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As far as we know, time and space are continuous. Various aspects of quantum field theories would not work in a discretized universe.

• naasking 4y ago
  > As far as we know, time and space are continuous. Our models are continuous. The map is not the territory. > Various aspects of quantum field theories would not work in a discretized universe. If you're referring to symmetries, that's not true [1]. Discretized theories have received barely any attention because physicists have simply built upon the formalisms they're used to from classical physics. We see people frequently saying that we should abandon classical intuitions now that we have quantum mechanics, but we haven't really even tried to abandon classical formalisms, which are just another form of classical intuition. IMO, baking continuity and uncountable infinities is what's responsible for many of the difficulties we've had, and various forms of discretization have resolved these issues in the past [2]. My conjecture is that one of the next big advances in physics will be to take discretization seriously. [1] https://arxiv.org/abs/1902.08997 https://arxiv.org/abs/1902.08997 [2] https://arxiv.org/abs/1609.01421 https://arxiv.org/abs/1609.01421
  • crazygringo 4y ago
    > Our models are continuous. The map is not the territory. Because all our evidence is that it is continuous. Our models are the best description of the evidence we observe -- i.e. the territory. Unless you have evidence of time and space being non-continuous?
    • naasking 4y ago
      > Because all our evidence is that it is continuous. No, we haven't really tested this to any appreciable degree, and existing tests rule out only certain types of discrete models just like they rule out certain continuous models. Our models are continuous because continuous models are what we've been using for centuries. I'm not sure why anyone still believes that science is a purely evidence-driven endeavour. History has clearly shown it's subject to fads, celebrity and inertia. > Unless you have evidence of time and space being non-continuous? General relativity produces unphysical nonsense like singularities, which is a form of internal inconsistency similar to Norton's dome. This isn't evidence that spacetime is discrete so much as that our continuous model is incomplete, but it seems quite clear that a discrete analogue of GR would not suffer from this problem. Furthermore, some new approaches to gravity are discrete theories, like loop quantum gravity, so clearly some physicists are already thinking along these lines.
      • crazygringo 4y ago
        We have oodles of everyday evidence that space time is continuous in the general case because we've never found it not to be. I don't know that you mean that this hasn't been tested. Essentially every experiment ever is consistent with it.
        • naasking 4y ago
          By that logic, every experiment ever conducted is consistent with discrete theories as well. Experiments that try to distinguish the fine structure of spacetime haven't really been a focus, and are probably impossible in a lab environment. Some studies of distant gamma ray bursts place some limits on some discrete theories, but those limits don't apply to covariant discrete theories that preserve other symmetries like the one I posted above.
          • deleted 4y ago
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          • fsh 4y ago
            Quantum electrodynamics is a continuous theory. Its predictions agree with measurements of the electron g-factor and of energy levels in atomic hydrogen to 12 digits of relative accuracy. It would be interesting if a discretized version (if at all possible to construct) makes the same predictions at that level.
            • naasking 4y ago
              I agree, that would be interesting! The paper I linked above suggests that discrete theories are simpler and require less formal structure (ie. no need to talk about gauges or gauge fixing), that's why I said above that I think a push towards discrete physics would provide many insights.