# The speed of gravitational field propagation

1. Oct 25, 2009

### blaksheep423

I am working on some interesting topics which relate to the speed at which gravity propagates. My question is this: within the frameworks of special and general relativity (or any other widely accepted theory, for that matter), is it necessary for gravitons/gravity waves to propagate at exactly the speed of light? Is it theoretically valid to suppose that gravitational fields could propagate at speeds of 0.9c, or 0.99c, etc.?

The limited amount of online research I've done concerning this has told me that, using a binary star system, the speed of gravity has been experimentally measured to within 0.95c, which, when coupled with a 0.25 experimental error, led to the assumption that gravity propagates at exactly c. Is there any theoretical work or research which refutes this, or any other reason to intelligently doubt it?

2. Oct 25, 2009

### rathat

I always kind of wondered how planets could keep a stable orbit around the sun while the suns gravity takes 500 seconds to reach the earth and the sun goes around the milky way at 486,000 miles per hour, i would figure that delay would stop things from orbiting but what do i know.

3. Oct 25, 2009

### JesseM

There's a good discussion of how certain effects of gravity "compensate" for the propogation delay here:

http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html

4. Oct 25, 2009

### rathat

wow, that can't be a more perfect article on my question.

5. Oct 25, 2009

### blaksheep423

this article sums up what i already knew, but is there any indication that the speed of gravity may not be exactly c? and is it absolutely essential to any standing theory that gravity propagate at the speed of light, or is it conceiveable that it could be slightly less?

6. Oct 25, 2009

### Creator

I've seen this argument many times in attempts to resolve the issue of grav. propogation delay causing orbital instability ...

I appreciate Carlip, et al, and their Gen Rel. point of view claiming that the speed of gravity explanation is analogous to Electrodynamic equations, but simply saying "when you solve the gravitational eqns. ...a cancellation of retardation effects occur" really seems like handwaving. Van Flandern and others do bring up some valid counter points..... (PLEASE, folks; no flaming about Van Flandern....that is NOT the point here.)

It would be nice if a little more in depth analysis could clear up a few questions which I find Carlip has not addressed.....
So let me start by asking you, Jesse, since I see you to be exacting in many of your responses.
If you don't feel you have a handle on this issue I understand....but I'm NOT looking for another link to Carlip Vs. Van Flandern debate.. (I've read all the counter punches and am not satisfied. )

First, let me say I agree with GR in most of its predictions, and I think Carlip tries to get to the real point by admitting , " Strictly speaking, gravity is not a "force" in general relativity,..." And I think he should have left it there. So there would be no need to address the non-centrality of forces...which causes the orbital instability problem.

But since he continues (in the weak field approx.), "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..."

Again apparent handwaving...

First, let me ask you....Is not this "velocity dependent" force in Gen Rel. based upon a v^2 term, namely v^2/c^2 ??

BTW, please give me simple answers WITHOUT using latex since all latex stuff is blacked out on my computer ( maybe that's asking alot , but try me). also, I post rather infrequently, and so it may be some time before I respond....so please be patient).

Thanks.

Last edited: Oct 25, 2009
7. Oct 26, 2009

### JesseM

Why do you think it is handwaving? Presumably there are technical details behind that statement, which was just a nonmathematical one for an article aimed at a general audience.
I am not very well-versed in the technical details of GR, so I can't help you with that. Perhaps someone else here can answer your questions. In the meantime you may find at least some useful info on these earlier physicsforums threads discussing the quadrupole dependence of gravity:

Just because it's not a force doesn't mean we don't still need to explain why there is no orbital instability problem. GR is still after all a local theory--I'm pretty sure it would be true for example that the curvature of spacetime in a given region is determined only by points in the past light cone of that region, so for example if the Sun were split into pieces which went in different directions at nearly the speed of light, this couldn't have an effect on the orbits of the planets until the event of the splitting entered their past light cones.
Do you really imagine there is no math behind it to make it precise?

8. Oct 26, 2009

### Creator

Jesse; thanks for your respnse but you are missing the point of my post entirely.

