[akvadrako]

I don't think we do define existence that way. Say you and your friend both go to opposite ends of the visible universe; due to inflation you'll never be able to communicate again.

I suspect most people would say their friend continues to exist. This is very analogous to the many worlds situation.

[tsimionescu]

Thinking about the extreme distances and time spans that entails makes it difficult, and of course relativity has its own "unreasonable" results. Still, they do exist in your past, and they also can assign coordinates in space-time to your current position, even though they are outside your light-cone. On the other hand, you can't meaningfully speak of them existing "now" in relativity, as there is no consistent definition of what "now" means for observers that are space-like separated.

I guess the best answers about MWI is that the other versions of these particles continue to exist at different coordinates in Hilbert space, and that they do interact with each other in observable ways, such as the interference patterns in double-slit experiments.