What if you invented a time machine and went back in time and grabbed the old you and then went forward in time to where you first left off? You wouldn’t exist for a period of time. Which would also potentially mean you weren’t there to invent said time machine. Which would then mean you wouldn’t be able to go back in time to stop yourself and so on.
If you were the first person to invent time travel, how hard would it be to resist wanting to try this experiment out?