Anyone else who is familiar with the 'speed of gravity' arguments want to give it a try?....again...the question is...

In Carlip's response as to how GR explains why the speed of gravity itself can have propogation delay without causing orbital instability , he says: "the 'force' in GR...... depends on velocity as well as position. The net result is that the effect of propagation delay is almost exactly cancelled..."

This apparent handwaving cannot be denied without more thorough examination.

My first question is: Does not this velocity dependent "force" in GR actually depend upon a v^2 term, or more precisely, upon v^2/c^2 ??

Anyone?

9. Oct 26, 2009

### Ich

Yeah, and saying that Carlip is "simply saying..." really seems like distorting the truth.

Yes.

Carlip presents a rigorous derivation which is hard to follow, of course. Therefore, additionally, he presents a less involved mathematical and physical argumentation from "first principles". To make sure that everybody understands, he also describes his findigs in plain English. What more could he do?

Accusing him of handwaving seems quite dishonest to me, as you surely must know the difference between "I don't understand his derivation" and "he gives no derivation".

10. Oct 26, 2009

### JesseM

Many of his comments are about gravitational waves. But I think I understand, your question is more about the "compensating effects" that occur even in situations where gravitational waves are not being emitted, correct?
Can you explain where specifically you get the idea that it depends on a v^2 term? I think it would help others to address your question. Again, have you seen this stated somewhere, are you deriving it from some equation, or what?

Also, I got the idea that when he said the force "depends on velocity as well as position", he meant that in the weak-field approximation, the gravitational force an object A feels from another object B which lies X light-seconds away is not directed at the position B was X seconds ago, but rather is directed towards where the object B would be if we took its velocity vector X seconds ago and used it to "extrapolate" its current position under the assumption it had moved at constant velocity for the last X seconds. So the force would be directed towards the actual present position of B if it had indeed moved at constant velocity, whereas if B was accelerated during the last X seconds than this wouldn't have any effect on A until a wave created by the acceleration reached A, until then A would continue to be pulled towards the position of an imaginary phantom version of B that had not accelerated. This would fit with what Carlip said about electromagnetism:
Am I incorrect in my understanding of what Carlip said? If my understanding is right, then what would be the corresponding physical meaning of your statement that the force depends on a "v^2 term"?

11. Oct 27, 2009

### Estif

Has no one noticed how "delay canceling " is a logical paradox?

To say delay gets canceled makes sense as much as if they said distance gets canceled.

What do you mean? Article very directly states speed of gravity is almost instantaneous. That is nowhere even close to the speed of light.

Article says:
- "In the simple newtonian model gravity propagates instantaneously"

- "The net result is that the effect of propagation delay is almost exactly cancelled, and general relativity very nearly reproduces the newtonian result."

v= s/t
v= s/delay

v= s/(delay - delay_almost_exact_cancel)
v= ~s/0.000000000000000000000000000000000000000000000001

Speed of gravity seem to be adjusting itself so it can act "almost instantaneously" regardless of distance. -- Has no one considered that gravity fields could be a fixed-part of the elementary particles and not something that propagates from it. Like a rigid-body fields would then move along with its center and that would explain instantaneous action over distance. How about it?

Last edited: Oct 27, 2009
12. Oct 27, 2009

### JesseM

Not if you pay attention to the context. In this case, they are saying that the delay that would be present in a hypothetical theory of gravity where the force vector always points to an object's "retarded" position (i.e. the position it was at when it was emitting a signal moving at the speed of light which would just be reaching you at this moment) is cancelled out when you calculate the actual direction of the gravitational pull in the "weak field" approximation to GR (or at least, it is cancelled for objects moving at constant velocity).

13. Oct 27, 2009

Staff Emeritus
Then I am afraid you shouldn't have brought him up.

I've actually had lunch with Tom van Flandern. He is a true gentleman. Unfortunately, he's also an object lesson in what happens when one becomes too enamored of one's own theory. During the course of this lunch, when presented with a counter-argument told me that this proves that not only is GR wrong, but Newtonian mechanics is wrong as well.

