I suggest that encountering yourself in your own past would be on the same order of difficulty as plotting the course of a photon across an entire galaxy, to hit a "mirror", precisely positioned to return that photon back across that same galaxy, this time apparently as an antiphoton, to another "mirror", that would bounce the photon back towards itself, prior to the time at which you redirected it across the galaxy. The precision required makes it effectively impossible.

But, given the nature of probabilities, if enough trials occurred, eventually one would succeed in causing something to interact with its past self. How would you even detect if that occurs? The particles that have the highest likelihood of doing this by chance all look pretty much the same anyway.