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I would go even a step further and question the randomness of the quantum realm, but IANAP and I might be saying something terribly stupid: apologies in advance

I would go even a step further and question the randomness of the quantum realm, but IANAP and I might be saying something terribly stupid: apologies in advance. What if the source of quantum randomness is not really random in the Kolmogorov sense? If any finite (computable, as physics seems to be) process has a bounded Kolmogorov complexity, is it correct to assert that infinite complexity can be originated only from an unbounded process? Then what about the constituent parts of that unbounded process? Shouldn't they have unbounded mass/energy and collapse into a blackhole? Equivalenty: shouldn't something with infinite entropy collapse into a blackhole per Bekenstein bound? Somehow I feel that this cosmic TRNG is as shady as the embedding of the real numbers in the real world. N.B.: - I don't think this line of reasoning contradicts Bell's theorem. - I reckon that, as digital cowboys, we have a bias for finiteness and discreteness I'm really curious about this, please contradict me. There must be something beautiful that I'm not seeing.

SamReidHughes 6y ago
With a deterministic universe, you'll need some way to produce discontinuous outcomes. For example, let's say you're on a walk on a trail in a deterministic universe, and there's a pole in the middle of the path. Let's assume you'll always walk left or right of it, as a function of your initial left/right position across the width of the path, in a bounded time t_max. (We assume there isn't some unstable center position, or set of positions, where you get stuck an arbitrarily long length of time before deciding which side to take, because you're human.) It follows that the laws of physics are discontinuous. It feels kind of like Arrow's Impossibility Theorem -- in both cases your cleanest way out of this jam is nondeterminism.
- SamReidHughes 6y ago
  Or, instead of nondeterminism, you have determinism + a separate free will package, which generates the discontinuity. Free will =~ being able to compute a decision in bounded time on a continuum of inputs.
- torotonnato 6y ago
  I can see your point, but the problem remains. Suppose to have a closed system that contains a random number generator and an observer. The observer can measure and extract (not store) an infinite amount of entropy. Where does that comes from? It seems to me to be unphysical. Possible way outs of this: - The randomness source has a state which is huge but finite. The finiteness should clash with the QM assumption that this kind of randomness is absolutely unpredictable - You can't even take an upper-bound of the Kolmogorov complexity of that bitstream without storing the bits. It's like saying: the universe can cheat because your are not looking (hypothesis that has a strong QM flavor) - The universe conspires to incrementally build one additional state for every measurement taken (non-sense) - The randomness source is not immanent in our physical universe (Occam's razor says no) Regarding your point, there are two options: discontinuous functions can be approximated with truncated series, for instance. Plus: the photoelectric effect doesn't logically need (for what I know) randomness to happen, there are already discontinuities without postulating non-determinism, discreteness suffices.

SamReidHughes 6y ago

With a deterministic universe, you'll need some way to produce discontinuous outcomes. For example, let's say you're on a walk on a trail in a deterministic universe, and there's a pole in the middle of the path. Let's assume you'll always walk left or right of it, as a function of your initial left/right position across the width of the path, in a bounded time t_max. (We assume there isn't some unstable center position, or set of positions, where you get stuck an arbitrarily long length of time before deciding which side to take, because you're human.) It follows that the laws of physics are discontinuous. It feels kind of like Arrow's Impossibility Theorem -- in both cases your cleanest way out of this jam is nondeterminism.

SamReidHughes 6y ago
Or, instead of nondeterminism, you have determinism + a separate free will package, which generates the discontinuity. Free will =~ being able to compute a decision in bounded time on a continuum of inputs.
torotonnato 6y ago
I can see your point, but the problem remains. Suppose to have a closed system that contains a random number generator and an observer. The observer can measure and extract (not store) an infinite amount of entropy. Where does that comes from? It seems to me to be unphysical. Possible way outs of this: - The randomness source has a state which is huge but finite. The finiteness should clash with the QM assumption that this kind of randomness is absolutely unpredictable - You can't even take an upper-bound of the Kolmogorov complexity of that bitstream without storing the bits. It's like saying: the universe can cheat because your are not looking (hypothesis that has a strong QM flavor) - The universe conspires to incrementally build one additional state for every measurement taken (non-sense) - The randomness source is not immanent in our physical universe (Occam's razor says no) Regarding your point, there are two options: discontinuous functions can be approximated with truncated series, for instance. Plus: the photoelectric effect doesn't logically need (for what I know) randomness to happen, there are already discontinuities without postulating non-determinism, discreteness suffices.