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" ... Anything massless would travel in a vacuum at the invariant speed, which is known as the vacuum speed of light. Light itself consists of massless photons, which travel at this speed in a vacuum. The only other thing we know that is massless and stable when free, would be the gravitational field (and its presumed quanta, the gravitons.) So like light (propagating waves of the electromagnetic field), gravitational radiation (propagating waves of the gravitational field) also travel at the vacuum speed of light. ... "
" ... But third off, it means that the speed of gravity is less than the speed of light, and that's harder to reconcile. In fact, there are observational and experimental limits on all three of these that tell us that if gravity is either not truly long-range, is not coordinate or boost invariant, or if its speed is not exactly equal to the speed of light, it has to be really, really close. ... "
" ... Einstein was responsible for the remarkable breakthrough of the concept of relativity, which identified which quantities were invariant, and didn’t change with the observer’s motion, and which ones were frame-dependent. The speed of light, for example, is the same for all observers, as is the rest mass of any quantum of matter. But the spatial distance you’d perceive between two points depended very strongly on your motion along the direction connecting those points. Similarly, the rate at which your clock ran as you journeyed from one point to another also depended on your motion. ... "
" ... Moving at high speeds relative to your environment has a number of other effects that you experience as well. Lengths and distances get contracted along your direction-of-motion, which is a similar requirement of relativity. Because the speed of light must be invariant for all observers in all reference frames, if time appears to pass more slowly (there's less time), then distances need to contract (there needs to be less distance) in order for the speed of light to remain constant. ... "
" ... The Standard Model is exactly Lorentz invariant. General Relativity is exactly Lorentz invariant. But many incarnations of quantum gravity are only approximately Lorentz invariant. Either the symmetry that mandates it is broken, or there's new physics that only appears at high-energy scales that breaks it. Although the low-energy Universe is observed to be Lorentz invariant, direct searches at particle colliders (like the LHC) are severely limited by the energies they can probe. ... "