beero1000
Veteran Member
Correct me if I'm wrong, but don't the presently measurable statistical consequences of discretization you're talking about scale with the size of the hypothetical spacetime quanta? So the nonappearance of these consequences can't ever rule out spacetime quanta, but can only put an upper bound on their size? For the sake of definiteness I used the Planck volume in my posts, and I take it that was way too big; but couldn't untermensche simply always postulate grains of unknown size far smaller than whatever the demonstrable upper bound is? This would make the spaceless interior of each quantum the Gap of the Gaps.Luckily for all of us, physicists are much smarter than you are, and they actually thought through the consequences of the different possibilities. They figured out that the potential discretized spacetimes imply a violation of Lorentz invariance, which in turn implies consequence that would be observable with today's technology. Specifically, the divergence from predicted results in vacuum Cherenkov radiation, particle decay, gamma ray bursts, etc, would all show as consequences of there being a 'smallest possible volume of space'. We've checked dozens of these as precisely as is currently possible (and that is VERY precisely, down to well below the Planck scale), and the consequences do not appear. You are wrong.
In a way, kind of, but in a sense it's also worse than just a single quantum 'god of the gaps' argument. You need two distinct steps, at least, and it's the second one that's harder to plausibly satisfy.
Discreteness is forbidden (even at arbitrarily small lattice sizes) in the standard model, due to the structure of the Lorentz group and how it would act on a discrete quantum spacetime lattice. So, the only way to show that space is discrete is first to show that the standard model is wrong. The negative experimental results for Lorentz violations show that we haven't found any issues with the standard model, so while you could 'god of the gaps' posit an issue outside our realm of measurement (IIRC, it's dozens of orders of magnitude smaller than the Planck scale, but that's at least a plausible experimental result), you're still facing the (worse) second issue -- that doesn't mean that spacetime is discrete, it just means that the standard model is wrong.
We'd need to then to replace it with a theory of discrete quantum spacetime and, importantly, there is no currently known discrete theory that could be expected to work to replace it. None of the ones that physicists have come up with in the last hundred years or so have survived experimental tests (if they even make any testable predictions at all). They just don't work -- and it's the discreteness itself that always seems to be the culprit.
So, in order for untermensche to be right, the single most supported theory of all time needs to be wrong, and then even if the standard model is wrong, it still needs to be replaced with a theory of discrete quantum spacetime when there are no solid theories of discrete quantum spacetime that are real contenders to replace it. The first is just an experimental result away, but the second needs a major theoretical breakthrough that has eluded the best physicists on the planet for a good long while.