Is the speed of gravitational waves constant in all inertial frames? If so, why isn't this included as one of the postulates of special relativity?
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Related: https://physics.stackexchange.com/q/5456/2451 and links therein. – Qmechanic Jul 11 '17 at 15:42
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Keep in mind that since what we call gravity is really the geometry of spacetime, gravitational waves can't exist in flat space. Gravitational waves are propagating fluctuations in spacetime curvature. Thus, there's no place for global Lorentz invariance here. However, in the linear approximation (limit of small amplitudes), the answer is clearly yes: gravitational waves propagate with the speed of light $c$. – Prof. Legolasov Jul 12 '17 at 00:15
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2Possible duplicate of How fast does gravity propagate? – Jason C Jul 12 '17 at 01:41
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Why would it need to be a postulate of SR? – Kyle Kanos Jul 12 '17 at 10:06
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The light speed postulate could have referred to anything applicable, or simply said there is an invariant speed. This implies Lorentz invariance instead of Galilean invariance. The resulting energy-momentum relation includes a parameter called the rest mass or invariant mass. We can then prove traveling at speed $c$ is equivalent to this parameter being $0$, which applies not only to photons of light but also to any massless particle or field.
J.G.
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1I'd replace the last part with "not only to photons but also any massless gauge boson." – JamalS Jul 11 '17 at 15:49
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@BradS Experimentally we don't, but the differential equations governing gravity allow us to verify the speed anyway. – J.G. Jul 11 '17 at 16:17
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@BradS Seconding what J.G. said, we can technically say that the speed of the as yet theoretical construct we call a graviton would travel at speed $c$. – JamalS Jul 11 '17 at 16:24
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@LightnessRacesinOrbit Based on this + the linked answer, "This has not yet been experimentally verified to everyone's satisfaction, but there are several excellent theoretical reasons to believe gravitational waves propagate at $c$", I think. – zwol Jul 11 '17 at 20:33
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2@zwol: I'm asking the author to summarise the answer in the answer! – Lightness Races in Orbit Jul 11 '17 at 20:56
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Your question is a bit more involved than one might think because it depends on exactly what you mean by a gravitational wave.
In relativity, both special and general, the local speed of a massless particle is always equal to the speed of light. Note that I say local speed because the speed of light is complicated in general relativity. For more on this see GR. Einstein's 1911 Paper: On the Influence of Gravitation on the Propagation of Light.
Now, when we say gravitational waves we normally mean an infinite plane wave of a magnitude small enough that it's propagation is linear. By this we mean that the energy if the gravitational wave is low enough that we can neglect the effect the energy of the wave has on the geometry of spacetime. In this case the local speed of the gravitational wave is always the same as the local speed of light. We don't include this as a postulate because it isn't a postulate. We get this for free from Einstein's equations.
When we get spacetime fluctuations so intense that we can no longer ignore backreaction life gets more complicated and I confess I'm not sure what the answer is. Part of the problem is that speed is not well defined for something that isn't an infinite plane wave. However my understanding is that the speed at which all changes to the spacetime geometry propagate is basically the speed of light.
John Rennie
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