of "action at a distance" in need of a common explanation. Newton is obviously right, action at a distance is out of the question. Neither instant gravity not entangled particles can be explained by action at a distance. This leaves us with a serious dilemma: how can the action of one body instantly affect the behavior of another millions of miles away? There is only one solution.
The Illusion of Distance
In my opinion (and this is something I've been saying for a long time) distance (or space) is an illusion. In my model of reality, there exist only particles, their properties and their interactions. The entire collection of particles comprise the universe. Nature keeps everything working through the law of conservation of energy.
Why is there no space? Because the concept of space is both selfreferential and redundant. If space exists, where is it? And if particles already have positional properties, what is the purpose of space?
If there is no space, position can no longer be viewed as a property of space but as an intrinsic property of the particles themselves, just like mass, charge or spin. To keep a long story short, I'll conclude by saying that, in my model, nonlocal phenomena (entangled particles) and instant gravitational actions (which I have recently come to accept as necessary) are due to the nonlocal principle of conservation of energy which acts almost instantaneously (in Planck time) to maintain a balance of energy in the universe. There is no need for action at a distance because there really is no distance.
Nemesis
Nasty Little Truth About Spacetime Physics: http://home1.gte.net/res02khr/crackpots/notorious.htm
> >  [tvf]: That is because widespread confusion exists between changes in gravitational fields and gravitational radiation (also called "gravitational waves"). These are two different, essentially unrelated phenomena. 
>  [mh]: Tom has a unique point of view on this subject. 
Uniqueness aside, I explained exactly why I made the above statement. See my complete exposition on this in section 3 of "The speed of gravity  Repeal of the speed limit" at http://metaresearch.org , "Cosmology" tab, "Gravity" subtab. If you find fault with my reasoning, please elaborate. For example, how can it be that we detect gravitational field variations in the solar system and in the laboratory, but have yet to detect a gravitational wave in either locale?
and "fred b mcgalliard"
>  A good clue is probably provided by analysing the problem your web site presents, but I am way not convinced that this shows gravity propagates faster than C. In fact, if we could show this in a more rigid study, it would not just overthrow all our existing physics, it would demand a lot of stuff that is shockingly absent. 
My conclusion was just the opposite. Fast gravity propagation is consistent with existing physics because nothing in the mathematical theories needs to change, just the interpretations thereof. And it helps physics in several areas where dilemmas now exist, such as the nonlocality problems in quantum physics. All we really need to do is replace Einstein's interpretation of the relativity of motion with Lorentz's, with no change in the math. Both interpretations are consistent with all eleven independent experiments that test various aspects of the relativity of motion. But with Lorentz's interpretation, the proof that nothing can go faster than the speed of light just goes away.
>  Consider what the universe must look like if gravity has an infinite top speed. How would this work if we send gravity wave info a light day to a space ship pushing 3/4C, and then send it back. How does this look if we are the ones moving and the ship and gravity sources are stationary in the ships view? 
Allow me to simplify and localize your example. Mars is several lightminutes away at all times. Suppose we send a signal to Mars that arrives one second later. Wouldn't all observers agree that was an ftl signal in forward time? If you think not, then let a Martian transponder send the ftl signal back to Earth, which takes another second. The signal then makes a round trip to Mars and back in two seconds, way faster than light (ftl).
In Einstein's interpretation of the relativity of motion, the signal would be traveling backwards in time. But in Lorentz's interpretation, the signal is simply ftl in forward time. So no causality violations or complications arise. If you haven't previously encountered Lorentzian relativity, this may be a fresh way of looking at physics. But it is also simple and rewarding, and most importantly it is consistent with all experimental evidence.
The essential point is that everybody agrees it takes light 8.3 minutes to get from the Sun to Earth. Something that makes the same trip in half the time is traveling ftl, but in forward time, and produces no causality violations (e.g., able to return before it was sent).
>  Every way I look at this I come to the conclusion that the two "frames" physics can't have exactly the same form and constants for this to be true, but the form and constants we get do not seem to be so frame dependant? 
In Lorentzian relativity, the dominant local gravity field is the "preferred frame". In the example I just gave, that would be the Sun's field. We synchronize all clocks in that frame. Then clocks moving relative to that frame slow down, but nothing happens to time itself.
This implies the (to some) surprising fact that all clocks with a uniform speed in the local gravity field, regardless of what that speed is, can be simultaneously synchronized (epochsynched) and syntonized (ratesynched), and will then remain in agreement indefinitely. But this was actually achieved in the Global Positioning System (GPS), where all ground clocks on the rotating Earth and all orbiting clocks in various nearcircular orbits in different planes, even those at different distances (Glonass), can all be synchronized and syntonized in this way. See a fuller discussion of this in "What the GPS tells us about relativity" in "Open Questions in Relativistic Physics", F. Selleri, ed., Apeiron, Montreal, pp. 8190 (1998), also available at the web site cited above.
and Nemesis Nemesis@nospam.com) writes:
>  If gravitational changes occur much faster than light speed, then Newtonian gravity is more or less correct since it assumes that changes are instantaneous. 
Yes, Newtonian gravity is an excellent approximation of reality, failing only for effects of order (v/c)^2 (typically 10^8 in the solar system) due to "spacetime curvature" or varying field density effects.
>  However, since Newton and the physicists of his day did not know the speed of light, they probably assumed that the observed positions of the various planets and the moon were their actual positions at the time of observation. In other words they did not compensate for the signal delay which can be many seconds to several minutes. Does anyone know if the delayed signal measurements were within the margin of error that would be expected in those days? 
Roemer was the first to notice the effect of a finite speed of light because the eclipse times of Jupiter's moons were delayed when Jupiter was farther away as compared with the eclipse times when Jupiter was closer. Roemer was a 17th century contemporary of Newton. But it was not until 1728 that Bradley discovered the aberration of light.
In short, yes, in those days the lightsignal delays were within the errors of position measurements until Roemer's discovery.
>  According to the essay on your site, you were taught at Yale that the correct astronomical answers are obtained only if gravitational changes induced by the movements of the sun and the planets are assumed to be felt instantly by all bodies. I find this amazing since all relativists insist that changes in gravity propagates at c. Is this still being taught the same way in physics classes around the world? 
Anyone can do a simple computer experiment with an orbit computation program and verify that the gravitational interactions must be nearly instantaneous compared to lightspeed to get reasonable orbits. So yes, celestial mechanics is still taught as it was, because that is what works. The disagreement with relativists is more semantic than substantive. Gravitational waves propagate at the speed of light, and many relativists aren't careful to distinguish those from changes in gravitational fields, which provably propagate faster than light in reality (binary pulsars) and in GR equations of motion (consider the field of any binary star at a distance of more than one lightperiod).
>  You quote Newton thus: [action at a distance is logically absurd] You also write in the introduction: "Indeed, far from upsetting much of current physics, the main changes induced by this new perspective are beneficial to areas where physics has been struggling, such as explaining experimental evidence for nonlocality in quantum physics..." I am not sure how instant gravity would explain nonlocality since they are both types of "action at a distance" in need of a common explanation. Newton is obviously right, action at a distance is out of the question. Neither instant gravity not entangled particles can be explained by action at a distance. This leaves us with a serious dilemma: how can the action of one body instantly affect the behavior of another millions of miles away? 
Of course, the speed of gravity is not instantaneous. That was Newton's point. It is simply too fast to measure at present. That is why it readily explains nonlocality experiments. However, the difference between any finite speed, however large, and infinite speed is still infinite.
>  In my opinion . distance (or space) is an illusion. 
Consider the varying times required by laser or radar beams to travel between points in space. These are proportional to distance. Moreover, we can measure distance by triangulating when we use two observers. I agree that, philosophically, the idea of empty space is absurd. But space is probably not really empty because we can detect such things as "zeropoint energy" (the Casimir effect). It is probably filled densely with entities too small for us to detect at present. These would provide meaning to distance.
You point out a legitimate philosophical problem. But I think your proposed solution is both impractical and inconsistent with experiment. Best wishes. Tom
Tom Van Flandern  Washington, DC  see our web site on replacement astronomy research at http://metaresearch.org
>  My conclusion was just the opposite. Fast gravity propagation is consistent with existing physics because nothing in the mathematical theories needs to change, just the interpretations thereof. 
This, of course, is complete nonsense. The field equations of general relativity rigorously and unambiguously imply that no gravitational effect can propagate faster than light. See, for example, R. Low, Class.Quant.Grav.16 (1999) 543.
(Tom knows about this paper. His first reaction was to claim that it said something different than it did. The author responded that Tom was wrong. Tom has subsequently simply ignored this and similar proofs, and persists in making statements about the ``mathematical theories'' that are demonstrably wrong.)
>  Anyone can do a simple computer experiment with an orbit computation program and verify that the gravitational interactions must be nearly instantaneous compared to lightspeed to get reasonable orbits. 
What Tom means, of course, is ``Anyone can do a simple experiment with an orbit computation program using Newtonian gravity and verify that in a Newtonian model, gravitational interactions must be nearly instantaneous.'' No one is arguing about this. But it's not the point, unless you think Newtonian gravity is right.
The same is true if you consider two oppositely charged particles held in orbit by their electromagnetic interactions. If you try to use Coulomb's law to describe the interaction, you'll find that the electric field must propagate much faster than light. But that's the wrong thing to do, of courseto get a correct description, you need to use the full electromagnetic interaction, including the various velocitydependent terms. If you do that, you find stable orbits even though the field propagates at the speed of light. The same is true in general relativity.
Tom believes, for whatever reason (I'll let him explain), that gravity must propagate much faster than light. But he also knows that general relativity is an extremely successful theory. So he tries to have it both ways, pretending that he can continue to use general relativity and just ``reinterpret'' it. He can't, but rather than learning enough general relativity to understand this, he evidently prefers to repeat claims about general relativity that are simply wrong.
Steve Carlip
In article <9n92gu$ssj$1@woodrow.ucdavis.edu>, Steve Carlip
> 
Tom Van Flandern 
>> 
My conclusion was just the opposite. Fast gravity propagation is consistent with existing physics because nothing in the mathematical theories needs to change, just the interpretations thereof. 
> 
This, of course, is complete nonsense. The field equations of general relativity rigorously and unambiguously imply that no gravitational effect can propagate faster than light. See, for example, R. Low, Class.Quant.Grav.16 (1999) 543. (Tom knows about this paper. His first reaction was to claim that it said something different than it did. The author responded that Tom was wrong. Tom has subsequently simply ignored this and similar proofs, and persists in making statements about the ``mathematical theories'' that are demonstrably wrong.) 
Maybe so but it seems to me that the equivalence principle assumes instantaneous gravitational effects. Using Einstein's thought experiment of a body in an elevator or a rocket, it's easy to see that any change in the acceleration of the elevator's floor instantly affects all bodies anywhere in the elevator. I may be overlooking something here but I'm not one to hold on to my erroneous views in the face of strong evidence to the contrary. If I am wrong, I'll stand corrected.
>>  Anyone can do a simple computer experiment with an orbit computation program and verify that the gravitational interactions must be nearly instantaneous compared to lightspeed to get reasonable orbits. 
> 
What Tom means, of course, is ``Anyone can do a simple experiment with an orbit computation program using Newtonian gravity and verify that in a Newtonian model, gravitational interactions must be nearly instantaneous.'' No one is arguing about this. But it's not the point, unless you think Newtonian gravity is right. 
I think it's a pretty good point. It seems to work pretty damn good by assuming instantaneous gravitational effects. In fact, some bodies in the solar system that were unknown in Newton's time were accurately predicted later using Newtonian gravity.
>  The same is true if you consider two oppositely charged particles held in orbit by their electromagnetic interactions. 
The only problem is that electrons are not in orbit around the nucleus. This model is hopelessly flawed. The most plausible model is that the electrons go right through the nucleus and oscillate back and forth.
>  If you try to use Coulomb's law to describe the interaction, you'll find that the electric field must propagate much faster than light. But that's the wrong thing to do, of courseto get a correct description, you need to use the full electromagnetic interaction, including the various velocitydependent terms. 
Which specific terms are you talking about? Even if you assumed that electrons are really orbiting the nucleus, the distances are so much smaller than astronomical distances as to make the analogy ludicrous.
>  If you do that, you find stable orbits even though the field propagates at the speed of light. The same is true in general relativity. 
>  Tom believes, for whatever reason (I'll let him explain), that gravity must propagate much faster than light. 
He explains the reason on his site. He says that it leads to unstable orbits because, if one assumes a gravitational propagation of c, planetary bodies in orbit would be reacting to the delayed positions of other moving bodies as opposed to their actual positions.
>  But he also knows that general relativity is an extremely successful theory. So he tries to have it both ways, pretending that he can continue to use general relativity and just ``reinterpret'' it. He can't, but rather than learning enough general relativity to understand this, he evidently prefers to repeat claims about general relativity that are simply wrong. 
You are attacking the man rather than his arguments.
Nemesis
Nasty Little Truth About Spacetime Physics: http://home1.gte.net/res02khr/crackpots/notorious.htm
> 
In article <9n92gu$ssj$1@woodrow.ucdavis.edu>, Steve Carlip

