Someone will probably pop up and say that one fundamental particle or somesuch is identical to another, but until they do I'll say that there's no such thing as an identical anything is there? For two universes to be identical over time, they would have to be totally deterministic - no possibility of chance, ruling out a universe like our own.
I guess the only scenario I could envision whereby both universes would be identical is if there is some kind of fundamental entanglement at the quantum level that is keeping both at parity. I have no idea how that mechanism might function or if it is even feasible given what we know about particle physics. I am kind of falling back on my tech knowledge with things like mirrored file systems and what not.
My instincts though lean more towards Tangle's view. If some replication event occurs that creates a duplicate universe, then specific uncertainty, randomness and chaos in each independent universe would eventual cause them to go out of sync.
So in my universes, despite their initial inherent similarities, only one Spock has a goatee.
Now, if the world is really probabilistic on a quantum level you may be right, since this could be a genuinely random element, but I've never been able to get my head around quantum physics.
This is what I was pondering as well. Maybe one of our resident physicists can chime in here with some more detail on quantum level aspects of how things operate. But from a holistic level, this leads me back to the whole nature of quantum physics, randomness and most importantly, uncertainty.
If one universe is replicated from another in its entirety, then this actually opens up a whole can of worms with regards to how one can achieve that knowing that the Heisenberg principle would need to apply; i.e. the actual nature of the particles at the quantum level is not certain. This is why I brought up entanglement. If there is a way to replicate the particles and entangle them exactly, then I suppose you could argue that the two universes could then be inexorably linked. Thereby having them progress identically and at the same rate.
Ultimately, the actual physics of this is beyond me. Anyone have a hotline to Stephen Hawking's cell phone?