Reality isn’t continuous according to quantum mechanics (at least with boundary conditions; for example the energy of a free particle/wave is continuous), but it is according to relativity (for example there’s nothing quantized about redshifting due to gravity or the expansion of the universe). Also what happens at a Planck scale is that quantum mechanics stop being able to model reality, but it doesn’t predict a quantum of distance or anything like that. There’s nothing preventing a particle from moving one meter+one Planck length. Really what happens at these scales is anyone’s guess, but whatever model succeeds the ones we use today will likely have to accommodate some continuity in order to model relativistic effects.
Reality isn’t continuous according to quantum mechanics (at least with boundary conditions; for example the energy of a free particle/wave is continuous), but it is according to relativity (for example there’s nothing quantized about redshifting due to gravity or the expansion of the universe). Also what happens at a Planck scale is that quantum mechanics stop being able to model reality, but it doesn’t predict a quantum of distance or anything like that. There’s nothing preventing a particle from moving one meter+one Planck length. Really what happens at these scales is anyone’s guess, but whatever model succeeds the ones we use today will likely have to accommodate some continuity in order to model relativistic effects.