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Could someone explain to me how Bell's theorem solves the EPR paradox and 'spooky action at a distance'?

From what I understand, when measuring a state, say spin up in the x direction, the wave function collapses and the other particle must be spin down in the x direction instantaneously no matter how far it is from its entangled partner.

I can't seem to put all the pieces together with local realism and local hidden variables.

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    $\begingroup$ Helpful: physics.stackexchange.com/q/114218 $\endgroup$
    – Yashas
    Commented Feb 21, 2017 at 12:37
  • $\begingroup$ It doesn't SOLVE the EPR paradox -- it doesn't resolve the factors EPR had a problem with -- what the Bell's Theorem experiments instead do is verifies that, whatever problems EPR thought existed in the QM view of entangled photons measurements, those problems are a feature of reality, and not just of QM. $\endgroup$
    – TKoL
    Commented Oct 14, 2022 at 15:04
  • $\begingroup$ To put it another way: EPR's problem with QM was that it said that unmeasured properties of these particles are indeterminate prior to measurement, and that creates issues with entanglement. The experiments we have around bell's theorem come out on QM's side of that, confirming that there's no way these properties (spin for example) could have had definite values prior to measurement. $\endgroup$
    – TKoL
    Commented Oct 14, 2022 at 15:04

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Bells inequality is derived by assuming 'local reality'. This inequality has been shown to be violated by experiment and by theory (quantum mechanics). So the conclusion is: nature doesnt always posess local reality. Assuming local reality made EPR a paradox, so without this it is resolved.

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  • $\begingroup$ Thank you. These three lines explain it better than any other explanation I have seen yet wherein they delve in the details without giving a clear overview. Perhaps I would add that for the first time an experiment was devised that would yield different results between local reality and spooky action at a distance, for which there is no obvious way to differentiate. $\endgroup$
    – DPM
    Commented Apr 12, 2020 at 0:13

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