>>  The field equations of general relativity rigorously and unambiguously imply that no gravitational effect can propagate faster than light. See, for example, R. Low, Class.Quant.Grav.16 (1999) 543. 
>  Maybe so but it seems to me that the equivalence principle assumes instantaneous gravitational effects. Using Einstein's thought experiment of a body in an elevator or a rocket, it's easy to see that any change in the acceleration of the elevator's floor instantly affects all bodies anywhere in the elevator. 
Only with a somewhat odd definition of ``affect.'' No body in the elevator acts any differently when the floor starts accelerating. No body even knows that the floor is accelerating until, at least, lighht from the floor reaches it. If my lab bench is freely falling inside a (very large) elevator and the floor starts moving, no measurement I can make on the bench will tell me that the floor has started until the lighttravel time from the floor to my bench.
I suggest that you look at Low's paper, which does this all very carefully.
>>  What Tom means, of course, is ``Anyone can do a simple experiment with an orbit computation program using Newtonian gravity and verify that in a Newtonian model, gravitational interactions must be nearly instantaneous.'' No one is arguing about this. But it's not the point, unless you think Newtonian gravity is right. 
>  I think it's a pretty good point. It seems to work pretty damn good by assuming instantaneous gravitational effects. 
Sure. Just as Coulomb's law works pretty damn good in describing interactions between charged bodies, provided that nothing is moving very fast. But we know that Newtonian gravity is just an approximation to general relativity. If we want to know how fast gravity propagates, it's not a very good idea to start with such an approximation, unless you know exactly how the approximation was made.
That's important here. In Newtonian gravity, lightspeed propagation would introduce aberration, and would give new velocitydependent accelerations that aren't seen. But general relativity is *not* just ``Newtonian gravity with lightspeed propagation''it has added velocitydependent effects that just aren't there in the Newtonian theory. And when you actually follow through the math that gives you the Newtonian approximation, you find that these extra velocity dependent terms almost exactly cancel the effects of aberration.
Now, I'm not trying to argue that general relativity is The Truth, and must be believed. If Tom wants to say that he thinks general relativity is wrong, and to develop a replacement, well, good luck to him. But he shouldn't go around claiming that ``nothing in the mathematical theories needs to change,'' and then provide an ``interpretation'' that is directly contradicted by ``the mathematical theories'' that he says don't need to be changed.
>>  If you try to use Coulomb's law to describe the interaction, you'll find that the electric field must propagate much faster than light. But that's the wrong thing to do, of courseto get a correct description, you need to use the full electromagnetic interaction, including the various velocitydependent terms. 
>  Which specific terms are you talking about? Even if you assumed that electrons are really orbiting the nucleus, the distances are so much smaller than astronomical distances as to make the analogy ludicrous. 
I'm not talking about electrons in atoms, but about what Maxwell's theory says about large, classical charged bodies. The specific terms I'm talking about are described in Volume II, Chapter 21 of the Feynman Lecturessee the discussion in section 211.
>>  Tom believes, for whatever reason (I'll let him explain), that gravity must propagate much faster than light. 
>  He explains the reason on his site. He says that it leads to unstable orbits because, if one assumes a gravitational propagation of c, planetary bodies in orbit would be reacting to the delayed positions of other moving bodies as opposed to their actual positions. 
That argument does, indeed, show that if gravity were described by Newton's theory, it would have to propagate much faster than light. It says nothing per se about general relativity.
>>  But he also knows that general relativity is an extremely successful theory. So he tries to have it both ways, pretending that he can continue to use general relativity and just ``reinterpret'' it. He can't, but rather than learning enough general relativity to understand this, he evidently prefers to repeat claims about general relativity that are simply wrong. 
>  You are attacking the man rather than his arguments. 
I apologize. It comes from the frustration of having explained Tom's errors over and over again, only to have him repeat them.
Once again, I have no objection to Tom's not liking general relativity, and trying to come up with an alternative in which gravity is more like Newton's gravity and propagates much faster than light. But I *do* object to his making false claims about what ``the mathematical theories'' do and do not say, and ignoring corrections from people who do, in fact, know much more about the details of general relativity than he does.
Steve Carlip
In article <9nbt1e$n3r$1@woodrow.ucdavis.edu>, Steve Carlip
> 
Nemesis 
>> 
In article <9n92gu$ssj$1@woodrow.ucdavis.edu>, Steve Carlip

