I don’t think that makes sense mathematically speaking. To turn the state of a group of atoms into numbers that can be represented by a random experiment, one would need to use continuous (i.e. non-quantized) variables. A continuous variable can take an uncountably infinite number of values, so it can’t be modeled by a countably infinite arrangement like the one you’ve described. It’s kind of like how you can choose real numbers at random for all eternity and never get the number 7.
Reality isn’t continuous, at least as far as we are aware. Past the plank scale at least our models don’t work. Infinite information to encode everything seems like it would all just collapse into a black hole immediately so having some limit somewhere makes sense at least in that way.
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.
I don’t think that makes sense mathematically speaking. To turn the state of a group of atoms into numbers that can be represented by a random experiment, one would need to use continuous (i.e. non-quantized) variables. A continuous variable can take an uncountably infinite number of values, so it can’t be modeled by a countably infinite arrangement like the one you’ve described. It’s kind of like how you can choose real numbers at random for all eternity and never get the number 7.
Reality isn’t continuous, at least as far as we are aware. Past the plank scale at least our models don’t work. Infinite information to encode everything seems like it would all just collapse into a black hole immediately so having some limit somewhere makes sense at least in that way.
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.