Why does the velocity of gravity wave equal to c?
Can you answer why speed of light is c? I think the reason should be same.
I'll take a crack at it, I'm a big time laymen myself
I think it is because like the photon (packets of light) which is a massless force communicating particle (a boson) the thereotical graviton is the massless force communicating particle carrying the force of gravity. Massless force carrying particles travel at the speed of light.
The FAQ entry below may be somewhat relevant here, although it's more of a "what," whereas you asked a "why" question.
TheTechNoir's answer is sensible, but there are a couple of problems with it. First, it's not true that gravitational waves always travel at c. The velocity is only c in the low-amplitude limit. Therefore any argument that proves v=c for all gravity waves can't be quite right. Also, general relativity is a classical field theory, so IMO supplying a quantum-mechanical answer is not very satisfying. We don't even know for sure that there are gravitons. Gravitons are a name for what you get when you apply standard methods of quantization to gravity -- but standard methods of quantization fail when you apply them to gravity.
In Newtonian gravity, gravitational effects are assumed to propagate at infinite speed, so that for example the lunar tides correspond at any time to the position of the moon at the same instant. This clearly can't be true in relativity, since simultaneity isn't something that different observers even agree on. Not only should the "speed of gravity" be finite, but it seems implausible that that it would be greater than c; based on symmetry properties of spacetime, one can prove that there must be a maximum speed of cause and effect.[Rindler 1979] Although the argument is only applicable to special relativity, i.e., to a flat spacetime, it seems likely to apply to general relativity as well, at least for ripples in spacetime that are relatively weak, so that space is approximately flat. As early as 1913, before Einstein had even developed the full theory of general relativity, he had carried out calculations in the weak-field limit that showed that gravitational effects should propagate at c. This seems eminently reasonable, since (a) it is likely to be consistent with causality, and (b) G and c are the only constants with units that appear in the field equations, and the only velocity-scale that can be constructed from these two constants is c itself.
Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51
FAQ: How fast do changes in the gravitational field propagate?
General relativity predicts that disturbances in the gravitational field propagate as gravitational waves, and that low-amplitude gravitational waves travel at the speed of light. Gravitational waves have never been detected directly, but the loss of energy from the Hulse-Taylor binary pulsar has been checked to high precision against GR's predictions of the power emitted in the form of gravitational waves. Therefore it is extremely unlikely that there is anything seriously wrong with general relativity's description of gravitational waves.
It is difficult to design empirical tests that specifically check propagation at c, independently of the other features of general relativity. The trouble is that although there are other theories of gravity (e.g., Brans-Dicke gravity) that are consistent with all the currently available experimental data, none of them predict that gravitational disturbances propagate at any other speed than c. Without a test theory that predicts a different speed, it becomes essentially impossible to interpret observations so as to extract the speed. In 2003, Fomalont published the results of an exquisitely sensitive test of general relativity using radar astronomy, and these results were consistent with general relativity. Fomalont's co-author, the theorist Kopeikin, interpreted the results as verifying general relativity's prediction of propagation of gravitational disturbances at c. Samuel and Will published refutations showing that Kopeikin's interpretation was mistaken, and that what the experiment really verified was the speed of light, not the speed of gravity.
A kook paper by Van Flandern claiming propagation of gravitational effects at >c has been debunked by Carlip. Van Flandern's analysis also applies to propagation of electromagnetic disturbances, leading to the result that light propagates at >c --- a conclusion that Van Flandern apparently sincerely believes.
Fomalont and Kopeikin - http://arxiv.org/abs/astro-ph/0302294
Samuel - http://arxiv.org/abs/astro-ph/0304006
Will - http://arxiv.org/abs/astro-ph/0301145
Van Flandern - http://www.metaresearch.org/cosmology/speed_of_gravity.asp
Carlip - Physics Letters A 267 (2000) 81, http://xxx.lanl.gov/abs/gr-qc/9909087v2
A technical note: the proper term for the phenomenon being discussed is gravitational wave. A gravity wave is a type of atmospheric wave, and has nothing to do with gravitational waves.
It seems the 'speed of gravity' question comes up twice a week on the forums.
A simple thought experiment - which is probably wrong. The Europran Gravity Field and Steady-State Ocean Circulation Explorer probe:
It can detect anomalies and features in Earth's gravitational field and has an Ion propulsion system.
Surely going over one spot and then going over the same spot at a different speed and noting if there is a delay (or not) in aquiring the same gravitational data will resolve the question once and for all?
Spikenigma -- The experiment you're proposing is basically an experiment involving propagation of electromagnetic waves between objects orbiting in our solar system. That's the same general class of observation that the Fomalont work falls into, and as discussed in #4, they can't tease apart this aspect of GR from other aspects.
GR assumes the speed of gravity is c, right? But, it must also predict that it is c, in the sense that I should be able to recover the speed of c from the field equations. How do you do that though? It is not obvious to me.
Surely, I must be able to apply GR so that if I blow up Krypton I can predict that the effect will reach Earth at the speed of light.
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