I raised this in an earlier post. As I see it, it would be impossible to exist in two places at once, so what happens if our traveller goes back say, five hundred years, does a bit of looking around for a couple of weeks and then returns to his/her point of departure? Would it be as though they had never left, that they return in the same instant they departed? And what would happen to them in the time zone they travelled to? Would everything be frozen at the instant of their arrival so that however long they lingered, nothing would change? Again, I couldn't see them travelling as a person, rather in a disassembled state - a projection if you like - that would hopefully all come back together when they get to where they're going, which raises all manner of problems that it's too late to discuss tonight.
Anyway, just musing. Back to the wine🍷.