by Pugugly001 » January 29th, 2011, 11:39 pm
I am not a quantum mechanic, so my logic here is almost certainly incomplete, but . . .
Bell's Theorem (Via Wikipedia) loosely translates as: "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics."
This seems to me to imply certain things about the kind of computer that could in theory simulate a quantum mechanical universe.
1) Since certain phenomena in the universe (ex radioactive decay) are 'truly random' Quantum Mechanics cannot be duplicated by a system that doesn't have a truly random generator.
2) Since the order of events in our universe is dependent on the frame of reference, the interaction of these random events cannot be calculated by a turing computer, in which the arrow of time is determined by the order of operations, not by frame of reference.
These two conditions seem, to me, to imply that even given a (simple) quantum mechanical computer of arbitrarily large memory but a lesser number of processors, that computer cannot simulate a quantum mechanical universe, because the very action of swapping memory to the processor will cause the simulation of a universe which has a definite order of time, and forces the quantum processor to utilize local variables to simulate a universe governed by quantum mechanics.
A creature living in a Universe simulated in that fashion would in fact not deduce Bell Theorem, because within his universe Bells Theorem would not apply. Nor could they deduce Relativity, because, again, in that universe the order of event being determined by relative frames would in fact not apply.
You might be able to make something that looks like our universe at first glance, but at the macro and micro level, the similarities would break down.
Now . . .
You could accurately simulate a universe subject to both QM and relativity in only one way that I can think of - doing away with the memory/processor dichotomy entirely, and creating a computer with a number of quantum processors working in parallel such that you have a one qubit to one planklength of space mapping (Because QM has virtual particles interacting with real particles, you can't map it one processor to one particle - any unit of space can potentially contain a particle).
But at that point, you're no longer 'simulating' a QM/Relativistic universe - you have in effect created a fully functional universe of a size equal to the number of processors you choose to devote to it.
I'm not a Physicist, nor even a Computer Scientist, but based on those two fundamentals, I honestly think this problem breaks down on the "Can you actually simulate the universe" level. The answer is "No", at least not unless you can find a Universe size box to put it in.
Pug