This article is from the Relativity and FTL Travel FAQ, by Jason W. Hinson jason@physicsguy.com with numerous contributions by others.
In this section we will explore a problem with FTL travel that doesn't
always seem to get consideration. The problem involves ones ability to
violate causality in certain frames of reference with the use of FTL travel.
While this in itself doesn't necessarily make FTL travel impossible, the
ability to go further and produce an unsolvable paradox would make the FTL
travel prospect logically self contradictory. So, I will start by discussing
the meaning of causality and the problems of an unsolvable paradox. I will
then try to show how any form of FTL travel will produce violation of the
causality principle. Finally, I will explain how, without special provisions
being in place, FTL travel can go further to produce an unsolvable paradox.
 
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