Aberration and the Speed of Gravity - by S. Carlip 1989 - Article review

This document contains article review "Aberration and the Speed of Gravity" by S. Carlip written in 1999
To order to read the article select: https://arxiv.org/abs/gr-qc/9909087



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In a recent paper in Physics Letters A [1], Van Flandern has argued that observations show that gravity propagates at a speed much greater than c.
From a technical point it is very important to handle this claim based on actual observations serious. The first step is to define the speed of light and how the speed is measured. The same with the speed of gravity.
In each process two events are important: the start of the lightsignal and the measurement
In the absence of direct measurements of propagation speed, Ref. [1] relies instead on directional information, in the form of observations of (the absence of) gravitational aberration.
What this implies is a good description between aberation and the speed of light versus the speed of gravity.
But the translation from a direction to a speed requires theoretical assumptions, and the implicit assumptions of Ref. [1]—in particular, that the interaction is purely central, with no velocity-dependent terms—do not hold for general relativity, or, for that matter, for Maxwell’s electrodynamics.
What is important is to understand the physical difference between aberation using light and graviational aberation. Secondly it is important how both are calculated and finally are measured in reality.
Although gravity propagates at the speed of light in general relativity, the expected aberration is almost exactly canceled by velocity-dependent terms in the interaction.

1. Aberration in Electromagnetism

By analyzing the motion of the Moon, Laplace concluded in 1805 that the speed of (Newtonian) gravity must be at least 7×10^6c. Using modern astronomical observations, Van Flandern raised this limit to 2 × 10^10c.
But this argument, at least in its simplest form, holds only if one postulates that the relevant force is purely central and independent of the source velocity
Any argumentation should be based on the physical interpretation of how the force of gravity operates. See also Reflection 2 - 3 body problem. . It should be mentioned that the only way to discuss this subject based on actual experiments or observations.
As a warm-up, let us first consider electrodynamics.
It is well known that if a charged source moves at a constant velocity, the electric field experienced by a test particle points toward the source’s “instantaneous” position rather than its retarded position.
It is very important to describe the experiment which describes this, in great detail. The question is how practicle this experiment is, beacause in all experiments there are is always accelerations involved.
Lorentz invariance demands that this be the case, since one may just as well think of the charge as being at rest while the test particle moves.
What Lorentz invariance always should imply that every process should be in agreement with actual experiments or actual observations.
It is also important what we mean with at rest.
If two observers are both in revolution around each other, it is physical impossible to assume for both observers, that one is at rest and the other moving.
The only solution is to assume one reference frame. This becomes more tricky if three objects are involved. This problem is discussed in more detail in Reflection 2 - 3 body problem.

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2. Aberration in Gravity

The Einstein field equations are consistent only when all gravitational sources move along the trajectories determined by their equations of motion, and in particular, we can consistently represent an accelerated source only if we include the energy responsible for its acceleration.
Both requirements are difficult to understand. How do you know that all objects move along the equations of motions. The physical evolution of any process is the result of all the forces active within the process. It should again be mentioned that in all physical system accelerations are involved.

3. Is the Cancellation a Miracle?


Reflection 1 - Length contraction versus length expansion

To test length contraction we can perform the following experiment: Assume a straight long train on a straight track. At the start of the experiment the train is positioned at the beginning of the track. There is one observer A at the beginning of the track and one observer B at the end of the track. There are also two observers C and D at both ends of the train.
train |C-------D>
track A----------------------------------------------------------------B
The whole experiment involves that the train moves from start to finish or from observer A to observer B. When the experiment is finished all the observers will be asked the same question: What did you observe?
  1. Observer A answers: From start to finish I saw, the back of the train become smaller and smaller.
  2. Observer B answers: From start to finish I saw, the front of the train become larger and larger.
  3. Observer C answers: From start to finish the front of train (the length of observer D) always had the same size.
  4. Observer D answers: From start to finish the back of train (the length of observer C) always had the same size.
Common sense reasoning requires that at each (next) moment the train can not, both become longer and shorter.
Using that it can be concluded that both observations are wrong.
The general conclusion is that based on all observations that the length and size of the train does not change.
A second conclusion is that what each observer observes is not always in agreement with the physical reality.

  • It is for example possible that when observer A looks careful, that observer C starts to move before observer D. This implies length contraction.
    This effects is caused because it takes more 'time' for a light signal to travel from observer D to A than from C to A. This is because D is futher away as C (from the point of view from A). As such A will see the state of observer C at an earlier moment as the state of observer D. That means C is further away and the train seems shorter.
  • It is for example possible that when observer B looks careful, that observer D starts to move before observer C. This implies length expansion. This effects is caused because it takes less 'time' for a light signal to travel from observer D to B than from C to B. This is because C is futher away as D (from the point of view from B). As such B will see the state of observer D at an earlier moment as the state of observer C. That means C is further away and the train seems longer.

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