> 
>>> 
The field equations of general relativity rigorously and unambiguously imply that no gravitational effect can propagate faster than light. See, for example, R. Low, Class.Quant.Grav.16 (1999) 543. 
> 
>> 
Maybe so but it seems to me that the equivalence principle assumes instantaneous gravitational effects. Using Einstein's thought experiment of a body in an elevator or a rocket, it's easy to see that any change in the acceleration of the elevator's floor instantly affects all bodies anywhere in the elevator. 
> 
Only with a somewhat odd definition of ``affect.'' No body in the elevator acts any differently when the floor starts accelerating. No body even knows that the floor is accelerating until, at least, lighht from the floor reaches it. If my lab bench is freely falling inside a (very large) elevator and the floor starts moving, no measurement I can make on the bench will tell me that the floor has started until the lighttravel time from the floor to my bench. 
I agree that "affects" was a poor choice of words on my part given that relativists believe literally in the PE and assume that falling bodies are not accelerating. What I meant to say (I am surprised you did not get my meaning) was that, if the floor suddenly accelerates, it does so *instantly*, relative to all bodies in the elevator regardless of the floor's distance from any given body.
IOW, there is no delay dictated by the speed of light that I can see. It seems that if there really is an equivalence (I have no reason to doubt that there is other than that I view it as an inverse equivalence) between acceleration and gravity, it is obvious that gravitational changes are "felt" instantly everywhere.
To PE or not to PE, that is the question. :)
>  I suggest that you look at Low's paper, which does this all very carefully. 
If it treats the subject the way you do in your online essay "Does Gravity Travel at the Speed of Light?" I am afraid I'll have to pass. I found your essay unconvincing. One is left with the impression that GR magically cancels gravitational propagation delays. You do not explain the physical mechanism. One does not cancel a propagation delay with math.
>>>  What Tom means, of course, is ``Anyone can do a simple experiment with an orbit computation program using Newtonian gravity and verify that in a Newtonian model, gravitational interactions must be nearly instantaneous.'' No one is arguing about this. But it's not the point, unless you think Newtonian gravity is right. 
> 
>> 
I think it's a pretty good point. It seems to work pretty damn good by assuming instantaneous gravitational effects. 
> 
Sure. Just as Coulomb's law works pretty damn good in describing interactions between charged bodies, provided that nothing is moving very fast. But we know that Newtonian gravity is just an approximation to general relativity. If we want to know how fast gravity propagates, it's not a very good idea to start with such an approximation, unless you know exactly how the approximation was made. 
It's just an inverse square approximation that works really well by assuming instant gravitational changes everywhere in the system. The only thing that seems to be missing is that it does not take time dilation into consideration, an "oversight" that Newton can be forgiven for.
>  That's important here. In Newtonian gravity, lightspeed propagation would introduce aberration, and would give new velocitydependent accelerations that aren't seen. But general relativity is *not* just ``Newtonian gravity with lightspeed propagation'' 
Apparently not since adding light speed propagation to Newtonian gravity destabilizes the system, which what Van Flandern correctly showed. But, as I mentioned above, I believe that adding "time dilation" to Newtonian gravity would probably correct any deviation from GR.
>  it has added velocitydependent effects that just aren't there in the Newtonian theory. And when you actually follow through the math that gives you the Newtonian approximation, you find that these extra velocity dependent terms almost exactly cancel the effects of aberration. 
Please don't tell me to follow the math because that would make your stance highly suspect. If it cannot be explained it in plain everyday language, it is snake oil from my point of view. As I explained above, the PE assumes instant gravity. If you feel that I am wrong about the PE, I am ready to listen to your counterargument.
>  Now, I'm not trying to argue that general relativity is The Truth, and must be believed. If Tom wants to say that he thinks general relativity is wrong, and to develop a replacement, well, good luck to him. But he shouldn't go around claiming that ``nothing in the mathematical theories needs to change,'' and then provide an ``interpretation'' that is directly contradicted by ``the mathematical theories'' that he says don't need to be changed. 
[cut]
>>>  Tom believes, for whatever reason (I'll let him explain), that gravity must propagate much faster than light. 
> 
>> 
He explains the reason on his site. He says that it leads to unstable orbits because, if one assumes a gravitational propagation of c, planetary bodies in orbit would be reacting to the delayed positions of other moving bodies as opposed to their actual positions. 
> 
That argument does, indeed, show that if gravity were described by Newton's theory, it would have to propagate much faster than light. It says nothing per se about general relativity. 
I don't see how Newtonian gravity can be so accurate by assuming instant propagation while GR assumes a propagation of c that magically gets canceled out. How else can one cancel a propagation delay? Sorry, mathematical magic is not an explanation. Nothing less than a physical explanation will do.
>>>  But he also knows that general relativity is an extremely successful theory. So he tries to have it both ways, pretending that he can continue to use general relativity and just ``reinterpret'' it. He can't, but rather than learning enough general relativity to understand this, he evidently prefers to repeat claims about general relativity that are simply wrong. 
> 
>> 
You are attacking the man rather than his arguments. 
> 
I apologize. It comes from the frustration of having explained Tom's errors over and over again, only to have him repeat them. Once again, I have no objection to Tom's not liking general relativity, and trying to come up with an alternative in which gravity is more like Newton's gravity and propagates much faster than light. But I *do* object to his making false claims about what ``the mathematical theories'' do and do not say, and ignoring corrections from people who do, in fact, know much more about the details of general relativity than he does. 
IMO, there is no propagation at all and this why the equivalence principle works so well. I am convinced that gravity is a nonlocal effect mitigated by the principle of energy conservation, which is a nonlocal principle.
Nemesis
Nasty Little Truth About Spacetime Physics: http://home1.gte.net/res02khr/crackpots/notorious.htm
> 
IMO, there is no propagation at all and this why the equivalence principle works so well. I am convinced that gravity is a nonlocal effect mitigated by the principle of energy conservation, which is a nonlocal principle. 
Nemesis, Read: http://www.cnde.iastate.edu/staff/swormley/eo/bkr/bkr.95.12
Starts down about 1/5 of the page.
To All Just a thought. Could gravity be what QM refers to as the fabric of space?Could we think of this like a spider web with all the strands of the web connecting all of the universe's energies and particles. This would answer "action at a distance".Wave function". In every book it tells us all is connected. A spider knows instantly where his prey has hit the web by the vibrations of the strings. This could play well in the "string theory" Best regards to all herb
Speed of G is time . Time dont chang space dose. Time is the only answer you have . I did not read any of the post on this but Im quite shure they are just stoopid .
Steve Carlip (carlip@dirac.ucdavis.edu) writes:
>>  [tvf]: Fast gravity propagation is consistent with existing physics because nothing in the mathematical theories needs to change, just the interpretations thereof. 
>  [sc]: This, of course, is complete nonsense. The field equations of general relativity rigorously and unambiguously imply that no gravitational effect can propagate faster than light. See, for example, R. Low, Class.Quant.Grav.16 (1999) 543. 
Allow me to provide a simple counterexample that exemplifies this whole discussion. When we look at a binary star in the sky, we see the components where they were in their mutual orbits when their light left the stars, not where they are now. If we could detect their gravity, would that agree with where we see the light from the stars, or with where the stars are now? The former would indicate a speed of gravity equal to the speed of light, and the latter would indicate an instantaneous speed of gravity. Agreed?
Here's the setup to answer this question. Consider the gravitational field of a binary star with orbital period P, as measured at a field point in the orbital plane of the binary and a distance R away from the binary's center of mass. Consider only large distances R > cP, where c is the speed of light. Then an observer at distance R will see light from the retarded positions of the binary stars as they were one lighttime (R/c) ago. Those orbital positions will differ from the actual instantaneous position of the stars by more than one complete revolution, so the retarded and instantaneous orbital phases of the stars will generally be quite different.
At the observer, the strength of the gravitational field oscillates up and down as the binary stars orbit one another. The combined field strength has a maximum when the binary stars are inline with the observer, and a minimum when they are at 90 degrees to the observer. Let's ask the GR equations of motion (e.g., those on p. 1095 of MTW) whether the gravitationa l field maxima at the observer are in synch with the instantaneous positions of the binary stars, or with their retarded positions. Surely, if the gravitational field propagates at lightspeed, the gravitational field maxima and minima will be in synch with the observed, retarded positions of the stars. But if and only if the field changes propagate with infinite speed (in GR) will the field for an arbitrarily distant observer remain in synch with the instantaneous positions of the stars. Are we still agreed so far?
Now we turn to the answer given by the GR equations of motion. MTW equation (39.64) has a Newtonian part factored by the bracket [1  (expr)], with two additional terms added on at the end. However, (expr) is an expression containing noncumulative terms that are very small compared with unity for ordinary binary stars, and therefore can be neglected here because we seek only the phase of the main field, and don't care about small perturbations thereof that cannot appreciably affect phase. To show that these terms are small compared to unity, note that every term contains either a potential or a velocity squared, with an implied c^2 in the denominator that makes the units correct. However, potential is generally of the same order as v^2, and (v/c)^2 is negligible compared with unity for our binary star and observer. In any case, nothing in the bracket can build up to produce an arbitrarily large phase displacement.
Next, we examine the last two addon terms. The first of these is the Newtonian acceleration multiplied by (v/c)^2, and the second is the Newtonian acceleration multiplied by a potential of the same order as (v/c)^2. So both of these are negligible by the same reasoning as before, and cannot appreciably affect orbital phase. Indeed, it was obvious at the outset that nothing in the equations of motion is related to the speed of light to the first power or the lighttime from the binary stars. We are then left with only the Newtonian acceleration to represent the gravitational field of the binaries at a great distance. This is reasonable and meets other known constraints because GR is supposed to approach Newtonian gravity in the weakfield, lowvelocity limit, which this example certainly represents.
But then we have the result that the distant field produces accelerations in synch with the instantaneous positions of the binaries, not their retarded positions in agreement with the prediction of Newtonian gravity. Therefore, in these GR equations of motion, changes in gravitational fields are propagated to great distances instantly.
So is there an error in my analysis? Is something important missing from the GR equations of motion even for this weakfield, lowvelocity case? Does GR not really approach the Newtonian approximation in the limit? . Or does this really illustrate gravitational field changes arriving at a distant target instantaneously in GR?
This is the most important point I would like to address to you in this message. The rest of this deals with details of lesser importance.
>  [sc]: Tom ... persists in making statements about the ``mathematical theories'' that are demonstrably wrong. 
Then why are you having such a difficult time demonstrating these errors, both here and in our private exchanges? In my last private message to you, I reaffirmed my openness to any reasonable argument showing an error I have made, with neutral parties as the judges, and asked you to make the same commitment to finding the truth, wherever it may lie. I have not yet heard that you are open to this suggestion.
>>  [tvf]: Anyone can do a simple computer experiment with an orbit computation program and verify that the gravitational interactions must be nearly instantaneous compared to lightspeed to get reasonable orbits. 
>  [sc]: What Tom means, of course, is ``Anyone can do a simple experiment with an orbit computation program using Newtonian gravity and verify that in a Newtonian model, gravitational interactions must be nearly instantaneous.'' No one is arguing about this. But it's not the point, unless you think Newtonian gravity is right. 
I was speaking of computer experiments using the GR equations of motion. I have corrected you on this misrepresentation before. This whole discussion is about the speed of gravity in GR and in reality, not its speed in Newtonian gravity, over which there is no controversy. Everybody agrees it is infinite.
Now that you know what I meant, that anyone can do simple computer experiments using GR equations of motion with an orbit computation program and verify that the gravitational interactions must be nearly instantaneous compared to lightspeed to get reasonable orbits, do you agree or disagree? Assuming you agree (many people have done this), how do you explain this with your interpretation of GR?
>  [sc]: Tom believes, for whatever reason (I'll let him explain), that gravity must propagate much faster than light. 
If we consider that (1) all six existing experiments indicate gravity propagates faster than light (Phys.Lett.A, v. 250, pp. 111, 1998) while no existing experiment sets this speed as slow as c; (2) the speed of gravitational waves (which is c) must not be mixed up with that of changes in gravitational fields; and (3) Lorentzian relativity is experimentally viable and allows fasterthanlight propagation in forward time (no causality violations); it then seems reasonable to conclude that gravity propagating at speed c is the "belief" unbacked by experiment, and gravity propagating at speeds faster than c is the reasoned deduction from the experimental evidence.
>  [sc]: Now, I'm not trying to argue that general relativity is The Truth, and must be believed. If Tom wants to say that he thinks general relativity is wrong, and to develop a replacement, well, good luck to him. But he shouldn't go around claiming that ``nothing in the mathematical theories needs to change,'' and then provide an ``interpretation'' that is directly contradicted by ``the mathematical theories'' that he says don't need to be changed. 
If we start with Newtonian gravity propagating at infinite speed, and add a refractive medium to produce the lightbending, redshift, radar timedelay, and pericenter advance effects, we get the same equations of motion as GR gives (except for a few small terms of no relevance here). Many authors (cited in my papers) have previously shown this. How, exactly, do you propose to make this model mathematically different? And if it is essentially the same mathematically, wouldn't if be unfair to represent it as a completely new theory with no credit to Einstein?
>  [sc]: I *do* object to [Tom's] making false claims about what ``the mathematical theories'' do and do not say, and ignoring corrections from people who do, in fact, know much more about the details of general relativity than he does. 
Are you suggesting that I (or anyone) should accept a point just because an expert says it is so? The "appeal to authority" is a tactic of the "unscientific method", as described in Chapter 20 of my book. And the history of science is filled with examples of where all the "experts" were wrong. So if you intend to defend a position under challenge, you must do the work of reasoning to that position, just as I must do the work of reasoning both that the standard interpretation has errors and that a replacement interpretation does not.
Here is a description of the precise point where the two of us differ. Steve notes correctly that the potential field around a mass is treated as a "retarded potential" in GR. In essence, potential is a scalar equal to M/r at a field point a distance r from a source mass M. A "retarded potential" is M/rv(r/c), where bold characters are vectors, so the denominator represents the distance from the source mass one lighttime ago. Then the scalar value of this retarded potential field is evaluated at every fixed field point in the space around the source mass; and those potential values are then used to calculate the gradient of the field (effectively, the slope of the potential) that gives rise to gravitational force.
However, this picture contains a serious error of physics that is hidden by using Minkowski diagrams, 4space, and the geometric interpretation of GR. If the "field point" is not fixed, but rather is a moving body such as an orbiting test particle, its motion changes the direction of the gradient of the potential field, and therefore the direction of the gravitational force applied. This is for the same reason that the direction of a light source is different as seen from a moving body than from a fixed one, the same reason that radiation pressure slightly retards the forward motion of a particle in a circular orbit around a star, and the same reason that an arrow always moving radially outward from the Sun will cross the cabin of a passing train diagonally rather than radially. This effect is called "aberration", and simply means that the apparent direction of the source and of any force it transmits are altered toward the direction of the particle's relative motion by the angle (v/V), where v is the particle's speed relative to the source and V is the arrow/photon/wave/field change's propagation speed. Minkowski diagrams hide this effect because the effect is visible only by comparing the perspectives of two different frames of reference at once  something the "curved spacetime" interpretation and 4space are illsuited to doing.
In physics, aberration necessarily exists in reality for any entity propagating linearly from a monopole source to a relatively moving target at a finite speed. Indeed, it is essentially just (v/V) in radians, which obviously exists for all v > 0 and 0 < V < infinity. Steve cites convenient cancellation of aberration by a deus ex machina in the math of GR that has no other need or purpose to exist than to cancel aberration. But as my binary star and computer experiment examples both show, this mechanism cannot avoid the common sense meaning of "gravity propagates faster than light" because changes in gravitational fields arrive at the target long before photons that show a picture of what is happening back at the source arrive.
and "Nemesis"
>  I may be overlooking something here but I'm not one to hold on to my erroneous views in the face of strong evidence to the contrary. If I am wrong, I'll stand corrected. 
You made some very good points in your messages, and this is an admirable scientific stance. I would go one step further. Being shown the errors in our present thinking is one of the best ways by which can we hope to expand our understanding and grow intellectually. It is something to look forward to, even if error should not be conceded lightly. Tom
Tom Van Flandern  Washington, DC  see our web site on replacement astronomy research at http://metaresearch.org
In article <9niu04$gnp$1@bob.news.rcn.net>, "Tom Van Flandern"
> 
and "Nemesis" 
>> 
I may be overlooking something here but I'm not one to hold on to my erroneous views in the face of strong evidence to the contrary. If I am wrong, I'll stand corrected. 
> 
You made some very good points in your messages, and this is an admirable scientific stance. I would go one step further. Being shown the errors in our present thinking is one of the best ways by which can we hope to expand our understanding and grow intellectually. It is something to look forward to, even if error should not be conceded lightly. Tom 
I appreciate your posts and your steadfastness in sticking with what you think is right. All too often we encounter a condescending group of people who think that only they are the legitimate oracle of truth and that the rest of the world has neither the right nor the capability to think for itself. I am a firm believer in both freedom of thought and speech.
You seem to favor the hypothesis that gravitational changes propagate at a fixed speed, albeit one that is much faster than c. This is where you and I disagree. Both the principle of equivalence and Newton's gravity equation assume that there is no propagation taking place. Changes in gravity are felt instantly by all bodies regardless of distance. It is for this reason that I am convinced that gravity is a nonlocal phenomenon. I believe that Newtonian gravity is essentially right and needs only minor corrections having to do with "time dilation."
Having said that, I don't believe for a second that there is a curved spacetime in which bodies are following their geodesics. The obvious reason is that nothing can move in spacetime. Therefore the answer to what causes gravity must be found somewhere else.
The locality of the spacetime of relativity is in direct contradiction with the nonlocal nature of gravity. Ironically, even though classical physics denies nonlocality, it turns out that nonlocality was an essential part of it from day one, witness Newton's instant gravitational effects. IMO, the only way to explain all this magic is by questioning our most cherished assumptions. I choose to question our concept of space or distance. You, OTOH, choose to believe that things can move much faster than c. I disagree for various reasons that I am not going to bore you with.
Although I belive that gravity effects are instantaneous, I do not make the mistake of thinking that everything about gravity is nonlocal. There is an aspect of it that can be explained only by assuming some form of radiation that emanates from bodies and propagates at c. I am talking about the inverse square nature of the field strength. I could go further but I think my post is already longer than it should be.
Nemesis
Nasty Little Truth About Spacetime Physics: http://home1.gte.net/res02khr/crackpots/notorious.htm
> 
Although I belive that gravity effects are instantaneous, I do not make the mistake of thinking that everything about gravity is nonlocal. There is an aspect of it that can be explained only by assuming some form of radiation that emanates from bodies and propagates at c. I am talking about the inverse square nature of the field strength. I could go further but I think my post is already longer than it should be. 
Ref: http://hepweb.rl.ac.uk/ppUK/PhysFAQ/grav_speed.html
updated 29Apr1998 by Steve Carlip, Matthew Wiener and Geoffrey Landis original by Steve Carlip
Does Gravity Travel at the Speed of Light?
To begin with, the speed of gravity has not been measured directly in the laboratorythe gravitational interaction is too weak, and such an experiment is beyond present technological capabilities. The "speed of gravity" must therefore be deduced from astronomical observations, and the answer depends on what model of gravity one uses to describe those observations.
In the simple Newtonian model, gravity propagates instantaneously: the force exerted by a massive object points directly toward that object's present position. For example, even though the Sun is 500 light seconds from the Earth, Newtonian gravity describes a force on Earth directed towards the Sun's position "now," not its position 500 seconds ago. Putting a "light travel delay" (technically called "retardation") into Newtonian gravity would make orbits unstable, leading to predictions that clearly contradict Solar System observations.
In general relativity, on the other hand, gravity propagates at the speed of light; that is, the motion of a massive object creates a distortion in the curvature of spacetime that moves outward at light speed. This might seem to contradict the Solar System observations described above, but remember that general relativity is conceptually very different from Newtonian gravity, so a direct comparison is not so simple. Strictly speaking, gravity is not a "force" in general relativity, and a description in terms of speed and direction can be tricky. For weak fields, though, one can describe the theory in a sort of Newtonian language. In that case, one finds that the "force" in GR is not quite central  it does not point directly towards the source of the gravitational field  and that it depends on velocity as well as position. The net result is that the effect of propagation delay is almost exactly cancelled, and general relativity very nearly reproduces the Newtonian result.
This cancellation may seem less strange if one notes that a similar effect occurs in electromagnetism. If a charged particle is moving at a constant velocity, it exerts a force that points toward its present position, not its retarded position, even though electromagnetic interactions certainly move at the speed of light. Here, as in general relativity, subtleties in the nature of the interaction "conspire" to disguise the effect of propagation delay. It should be emphasized that in both electromagnetism and general relativity, this effect is not put in ad hoc but comes out of the equations. Also, the cancellation is nearly exact only for constant velocities. If a charged particle or a gravitating mass suddenly accelerates, the change in the electric or gravitational field propagates outward at the speed of light.
Since this point can be confusing, it's worth exploring a little further, in a slightly more technical manner. Consider two bodies  call them A and B  held in orbit by either electrical or gravitational attraction. As long as the force on A points directly towards B and vice versa, a stable orbit is possible. If the force on A points instead towards the retarded (propagationtimedelayed) position of B, on the other hand, the effect is to add a new component of force in the direction of A's motion, causing instability of the orbit. This instability, in turn, leads to a change in the mechanical angular momentum of the AB system. But total angular momentum is conserved, so this change can only occur if some of the angular momentum of the AB system is carried away by electromagnetic or gravitational radiation.
Now, in electrodynamics, a charge moving at a constant velocity does not radiate. (Technically, the lowest order radiation is dipole radiation, which depends on the acceleration.) So to the extent that that A's motion can be approximated as motion at a constant velocity, A cannot lose angular momentum. For the theory to be consistent, there must therefore be compensating terms that partially cancel the instability of the orbit caused by retardation. This is exactly what happens; a calculation shows that the force on A points not towards B's retarded position, but towards B's "linearly extrapolated" retarded position. Similarly, in general relativity, a mass moving at a constant acceleration does not radiate (the lowest order radiation is quadrupole), so for consistency, an even more complete cancellation of the effect of retardation must occur. This is exactly what one finds when one solves the equations of motion in general relativity.
While current observations do not yet provide a direct modelindependent measurement of the speed of gravity, a test within the framework of general relativity can be made by observing the binary pulsar PSR 1913+16. The orbit of this binary system is gradually decaying, and this behavior is attributed to the loss of energy due to escaping gravitational radiation. But in any field theory, radiation is intimately related to the finite velocity of field propagation, and the orbital changes due to gravitational radiation can equivalently be viewed as damping caused by the finite propagation speed. (In the discussion above, this damping represents a failure of the "retardation" and "noncentral, velocitydependent" effects to completely cancel.)
The rate of this damping can be computed, and one finds that it depends sensitively on the speed of gravity. The fact that gravitational damping is measured at all is a strong indication that the propagation speed of gravity is not infinite. If the calculational framework of general relativity is accepted, the damping can be used to calculate the speed, and the actual measurement confirms that the speed of gravity is equal to the speed of light to within 1%. (Measurements of at least one other binary pulsar system, PSR B1534+12, confirm this result, although so far with less precision.)
Are there future prospects for a direct measurement of the speed of gravity? One possibility would involve detection of gravitational waves from a supernova. The detection of gravitational radiation in the same time frame as a neutrino burst, followed by a later visual identification of a supernova, would be considered strong experimental evidence for the speed of gravity being equal to the speed of light. However, unless a very nearby supernova occurs soon, it will be some time before gravitational wave detectors are expected to be sensitive enough to perform such a test.
See also the section on gravitational radiation
References
There seems to be no nontechnical reference on this subject. For a technical reference, see
T. Damour, in Three Hundred Years of Gravitation, S.W. Hawking and W. Israel, editors (Cambridge Univ. Press, 1987)
For a good reference to the electromagnetic case, see
R.P. Feynman, R.B. Leighton, and M. Sands, The Feynman Lectures on Physics, chapter II21 (AddisonWesley, 1989)
> 
A spider knows instantly where his prey has hit the web by the vibrations of the strings. This could play well in the "string theory" Best regards to all herb 
No, the spider knows only after the mechanical wave has propagated along the web between the trapped prey and the spidera finite time interval.
In article <3B9DA380.EEDF0945@cnde.iastate.edu>, Sam Wormley
>  Nemesis wrote: 
>> 
Although I belive that gravity effects are instantaneous, I do not make the mistake of thinking that everything about gravity is nonlocal. There is an aspect of it that can be explained only by assuming some form of radiation that emanates from bodies and propagates at c. I am talking about the inverse square nature of the field strength. I could go further but I think my post is already longer than it should be. 
> 
> 
updated 29Apr1998 by Steve Carlip, Matthew Wiener and Geoffrey Landis original by Steve Carlip 
I've already read this article and I disagree with it. I don't care what the GR experts believe in. I like to do my own thinking, thank you very much. The principle of equivalence squarely and irrefutably contradicts the notion that gravity propagates at the speed of light. Besides, if gravity effects were not instantaneous, Newtonian gravity would be completely useless. As it is, it's almost perfect. Its only shortfall is that it does not take time dilation into consideration, something for which Sir Isaac can be forgiven.
Nemesis
Nasty Little Truth About Spacetime Physics: http://home1.gte.net/res02khr/crackpots/notorious.htm
> 
In article <3B9DA380.EEDF0945@cnde.iastate.edu>, Sam Wormley

