It is said that during sleep our brain sorts out the thoughts we had during the day, and thus humans need sleep. But with sleep come dreams, and dreams are a different beast altogether. Could it be that during dreams we visit our other incarnations in parallel dimensions?
The fact I have remembered different dreams that seemed to be continuation episodes, I believe this is quite likely. Just this week I remembered visiting a family I had met in an earlier dream, thus giving the idea of a consistent existence in my dreams more likely.