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Let's say that a being or a machine has nearly infinite amount of information, about the world around us. It could easily find the outcome of a flipped coin knowing the force it was thrown, the atmospheric pressure, etc... It could also predict the place and action for every person on earth in a year from now by calculating all the possibilities.

So the question is, is there any event that could happen that this machine has no way to predict? A trully unpredictable event no matter how much information it has?

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The way physics stands now, quantum mechanics is truly unpredictable. The 'hidden variables' theory has very few proponents. And hence even coin throws are 'truly unpredictable' because to have a perfect theory, you would have to model the quantum interactions of the metal atoms in the coins with those of the atmosphere and the table. However you could have a theory that gives correct results within certain error limits.

This also links with the PvsNp issue, and the BQP issue in theoretical computer science. But then again, it is all grounded in a certain 'assumed ontology', which can change, with new advances in human understanding.

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    I disagree with this statement; the fact that QM resolves in a probabilistic manner to any attempt to quantify (measure) it is not a result of unpredictability, it's a result of observations changing the phenomena under observation. If this was not the case, then QM could not exist as a model of quantum behaviour because there would be no 'trend' that can be observed as accurately as it can be. The fact that we have laws of physics at all implies that if there is something truly unpredictable, it has to exist outside the fundamental physical laws.
    – Tim B II
    Commented Feb 17, 2018 at 10:49
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    Both of us are using 'predictable' and 'observation' in a very different sense. But I think that my assessment about coin throws, still stands. Quantum mechanics forces you to be satisfied with 'error bounds'. And the only predictable are these bounds.
    – user2277550
    Commented Feb 17, 2018 at 10:53
  • Could really quantum interactions influence an event like coin throw? I know a single electron can pass through a wall but a whole coin, no... I believe a coin throw, and most of the events we can observe can be predicted without quantum mechanics.
    – Alex Michailidis
    Commented Feb 17, 2018 at 13:35
  • @alex-rokabilis To predict a coin throw, you would take the initial conditions, plus the law of physics, simulate the throw and use the result of the simulation to predict the outcome. Sometimes the initial conditions are such that a very small change in the initial conditions would change the outcome. When that happens, the radioactive decay of a single carbon atom in the coin could change the outcome.
    – gnasher729
    Commented Feb 17, 2018 at 14:19
  • +1 However, I think "truly unpredictable" means "not perfectly predictable for a single quantum event". QM does allow a probabilistic predictability which is all I think we can expect of any theory of science even gravitation theories.
    – Frank Hubeny
    Commented Feb 17, 2018 at 15:15

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