>> 
Nemesis wrote: 
>>> 
Although I belive that gravity effects are instantaneous, I do not make the mistake of thinking that everything about gravity is nonlocal. There is an aspect of it that can be explained only by assuming some form of radiation that emanates from bodies and propagates at c. I am talking about the inverse square nature of the field strength. I could go further but I think my post is already longer than it should be. 
>> 
Ref: http://math.ucr.edu/home/baez/physics/Relativity/SR/grav_speed.html updated 29Apr1998 by Steve Carlip, Matthew Wiener and Geoffrey Landis original by Steve Carlip 
> 
I've already read this article and I disagree with it. I don't care what the GR experts believe in. I like to do my own thinking, thank you very much. The principle of equivalence squarely and irrefutably contradicts the notion that gravity propagates at the speed of light. Besides, if gravity effects were not instantaneous, Newtonian gravity would be completely useless. As it is, it's almost perfect. Its only shortfall is that it does not take time dilation into consideration, something for which Sir Isaac can be forgiven. 
"That one body may act upon another at a distance through a vacuum, without the mediation of any thing else, by and through which their action and force may be conveyed from one to the other, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it."
So, if you think gravity propagates instantaneously, take comfort in the knowledge that Sir Isaac has reached down through the centuries simply to call you a complete jerk.
Regards
 Charles Francis
In article <223943B9A1A42130@storefull131.iap.bryant.webtv.net>,
G=EMC^2 Glazier
>  To All Just a thought. Could gravity be what QM refers to as the fabric of space?Could we think of this like a spider web with all the strands of the web connecting all of the universe's energies and particles. This would answer "action at a distance".Wave function". In every book it tells us all is connected. A spider knows instantly where his prey has hit the web by the vibrations of the strings. 
I have not heard that QM refers to the "fabric of space", but this is basically true. Gravity is simply the rate of change of velocity of an inertial body whose position is being monitored by another inertial body. It arises from measurement of position, and measurement of position could be described as your "spiders web". The speed of the effect being transmitted with the messages required to measure position, i.e. light speed.
>  This could play well in the "string theory" Best regards to all herb 
No. String theory is quite different, and takes for granted the things it supposedly sets out to explain.
Regards
 Charles Francis
In article <6v3jptom0onje5sh7bmjt5nj7buioheart@4ax.com>, Nemesis
> 
In article <9nbt1e$n3r$1@woodrow.ucdavis.edu>, Steve Carlip

