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I often heard physicists mentioning the EPR paradox or the quantum entanglement when talking about the non-locality of quantum mechanics, but wasn't quantum mechanics already non-local from the beggining? I mean when the measurement it's being made, the wavefunction of the quantum system is affected everywhere instantaneously.

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    $\begingroup$ when the measurement it's being made, the wavefunction of the quantum system is affected everywhere instantaneously This is only in the Copenhagen interpretation, not in standard quantum mechanics. $\endgroup$ – Ben Crowell Oct 3 '18 at 15:53
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Yes, and in a sense EPR and entanglement are just ways of seeing this feature directly. In other words the formalism of quantum mechanics had this non local feature but it's through EPR and entanglement that you can actually see it manifest

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