> 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.
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.
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.
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.
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.