Re: The speed of gravity revisited

Tom Roberts writes:

[Carlip]: a gravitating object -- call it A -- moving at a constant velocity suddenly stops. What happens to the motion of a test body B a distance R away from the point that A stops?

{TomVF]: This has nothing to do with the issue on the table, the propagation speed of gravitational force. It concerns only the propagation speed of changes in the gravitational potential field, about which there is no dispute -- it is speed c. We don't need A to be moving, then stop, as in your example. The issue of relevance here is present even when A is permanently at rest and its field is completely static. The direction of the source mass as sensed by an orbiting target body is toward its true instantaneous position when the target body or field point is at rest. And it is toward the source mass's retarded position (retarded by the speed of gravitational force) when the target body is orbiting. That's elementary physics.

[Roberts]: So you claim that the "gravitational force" in Steve's example is not the "gravitational force" in yours (in general, abstracting away the differences in physical situations). That is ridiculous.

No, it is not ridiculous, and you are apparently not following the discussion. I objected to Steve's example because it tried to insinuate that my position required field changes to occur faster than light, which no one claims. Gravitational aberration much exist even for perfectly static (unchanging) fields, as well as for fields experiencing a sudden impetus to change, as in Steve's example. So his example serves to obscure the issue, not to clarify it.

As is well known, the unique math of GR has more than one physical interpretation. In particular, physics is concerned about the direction of the arrow of causality, whereas math is not. So when we say "force is the gradient of potential", the geometric interpretation of GR simply assumes that the gravitational potential field, as described by the Einstein field equations, governs; and that a gradient in that field causes a force. However, the geometric interpretation of GR is no longer viable because it violates physical principles. So we are forced to adopt the other physical interpretation, that gravitational force induces a gradient into the gravitational potential field. The arrow of causality is reversed. The math, of course, is insensitive to this and remains unchanged.

So in Steve's example, when a source mass "A" changes its state of uniform motion (as happens for binary pulsars in their mutual orbits), observations are very clear that the force on distant target bodies changes almost instantly, and always operates in the new direction of A. (Any delay is immeasurably small.) Then this changed force operates on the field, and alters the density of the physical potential field surrounding A. Field changes occur at the speed of light, and eventually conform to the new location and motion of A, but only after a delay, just as the Einstein field equations specify.

I gather from our past exchanges that you have not been trained in classical physics, and are familiar only with the geometric interpretation of GR. I highly recommend you broaden your horizons. True understanding of nature cannot be achieved through math alone. You need to study the two different physical interpretations of GR, then come to understand why one of them (the geometric interpretation) is now off the table, and why the other (the field interpretation) makes the physics of gravity easier to understand for everyone.

[Roberts]: You claim Steve's example is "propagation speed of changes in the gravitational potential field". But the gradient of the potential gives the force (in your model), so "gravitational force" also "is speed c" -- either that is true or you disbelieve mathematics.

The field interpretation of GR existed before I was born, and is therefore not "my model" even though I have published extensively about it. In the field interpretation, the force causes the gradient in the potential field instead of vice versa. The force propagation speed (the "speed of gravity") is much faster than the speed c at which the physical field can change in response to changes in the force.

In modern expositions of the field interpretation of GR, the gravitational potential field is synonymous with the light-carrying medium, now called "elysium". Einstein hinted at this, but did not state it quite so clearly. Gravitational force is responsible for most orbital motion (except the perihelion advance), and it makes elysium denser near large masses, just as it does for planetary atmospheres. The special GR effects such as light-bending are then simply refraction in elysium because of this density gradient near masses. This is simple, classical physics, and is well known in the relativity literature. Even Eddington spoke of it in his 1920 book "Space, Time and Gravitation".

[Roberts]: The problem is: your model is inconsistent with "gravitational force" propagating at speed c; but the appropriate approximation to GR is not inconsistent with that, nor is GR itself.

That statement is flatly wrong. You really need to get yourself straightened out about that point. Ask Steve Carlip or anyone who knows relativistic dynamics. No model that has gravitational forces propagating at speed c can reproduce the orbital motions of the planets. GR itself is about the field, and says nothing about forces without making additional assumptions about the nature of potential gradients. What you call the "approximation" to GR has explicitly instantaneous forces with propagation delay set to zero. The only light-speed propagation delays anywhere in GR occur in the field. But the most important manifestation of propagation delay, gravitational aberration, is set to zero when field gradients are used to calculate forces or when it is applied to an orbiting body.

