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Comment by angrais | Hacker News Reader

>> What's randomness in a coin toss? If we had all the information we could perfectly predict the result of a toss. But if we know nothing then at most we can say is that both outcomes are equally probable.

Perhaps I'm being dense or overall don't understand, but how is this possible? What is "all the information"? Isn't it at most likely they the outcome is 50/50?

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Each coin-toss is a deterministic physical process governed by laws of motion. If we had perfect information about the motion of all components in the system (hand, coin, air, floor, etc.), then we could, in principle, perfectly predict the outcome of every toss. Each individual toss would have a 100% probability of its predicted outcome.

Since we typically lack any of that information, we are stuck with the 50 / 50 prior distribution.

This is very debatable if you throw QM into the mix. From all what we know, we cannot predict everything with 100% success rate -- QM cannot be explained by a hidden variables model.

Argh - yes it can. Bell explicitly have a pretty trivial one in one of his early papers. QM cannot be explained by a non-contextual hidden variables model. (The simplest physical version of contextuality is locality - so as Bell showed you cannot explain quantum theory with a local hidden variables model).

Let's not break causality by observing non-local hidden variables.

Presumably talking to the wind here as this thread is old, but nonlocal hidden variables do not break causality! This can be seen explicitly in Bell's trivial model, where the state of a system is just the regular quantum state plus a uniform random number between 0 and 1 (hidden). Or put it this way, if this model "breaks causality" then so does regular non-relativistic quantum theory.

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