>> 
Nemesis 
>>> 
In article <9n92gu$ssj$1@woodrow.ucdavis.edu>, Steve Carlip

>> 
>>>> 
The field equations of general relativity rigorously and unambiguously imply that no gravitational effect can propagate faster than light. 
Steve, What we want are intuitive reasons to see that this is true, not obtuse equations. I believe that there is an intuitive reason for it. Namely that the metric is determined by two way photon exchange, and so changes in the metric are transmitted by photons, at light speed.
>>>  Maybe so but it seems to me that the equivalence principle assumes instantaneous gravitational effects. Using Einstein's thought experiment of a body in an elevator or a rocket, it's easy to see that any change in the acceleration of the elevator's floor instantly affects all bodies anywhere in the elevator. 
Actually it is easy to see that it doesn't. The change in acceleration of the elevator's floor is not detectable by an inertial body at the centre of the elevator until light passes between the two. Fairly conclusively illustrating the speed of the gravitational effect.
>  I agree that "affects" was a poor choice of words on my part given that relativists believe literally in the PE and assume that falling bodies are not accelerating. What I meant to say (I am surprised you did not get my meaning) was that, if the floor suddenly accelerates, it does so *instantly*, relative to all bodies in the elevator regardless of the floor's distance from any given body. 
I think we got that, but it is simply not true. the acceleration is change in position, and position is just a number determined by photon exchange, so position cannot change until the photons can return.
> 
IOW, there is no delay dictated by the speed of light that I can see. 
Can you see it now?
> 
If it treats the subject the way you do in your online essay "Does Gravity Travel at the Speed of Light?" I am afraid I'll have to pass. I found your essay unconvincing. One is left with the impression that GR magically cancels gravitational propagation delays. You do not explain the physical mechanism. One does not cancel a propagation delay with math. 
The way gr is normally done does not explain physical mechanisms. The cancellation does take place in the math, its just that math does not explain physics, it only tells us what is true of the answer. Someone following the math of gr will definitely know the right answer, but they will not definitely understand the physical reason for it.
>  It's just an inverse square approximation that works really well by assuming instant gravitational changes everywhere in the system. The only thing that seems to be missing is that it does not take time dilation into consideration, an "oversight" that Newton can be forgiven for. 
Yes. But there is more to time dilation than we find in special relativity. When we use time dilation to adjust Newton's laws for flat space then we find the accelerations due to gravity, without needing to postulate anything else. That is basically what gr says.
>  But, as I mentioned above, I believe that adding "time dilation" to Newtonian gravity would probably correct any deviation from GR. 
As I say, adding time dilation to Newtonian flat space exactly reproduces GR and explains Newtonian gravity.
>  IMO, there is no propagation at all and this why the equivalence principle works so well. I am convinced that gravity is a nonlocal effect . 
The fundamental point is that gravity just arises from measurement of position, and measurement of position requires two way messaging. Messaging is a nonlocal thing to do, by definition. So you are right, gravity is a nonlocal effect. As is position itself.
Regards
 Charles Francis
In article
> 
In article <6v3jptom0onje5sh7bmjt5nj7buioheart@4ax.com>, Nemesis

>> 
In article <9nbt1e$n3r$1@woodrow.ucdavis.edu>, Steve Carlip

>>> 
Nemesis 
>>>> 
In article <9n92gu$ssj$1@woodrow.ucdavis.edu>, Steve Carlip

>>>  [cut] 
>>>>  Maybe so but it seems to me that the equivalence principle assumes instantaneous gravitational effects. Using Einstein's thought experiment of a body in an elevator or a rocket, it's easy to see that any change in the acceleration of the elevator's floor instantly affects all bodies anywhere in the elevator. 
> 
Actually it is easy to see that it doesn't. The change in acceleration of the elevator's floor is not detectable by an inertial body at the centre of the elevator until light passes between the two. Fairly conclusively illustrating the speed of the gravitational effect. 
The point I wanted to make is that all bodies start accelerating toward the elevator floor immediately when the floor begins accelerating. In the case of gravity, for the equivalence to hold, all bodies must feel a change in a gravitational field instantly.
>>  I agree that "affects" was a poor choice of words on my part given that relativists believe literally in the PE and assume that falling bodies are not accelerating. What I meant to say (I am surprised you did not get my meaning) was that, if the floor suddenly accelerates, it does so *instantly*, relative to all bodies in the elevator regardless of the floor's distance from any given body. 
> 
I think we got that, 
Others may have gotten it but apparently you didn't.
>  but it is simply not true. 
So say you but it's obviously true.
>  the acceleration is change in position, and position is just a number determined by photon exchange, so position cannot change until the photons can return. 
Position is a number determined by photon exchange *only* according to your silly theory. When something accelerates, it does so relative to all objects in the universe,instantly, your opinion to the contrary notwithstanding.
>>  IOW, there is no delay dictated by the speed of light that I can see. 
> 
Can you see it now? 
How can I see something that is a figment of your imagination?
>>  If it treats the subject the way you do in your online essay "Does Gravity Travel at the Speed of Light?" I am afraid I'll have to pass. I found your essay unconvincing. One is left with the impression that GR magically cancels gravitational propagation delays. You do not explain the physical mechanism. One does not cancel a propagation delay with math. 
> 
The way gr is normally done does not explain physical mechanisms. The cancellation does take place in the math, its just that math does not explain physics, it only tells us what is true of the answer. Someone following the math of gr will definitely know the right answer, but they will not definitely understand the physical reason for it. 
There is no physics behind it only because gravitational effects are instantaneous and are mediated by the nonlocal application of conservation principles.
>>  It's just an inverse square approximation that works really well by assuming instant gravitational changes everywhere in the system. The only thing that seems to be missing is that it does not take time dilation into consideration, an "oversight" that Newton can be forgiven for. 
> 
Yes. But there is more to time dilation than we find in special relativity. 
I was referring to gravitational time dilation in strong fields *and* SRtype dilation of moving bodies.
>  When we use time dilation to adjust Newton's laws for flat space then we find the accelerations due to gravity, without needing to postulate anything else. That is basically what gr says. 
Not according to Carlip et al since they keep insisting that gravity propagates at c. Adjusting Newton's laws to include time dilation does not change the fact that gravitational effects are instantaneous.
>>  But, as I mentioned above, I believe that adding "time dilation" to Newtonian gravity would probably correct any deviation from GR. 
> 
As I say, adding time dilation to Newtonian flat space exactly reproduces GR and explains Newtonian gravity. 
What the point of repeating what I wrote?
>>  IMO, there is no propagation at all and this why the equivalence principle works so well. I am convinced that gravity is a nonlocal effect . 
> 
The fundamental point is that gravity just arises from measurement of position, and measurement of position requires two way messaging. 
Gravity does not arise from measurement of position since particles do not measure one another's position.
>  Messaging is a nonlocal thing to do, by definition. So you are right, gravity is a nonlocal effect. As is position itself. 
Messaging is nonlocal? Since when? Nonlocal phenomena is specifically not about messaging since messaging must happen at the speed of light. Entangled particles do not communicate their states via messages. That is the whole point of nonlocality. You are a truly confused man, Francis.
Nemesis
Nasty Little Truth About Spacetime Physics: http://home1.gte.net/res02khr/crackpots/notorious.htm
In article
> 
In article 
>> 
In article <3B9DA380.EEDF0945@cnde.iastate.edu>, Sam Wormley

