The problem I have with time travel stories is the law of conservation of mass (and energy). Moving a person from the present to either past or future removes mass from the present. There is a net loss of mass (the person) with no mass to replace it. The present universe now violates this fundamental law of the physical universe, which logically and provably can’t happen. That alone negates the possibility of time travel. So there.

Antimatter is a different thing.