Re: The speed of gravity revisited
- From: "Tom Van Flandern" <tomvf@xxxxxxxxxxxxxxxx>
- Date: Tue, 30 Sep 2008 17:14:44 -0700
Tom Roberts writes:
[TomVF]: As even you know, the propagation speed of gravitational force in Newtonian gravity (NG) is infinite. And as every student of celestial mechanics knows, when the propagation speed is reduced in NG (with no other changes), orbits become open spirals instead of closed ellipses.
[Roberts]: Yes. But why bring up a FANTASY theory? As even you OUGHT TO know, this has NOTHING WHATSOEVER to do with GR.
You claim GR reduces to NG in the weak-field, low-velocity limit. Therefore GR reduces to a theory with infinite force propagation speed in that limit. Right?
The difference between infinite force propagation speed and forces propagating at the speed of light is *huge* in all theories, even for weak-field, low-velocity cases. Right?
Therefore, for all cases near this limit, GR must approximate infinite force speed, not forces propagating at the speed-of-light. Right?
That is why the point matters to this discussion.
[TomVF]: The original point is that it is impossible to have a system in which gravity is the only operating force, yet have that force propagate at less than infinite speed and still have closed orbits.
[Roberts]: This is just plain not true. Yes, it is impossible to combine the equations of NG with a finite propagation speed and still have a valid theory, but that is just your personal FANTASY. GR itself has no "propagation speed", and the linear APPROXIMATION to GR I have discussed combines a finite propagation speed with DIFFERENT EQUATIONS.
Stop changing the meaning of words in mid-argument. We are talking 3-space, in which orbiting bodies experience force by definition of the word ("the time rate of change of momentum"). And all forces have a velocity of propagation because they carry momentum, which is normally the product of mass and the velocity of propagation of the force carriers.
In this 3-space context, your shouted claims make no sense. In a 3-space context, any physical interpretation of gravity that lacks force or carries no momentum is useless because no target body could be induced to begin moving or change its existing motion.
[Roberts]: Just because NG plus finite propagation speed fails does NOT mean that it is "impossible" for a valid theory to have finite propagation speed. The linear approximation to GR is an explicit counterexample to your claim.
If gravity is the only force acting, then yes, it is impossible for a theory with force propagating at the speed of light to conserve angular momentum. The proof is elementary. I quote Eddington's succinct argument:
"If the Sun attracts Jupiter towards its present position S, and Jupiter attracts the Sun towards its present position J, the two forces are in the same line and balance. But if the Sun attracts Jupiter toward its previous position S', and Jupiter attracts the Sun towards its previous position J', when the force of attraction started out to cross the gulf, then the two forces give a couple. This couple will tend to increase the angular momentum of the system, and, acting cumulatively, will soon cause an appreciable change of period, disagreeing with observations if the speed is at all comparable with that of light."
That argument has full generality and applies to all theories where gravity is the only force acting. Do you see any way to refute it?
[TomVF]: "GR becomes a theory with infinite force propagation speed in the weak-field, low-velocity limit."
[Roberts]: Hmmm. GR does not "become" such a theory, it is APPROXIMATED by such a theory. As others have pointed out, "reduces" implies a rigorous process, and this is an APPROXIMATE relationship, not a rigorous one.
I too have argued that infinite propagation speed is only an approximation for a very fast speed. But that does not change the fact that forces propagating at the speed of light are ruled out. To represent real orbits, the force propagation speed must be very much faster than light propagation speed. Astronomers easily see the retardation of light and of radiation pressure forces caused by light, but they see zero retardation for gravitational forces.
[Roberts]: In GR, nothing that carries energy, momentum, or information can travel faster than c. This is a rigorous result based on the structure of the ACTUAL THEORY.
[TomVF]: That *belief* of yours is definitely NOT a rigorous result based on the structure of the actual theory, and you cannot defend such a claim that it is.
[Roberts]: Nonsense. This is not merely my claim or "belief" -- there is literature on this.
Be careful. You came dangerously close to supplying an actual citation instead of just another unsupported claim. :-)
In point of fact, the proof that your claim is false is the existence of Lorentzian relativity as a still-viable theory for the relativity of motion, yet one that lacks *any* universal speed limit. And GR is based on LR rather than SR because the Lorentz transformations are used only from the local gravitational potential frame to any moving frame, but not back again.
GPS satellites are an obvious example of this. The orbiting satellites are synchronized with the master ground clock, but never the reverse. In that way, GPS uses an effective frame-independent time scale for all clocks in all frames.
[TomVF]: This has nothing to do with ordinary gravitational force that causes elliptical orbits. It relates only to light-bending, perihelion advance, and other small (c^-2) GR effects that arise from the potential field (or whatever you want to call it in 4-space).
[Roberts]: No. Just look at the equations -- the ENTIRE equation is solved with a Green's function that has the interaction propagation at c. This is not a perturbation or add-on, it is the complete solution.
