The textbook example would be the energy levels of the hydrogen atom. An electron in a hydrogen atom can have an energy of -13.6 electron volts, or -3.4 eV, or -1.51 eV, or -0.85 eV, and so on, but not any energy in between (the general formula is -13.6 eV/n^2, where n is any integer).
So, yes, distance and time in spacetime do seem to be based on integer values – but the integers are not very big. The Planck length is more that 24[sub]10[/sub] orders of magnitude smaller than the ångström unit.
It’s widely believed to be the shortest meaningful length, but there’s no real basis for that wide belief. Physicists wouldn’t be surprised if it turns out to be true, but we’d be even less surprised if it turns out not to be. It’s just that, if there is a smallest meaningful length, we don’t have any better guesses for what it might be… but there’s nothing that says that it has to be something that we would guess.
Cynthia thinks I should cut back on my neutronium consumption anyway.