>>> 
Nemesis wrote: 
>>>> 
Although I belive that gravity effects are instantaneous, I do not make the mistake of thinking that everything about gravity is nonlocal. There is an aspect of it that can be explained only by assuming some form of radiation that emanates from bodies and propagates at c. I am talking about the inverse square nature of the field strength. I could go further but I think my post is already longer than it should be. 
>>> 
http://hepweb.rl.ac.uk/ppUK/PhysFAQ/grav_speed.html updated 29Apr1998 by Steve Carlip, Matthew Wiener and Geoffrey Landis original by Steve Carlip 
>> 
I've already read this article and I disagree with it. I don't care what the GR experts believe in. I like to do my own thinking, thank you very much. The principle of equivalence squarely and irrefutably contradicts the notion that gravity propagates at the speed of light. Besides, if gravity effects were not instantaneous, Newtonian gravity would be completely useless. As it is, it's almost perfect. Its only shortfall is that it does not take time dilation into consideration, something for which Sir Isaac can be forgiven. 
> 
Sir Isaac obviously thought its shortfalls were much more serious: "That one body may act upon another at a distance through a vacuum, without the mediation of any thing else, by and through which their action and force may be conveyed from one to the other, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it." So, if you think gravity propagates instantaneously, take comfort in the knowledge that Sir Isaac has reached down through the centuries simply to call you a complete jerk. 
I am sure he would say that I was wrong but I doubt that he would call me a complete jerk since his own equation assumes instantaneous action at a distance. However, once shown the evidence for nonlocality (really nonspatiality), he would have to agree with me that distance/space is an illusion and that therefore, there is no contradiction in saying that a principle can be applied instantly even over what you think are vast distances.
The "complete jerk" part is your wanting to ascribe to Newton your personal emotional frustration at not being regarded as the great physicist that you want others to think you are. Oh well!
Nemesis
Nasty Little Truth About Spacetime Physics: http://home1.gte.net/res02khr/crackpots/notorious.htm
> 
In article 
>>>  I've already read this article and I disagree with it. I don't care what the GR experts believe in. I like to do my own thinking, thank you very much. The principle of equivalence squarely and irrefutably contradicts the notion that gravity propagates at the speed of light. Besides, if gravity effects were not instantaneous, Newtonian gravity would be completely useless. As it is, it's almost perfect. Its only shortfall is that it does not take time dilation into consideration, something for which Sir Isaac can be forgiven. 
>> 
Sir Isaac obviously thought its shortfalls were much more serious: "That one body may act upon another at a distance through a vacuum, without the mediation of any thing else, by and through which their action and force may be conveyed from one to the other, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it." So, if you think gravity propagates instantaneously, take comfort in the knowledge that Sir Isaac has reached down through the centuries simply to call you a complete jerk. 
> 
I am sure he would say that I was wrong but I doubt that he would call me a complete jerk since his own equation assumes instantaneous action at a distance. 
And as he pointed out anyone who assumes that the equation is perfect, or that it really implies instantaneous action at a distance is a complete jerk.
>  However, once shown the evidence for nonlocality (really nonspatiality), he would have to agree with me that distance/space is an illusion and that therefore, there is no contradiction in saying that a principle can be applied instantly even over what you think are vast distances. 
As this is one of the big things he argued with Leibniz about, it is quite certain that he would not have agreed with you. Leibniz or Descartes adopted the view that distance/space is an illusion, Newton seems to have thought there really was something like it, even if not exactly.
Regards
 Charles Francis
In article <8dirptgdlpt77pekb1av9e97sc1i49ke5d@4ax.com>, Nemesis
> 
In article 
>>>>>  Maybe so but it seems to me that the equivalence principle assumes instantaneous gravitational effects. Using Einstein's thought experiment of a body in an elevator or a rocket, it's easy to see that any change in the acceleration of the elevator's floor instantly affects all bodies anywhere in the elevator. 
>> 
Actually it is easy to see that it doesn't. The change in acceleration of the elevator's floor is not detectable by an inertial body at the centre of the elevator until light passes between the two. Fairly conclusively illustrating the speed of the gravitational effect. 
> 
The point I wanted to make is that all bodies start accelerating toward the elevator floor immediately when the floor begins accelerating. In the case of gravity, for the equivalence to hold, all bodies must feel a change in a gravitational field instantly. 
Yes I know. I was explaining why that is not true. Think of it from the point of view of the inertial body. The distance to the floor is half the time taken for light to travel to the floor and back to the body. When the floor starts to accelerate the inertial body cannot know anything about it until the light arrives back from the floor. So it cannot be aware of a change acceleration of the floor, and it cannot therefore be affected by it.
>>>  If it treats the subject the way you do in your online essay "Does Gravity Travel at the Speed of Light?" I am afraid I'll have to pass. I found your essay unconvincing. One is left with the impression that GR magically cancels gravitational propagation delays. You do not explain the physical mechanism. One does not cancel a propagation delay with math. 
>> 
The way gr is normally done does not explain physical mechanisms. The cancellation does take place in the math, its just that math does not explain physics, it only tells us what is true of the answer. Someone following the math of gr will definitely know the right answer, but they will not definitely understand the physical reason for it. 
> 
There is no physics behind it only because gravitational effects are instantaneous and are mediated by the nonlocal application of conservation principles. 
You're just making that up. The physics of measurement is behind it, just as the physics of measurement is behind the existence of conservation principles. But you do have to look into the maths to prove it.
>>>  It's just an inverse square approximation that works really well by assuming instant gravitational changes everywhere in the system. The only thing that seems to be missing is that it does not take time dilation into consideration, an "oversight" that Newton can be forgiven for. 
>> 
Yes. But there is more to time dilation than we find in special relativity. 
> 
I was referring to gravitational time dilation in strong fields *and* SRtype dilation of moving bodies. 
Good. Just making sure.
> 
>> 
When we use time dilation to adjust Newton's laws for flat space then we find the accelerations due to gravity, without needing to postulate anything else. That is basically what gr says. 
> 
Not according to Carlip et al since they keep insisting that gravity propagates at c. Adjusting Newton's laws to include time dilation does not change the fact that gravitational effects are instantaneous. 
In fact it does. But you have to do the maths to see the possible ways in which time dilation can work, and how its effects propagate.
> 
>>> 
But, as I mentioned above, I believe that adding "time dilation" to Newtonian gravity would probably correct any deviation from GR. 
>> 
As I say, adding time dilation to Newtonian flat space exactly reproduces GR and explains Newtonian gravity. 
> 
What the point of repeating what I wrote? 
You wrote that you should add time dilation to Newtonian gravity. All you have to do is add time dilation to Newtonian flat space without gravity. The time dilation itself is what is described in gtr as "curved spacetime" (a grossly misleading phrase btw, it is better just to think of it as a "time dilation field" or something like that). Time dilation causes what we percieve as gravity.
>>>  IMO, there is no propagation at all and this why the equivalence principle works so well. I am convinced that gravity is a nonlocal effect . 
>> 
The fundamental point is that gravity just arises from measurement of position, and measurement of position requires two way messaging. 
> 
Gravity does not arise from measurement of position since particles do not measure one another's position. 
But they do. Are you not composed of particles, and are you not able to measure the position of other particles?
>>  Messaging is a nonlocal thing to do, by definition. So you are right, gravity is a nonlocal effect. As is position itself. 
> 
Messaging is nonlocal? Since when? 
Since a message passed from one location to another, obviously.
>  Nonlocal phenomena is specifically not about messaging since messaging must happen at the speed of light. Entangled particles do not communicate their states via messages. That is the whole point of nonlocality. 
Particles cannot be entangled. Only the information we have about the particles is entangled. Entanglement appears precisely when there is no communication of state via messages. Without the messages there is not enough information to say much about the particles, and they seem entangled.
Regards
 Charles Francis
Hi Sam I know there is some time lapse with the spider and the web vibrations. My point was to show gravity as a lattice of space. Much like space is used as a rubber sheet to show how gravity works. If everything in the universe is connected my thoughts show how it is connected. Now if you want my thoughts that there is a time lapse my answer is no. Nature has made the universe to big for gravity to move at the speed of light. Gravity has to move the way Newton saw it "instantaneously" It would make no sense to have gravity move at light speed. Instantaneous action I'm sure would be well received by QM. Like lots of stuff in the QM theory we in our macro realm can't relate. Hard to find a frame of reference to instantaneous action. That is the way nature keeps its best kept secret from us. Best regards herb
>  When we look at a binary star in the sky, we see the components where they were in their mutual orbits when their light left the stars, not where they are now. If we could detect their gravity, would that agree with where we see the light from the stars, or with where the stars are now? 
Neither. The direction of each star's gravity is determined by starting with the position ``where we see the light from the stars'' and extrapolating it forward, in a somewhat complicated way that depends on the star's velocity and acceleration at its propagationdelayed position. The result is generally very close to ``where the stars are now,'' though there can be small differences.
This isn't just a quibble. Consider the electric field of a moving charge, which has roughly the same behavior (details differ) and has the advantage that we can actually run experiments. Suppose first that the charge is moving at a constant velocity, and that at time t=0 it is one lightsecond away from us. Then at t=1 second, we will indeed see the field pointing to ``where the charge is.'' Here's an attempt at a picture:
t=1 t=0 t=1We are at o. At t=1, the observed field will point toward point c, not point b. ``Instantaneous,'' right?a > b > c
o
Wrong. Suppose that at t=.5, the charge suddenly turns around, so that at t=1 it's back where it was at t=0.
t=1 t=0 t=.5In this situation, at t=1, we will *still* see the field pointing toward the ``extrapolated'' position, point X in this picture, even though the charge never got there and is actually back at d. Then very soon after t=1  the exact time depends on exactly where the charge turned around  the field will swing around toward the actual location of the charge. (If the charge has stopped at d, the field will actually overshoot, and then swing around again to point toward d.)a > b > c X d < t=1
o
This is the prediction of Maxwell's equations. But it's more than a prediction  it's tested every time you turn on a radio. The sudden swing of the electric field in a delayed response to the ``extrapolation error'' *is* an electromagnetic wave. I don't just mean this figuratively; this picture, combined with Gauss's law, is enough to actually calculate the strength and direction of the radiation field, and the power radiated. You'll find a nice derivation in Appendix B of Purcell's undergraduate textbook, _Electricity and Magnetism_.
>  Now we turn to the answer given by the GR equations of motion. MTW equation (39.64) has a Newtonian part factored by the bracket [...] 
MTW equation (39.64) is not ``the GR equations of motion.'' It is an approximation in which the extrapolation I described above has already been accounted for.
Tom, I note that you once again refused to address Low's paper. If you think it's wrong, please let me know exactly where.
>  If we start with Newtonian gravity propagating at infinite speed, and add a refractive medium to produce the lightbending, redshift, radar timedelay, and pericenter advance effects, we get the same equations of motion as GR gives (except for a few small terms of no relevance here). 
Exact reference, please. Preferavbly to a paper published in a real journal.
>>  [sc]: I *do* object to [Tom's] making false claims about what ``the mathematical theories'' do and do not say, and ignoring corrections from people who do, in fact, know much more about the details of general relativity than he does. 
>  Are you suggesting that I (or anyone) should accept a point just because an expert says it is so? 
If the issue is what a particular theory (in this case, GR) says, and if the experts understand the details of the theory and you don't, then, yes, that's what I'm suggesting. Or alternatively, you should learn the theory well enough to be an ``expert'' yourself. For example, if you think Low's paper is wrong, find a mistake, and publish. But if the ``experts'' unanimously say, ``GR predicts X,'' you really shouldn't go around saying ``GR predicts Y'' without at least acknowledging that people who know much more about GR than you all disagree.
Steve Carlip
The behavior of the gravitational (or electric) field of a moving body is somewhat unintuitive, as is apparent from my last post. Here's one way to think about it that might help. For simplicity I'll talk about electromagnetism rather than gravity; this will let lots of readers check my claims, since Maxwell's equations are a lot easier than the Einstein field equations. Note: the speed of light is approximately one foot per nanosecond (ns).
It's often said (by me, among others) that if a charge moves at a constant velocity, its electric field points directly toward its ``instantaneous'' position. Strictly speaking, this is only true of the charge has been moving at a constant velocity for an infinite amount of time. It's helpful to think about what happens when the charge first *starts* to move.
Suppose you have a charge that is at rest (and has been at rest for a long time) at point x. Say that at time t=0, it starts to move at a constant velocity. At t=1 ns, the field within a foot of the origin will point toward the instantaneous position of the charge, but the field 1.1 feet away will still point toward the origin. At t=2 ns, the field within two feet of the origin will point toward the instantaneous position, but the field 2.1 feet away will still point toward the origin. The region of transition between ``pointing toward the instantaneous position'' and ``pointing toward the origin'' will move outward at the speed of light, and will have a shape that depends on the details of the charge's initial acceleration. It is what we call an electromagnetic wave specifically, ``the electromagnetic wave emitted by an accelerated charge.''
Now picture the electric field itself. It does *not* respond instantly to the charge's acceleration. But once it has begun to move, it will continue to move along with the charge. So after t=1 ns, for instance, the field within a foot of the charge will continue to point to the charge, because, roughly speaking, it's moving at the same velocity that the charge is.
This isn't so difficult to picture, I think. It won't make sense if you don't really believe the field exists as an independent phenomenon, or if you think (as Tom does) that it has to be continuously ``renewed.'' But the field doesn't move because it's somehow just an outgrowth of the charge. It moves because it has started moving, and nothing has stopped it. The charge couples to the field, and can *start* it moving, but that's all it has to do.
Hence, for example, if the charge suddenly stops (at t=100 ns, say), the field won't instantly stop moving, either. At t=101 ns, the field within a foot of the charge will have stopped moving, and will point to the charge. But the field 1.1 feet away will continue to move, and thus will point to the ``extrapolated'' position, the place where the charge would have been if it hadn't stopped. At t=102 ns, the field within two feet of the charge will have stopped moving, and will point to the charge, but the field 2.1 feet away will still be moving. Once again, the transition region between ``pointing toward the instantaneous position'' and ``pointing toward the extrapolated position'' will move out from the charge at the speed of light. This is what we call ``the electomagnetic wave emitted by a decelerated charge.''
Let me emphasize again that this picture leads to quantitative predictions about the electromagnetic radiation emitted by an accelerated charge, and that these predictions are verified extremely well. If you believe instead, as Tom does, that the electric field propagates (almost) instantaneously, then you have to postulate some other, separate cause of radiation, which just by coincidence also couples to charge, and by some *enormous* coincidence happens to agree exactly with the predictions of the picture I've just described.
The situation for gravity is more complicated, of course. The main difference is that you can start or stop a charge by using uncharged matter, so you only have to worry about the electric field of the charge itself. To start or stop a mass, you have to use some other mass (or energy), and the gravitational field depends on that as well. But the basic principle is the same.
Steve Carlip
In article <9noff8$9k6$1@woodrow.ucdavis.edu>, Steve Carlip
> 
Following up my own post:
The behavior of the gravitational (or electric) field of a
moving body is somewhat unintuitive, as is apparent from
my last post. Here's one way to think about it that might
help. For simplicity I'll talk about electromagnetism rather
than gravity; this will let lots of readers check my claims,
since Maxwell's equations are a lot easier than the Einstein
field equations. Note: the speed of light is approximately
one foot per nanosecond (ns).
It's often said (by me, among others) that if a charge moves at a constant velocity, its electric field points directly toward its ``instantaneous'' position. Strictly speaking, this is only true of the charge has been moving at a constant velocity for an infinite amount of time. It's helpful to think about what happens when the charge first *starts* to move. 
Hi, Steve,
I have found these two posts fascinating, thanks. I have been working on an intuitive approach to gtr [1], and I think it is possible to see from what you said about e.m. how this works for gravitation without getting too heavily into the field equations. Please comment on the accuracy of these intuitive notions.
The starting point is the radar method of measuring spacetime coordinates. The position I take is that the manifold consists only of the measurements, what is actually measured and what would be measured if we were to do a measurement  I take this last phrase from a Dirac Von Neumann type interpretation of qm. The overall philosophy is that the equations of physics apply to the information we have about what is and what would be, not what actually is, and that this applies as much to curvature as it does to the quantum domain.
I will consider the conditions in turn:
A Static Gravitating Body.