To show otherwise, all you have to do is show where the gravitational aberration exists in the equations of motion. Such a term is easily spotted: It must be proportional to v/v_g, where v is the relative transverse speed of any orbiter and v_g is the speed of gravity, which (you wish to argue) has been set equal to c. No such term exists. Steve Carlip knows that full well, and he argued that some "velocity-dependent term" must exist to cancel gravitational aberration. My 2002 paper with Vigier in Foundations of Physics showed that, while such a hypothesis would be required to conserve angular momentum when forces propagate at speed c, no possible physical justification exists.

However, I infer that you would rather continue to hurl insults on USENET than to read the published literature and judge the merits of the arguments for yourself, or possibly even make a useful contribution to the on-going dialogue.

[Roberts]: Steve's example is a COUNTEREXAMPLE to your claim "The direction of the source mass as sensed by [the] target body is toward [the source's] true instantaneous position". That is, of course, why he mentioned it.

On the contrary, binary pulsars prove that when the source mass accelerates (as in Steve's example), the target body responds almost instantly. Your impression to the contrary is indefensible, and is keeping you from seeing the validity of our criticism of the geometric interpretation of GR. Unless you remedy this knowledge deficit, you will die no wiser than you are now about relativity and the physical nature of gravity. No one in the know challenges the fact that much better than a linear extrapolation of the field is required to explain orbital dynamics.

[Roberts]: As has been repeatedly pointed out, for the situation you discuss an approximation to GR is valid, and in that approximation the "gravitational force" points directly to the EXTRAPOLATED position of the source. For the situations you consider, that EXTRAPOLATED position is indistinguishable from its present position [#]. But for Steve's situation they are different, and clearly show the error in your claims, WHEN USING THIS APPROXIMATION TO GR.
[#] This is why the experiments you cite do not refute GR.

Once again, you are dead wrong on your two major points. (1) For the situations I consider, one of which is binary pulsars, the linearly extrapolated position is easily distinguished from the present position. The difference is major because the accelerations during the light-time between the two stars are large and significant. (2) Please write a reminder to yourself, because this is the nth time I've had to remind you: I do not claim any experiment refutes GR, meaning the mathematical theory. Not one iota of it needs to change. But one of the two physical interpretations of GR (the geometric) that have existed for nearly nine decades is now falsified in favor of the other (the field interpretation).

If you don't know or care anything about the physics behind GR, then this change of physical interpretation need not concern you. But then you will never understand what this discussion is about.

[Roberts]: I repeat: your basic problem is confusing NG with GR. Indeed, you even confuse NG with this approximation to GR.

All of my statements are in a GR context. You seem to be so unfamiliar with the physics behind GR that you are unable to distinguish GR physics from NG physics. If so, that's not my problem; it is something you must remedy.

[Roberts]: It is not possible to ascribe a "speed" to a static field. That is, in a static situation it simply is not possible to distinguish among models in which "gravitational force" propagates with different speeds, because for any propagation speed whatsoever one obtains the same "gravitational force" and its direction.

When changes are imposed on a static field, they spread out with a certain speed. In the case of the gravitational potential field, that speed is the speed of light. But whether the field is changing at speed c or static with no speed, that has no bearing on gravitational force and its propagation speed.

Your statement about gravitational force betrays a lack of understanding of the physics of forces. When two bodies have a relative transverse motion, and a force (or anything else) passes linearly between them at a uniform speed, the receiving body will sense the force approaching from the retarded direction of the source, not its instantaneous direction. That much is unconditionally true.

The ratio of the relative transverse speed of the two bodies to the force propagation speed passing between them is called "aberration". If the force appears to come from the instantaneous position of the transmitting body (as it does for gravity), the aberration angle (measuring apparent motion during the light-time) is zero. Since the relative speed is not zero, the force propagation speed must be infinite (or at least very large) to make the aberration speed ratio approximately zero. Again, this basic physics has full generality.

When the propagating force is light (e.g., radiation pressure force) and travels at light-speed, the aberration angle is large and easily seen. But for gravity, that aberration angle is zero to the accuracy of our best observations. Hence, the speed of transmission of gravitational force from source to receiver must be much faster than light-speed. It simply does not matter that field changes (if any are needed) happen much slower.

[Roberts]: The other problem is you keep assuming that "gravitational force" is a central force, and in the approximation to GR it simply is not. In GR itself there is no quantity that can be identified as "gravitational force"

What you call "GR itself" appears to refer to the field equations and their solutions. I agree, these describe only the field, not the forces that form and change that field. Once again, when thinking physics, "field" can be considered a synonym for "light-carrying medium".

The GR equations of motion are expressions for the 3-space acceleration of target bodies with respect to source masses. Because "force" is by definition the time rate of change of momentum, and momentum is the product of target mass and target relative velocity, it follows that the force acting on the target body is given by the product of its own mass and the 3-space acceleration from the GR equations of motion. But those equations of motion are based on central forces. Any deviations from central forces are second order in the speed of light (i.e., proportional to 1 / c^2), and are too small to significantly affect aberration or any of the experiments or reasoning I described above.

