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I don't really get your point - the time evolution operator is deterministic, but it describes the wave function, which itself gives a probability distribution

I don't really get your point - the time evolution operator is deterministic, but it describes the wave function, which itself gives a probability distribution for the outcome of measurements. Typically exegeses of QM are roughly given in two parts: deterministic time evolution of the wave function and random selection of the outcome of measurements. So it really is just right there in the formalism: some stuff is random. From the point of view of foundations of physics there really is no easy way out of this apparently fundamental randomness. We can be wave-function substantivalists and then we must explain why and how we don't see wave functions but concrete outcomes. We can adopt t'Hooft's cellular automata interpretation but that framework cannot easily support even something as simple as basic interactions in QFT (last I checked). We may list any number of ways of interpreting QM but all of them that I know of only at most banish randomness to the initial conditions, but not totally eliminate it from the ontology. I'm not saying that reality is fundamentally non-deterministic. But I am saying that most of the ways one squares basic quantum mechanical predictions with basic physical measurements suggest a type of uncertainty that is at least very close to being "fundamental."

GoblinSlayer 1y ago
Evolution operator shows that state evolves deterministically and doesn't hide randomness anywhere. You use probabilities when you want to explain human experience, because you can't practically compute human's state. But you don't strictly need fundamental randomness for this optimization, Bayesian probabilities work in the same way, whether randomness is fundamental or not is difficult to observe. That said, computational difficulties start in the measurement device, that's where you should do collapse if you don't want exponentially complex calculations. Outcomes of observation are explained by linearity of evolution operator and decoherence, but then you get human factor: different people have different problems with this explanation, I think it's because unitary motion is unintuitive, Aristotle knew explanation of heliocentrism, but it didn't work, because geocentrism was more intuitive for him. Some apparently suggest that to explain human experience you need to calculate mind from physics, which needs to solve the hard problem of consciousness, which is impossible.

GoblinSlayer 1y ago

Evolution operator shows that state evolves deterministically and doesn't hide randomness anywhere. You use probabilities when you want to explain human experience, because you can't practically compute human's state. But you don't strictly need fundamental randomness for this optimization, Bayesian probabilities work in the same way, whether randomness is fundamental or not is difficult to observe. That said, computational difficulties start in the measurement device, that's where you should do collapse if you don't want exponentially complex calculations. Outcomes of observation are explained by linearity of evolution operator and decoherence, but then you get human factor: different people have different problems with this explanation, I think it's because unitary motion is unintuitive, Aristotle knew explanation of heliocentrism, but it didn't work, because geocentrism was more intuitive for him. Some apparently suggest that to explain human experience you need to calculate mind from physics, which needs to solve the hard problem of consciousness, which is impossible.