greywolf42 wrote:
The speed of gravity could indeed be greater (different) than the speed of
light. Einstein assumed that the speed of gravity was equal to the speed
of
light, when he developed his General Relativity. However, the only direct
measurements of the speed of gravity are the perihelion advances of
orbits.
Mercury in this solar system, and a few stars.


Consider the weak field limit where SR is a good approximation. Very
general considerations preclude signals (and that would include
gravitational effects) being sent faster than light.

Consider sending information from P to Q FTL at some speed U in some frame
S. Chose coordinates so both events occur on the x axis and let their time
and distance representations be delta t and delta x respectfully. Consider
another reference frame S' moving at velocity v so we have from the Lorentz
transformation:
delta t' = lambda (delta t - v delta x/c2) = lambda delta t (1 - Uv/c2).
Choose v such that c2/U v c then delta t' would be less than 0 implying
in that frame the signal left before it arrived. This violates causality so
FTL signaling is not possible.

Also the assumption that gravity travels at the speed of light is not
necessary to justify general relativity (GR). The basic ideas of GR are as
follows:

1. The principle of general invariance which asserts that the laws of
nature should be put in a form that is the same in all coordinate systems.
When put in this form it is assumed that natures laws obtain their most
elegant and transparent form. The specific physical assumption made is that
you are able to determine the nature of the terms in the equations when put
in such a form.

2. Coordinate systems can be found such that locally any point in space time
behaves for all practical purposes like an inertial frame ie by suitable
choice of coordinates gravitation can in any very small region and for a
very small instant of time be made as small as we like so that it can be
considered inertial. This is the basically Einstein's equivalence
principle. In such a small regions Special Relativity (SR) applies - but it
may not apply in other coordinate systems so that the speed of light is not
constant as in SR. However it would still not be possible to send
information faster than whatever that speed is - if you could then you could
go to the locally inertial coordinate system and send signals faster than
light - in violation of the argument above.

2. Nature has no prior geometry. The physical consequence is that something
called the metric is then a dynamical variable. Once this assumption is
made general considerations on the most reasonable lagrangian lead
immediately to Einstein's Field Equations (EFE) which is the crux of GR.

As you can see no assumption was made about the speed of gravity; but quite
general consideration preclude gravity propagating faster than light. Also
an analysis of the weak field limit of the EFE's show gravitational waves
and other effects can not propagate FTL. In fact it predicts gravitational
waves propagate at the speed of light.

Thanks
Bill