The Physics of Time Travel: II
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So far we have limited our consideration of relativity theory to speeds below the speed of light—that is, to the condition v < c, where v is the relative velocity of two reference frames. There was nothing, however, in the derivation of the Lorentz transformation equations discussed in Chap. 3 that actually used that self-imposed constraint. So, just what, in fact, does happen for v > c? This is not an empty question, because the second half of the above quote that opens this section is simply not true. That isn’t to say we can have FTL for free; there is a high price to pay, that of causality violation (although, if you are a fan of time travel, it’s a price you are probably happy to pay). If a material object goes FTL, then the mathematics seems to say that the object could travel into the past, just as the caped crusader does in the first (1978) Superman movie, in order to change the past (to save Lois Lane from dying in an earthquake). In addition, the mathematics also seems to say that if a signal bearing information could achieve FTL, then that information, too, would travel back into the past (see Fig. 6.1).