When you travel back and change the history you spilt off into an alternative timeline - isn't that the standard answer to that problem?
Yeah, in weak sci-fi
But the usual way is "consistency". In General Relativity, any possible space-time is a full 4d entity: past, present, future. You cannot start with some fixed past and generate arbitrary futures. The space-time comes as the whole package. Does wonders for thoughts of pre-destination and free-will.
A paradoxical scenario as described by Guido is not a valid space-time... hence it can't happen. Only consistent space-times are allowed.
By the way, we actually have a name for Guido's experimental set-up: wormhole billiards, the subject of my very first research. One really intersting part of this is if we fix the initial and final conditions, say ball rolls towards the in-hole, and ball rolls away from out-hole, then classically there should only be one solution.
But with the time-machine aspect, we get an infinite number of solutions which we must sum over to get some average: ball goes in in-hole, comes out of out-hole; ball goes in in-hole, comes out out-hole, goes back in in-hole and finally come out of out-hole again; ball isn't going in, but collides with it-self, knocking it in... it comes out, just in time to make the collison with itself and heads out; etc, etc, etc.
This is suspiciously like Feynman sum-over-histories quantum mechanics...
Edited by cavediver, : No reason given.