It's one of those things which would be pretty much impossible to prove, but it holds well with the effects we currently see. Electrons can annihilate by colliding with positrons. But the collision we see could be a single electron changing from moving forwards in time to moving backwards in time. It holds that it's the same particle in the equations by cancelling out the minus sign of the charge with the minus sign in the time. So while we see a collision, the electron would just see itself changing charge and start moving backwards in time instead.

It's a beautiful hypothesis, and fills me with chills to think about the electron "experiencing" all of history an unimmaginable amount of times.