Theory fails to forbid travelling backwards in time. But practice suggests it might just as well be forbidden. Perhaps that is for the best. If backward time travel were possible, some fool would no doubt try testing the grandfather paradox, another invention of time-travelling fiction writers. In this, a visitor to the past kills his or her grand-father before the conception of the protagonist’s own parent, meaning the protagonist could never have been born, and the murder could not have taken place.
The grandfather paradox—the observation that causality cannot work backwards—is probably crucial to an understanding of the arrow of time. It is implicit in explanations that rely on thermodynamics and the like, but has not yet been translated into a coherent mathematical theory. For the person who does translate it, however, or who otherwise solves the conundrum of time’s arrow, a Nobel prize surely beckons.
But it remains, understandably, a staple of science fiction.