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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?

Alex Michailidis
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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.

user2277550
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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 Feb 17 '18 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 Feb 17 '18 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 Feb 17 '18 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 Feb 17 '18 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 Feb 17 '18 at 15:15
  • @TimBII We've been over this before; since you won't read up on it, let me try it this way. When you say this: "is not a result of unpredictability, it's a result of observations changing the phenomena" ...then the _phenomena_ you're referring to, assuming it's _predictable_, is called a "Hidden Variable"; and such theories are called "Hidden Variable Theories". There's also such a thing as "No Go Theorems". Bell's Theorem is a No Go Theorem demonstrating that there _cannot_ be any classical local Hidden Variable Theories; IOW, your _description_ is wrong. – H Walters Feb 17 '18 at 17:36
  • ...now there can be determinism in QM, but it requires something like non-locality, or non-realism of classical physics. There is indeed something more fundamental about this than observations merely interfering. Read up on Bell Inequalities. – H Walters Feb 17 '18 at 17:39
  • Good to see you around again @HWalters. First, it's not a question of 'won't'; it's on my reading list and I'll get to it when I have time to do it justice which isn't now. Second (respectfully), you're using a sledgehammer to crack a nut. If the universe is deterministic, then any subset of it (including QM) is deterministic and hidden variables and Bell Inequalities are irrelevant. If the universe is non-deterministic, then QM is certainly a candidate for non-deterministic behaviour, although it's influence on the classical scale is nominal at best, non-existent at worst. – Tim B II Feb 18 '18 at 06:08
  • @alex-rokabilis, you are essentially correct, although gnasher729 does raise a valid objection only because of our inability to measure accurately below the Newtonian scale. What is unclear is whether or not the decay of the carbon atom could be predicted; Many physicists say yes, meaning that the universe is deterministic and nothing is unpredictable. Some, like gnasher729 and HWalters say no. The truly wonderful part of the universe is that we don't know who is right yet, although a non-deterministic QM doesn't seem to impact the classical scale enough to change a coin toss much if at all – Tim B II Feb 18 '18 at 06:15
  • @TimBII This: "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." ...is wrong. You're describing classical Heisenburg Uncertainty, which is simply classical physics without precise knowledge; IOW, this is a classical local HVT. Classical local HVT's are forbidden by Bell's Theorem. The type of determinism allowed in QM has nothing to do with this wrong statement you keep making. – H Walters Feb 18 '18 at 08:34
  • @HWalters - I disagree. What I'm saying is that IF the universe is deterministic, then so MUST be QM. It's that simple and I don't see anything in your response that disproves that. – Tim B II Feb 18 '18 at 10:41
  • Let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/73324/discussion-between-h-walters-and-tim-b-ii). – H Walters Feb 18 '18 at 14:26