The speed of light is now defined as 299792458. m/s
But what is the speed of gravity ?
One can show that gravitational waves propagate at c, just like the e-m ones.
Almost a century ago Einstein predicted gravitational waves, they have yet to be observed. I do find it interesting that the velocity of gravitational wave propagation is asserted to be c. But without seeing some basis for that assertion, it strikes me as wishful thinking, and so requires me to have faith. That gravitational waves propagate at c seems at first sight to be eminently acceptable, and sure is neat. But “It can be shown” does not really convince me as I am stubborn and of little faith.
I know that c, the velocity of EM waves in space, is determined by the product ε0 μ0 = 1 / c2
So just what fundamental universal parameters determine the speed of gravitational wave propagation in space.
Do we even have a concrete definition of what "the speed of gravity" means outside of linear gravity?
I mean in EM we could solve the vacuum wave equations, where c just emerged out of, but in full blown non-linear GR we of course don't have those neat equations.
On the other hand, the speed at which gravitational waves propagate must be frame invariant, which means it must locally be C.
There is only one fundamental constant in Maxwell's Equations, namely c. The so-called 'permeability of free space' μ0 is inserted solely for the benefit of Electrical Engineers. It's unfortunate that introductory E & M courses make it seem otherwise. In fact μ0 has the exact defined value of 4π x 10-7. Maxwell's Equations written in Gaussian units, for example, contain neither ε0 or μ0, only c.
There are a bunch of good references in the FAQ at the top of this forum:
Yes, this is a good explanation, and serves to remind us that General Relativity is not the only nonlinear theory in the world. The theory of nonlinear PDE's and their associated wave motions is well developed.
The velocity of wave propagation is studied as high frequency, small amplitude perturbations on a background, or equivalently as the propagation of discontinuities on that background. Wave fronts are the characteristic surfaces, and information propagates along the generators of those surfaces, i.e. the bicharacteristics.
In the high frequency limit we keep only the highest derivative terms in the PDE, and for GR this means the wave operator on a curved background. The characteristics are the null surfaces in the background geometry, and the bicharacteristics are its null geodesics.
I see Bcrowell raises the same objection in this ref as he did here when the subject last came up, namely the existence of wave tails, a nonlinear effect which trails behind the wave. But it is only the leading edge of the wave which matters, and the wavefront always propagates at c.
DO you happen to know of a good textbook delving into detail on these and related topics (non-linear wave PDEs)? Thanks Bill.
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