[yk]

The electron goes forward and backward in time and interacts with itself. (In quantum field theory you can replace a positron with an electron going backwards in time). Regrettably the theory does not work, since it would predict the same number of electrons and positrons in the universe.

[txdv]

Feynman later proposed this interpretation of the positron as an electron moving backward in time in his 1949 paper "The Theory of Positrons".[2] Yoichiro Nambu later applied it to all production and annihilation of particle-antiparticle pairs, stating that "the eventual creation and annihilation of pairs that may occur now and then is no creation or annihilation, but only a change of direction of moving particles, from past to future, or from future to past."[3]

This sounds like SciFi material.

[yolesaber]

The positrons might be hiding in the protons!

[andrewflnr]

Physics is sufficiently weird that I can't tell if this is just spitballing or an actual theory I haven't heard of before.

Edit: holy crap, these people think nucleons are made of muons that are made of electrons and positrons: http://wlsprojects.com/structure-inside-proton.html . Solves the matter vs antimatter problem, I guess.

[yolesaber]

The explanation I gave was the one used by Wheeler in a famous phone call with Feynman.