A world where you can go into the past and meet your younger self implies one of two things, both of them unlikely:

1. Linear time is not only illusory, but all time exists simultaneously, and there is no free will whatsoever, and all things have all happened, and ones travel to the past to change it is also part of the original expression.
2. The "many worlds interpretation of quantum mechanics" is literally true, and there is an entirely new, complete universe hyperdimensionally branching off of every possible quantum state flux in all of existence, and this is the way the universe could accommodate timestream bifurcations like altering the past. You'd never ever be able to return to ones original timestream.