You simply cannot take Tom van Flandern to be a reliable source.

You will not learn anything whatever about the speed of gravity by looking at orbits around a static gravity source. The source is static. Specifically, the potential is just a function of distance, and the force is just the gradient of the potential. The relevant time scale is not the 8 minutes it takes gravity to reach the earth from the sun, it's the 4.5 billion years the sun has been here.

All this talk of aberration and remarkable cancellations, while true, is simply an artifact of working in a geocentric frame, where things are a mess. In a heliocentric frame, everything looks simple - there's a static potential, which has a gradient, the force, and the earth responds to this force.

Measuring the speed of gravitational waves is difficult but straightforward. The radiated power depends on the speed of gravitational radiation, and it's straightforward to measure the energy loss in a binary pulsar system. One gets that the speed of gravity is close to and compatible with the speed of light.

Measuring the speed of static gravity (assuming it even can be different from radiation - this is far from clear) is very difficult. You need two large masses, close enough to each other that one's field doesn't dominate, but far enough apart that there is a measurable delay in propagation time - and you need something to act as a test probe to measure the local spacetime curvature. This is incredibly difficult, as few such systems exist, and placing a test probe where you want it adds even more complications. People have tried this using the sun, Jupiter (already not ideal) and EM radiation as a test probe. This has proved to be even more difficult than expected, as the use of EM radiation as the test probe mixes the speed of light in to the problem in a non-trivial way, and the interpretation of the results have been controversial.

14. Oct 28, 2009

### Estif

Are you saying this delay (8 minutes) does not actually get canceled, and so Earth does not orbit Sun, but the point where Sun was 8 minutes ago? What does it matter what happened in the past, is there some accumulative effect that impacts potentials and delays? I thought orbitals depend ONLY on distance, mass and velocity (initial conditions so to say).

What formula are you using instead of F= k* m1*m2/r^2 ?

15. Oct 28, 2009

### A.T.

There is no frame of reference in which this question makes any sense:
- In the frame of the Sun, the Sun and the point where Sun was 8 minutes ago is the same.
- In the frame of the Earth, the Earth does not orbit anything.

16. Oct 28, 2009

### JesseM

Am I correct in understanding that the "weak field" approximation to general relativity treats gravity as a type of field in flat minkowski spacetime? (see p. 468 of this book). If so, can you pick an "inertial" coordinate system where the Sun has some constant velocity and figure out whether the Earth is being accelerated towards its current position at each moment?

17. Oct 28, 2009

### A.T.

Yes, right. Stating "There is no frame of reference in which this question makes any sense" was wrong. I just considered the two mentioned frames.

The fact that the Earth is being accelerated towards the inertially moving Sun's current position doesn't imply that the speed of gravitational field propagation is infinite. The field could have a velocity component.

Last edited: Oct 28, 2009
18. Oct 28, 2009

### JesseM

Right...when people like Van Flandern claim the speed is infinite (or faster than c), are they actually claiming gravitational information is traveling faster than light, so if you shake one planet, observers on other planets would feel the gravitational effect earlier than the light from the shaking-event would reach them? If so, could this be debunked just by showing that in GR, the curvature in some finite region of spacetime can be determined by what's in the past light cone of that region, not by anything outside outside the past light cone?

19. Oct 28, 2009

Staff Emeritus
But van Flandern doesn't (well, didn't) believe in GR. Or SR. So he's not going to be convinced by that argument.

Like I said, he's an object lesson in what happens when one loves one's own theories too much. When faced with a contradiction between his theories (intended to preserve Newtonian mechanics) and Newtonian mechanics, he concluded Newtonian mechanics is wrong.

20. Oct 28, 2009

### Estif

That would be true if those two masses were the only ones in the universe and the distance between them was constant.

A third mass with an orbit in a different plane should make for a very good vantage point to judge what is going on with the first two. From this planet we would still not know if the system is moving or not as a whole, position of the Sun and where Sun was 8 minutes ago would still be the "same", but we should be able to see all the other relations.

