I'm a bit late to the game on this one, but according to current physical theory, two universes that began identically would not stay identical due to quantum mechanical fluctuations.
Regarding hidden variables (by which I mean the possibility that Quantum events are actually determined by some unknown physics) several results restrict these theories. We know that they would have to be: (a) non-local, communicate faster than light (b) contextual, particles are aware of and contain information on the state of every other particle in the universe (c) have essentially infinite complexity, each particle stores an infinite amount of data
Which I think is just as strange as quantum mechanics.
Let us say an atom emits red light if it decays and green light if it remains undecayed. If this atom is next to a photosensitive chemical that contracts under green light and expands under red light, that would be an example of a classical system reacting differently depending on a quantum event.
In fact technically all nearby classical systems react differently to different outcomes of a quantum event. The quantum mechanical decays that power phosphorescence of certain minerals would result in completely different physical states of a cave wall the minerals were embedded in. Wouldn't this be the same as a human going to the right or left depending on the outcome.
I know, I am agreeing with him (not that I could disagree with his physics) but NoNukes appears to be making distinctions between stuff at quantum level - which we all agree appears to be prperly random - and stuff at a macro level. I'm giving an example how a macro sized lump of stuff - me - could use quantum level randomness to create a non-deterministic outcome.
Ah, I see, you are talking about bootstrapping indeterminism up to the macro scale by making a classical object's next state depend on a quantum event. In which case, certainly yes macroscopic objects can be made indeterminate in this sense.
In fact such issues (how quantum indeterminism propagates up to the classical world) is the "real" point of Schrodinger's cat.