There is no issue. The measurement tells us where the body was at the
time of radar reflection. It is still in the same place, and hence that
is where curvature is centred.
A Uniformly Moving Gravitating Body

Lorentz transform to the case of a static gravitating body. The centre
of curvature is always where the body is, so when we transform back to
the moving case, that is where the centre of curvature has to be. I.e.
the centre of curvature is where the body is now, not where it was at
the time of measurement.
A Inertially Moving Gravitating Body

This is really a correction to the uniformly moving case. To do it
properly we have to think in terms of inertial reference frames, and
uniform movement is not necessarily inertial. So the centre of curvature
is where the body is now as a result of inertial motion, not uniform
motion.
Corollary: Precession of the Perihelion. Considered from a reference frame on a planet using a zaxis radial to the sun, the centre of gravity of the sun is always just ahead of the point where it is seen in the sky.
An Instantaneously Accelerated Gravitating Body

Consider a body following an inertial path, instantaneously accelerated,
and then following an inertial path again. Up until the time when we
receive light from the body at the moment of acceleration the situation
is exactly as for the inertially moving gravitating body. There being no
other information, the prediction must be identical. The centre of
gravity is where the body would have been had the body continued
inertial motion, and starts to move away from that point after we
recieve information about the acceleration.
An Accelerated Gravitating Body

Future accelerations cannot be predicted, so the centre of gravity
should always be at the point where we predict the body would be based
on inertial motion following the last information we had about it.
[1] Is there any chance I could get you to read it before I send it to journals? Unlike my previous attempt, which I now feel looks pretty lame in comparison, I do actually get the equations out of it instead of just a hand wavy account, which to my chagrin, no one recognised as gtr. I feel I cover 75% of Dirac's nice short account in about 1/3rd the space and with much easier ideas (about 1st year undergraduate), so I really hope it will have pedagogical value as well as insight.
Regards
 Charles Francis
In article
> 
In article <8dirptgdlpt77pekb1av9e97sc1i49ke5d@4ax.com>, Nemesis

>> 
In article 
> 
>>>>>> 
Maybe so but it seems to me that the equivalence principle assumes instantaneous gravitational effects. Using Einstein's thought experiment of a body in an elevator or a rocket, it's easy to see that any change in the acceleration of the elevator's floor instantly affects all bodies anywhere in the elevator. 
>>> 
Actually it is easy to see that it doesn't. The change in acceleration of the elevator's floor is not detectable by an inertial body at the centre of the elevator until light passes between the two. Fairly conclusively illustrating the speed of the gravitational effect. 
>> 
The point I wanted to make is that all bodies start accelerating toward the elevator floor immediately when the floor begins accelerating. In the case of gravity, for the equivalence to hold, all bodies must feel a change in a gravitational field instantly. 
> 
Yes I know. I was explaining why that is not true. Think of it from the point of view of the inertial body. The distance to the floor is half the time taken for light to travel to the floor and back to the body. When the floor starts to accelerate the inertial body cannot know anything about it until the light arrives back from the floor. So it cannot be aware of a change acceleration of the floor, and it cannot therefore be affected by it. 
I once called you a moron Francis. I now realize I was mistaken. You are not a moron. You are a *fucking* moron. And you're wasting my time. Goodbye.
Nemesis
Nasty Little Truth About Spacetime Physics: http://home1.gte.net/res02khr/crackpots/notorious.htm
>  Yes I know. I was explaining why that is not true. Think of it from the 
>>  point of view of the inertial body. The distance to the floor is half the time taken for light to travel to the floor and back to the body. When the floor starts to accelerate the inertial body cannot know anything about it until the light arrives back from the floor. So it cannot be aware of a change acceleration of the floor, and it cannot therefore be affected by it. 
> 
I once called you a moron Francis. I now realize I was mistaken. You are not a moron. You are a *fucking* moron. And you're wasting my time. Goodbye. 
Well you are obviously totally fucking pissed off that I have used your own argument to show that you were wrong, and you are not talking about it because, many days later, you still have no answer to it.
Regards
 Charles Francis
In article
> 
In article 
>>  Yes I know. I was explaining why that is not true. Think of it from the 
>>>  point of view of the inertial body. The distance to the floor is half the time taken for light to travel to the floor and back to the body. When the floor starts to accelerate the inertial body cannot know anything about it until the light arrives back from the floor. So it cannot be aware of a change acceleration of the floor, and it cannot therefore be affected by it. 
>> 
I once called you a moron Francis. I now realize I was mistaken. You are not a moron. You are a *fucking* moron. And you're wasting my time. Goodbye. 
> 
Well you are obviously totally fucking pissed off that I have used your own argument to show that you were wrong, and you are not talking about it because, many days later, you still have no answer to it. 
What I have written is enough and I don't need to defend it against your stupidity.
Nemesis
Nasty Little Truth About Spacetime Physics: http://home1.gte.net/res02khr/crackpots/notorious.htm
Steve Carlip
> 
SNIP
In this situation, at t=1, we will *still* see the field pointing toward the ``extrapolated'' position, point X in this picture, even though the charge never got there and is actually back at d. Then very soon after t=1  the exact time depends on exactly where the charge turned around  the field will swing around toward the actual location of the charge. (If the charge has stopped at d, the field will actually overshoot, and then swing around again to point toward d.) This is the prediction of Maxwell's equations. But it's more than a prediction  it's tested every time you turn on a radio. 
I do not understand when I turn on my radio that that proves that the electric(magnetic) field points towards its "extrapolated" position. IMO my radio is not accurate enough to demonstrates any effect that depents on c
Consider two observers O and M which are a distance 3 light seconds a part. Observer O is positive charged and observer M negative charge. Both observers have a clock which are synchronised. The time at both's clocks is 12.00
1. IMO when O's clock shows 12.00 he will see that M's Clock shows 11.57 because it takes 3 secs for the image of M's clock to reach O.
2. IMO the same for M. At 12.00 at M's clock he will see that O's clock shows 11.57
At 12.00 M starts to move with a lineair speed around O.
O will see this (change in position) at 12.03 at his clock
i.e. when M's clock shows 12.00
At 12.03 M has moved forward.
3. That means O sees M at a retarded position.
For the electric field generated by M the same is true.
Before 12.00
4. O will agree that the electric field generated by M points towards
the instantaneous position of M.
5. For M the same is true.
O will also agree that the electric field points to that same position
untill 12.03.
At 12.03 O will detect a change in the electric field.
6. That means (IMO) that O does not agree that the electric field points
to its "extrapolated" position.
Because then already at 12.00 O should detect a change.
(For M this is different).
The question is how do we test (with an experiment) if statement 6 is right or wrong.
IMO this is difficult and may be imposible.
If it is impossible than which is the best experiment that we can perform that most closely describes this situation.
>  The sudden swing of the electric field in a delayed response to the ``extrapolation error'' *is* an electromagnetic wave. I don't just mean this figuratively; this picture, combined with Gauss's law, is enough to actually calculate the strength and direction of the radiation field, and the power radiated. You'll find a nice derivation in Appendix B of Purcell's undergraduate textbook, _Electricity and Magnetism_. 
SNIP
>  Steve Carlip 
My apologies for a slow response in this discussion, but I live in Washington, DC, and have family living in Manhattan and Brooklyn. So I have had to think about matters more pressing than the "speed of gravity" during the past week.
>>  [tvf]: When we look at a binary star in the sky, we see the two 
>  [sc]: Neither. The direction of each star's gravity is determined by 
Do we agree on the meaning of "speed"? For a gravitational signal from a binary star, do we agree the speed of the signal is equal to the distance traveled divided by the time interval elapsed during its travel? You agree the gravity field oscillations of a binary star would be "very close to" in phase with "where the stars are now", as opposed to in phase with their retarded positions. So if you agree that a gravitational signal (phase oscillations for a binary star) reaches an arbitrarily large distance in much less than the light time, doesn't that mean the signal is traveling much faster than light by definition?
This binary star example does not depend on aberration, so the invisible "velocitydependent terms" you claim cancel aberration are irrelevant here. But your response here seems atypically vague and irrelevant. Is that because you are still thinking about the example or because you have no better response? I don't ask that you work out the equations here for what you call "a somewhat complicated way"; but you should be able to explain the concept behind it, if one exists.
BTW, notice how easy the explanations become if one simply recognizes that gravitational signals propagate at infinite speed in GR.
>  [sc]: This isn't just a quibble. Consider the electric field of a moving 
This claim is in contradiction to the results of the SherwinRawcliffe experiment (previously cited), which attempted to look for this hypothetical "overshoot" effect. In the experiment, a pair of like charges a fixed distance apart are simultaneously and continually accelerated from rest. According to your description, the field of the forward charge should lag, producing an increased repulsion on the rearward charge. The experiment showed that did not occur. It follows that, if the experiment was conducted competently, something is wrong with the picture you describe.
>  [sc]: The sudden swing of the electric field in a delayed response to the 
That is an *interpretation*, not a fact. I don't wish to confuse the issue here by introducing any other model. But just to illustrate a different interpretation (without mentioning any model to support it), the electric field could exist apart from a "universal aether" (defined as the wavecarrying medium for light), and act upon that aether. Then a sudden acceleration of the source charge would then set off a wave in the aether while the electric field itself imitated the source charge motions nearly instantly.
As you know, part of our problem in reaching a meeting of the minds is due to some confusion between what is established fact and what is still open to interpretation, and your apparent insistence that any interpretation of GR other than the one you favor is not GR, but some other theory. I remind you that Feynman, no slough in such matters, said in Feynman Lectures on Gravitation [AddisonWesley, New York (1995). Section 8.4, p. 113]: "It is one of the peculiar aspects of the theory of gravitation, that it has both a field interpretation and a geometrical interpretation. ... The geometrical interpretation is not really necessary or essential to physics."
>>  [tvf]: Now we turn to the answer given by the GR equations of motion. MTW 
>  [sc]: MTW equation (39.64) is not ``the GR equations of motion.'' It is an 
Those equations are more than accurate enough for our purposes here, as we have discussed earlier and in my last message. They show the distant field of a binary star being inphase with the instantaneous positions of the stars, no matter how many complete revolutions the two stars have made during the light transit time to the distant field point (which can be as far away as we please). No extrapolation based on position, velocity, and acceleration at a retarded emission time can be good for multiple revolutions. Please address yourself to explaining that fact if, as you claim, the speed of gravity is the speed of light. My binary star example obviously cannot be explained by nature extrapolating the velocity and acceleration of the sources based on their values when the gravitational signal leaves the stars. The gravitational signal arriving nearly inphase with the instantaneous positions of the stars, even over arbitrarily large distances, meets the ordinary definition of a field propagation speed traveling much faster than light.
There is no aberration to cancel, and no "velocitydependent terms" can cancel an effect that lasts for multiple revolutions. This example is a simple, direct demonstration of the point of this discussion. The oscillating gravitational signals from a binary star pair are nearly in phase with the instantaneous positions of those stars, and badly out of phase with the lighttimeretarded optical positions of those stars, over arbitrarily large distances. And this happens right in the GR equations describing the motion of just such systems, even though no important or relevant terms are truncated from those equations.
>  [sc]: Tom, I note that you once again refused to address Low's paper. If 
I answered you in our previous discussion last year, which you can look up as well as I can. I'm not fresh on Low's paper now, since it seemed at the time I read it to have little relevance to this discussion. In fact, that author seemed not to understand why aberration is necessary, or why propagation speeds of c for the distance factor (denominator) in a retarded potential have no observational consequences at present  which is why they are irrelevant here.
>>  [tvf]: If we start with Newtonian gravity propagating at infinite speed, 
>  [sc]: Exact reference, please. Preferably to a paper published in a real 
Here's a mainstream journal article with a good bibliography to other similar articles that shows how an optical medium can produce general relativistic effects: Gen.Rel.&Grav. 2 #4, 347357 (1971) by Fernando de Felice, titled "On the gravitational field acting as an optical medium". He notes that Einstein himself first suggested the idea that gravitation is equivalent to an optical medium. From the abstract: ". Maxwell's equations may be written as if they were valid in a flat spacetime in which there is an optical medium . this medium turns out to be equivalent to the gravitational field. . we find that the language of classical optics for the 'equivalent medium' is as suitable as that of Riemannian geometry."
Tom Van Flandern  Washington, DC  see our web site on replacement astronomy research at http://metaresearch.org
Gravity. All mater regardless of its atomic mass falls at the same
rate.
1 Before anything can fall more force must be one one side of each
atom then the other AND it must allways be displaced twards less energy.
2 it dose not mater the atomic sise . It wil be displaced twards less
at the sae rate. SO all mater is proportional to the rate energy
expands in space. Because space is bent the energy rate becomes less
near mater. Mater dose not expand so is allways proportional to
expanding space ( expanding energy) .
Our universe is still a big bang expanding . The presure of energy
filling space still pushes outward . Mater is still condenced energy .
In article <9niu04$gnp$1@bob.news.rcn.net>
"Tom Van Flandern"
... about general relativity in sci.physics ...
>
Aren't you aware of the fact that posting about relativity in sci.physics without setting followups to sci.physics.relativity is an indicator of crankdom? That Carlip failed to notice that your comments were offtopic is no excuse.

