Why Things Don't Travel Faster than Light

Maxwell's equations imply that all electromagnetic fields in vacuum travel at the speed of light . Thus no electromagnetic phenomena or signals can travel faster than light. Moreover, in all quantum field theories, phenomena connecting massive particles must occur inside the light cone, meaning that no particles or signals can travel faster than light. It can therefore be surmised that is a universal "speed limit" for material particles. Or, at the very least, this can be stated as an additional postulate in the special theory of relativity. (This doesn't apply in general relativity, where one could, in concept construct spacetimes allowing particles to travel faster than light. For example, the Alcubierre drive, a speculative although valid solution of Einstein's field equations. And science fiction is replete with "warp drives," which enable rocket ships to routinely travel faster than light.)
A signal from to at a speed slower than light (inside the light cone, colored magenta) and another signal from to faster than the speed of light, are observed in the frame of reference - with velocity (fraction of the speed of light), following the lines parallel to . In the case of events and , it is clear that the "cause" happens before the "effect", but in the case of and , the observer in this frame can observe that causality is broken (when appears before in the axis). So very weird things can happen, such as a hypothetical traveler reaching a designated destination before leaving home or at the same time (when overlaps ).


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[1] T. Takeuchi, An Illustrated Guide to Relativity, Cambridge: Cambridge University Press, 2010.
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