# Carlip's explanation of lack of gravitational aberration

• hkyriazi
This problem with trying to determine the "speed" of anything is a longstanding one, and has been the subject of numerous papers and discussions.

#### hkyriazi

Last month I asked here whether there's a consensus about Van Flandern's speculations about the speed of gravity. I quickly learned that he's not well-regarded. Fine. I was hoping to be able to get something out of Steve Carlip's explanation for how GR explains the apparent almost instantaneous speed with which planets know about each other's current positions. (In 1805, Laplace estimated that the speed of Newtonian gravity would have to be at least 7 million c for the moon's orbit to be as stable as it is -- Van Flandern estimated at least 20 billion c, based upon more precise experimental findings.)

Carlip's article is at: http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9909/9909087.pdf

But, sad to say, I find the mathematics impenetrable, and wasn't able to get anything out of the prose, either (although his intro was excellent).

Can anyone here give me a "common sense" explanation of these velocity dependent terms that Carlip talks about, and/or the quadrupole nature of gravity? Here's Carlip's abstract:

"The observed absence of gravitational aberration requires that
“Newtonian” gravity propagate at a speed cg > 2 × 1010c. By
evaluating the gravitational effect of an accelerating mass, I show
that aberration in general relativity is almost exactly canceled by
velocity-dependent interactions, permitting cg = c. This cancella-
tion is dictated by conservation laws and the quadrupole nature of

I guess the level of explanation I'm looking for is, "the gravitational field of an accelerating object [somehow] warps spacetime preferentially in its direction of acceleration, such that its future position seems to be telegraphed ahead, and uniformly accelerating objects such as orbiting planets thereby achieve stable orbits..."

(I've read Purcell's E&M textbook's similar treatment of electrical charges with constant velocity telegraphing their future position, but the gravitational case is different.)

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Carlip's article is not dispositive of the issue nor was it intended to be - he makes the point that Van Flanderen's argument based upon the the apparent
lack of aberration is not valid evidence for faster than c gravitational action - Feynman discusses the same problem in the context of electrostatic fields.

I do not know if this is worth consideration - but the situation is somewhat analogous to what is observed with light from distant stars - we use the aberration angle to measure the Earth's motion relative to the light source - but it is not reciprocal - we cannot conclude anything about the relative motion of the light source from our measurment of the aberration angle- there are a number of radial photon paths eminating from the source - and if the source moves we are simply capturing a different ray to use when we measure the aberration due to the Earth's motion about the Sun - in the case of the gravitational effect of the Sun, the G field is radially divergent so as the Earth moves from one position to another our motion is affected by a different element of the radial spoke (so to speak)... so the next position of the Earth is influenced by a different radial angle. The effect is to appear as though the line of communication is instantaneous - this crude explanation works for the path of the Earth if it were moving in a straight line - but there is almost no curvature to the Earth's motion in a very short time element - so the effect "almost" exactly corresponds to a situation where the force points in the direction of the present position rather than the retarded position of the earth.

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As for gravitational radiation entering the equation in our solar system, the only bodies we have seen that emit this are massive binary pulsars, black holes, and extremely large bodies moving at extreme speeds, and last I looked we had no dual pulsars or other such in our solar system.

http://en.wikipedia.org/wiki/Gravitational_wave" [Broken]

All other gravitational radiation emitted from smaller bodies has already been shown to be virtually undetectable. So this may indeed apply to light passing binary pulsars, but no such explanation can be used for objects within our solar system.

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Consider the following problem. Determine the "speed of electromagnetism" based on an analysis of the coulomb force law.

One of Carlips many points is that if you analyze this simple E&M problem, you'll find that the "speed of electromagnetism" is "infinite", using the same logic one used to determine that the "speed of gravity" is infinite. This suggests that said notion of "speed" is flawed, otherwise we'd be arguing that the "speed of light" is infinite, and we know that is not the case from multiple experiments.

The usual issue is that people have some pre-existing intuitive notion of how this sort of "speed" is determined, rather than thinking it through. This makes any discussion of the point hard, because one can't demonstrate the errors in a chain of logic where there is no chain of logic.

If one makes some incorrect assumptions, it's possible to formalize the argument a bit more as to why the direction of a force should indicate it's speed, which helps to see where the problem is.

These incorrect assumptions would be that the E&M force is carried by a particle (which is pretty close, but the actual correct assumption is that it's carried by VIRTUAL particles ), that these VIRTUAL particles have an actual "speed" which is equal to the "speed of light" and is in a radial direction (I don't know if this is correct or not, it's a suspect assumption), that the momentum of a particle must point in the same direction as its velocity, (definitely untrue for VIRTUAL particles - see http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html which illustrates how the momentum might even be in the opposite direciton of travel, which is required for attractive forces ), and that said virtual particle is absorbed by the receiving particle transferring its momentum (probably an OK assumption).

Given these incorrect assumptions, one can envision detecting the change in state of the motion of a test charge by observing the force on a stationary test charge some distance away. Unfortunately, these assumptions are still incorrect.

One of the points of Carlips paper is that if you actually analyze Maxwell's equations to get the E&M field of a moving charge, this simple scheme for measuring "speed of propagation" doesn't actually work. To see this requires that one have the mathematical / physical background to actually work with Maxwell's equations - div, grad, curl and all that. Sorry, but sometimes one DOES have to actually sit down and study the math to get good physics!

One will find discussion of this issue in E&M textbooks as well as in Carlips paper - it's usually talked about as the Coulomb gauge vs the Lorentz gauge - but typically said discussion is even more technical than Carlip's paper.

hkyriazi said:
(I've read Purcell's E&M textbook's similar treatment of electrical charges with constant velocity telegraphing their future position, but the gravitational case is different.)

The only real difference, as Carlip points out in his paper, is that gravitational radiation is quadrupole whereas electromagnetic radiation is dipole. That means that, in gravity, objects with constant *acceleration* will "telegraph their future position", instead of objects with constant *velocity*. (The relationships, "dipole <-> constant velocity telegraphing future position, and quadrupole <-> constant acceleration telegraphing future position, are dictated by conservation laws.) Other than that, everything works the same.