But you know math. You should have been able to see that for yourself, and not raise this straw man argument about central vs. non-central forces as if it had some relevance to this discussion. The difference is too small to affect this discussion by a substantial margin (many orders of magnitude).

[Roberts]: Your claims about the orbiting body are basic math: in the frame of the source the "gravitational force" is central. Transform to the instantaneous rest frame of the orbiting object and of course the "gravitational force" will still point directly at the source.

This statement refers to a "non-propagating force", something that has no meaning in physics, where forces involve momentum by definition. If a force propagates, then a snapshot of the system with nothing moving is meaningless for understanding its dynamics. For a propagating force, your statement is false. The direction of the force in the rest frame of the orbiting body is the retarded position of the source, not its instantaneous position.

If you might benefit from a refresher on propagation delay and aberration, see our animation #4 at http://metaresearch.org/media%20and%20links/animations/animations.asp

[Roberts]: The problem is: this is NOT the math of GR. It is the math of Newtonian gravitation. It is also not the math of the approximation to GR that I am discussing.

What I've said here is in a relativistic context, not a Newtonian one. If you choose to define GR so narrowly that relativistic physics, relativistic dynamics, and relativistic celestial mechanics are excluded, that would make your claim that it "is NOT the math of GR" true but of no practical value. [shrug]

[Roberts]: you do not understand GR, which you repeatedly demonstrate, but refuse to admit.

Then why are my papers published and yours are not? And why do you continue to make claims that are in hard conflict with experimental facts when attempting to show that you understand GR better than I do?

[Roberts]: why do you keep claiming you are using GR when you QUITE CLEARLY are not?

Perhaps it is because I deal with the real world and you deal with a mathematical idealization for which the only physical interpretation you are familiar with has now been discarded.

[Roberts]: You repeatedly claim Steve (and I) are ignoring the "physics behind the math". The problem is YOURS, not Steve's or mine -- you are confusing Newtonian gravitation with General Relativity. The physics is DIFFERENT. Until you actually learn about GR, you will remain confused.

In this discussion, one of us is answering every point by addressing observations, experiments, citations, or argumentation. And one of us is simply repeating bold claims without any new attempt to justify them. Shall we let the readers decide which of us matches which description? :-) -|Tom|-


Tom Van Flandern - Sequim, WA - see our web site on frontier astronomy research at http://metaresearch.org

.

Relevant Pages

  • Re: Tom Van Flandern and Newtonian Gravity
    ... replacement physics interpretations for the math of GR and QED. ... to the notion that superluminal speeds contradicted causality. ... propagation of gravity in forward time, ...
    (sci.physics.relativity)
  • Re: The speed of gravity revisited
    ... Special relativity has now been falsified in favor of Lorentzian relativity. ... ** six experiments showing that the propagation speed of gravitational force is>> c, which contradicts SR, but is in accord with LR having no speed limit. ... If your only concern is that the Lorentz transformations do not work for speeds above c, the references explain why this is not a problem for LR. ... I am always careful to state that "the speed of gravity" measured by the six available experiments always means the 3-space propagation speed of gravitational force, and has nothing to do with changes in gravitational potential. ...
    (sci.physics.relativity)
  • Re: The speed of gravity revisited
    ... Carlip's paper showed that orbits are also consistent with light speed propagation, due to a subtlety of retarded potentials also present in the Lienard-Wiechert potentials of electromagnetism. ... Yet you are so accustomed to assuming that the speed of field changes must be the same as the speed of the associated force that your mind is resisting the obvious: the two speeds are quite different and have no connection to one another. ... The orbits of the Moon and artificial satellites would change because the Sun would no longer be perturbing them. ... And that would coincide with the moment the Sun's gravity ceased, not the moment when the Sun's light showed us the disaster. ...
    (sci.physics.relativity)
  • Re: The speed of gravity revisited
    ... a theory with infinite force propagation speeds that gives strongly spiral orbits if the force ... 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. ... The instantaneous and retarded source positions of the source mass are well-distinguished for target bodies with ordinary solar system speeds. ... In physics, something must contact something else to produce any action. ...
    (sci.physics.relativity)
  • Re: Van Flandern & Rethinking Relativity?
    ... are both propagation delay effects which by themselves produce orbital ... See "The speed of gravity - What the experiments say", ... > particle is always moving in time; for weak fields and slow speeds, ... can be done without accelerations, turn-arounds, or frame changes. ...
    (sci.physics)