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
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.
Okay
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.
Okay
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.