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This question has a basis in what I would call theoretical and metaphysical computer science. Naturally, it would not be welcome on CS SE. Hopefully it fits here and there are those of you here interested enough in both philosophy and computers to answer.

I have asked a question here related to the possibility of our world being a computer simulation, which received an interesting answer in response.

As explained in answers to this programming question (bear with me), in order to achieve the simulation of simultaneous actions in any computer simulation, (in computers, things are processed one after the other, never at the same time) one must observe actions in a series of ticks, each tick representing the smallest unit of time in the simulation. This, I think, is a fairly common concept.

So, the relevance? I'm curious to know:

A) Whether we could ever observe or measure the existence of a limitation in time divisibility (tick) - this part is possibly just a physics question, perhaps not even metaphysical, but it's pertinent to the real question:

B) If we can measure one (or rather the absence of one, should it not exist), would the absence of a smallest divisible unit (meaning time is infinitely divisible) disprove the theory of the universe being a computer simulation?

This seems to me like a fairly challenging question.

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It wouldn't prove anything except that at least it's a simulation that uses something equivalent to adaptive mesh refinement. Basically, the simulator detects when it needs to divide time more finely to get accurate (i.e. not-quantized) results, and then does so.

So it doesn't really matter how accurately we can measure.

Also, the universe could be not-a-simulation and yet still have quantized time. So it really doesn't matter what we measure.

(As an aside: Planck time is a theoretical idea of how finely time can be divided and still be sane quantum-mechanically. But whether or not people find ways around it, it still doesn't solve the adaptive refinement issue.)

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It depends, of course, on what counts as a computer simulation, which in turn depends, of course, on what counts as a computer. If the universe is anything like current physics says it is (with time infinitely divisible) then it can't be simulated on a (finite) digital computer, but there's no barrier to simulating it on a quantum computer --- in fact, the Universe itself can be that quantum computer.

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  • A quantum computer doesn't have sequential processing behavior? – CuriousWebDeveloper Dec 28 '14 at 2:01
  • @CuriousWebDeveloper: The range of possible behaviors for a quantum computer depends on how you define a quantum computer. But if you're willing to allow the contents of the registers evolve according to the Schrodinger equation, then you've got continuous behavior, no? – WillO Dec 28 '14 at 15:39
  • I think I remember watching a documentary recently that explained a quantum computer could do many many things at once, rather than one after the other. Just to make sure I've got it right, I'm thinking the simulation, via your explained method, would require as many processing units as there are simultaneous actions to be processed, correct? – CuriousWebDeveloper Dec 28 '14 at 18:24
  • You probably shouldn't get your technical information from documentaries. A quantum computer, as generally understood, has a finite number of registers. Therefore at any given moment, only a finite number of them are changing. – WillO Dec 28 '14 at 21:36
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To answer (A), I will point you to Planck time, which is a theoretical lower bound on the smallest possible time duration if one should exist.

(B) is obviously much more difficult to answer. As a primer, I would direct you to Nick Bostrom's seminal Oxford paper in which he discusses the Simulation Argument. You'll notice that his discussion is underpinned by various stochastic arguments, and not so much on the hypothetical simulation having particular kinds of features (e.g. discreteness). In fact, having these kinds of constraints on the simulation is probably counterproductive.

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  • That Oxford paper was immensely intriguing, thanks. However, (unimportantly) I actually had in mind perhaps a 4+ dimensional being owning the computer simulation. For some reason, I feel like the dimensions going up might make computation that much more powerful compared to our own, making 3D universal computer simulations more feasible. In the article he talks of simulating our own universe. I'm imagine the simulation of our physics. Our origin. – CuriousWebDeveloper Dec 28 '14 at 3:16
  • ^ or perhaps, I think better fits: A different universe and different physics all together regardless of dimension. – CuriousWebDeveloper Dec 28 '14 at 3:26

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