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All electromagnetic waves travel at speed of light in vacuum. Gravitional waves also travel at speed of light. I am having this vague notion that all waves in vacuum must travel at speed of light. Is there any theorem like that? If yes, please elaborate. If not, please give some counterexamples.

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    $\begingroup$ What types of waves do you know, except gravitational and electromagnetic, which can travel through a vacuum? $\endgroup$
    – alephzero
    Feb 9, 2019 at 12:35
  • $\begingroup$ I don't know any other. But I was just wondering if it were possible for a wave to travel at subliminal speed in vacuum. And if not, is this mere coincidence. $\endgroup$
    – user215736
    Feb 9, 2019 at 12:36
  • $\begingroup$ For EMW it is an established experimental fact. For the others it is a hypothesis with some experimental support. $\endgroup$ Feb 9, 2019 at 18:16

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All zero mass particles travel at the speed of light in vacuum is not a theorem, but a result of imposing special relativity on the description of particles in quantum mechanics.

Electromagnetic waves are emergent from zillions of photons, and the same would be true for gravitational waves , emergent from zillions of gravitons, once gravity is definitively quantized.

In the standard model of particle physics before symmetry breaking , all particles have zero mass, acquiring mass by the mechanisms as the Higgs mechanism of symmetry breaking for the electroweak case. So in the cosmological models, before electroweak symmetry breaking one could have the table of particles at zero mass, and in this sense the emergent "radiations" would travel at the speed of light in vacuum. The same for GUTS symmetry breaking. By construction as long as special relativity holds.

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