It would be nice if you could cite such an equation so we could both look at it and see what it really says. As my cited journal articles showed, the only places where light-speed interactions occur in GR is analogous to where they occur in electrodynamics: retardations in the potential field with changing mass distribution or changing distances. However, the main effect of retardation, the aberration that must occur for any target body with a transverse speed, is neglected. Therefore, zero aberration (infinite force speed) is being used whether one says so or not. The places where retarded potentials are used have no observable consequences, and are therefore untestable.
The reference for this is: T. Van Flandern, "Reply to comments on 'The speed of gravity'", Phys.Lett.A 262:261-263 (1999).
[Roberts]: GR is consistent with the experiments. So is the linear approximation to GR in which the interaction between source and object propagates rigorously at c ...
Nope. The linear approximation to GR uses infinite force propagation speed. Vigier and I demonstrated that in our "Foundations of Physics" paper (previously cited), where we show the linear approximation of GR with and without the speed of gravity term. So we have our reasoned, published, peer-reviewed demonstration against your unsupported claim. Do you care to add any substance to your side of this debate?
[Roberts]: using the extrapolated position gives results indistinguishable from using the instantaneous position (as NG itself does). This is essentially what the linear approximation to GR does.
Originally, you spoke of linear extrapolations. Apparently, you have now learned that linear extrapolations are not good enough. So now you refer vaguely to "extrapolated position" without defining that term.
It should be evident to anyone who knows basic math and geometry that the instantaneous position can be decomposed into any number of components; for example, a retarded position (retarded by any amount) combined with an extrapolation of sufficiently high accuracy. While it is trivial that such a thing can be done, there is no physics behind such a decomposition. Even a linear extrapolation would be unjustified in physics because the field is static. But a quadratic extrapolation has no imaginable physical justification. And it is trivial to claim that one can do it. I could use the same process to argue that the speed of gravity was the speed of a snail. All I need is an elliptical extrapolation from that "snail-retarded" position.
Basically, any speed whatever could be justified by such a process, because all lead to the only position that matters: the true, instantaneous position of the source mass.
[TomVF]: Yet the only way to predict the correct orbits is with zero retardation of gravitational force in both theories.
[Roberts]: Again this is just not true. In the linear approximation to GR, one uses the extrapolation from the retarded position of the source. The equations have no term with "zero retardation", yet the equations accurately agree with measurements
You can call it the extrapolated retarded position if you like. The same terminology covers the snail-retarded position as well. But by any name you choose, it remains a fact that orbits depend only on the instantaneous position of the source mass, no matter how you choose to get there. And there is no possible physical justification for nature doing any extrapolating for static field cases in which gravity is the only force acting.
[Roberts]: the equations actually involve only the retarded position, retarded velocity, and retarded acceleration of the source. That, in turn, rigorously shows that the interaction propagates with speed c.
Not so. You could use any imaginable retardation and corresponding propagation speed in the neighborhood of c or faster and do the same thing. There is nothing about the real world that suggests a speed as slow as c for gravitational force. On the contrary, all relevant experiments show FTL propagation of gravity.
[Roberts]: the rest of us do not have that special "channel to God" that you have, which tells you what "causality" means.
My college physics teacher might be flattered by being compared to God, but I confess that my basic physics education and a handy dictionary were sufficient for me to learn what "causality" means. For example, my Encarta dictionary says: "cause: a person or thing that makes something happen or exist or is responsible for something that happens"; "effect: a change or changed state occurring as a direct result of action by somebody or something else"; "causality principle: every effect has an antecedent, proximate cause". Didn't you take that course?
Physics is all about the material, tangible objects that act as causes and produce effects. Math is as oblivious to the causality arrow as it normally is to time's arrow, which is why it needs continual guidance from physics if it is expected to apply to reality.
[TomVF]: In 3-space, curvature alone cannot initiate motion in the absence of a force.
[Roberts]: Again that is your FANTASY theory, not GR. in GR, the curvature is in spaceTIME, and it most definitely CAN "initiate motion" in the absence of "force" (e.g. it accurately predicts the trajectory of a dropped stone, which is initially at rest wrt the surface and starts moving wrt that surface just due to the form of the geodesic path it follows once released).
You switched the conversation back to math and 4-space. I'm talking physics and 3-space. Kindly make an argument, if you can conceive of one, that curvature of anything in the absence of a force can initiate motion in 3-space. Otherwise, kindly concede that your argument does not apply to reality.
The entire point of relevance here is that nothing can change a body's state of 3-space motion or non-motion unless a force is applied to it. It is not relevant here to show an equation that can describe the motion because equations cannot *cause* motion.
[TomVF]: If a small body is at rest in a gravitational field, "curvature" of anything cannot make it begin to move. It will just stick there on the side of a potential hill forever, until a force acts.
[Roberts]: Again you display your ignorance of GR -- if what you say were true, GR would be immediately refuted by everyday observations; GR has not been so refuted.
Don't be melodramatic. Only your understanding of GR is at risk here, not the theory itself. The field interpretation of GR works just fine and requires no changes in its math. But the field interpretation says gravity is an ordinary force operating in 3-space.
Do you claim that something *can* initiate 3-space motion in the absence of a force? I'd love to see you try to defend *that* claim. -|Tom|-
Tom Van Flandern - Sequim, WA - see our web site on frontier astronomy research at http://metaresearch.org
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