If I could travel back to 1961 I might encounter my 10-year-old self. If I am experiencing my life as my current self, "who" is experiencing life as my 10-year-old self?

If I can travel to a time in the past, that time must exist independently of my being there. That means that each past moment continues to exist. "Someone" must experience each moment of my past life. Each moment must be continuously experienced by "someone." How does that work?

If I could travel to the future, I could encounter my descendants after I am dead.

I will believe that someone has traveled to the future when they can tell me tomorrow's winning powerball numbers.