Or the less click-baity headline: "Physicists to Test if Universe is Computable"

tantalor · on April 17, 2013

Of course it's computable. Planets aren't going to orbit by themselves; something has to add up all those force vectors for every molecule everywhere.

I think the question is whether the compution is discrete (i.e., cheats) or is everywhere continuous.

midnightsine · on April 17, 2013

Are you sure? Is the universe described by an equation s=t*v, v=10 untrue unless we compute it? Does moving electrons on a CPU die suddenly give it meaning? Do scraps of graphite left on paper by a pencil? The simplest turing complete cellular automaton can be computed using ordinary rocks.

Are there no infinitely many natural numbers unless we observe them? And then finally is actually computing a universe described by a set and a step function the only way to make it real? Is it not "real" by simply being possible?

As for discreteness of time, in quantum mechanics changes in state are modeled by square matrices over complex numbers. GL(n, C) is complete - for every matrix M you also have M^1/2, representing half the state chance. It follows that our time, at conceptual level, is at least as "dense" as rational numbers.