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Can Quantum Entangled particles convey information faster than speed of light. If they don't what was wrong with John Bells experiment?

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You cannot convey information faster than light using quantum entanglement. For a mathematical proof of this result, which is commonly called the "no-communication theorem", see e.g. https://en.wikipedia.org/wiki/No-communication_theorem.

Nothing was wrong with Bell's experiment. Communication was not demonstrated, only correlation between outcomes. In order to derive information from correlation, you either have to:

  • Compare the results of experiments on one particle with experiments on the other, which requires communicating the results of both experiments classically (i.e. slower than light), or
  • Know beforehand exactly how the entanglement is set up, in which case information wasn't really communicated using the experiment at all; once you measure your particle, you know what state the other particle is in, but you already knew that, conditionally (just like you already knew what the other particle's state would be for every other experimental outcome), so it's more a case of selecting a relevant piece of information than actually communicating anything.

If neither of these conditions is fulfilled, and you just look at the results from one of the particles, then you'll just see randomness. Importantly, you can't actually control the outcome of the measurement; this is one of the basic postulates of quantum mechanics.

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    $\begingroup$ Murray Gell-Mann said if we split 30 cents and I go back to New York and look in my pocket and see a quarter, I instantly knew you have a nickel back in LA. So what? $\endgroup$ – JEB May 9 at 16:29
  • $\begingroup$ @JEB That's an excellent analogy for the second case. You know beforehand how the splitting is set up (namely, you know that your money and your friend's should sum to 30 cents), so the fact that you now know something about your friend's money is just selecting the relevant piece of information from the list of already-known facts ("if I have 1 cent, my friend has 29 cents," "if I have 2 cents, my friend has 28 cents," etc.), rather than communicating anything. $\endgroup$ – probably_someone May 9 at 16:33
  • $\begingroup$ @JEB: I find it impressive you would know the nickel was in LA simply based on the contents of your pocket. Sorry, j/k. $\endgroup$ – Exocytosis May 9 at 17:31

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