Astrophysicist Ethan Siegel offers two scenarios where it wouldn’t:
The second way out is to assume that the past isn’t written, and your actions do matter. The Universe, as it exists today, is not bound to the state its in right now if you travel back to the past. In a way, every action you take creates a new, alternate history for the Universe. You can kill your own grandpa before your parents are conceived; you can prevent your parents from meeting and falling in love; you can kill Hitler before World War II or assassinate Brutus and Cassius and Marc Antony before they assassinate Caesar.
In short, you can change history. The only thing you have to give up, then, is that the Universe you inhabit after traveling back in time is the same as the Universe you inhabit before you went back.
And in this new future, you may not even be born. You may simply have come into existence at the moment you arrived at your time-traveling destination. You would literally be a visitor from another Universe.Ethan Siegel, “Ask Ethan: Would Traveling Back In Time Destroy The Universe?” at Forbes
Except that there isn’t another universe; that one didn’t exist, remember? So then how could one have come to exist in order to go back?
Maybe it works better as science fiction.
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See also: Astrobiologist: Why time travel can’t really work
Carlo Rovelli: Future time travel only a technological problem, not a scientific one. Rovelli: A starship could wait [near a black hole ] for half an hour and then move away from the black hole, and find itself millennia in the future.
Rob Sheldon’s thoughts on physicists’ “warped” view of time An attempt to force complete symmetry on a universe that does ot want to be completely symmetrical