Billy and Pete theorem

The theory that Billy and Pete cease to exist once their objective had been completed. They are seen in the same clothes everyday, despite weather, and never seem to leave nor enter where they are. They only come into existence when they are needed and leave when they are not, nobody can see them leave or enter, they just enter

It's a shame that Einstein died when he was about to solve the Billy and Pete theorem, what a shame, and a coincidence...