James Carr
> 
"Steve Carlip" 
>  Do we agree on the meaning of "speed"? For a gravitational signal from a binary star, do we agree the speed of the signal is equal to the distance traveled divided by the time interval elapsed during its travel? 
Yes. Do we agree that ``speed'' means a different thing from ``direction''?
>>  [sc]: This isn't just a quibble. Consider the electric field of a moving 
>  charge . we will *still* see the field pointing toward the ``extrapolated'' position . even though the charge never got there . If the charge has stopped at d, the field will actually overshoot, and then swing around again to point toward d. 
>  This claim is in contradiction to the results of the SherwinRawcliffe experiment (previously cited), which attempted to look for this hypothetical "overshoot" effect. 
Ah, yes. The famous experiment that shook the foundations of modern physics, showing that special relativity was wrong, that signals could be sent faster than light, and that Maxwell's equations had to be dumped ... and that somehow never got published. Very convincing.
>>  [sc]: The sudden swing of the electric field in a delayed response to 
>  the ``extrapolation error'' *is* an electromagnetic wave. 
>  That is an *interpretation*, not a fact. 
It is an unambiguous prediction of Maxwell's equations. It's easy enough to write down the (unique) exact solution for this situation, graph out the field lines, and see how they behave.
Of course, this is an ``interpretation'' of the observational results, in the sense that there could conceivably be a different theory that explained electromagnetic waves in a different way. In this, it's no different from any of the rest of physics. But Maxwell's equations don't just say, ``This is what an electromagnetic wave is.'' They give exact, quantitative predictions for the behavior of such wavestheir amplitude, their direction, their dependence on the acceleration of the charge, their polarizationthat are all quantitatively confirmed by experiment.
It bewilkders me that you are prepared to call this an ``interpretation'' and yet don't understand that your arguments about aberration and speed are also an ``interpretation,'' based on a particular model (that *hasn't* had the successes of Maxwell's theory).
>  I remind you that Feynman, no slough in such matters, said in Feynman Lectures on Gravitation [AddisonWesley, New York (1995). Section 8.4, p. 113]: "It is one of the peculiar aspects of the theory of gravitation, that it has both a field interpretation and a geometrical interpretation. ... The geometrical interpretation is not really necessary or essential to physics." 
My goodness! You think this somehow supports your bizarre idea that gravitational fields propagate instantaneously? I suggest that you go back to the book and try to understand the remark after eqn. (3.2.9). The ``field theory'' approch Feynman is writing about makes it, if anything, much easier to see that the propagation speed is c.
>>  [sc]: MTW equation (39.64) is not ``the GR equations of motion.'' 
>  It is an approximation in which the extrapolation I described above has already been accounted for. 
>  Those equations are more than accurate enough for our purposes here 
No, they're not.
>>  [sc]: Tom, I note that you once again refused to address Low's paper. If 
>  you think it's wrong, please let me know exactly where. 
>  I answered you in our previous discussion last year, which you can look up as well as I can. I'm not fresh on Low's paper now, since it seemed at the time I read it to have little relevance to this discussion. In fact, that author seemed not to understand why aberration is necessary, or why propagation speeds of c for the distance factor (denominator) in a retarded potential have no observational consequences at present 
You're being silly. Low demonstrates an exact, rigorous consequence of the Einstein field equations. If you think the conclusion does not describe nature, then you necessarily believe that the Einstein field equations are wrong. Fine...but stop pretending otherwise.
>>>  [tvf]: If we start with Newtonian gravity propagating at infinite speed, 
>  and add a refractive medium to produce the lightbending, redshift, radar timedelay, and pericenter advance effects, we get the same equations of motion as GR gives (except for a few small terms of no relevance here). 
>>  [sc]: Exact reference, please. Preferably to a paper published in a real 
>  journal. 
>  Here's a mainstream journal article with a good bibliography to other similar articles that shows how an optical medium can produce general relativistic effects: Gen.Rel.&Grav. 2 #4, 347357 (1971) by Fernando de Felice, titled "On the gravitational field acting as an optical medium". 
You haven't actually read this paper, have you? I have; it has nothing to do with your claims quoted above. It doesn't ``start with Newtonian gravity propagating at infinite speed''; it applies only to stationary fields; and it has nothing to do with pericenter advances. It does show that the effects of a stationary gravitational field on light can be mimicked by a suitably complicated optical medium. But it gives no ``equations of motion'' that would determine the properties of that medium from the distribution of surrounding massesto get those, it has to go back to GR, solve the Einstein field equations, plug the resulting metric into Maxwell's equations as a background, and then reinterpret the results. In particular, all of the properties of the ``optical medium'' are determined by the standard Einstein field equations, and Low's proof that they propagate at the speed of light stands exactly as it does in conventional GR.
Steve Carlip
Steve Carlip
>  My goodness! You think this somehow supports your bizarre idea that gravitational fields propagate instantaneously? I suggest that you go back to the book and try to understand the remark after eqn. (3.2.9). The ``field theory'' approch Feynman is writing about makes it, if anything, much easier to see that the propagation speed is c. 
I shall try to attract your attention in the possible alternate approach to a problem of speed of propagation of interaction considered in this thread.
The presented below example should be considered as allegorical.
Let's consider own oscillations of a string with the fixed ends. In this case oscillations of a string represent standing waves. All points of a string make oscillations in the same phase (analogy  in a problem of two bodies, the bodies make motion in the same phase too).
Here there is no aberration during motion of parts of a system and we _have _illusion of an _infinite _transfer _rate of _interaction_ between parts of a system  a string or two bodies.
But we perfectly know, that the speed of propagation of elastic interaction between parts of a string is limited.
You can ask what analogy can be between own oscillations of a string and problem of two gravitating bodies? In case of own oscillations of a string or own oscillations of a rectangular elastic thin plate we deal with a class of physical systems located in a _stationary_ _state_.
_stationary_ _state_ !!!
For this reason indicated by Tom Van Flandern the absence of aberration in gravitational systems can be connected with a stationary state of gravitational systems.
The given approach is the alternate approach to a problem of speed of propagation of gravitational interaction considered in this thread, but the given point of view empirically is justified by existence of the empirical data for the benefit of a stationarity of the Solar system and so on.
The paradox of a problem of speed of propagation of gravitational interaction consists of impossibility to determine speed of propagation of interaction by motion of parts of a system located in a stationary state.
The Stationary gravitational system is a system located in a state of own free oscillations, when all bodies of a system make motion in the same allegorical "phase".
Comments.
[snip]
>   Aleksandr Timofeev http://groups.google.com/groups?ic=1&q=msgid:3B372CA5%40MailAndNews.com 
Having reread Tom's illustration, I realized that I had initially misunderstood, and had given an incorrect answer. Here's the right answer.
The question, again, was this:
>  When we look at a binary star in the sky, we see the components where they were in their mutual orbits when their light left the stars, not where they are now. If we could detect their gravity, would that agree with where we see the light from the stars, or with where the stars are now? 
In my hasty reading, I thought the question was where each star saw the other one's gravity. I now see that the question is where we, far away from the system, see the gravity. This is a nice question. Let's first look at the answer in Newtonian gravity.
The first, and crucial, point, is that we can only see the combined gravitational fields of the two stars. Forces don't come with little name tags (``Hi, I'm the gravitational field of star #1''). While each star has its own field, we can only observe the sum.
Now, let the two stars have masses m_1 and m_2 and position vectors r_1 and r_2. The center of mass position R is defined as (m_1 = m_2)R = m_1 r_1 + m_2 r_2. The distance between the stars is d = r_1  r_2, and by assumption d<< R.
Then to a very good approximation, the gravitational field of the system has magnitude G(m_1 + m_2)/R^2, and points to the center of mass. Since the center of mass doesn't change position as the stars orbit each other, the field doesn't change direction. It looks just the same whether it comes from ``where we see the light from the stars'' or from ``where the stars are now.''
This isn't quite the whole story, of course. There will be small corrections to this force that do change with time. The easiest way to describe them, in Newtonian gravity, is to expand the total force in powers of the small quantity d/R. This is just the multipole expansion, and should be familiar to anyone who's taken an introductory course in electromagnetism.
The first correction, the dipole contribution, turns out to be exactly zero for gravity. This is a straightforward computation: the dipole force comes out to be proportional to the mass dipole moment m_1(r_1  R) + m_2(r_2  R), which vanishes by the definition of the center of mass position R.
The next correction, the quadrupole term, *does* depend on time. The Newtonian prediction is that it depends on the value of the quadrupole moments ``where the stars are now.'' The prediction of general relativity is, completely unambiguously, that it depends on the value of the quadrupole moments ``where we see the light from the stars.'' The quadrupole approximation is exactly the point in GR at which the cancellations due to velocitydependent interactions stop, and propagation delay becomes obvious.
Note that the quadrupole term is smaller than the leading center ofmass term by a factor on the order of (d/R)^2. This is very small, and this difference between Newtonian gravity and GR has not been tested. For electromagnetism, on the other hand, exactly the same type of analysis holds (although there the dipole contribution is nonzero as well), and the time dependence is very well tested; it is the basis of antenna theory.
>  Now we turn to the answer given by the GR equations of motion. MTW equation (39.64) 
MTW equation (39.64) is, among other things, a multipole expansion that stops before the quadrupole term. It is exactly the wrong approximation for your question.
Steve Carlip
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