Here is a more enigmatic paradox than the "grandfather paradox." Could "self-healing time” resolve this one?

Suppose I travel back in time to 1961 and encounter my ten-year-old self. If I am still experiencing my existence as my current self, then "who" is experiencing the existence of my ten-year-old self?

If I can travel to the past, would it not have an existence independent of my being there? If so, then someone would have to continue experiencing each moment of everyone's existence. Who would that be?