Can a *perfectly* accurate physical simulation be faster than the real process?
Question: assuming one day we know the exact laws of the physical universe, and assuming we have enough computing power, is it possible to simulate a part of the universe (even a tiny one like a molecule) with perfect accuracy (i.e, indistinguishable form the real thing for EVERY experiment we can imagine) but faster than the real process? Or does a perfect simulation require at least exactly the same duration (and/or physical space, energy, etc)? The question may seem stupid but it's more complicated that it appears at first thought. Think about this: assuming a classical, newtonian universe, and a perfectly isolated particle, we can easily compute at any time, say, the position by using a simple mathematical formula. Then the "simulation" does not need approximating the behavior of the system using any sort of time step: the computation time may be much less than the time required by the real particle to actually reach the position. But as soon as we introduce r