If we consider we live in an infinite universe then there are an infinite number of "spaces" in that universe. Each space must have a number of particles within it which is finite and thus a number of configurations for those particles in that space which is also finite. The number of particles and number of configurations will be very large but they both will be finite. In an infinite universe of infinite spaces there must be a space where the number of particles and their configuration is exactly the same as any specific space you so choose.
If the space we choose is our own space, our known "universe" as we see it, then in an infinite universe there must be another such space of exactly the same number of particles in exactly the same configuration as we see here. An identical "universe" to our own. And, infinities being what they are, there are an infinite number of such "universes" identical to our own. And an infinite subset of those infinite universes like our own will have the exact same histories, past, present and future.
What I cannot fathom is how any event can happen without a preceding event.
Yes, events do have preceding events. No one is saying otherwise. But, in a probabilistic universe, if you wind the clock back far enough from that event and start over the play out of the probabilities on the second run may not produce the same event from the first run. Whatever different event does happen on the second run will, of course, have had a different set of preceding events.
Clockworks always play out the same way and so we can predict the position of the clock at some future time with precision.
Are you sure about that? QM and GR might disagree.
I guess my question is how do you prove that no hidden variables exist?
Hidden variables has been a contentious point with QM since Einstein and the EPR paradox. But, the worm has turned, as they say, and the present consensus is hidden variables do not exist. The Bell Inequities, Alain Aspect's and Nicolas Gisin's experiments show that hidden variables has some fatal flaws that preclude their reality.
One does not prove that hidden variables do not or cannot exist. One can only show the preponderance of the evidence is against such things.
IMO one of the best, comprehensive and lay-friendly write ups on whole controversy is here