I feel like “deterministic” and “predictable” are often conflated. Suppose I give you the output of encoding a secret message with a one-time pad. Can you predi

I feel like “deterministic” and “predictable” are often conflated. Suppose I give you the output of encoding a secret message with a one-time pad. Can you predict the message contents without the one-time pad? No. Does that mean the output was generated non-deterministically? No. More generally, there are strings with Kolmogorov complexity of at least the length of the string but for which the conditional Kolmogorov complexity is very small given some other string. In this sense, it’s quite possible that quantum mechanics is fully deterministic and there is a hard limit on our ability to predict the future (so for all intents and purposes, quantum mechanics is at some level indistinguishable from true randomness to us despite there being no randomness whatsoever in the laws of physics). In fact, I think the former actually implies the latter: Consider a completely classical, deterministic universe (or at least imagine a high fidelity molecular dynamics simulation of our lightcone of the universe). Then all of the actions that humans take in an attempt to predict future observations are fully pre-ordained. Why should it be the case that these actions just so happen to lead to output that describes another subsystem’s behavior to arbitrary precision? That would be a strange coincidence to have for whatever set of laws describes the time evolution of this hypothetical universe. Mathematically, how many universes like that are even possible? What sort of bizarre initial conditions would there have to be for this to be the case? My take is pretty simple: 1) the universe is fully deterministic and 2) quantum mechanics appears inherently random to us because we are inescapably part of the system we are trying to study and predict. So now the interesting question: is there is an experiment that can distinguish between the case of a fully deterministic universe and one with non-deterministic processes, given that the two would seem to appear the same as far as human observation is concerned?