These two related questions cover the potential effects of quantized spacetime:
This question extends the above discussions with questions about the potential effects of discretized spacetime on conservation laws. (The reason this is important to me is that I'm writing a book that doesn't have a lot to do with quantum physics, but one of the arguments I'm considering for inclusion is related to the degree by which layers of cellular automata could "directly" simulate this universe, meaning each possible branch from quantum decoherence would have its own layer, with each layer being a physical approximation of particles including the "stringy" dimensions. Suggestions on this topic are also welcome in the comment section.)
The Planck distance is incredibly tiny, but its existence does not imply quantized spacetime. Ignoring the uncertainty principle for a moment, there's nothing that suggests one couldn't arrange "elsewhere" (noncausal) events that are a non-natural number of Planck distances apart, just so long as they're at least 1 Planck distance apart. This implies that noncausal events could be packed more tightly if arranged in a triangular tiling as opposed to a square tiling—again, without quantization of spacetime. But it does not imply that there is an underlying "tiling" of spacetime.
However, if spacetime were quantized, my intuition tells me this would mean otherwise-identical experiments could produce ever-so-slightly different results depending on whether the experiment is oriented in line with or skew with the underlying "grid" of spacetime (even if it is an irregular tiling). There would never be a way to detect this in practice, but if experiments were absolutely perfect and you did unimaginably many of them, over time the tiniest probabilistic difference might appear.
Emmy Noether proved that every experimental invariant implies a corresponding conservation law, and based on her theorem, we can (and do) infer that experimental invariance to "direction" implies that angular momentum is conserved. However, if spacetime were discretized, this invariant would not truly exist.
0) Does the uncertainty principle "blur" any possible effects from discretized spacetime to such a degree that the effects would not show up under any circumstance, thus "accidentally saving" the conservation of angular momentum?
1) If not, does the loss of the directional invariant suggest angular momentum might not be perfectly conserved, or is there another invariant which also implies the conservation law?
2) If conservation of momentum is not conserved, where might the nigh-infinitesimal energy go (or come from)? Put another way, does a loss of conservation of angular momentum also imply a loss of any other conservation laws, for example, conservation of energy?
3) Might any other physical laws be affected by loss of the directional invariant?