But, even if the first two masses were the only ones, without instantaneous action and orbits being exactly around their present centers they would not be able to keep a constant distance and stable orbits, according to Newtonian mechanics, as I've have heard.

However, having a sky full of distant stars it's like having a grid or millimeter paper (absolute reference frame) that can serve as a guide for plotting mathematical functions and deduce relative motion, if not absolute one.

If we can easily measure 8 minutes delay with the light, why can't we do the same with gravity? Eight minutes is quite a delay, and if you try to simulate solar system with this delay, it will fall apart, according Newtonian mechanics, as I have heard.

What formula are you using instead of F= k* m1*m2/r^2?

How do you know it's more correct?

21. Oct 28, 2009

### JesseM

Oh, somehow I thought he was saying physicists are misunderstanding what GR says about the speed of gravity on a theoretical level. So what's his deal, he agrees GR predicts gravity travels no faster than light, but thinks there is empirical evidence that it actually does? But for any observation he might point to about how planets move in our solar system, isn't it possible to show that the movements match the predictions of GR, using a weak-field approximation or a numerical approximation or something?

22. Oct 28, 2009

### Estif

Are scientists equally divided in their opinions about this, or is there a majority? If there is a majority, then what is their explanation, what is their _official document explaining all this?

Is there an "official" kind of document for anything in science at all? I mean, we can't even agree if we are to consider a virus living or non-living thing, and I'm pretty sure there are many even more extreme examples of the division of opinions.

So, what do we do without majority?

And what do we do if majority is wrong, like in Galileo time?

23. Oct 28, 2009

### A.T.

Instantaneous action is merely the simplest way to make orbits work like they do, so Newton went with it. This doesn't mean it is the only way or the correct way.

Even without GR, you could modify Newtons gravity field to be non-instantaneous but have a velocity component inherited from the velocity of the field's source. The field lines in such a field emitted from a inertially moving source would point towards the current position of the source, not the position of their emission. See the electric field. No information is transported instantaneously, because the information about the source's velocity was already available at emission time.

I'm not saying that this is a good law of gravity. I'm just pointing out the flaw in the simplistic argument which goes like: "If objects are pulled to the current position of a moving mass, information must travel instantaneously"

Last edited: Oct 28, 2009
24. Oct 28, 2009

### Estif

I must agree, somewhat reluctantly though, because as a logical principle Occam's razor would demand that scientists accept the simplest possible theoretical explanation for existing data. It is the same principle that led to abandonment of the aether theories. But yeah, I'm with you... even if all seemed to fit perfectly well, it doesn't hurt to look for an alternative answers or interpretations.

You lost me. I like mathematics definitions and formulas most of all, they are much harder to misinterpret than worded theories, so if you can point some link where this is explained in a bit more depth?

I agree, but I do not see any other explanation.

So, what can we do?

First we have to assume quite a bit of determinism in this universe. Then, we can measure the real-world and come up with some theories, and these theories we should be able to re-phrase in mathematical formulas.

With this math all we need to do now is to predict the real-world measurements.

Prediction in deterministic universe should be straight forward... if we only had a power of precision, infinite divisibility, parallelism and continuity universe has. In other words, we need to do kinematic simulation, we need to integrate our equation over time and calculate trajectories, but we are bound to have errors.

So, we plug "F=k* m1*m2/r^2" in our numerical integration and we plot trajectories, step-by-step, the smaller the better, and we find this simple equation works remarkably well, especially considering all the imprecision that came in, not only due to limited computer precision, but also due to measurements of initial condition.

Hence, considering all that, this equation makes me happy.

To convince me otherwise, just give me a better equation, that's all.

25. Oct 28, 2009

### A.T.

Yes, but instantaneous Newtonian gravity doesn't explain all existing data: amount of light bending, orbit precession.

Take the electric field of an inertially moving electron. Even at a distance the field lines always point to the current position of the electron. Yet if the electron suddenly stops you see that the information about the stop propagates only at c. At distant points the field lines still point to the extrapolated position where the electron would be, if it didn't stop.
On the electric field;
http://farside.ph.utexas.edu/teaching/em/lectures/node125.html
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