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Digital Physics are a branch of hypotheses about the fundamental physics of our universe. They basically describe the universe as an analogy to a computer and defend that everything in the universe is computable.

(https://en.wikipedia.org/wiki/Digital_physics)

Important proponents of these hypotheses, like nobel laureate Gerard 't Hooft, defend that...

(...) the probabilistic nature of quantum physics is not necessarily incompatible with the notion of computability

But is this the same as quantum randomness? (https://en.wikipedia.org/wiki/Probability)

I've read everywhere that quantum randomness is utterly uncomputable*, so how can this be compatible with what these authors hold?

*for example here: https://books.google.es/books?id=gjf3BwAAQBAJ&pg=PA4&lpg=PA4&dq=quantum+randomness+uncomputable&source=bl&ots=oyr7paY2Nm&sig=ACfU3U1ra3Dk0FLBbgCvr5RCXmA5aZ93Mg&hl=es&sa=X&ved=2ahUKEwi3qMy1q7LhAhVO1hoKHU2SCWUQ6AEwCHoECAgQAQ#v=onepage&q=quantum%20randomness%20uncomputable&f=false

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  • $\begingroup$ Can you provide a more specific citation of how quantum mechanics is compatible with computability? Surely the probability distributions in quantum mechanics are computable. The only difficulty is then effectively sampling those probability distributions on a computer as is always the case with probablility distributions. $\endgroup$ – Ian Apr 7 at 0:51
  • $\begingroup$ @Ian you said that the probability distributions are computable, but I've always read that quantum randomness is not computable. Are these two concepts (probability distributions and quantum randomness) the same? $\endgroup$ – user226436 Apr 7 at 22:59
  • $\begingroup$ Probability distributions in quantum mechanics are certainly computable. The computation is exponentially complex, and it requires solving the Schrodinger equation exactly for a many-body system, but with enough computer time it is certainly possible. Any undergraduate quantum mechanics textbook demonstrates several solvable problems in quantum mechanics that can even be solved by hand, and they certainly involve quantum randomness! $\endgroup$ – Ian Apr 8 at 21:52
  • $\begingroup$ Now the problem is how to sample the resulting distributions. Just like sampling a normal distribution on a computer requires a pseudo-random number generator, sampling quantum probability distributions may only be done pseudo-randomly on a computer. I assume that it is in this sense that quantum randomness is not computable. $\endgroup$ – Ian Apr 8 at 21:53
  • $\begingroup$ @Ian here there are some examples of texts that indicate that quantum randomness is uncomputable. Are these texts proposing what you are saying?: Example 1: books.google.es/… $\endgroup$ – user226436 Apr 9 at 21:05

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