N. David Mermin wrote a proof of Einstein's theory of special relativity that did not assume the speed of light was constant. Mermin's version, called "Relativity Without Light", assumed some basic properties of the universe (like the fact that it looks the same in every direction), and proved from that the same conclusions, that there is some maximum speed in the universe. Nothing with mass can go that speed because the faster anything with mass goes, the more energy it takes to accelerate just a little bit more. It would take infinite energy to accelerate to the maximum speed. The theory also shows that nothing without mass can go at any other speed. Light is one of very few massless particles out there. It travels at the maximum speed of the universe. Light travels so fast because it travels at the fastest possible speed.
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