There will never be true knowledge of both a particle's location and momentum a la uncertainty principle, and will always have to be estimated.
And, like, there is still uncertainty about the position of the "center of mass" pretend particle, as well as for the position of the "displacement" pretend particle.
(the operators describing these pretend particles can be constructed in terms of the operators describing the actual particles, and visa versa.)
I don't know for sure if this works for many electrons around a nucleus, but I think it is rather likely that it should work as well.
Main thing that seems unclear to me is what the mass of the pretend particles would be in the many electrons case. Oh, also, presumably the different pretend particles would be interacting in this case (though probably just the ones that don't correspond to the center of mass interacting with each-other, not interacting with the one that does represent the center of mass?)
So, I'm not convinced of the "nuclei have to be treated as frozen, otherwise electrons don't have a reference point" claim.
People have done simulations with quad precision (very slow) but very few terms in molecular dynamics would benefit from that. In fact, most variables in MD can be single precision, exceptt for certain terms like the virial.
If the universe is discrete, how does one voxel communicate to the neighboring voxel what to update without passage through ‘stuff in between’ that doesn’t exist? Heh
It seems physics is going the opposite way with infinite universes and multiple dimensions to smooth out this information transfer problem and make the discrete go away.
I don't think your "voxel" intuition can be right because it's a small jump from that to (re)introducing an absolute reference frame.
That kind of reminds me of the 'aether' that was once hypothesized as a medium of transmission for light and radio waves [0].
Also, voxel's communicating sounds an awful lot like a higher-dimensioned cellular automata.
How much smaller?
But photons resulting from the same event but with different energies arrive at detectors an appreciable distance away to all intents and purposes simultaneously, something that would not happen if spacetime were discrete at a level close to the Planck length. So it would have to be quite a big difference for an effect not to show up as a difference in time-of-flight.
What accounts for the expectation that they do not arrive simultaneously in a voxel-based universe?
As in, photons that leave the surface of the sun always strike those specific points in space-time which are at a zero spacetime interval from said surface. If you take the described geometry seriously, then "spacetime interval" is just the square of the physical distance between the events.
(And any FTL path has a negative spacetime interval. If that's still the square of the distance, then I think we can confidently state that FTL is imaginary.)
In practice, none of this matters though and we can still get very useful results at the resolution we care about.