Let’s see two paradoxes that can exist if you can time travel.
The first one is the grandfather paradox. Imagine you can time travel, go back to the past, and kill your grandfather before he met your grandmother. That means he did not have children, and you could not be born in the first place (to time travel)!
The second one is the bootstrap paradox. You buy a copy of Hamlet from a bookshop and go back to the time before William Shakespeare has written Hamlet. You give the book to William. He then copies it and claims his own. Years passed, and the book made several copies. One of them enters the same bookshop you originally visited. The question is: who wrote Hamlet?
A direct consequence of these paradoxes could be that there is no time travel possible. Another possibility is that a parallel universe is created as a result, and your existence (and Hamlet’s) is real in one of them.
