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What did Bell’s theorem actually prove? I keep hearing three different answers

Ethan Mercer Fellow
· 4 replies
Physics & cosmologyAnalyticModern EuropeanAlbert EinsteinDavid BohmJohn BellNiels Bohr#bell-theorem#hidden-variables#locality#quantum-mechanics
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I'm doing philosophy with some physics. In the space of one week I have been told by three different people that Bell's theorem proves:

  1. that the universe is non-local;
  2. that there are no hidden variables in quantum mechanics;
  3. that Einstein was wrong.

They can't all be right in the strong form, and I suspect none of them is quite right. The textbook I have goes straight into the maths of the inequality and I lose the thread of what is being assumed.

Could someone explain, without too much notation, what Einstein's original worry was, what exactly Bell showed, what the experiments then found, and what follows and what does not? I'd especially like to know which of my three slogans is closest to true, and why the other two overreach.

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4 answers

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  1. Lars Eriksen

    ✓ Accepted answer Fellow

    Good instinct: all three overreach.

    Einstein's worry. In the 1935 EPR paper, Einstein, Podolsky and Rosen argued that quantum mechanics is incomplete. Particles must have definite properties before measurement; the theory's probabilities just reflect our ignorance. Underneath that is an assumption of locality: nothing done here can instantly affect what happens over there.

    Bell's step (1964). Bell derived an inequality that any theory satisfying both assumptions must obey: locality, and definite pre-existing values for the measured quantities. Quantum mechanics predicts that certain correlations violate it. That turned a philosophical stand-off into an experimental question.

    The experiments. Done repeatedly from the 1970s and 80s onwards, with the main loopholes closed in 2015. The inequality is violated, as quantum mechanics predicts.

    What follows. No theory can be both local and give every measurement a definite pre-existing value. One of the two must go. Bell does not tell you which.

    So: slogan 2 is wrong as stated, because Bohm's 1952 pilot-wave theory has hidden variables; it simply gives up locality. Bell admired it. Slogan 1 is too strong, because many-worlds keeps locality by giving up single definite outcomes. Slogan 3 is half true: Einstein's particular combination of hopes cannot be had. Whether he was wrong about what matters is still argued.

    1. Pieter van Dijkhuizen

      Fellow

      Adding one footnote to Lars: there is also a small minority escape route, usually called superdeterminism, which denies that the experimenters' choice of settings is statistically independent of the particles being measured. Most physicists find it unattractive because it seems to undermine experimental reasoning generally, but it is the reason careful writers say Bell's result depends on three assumptions, not two.

      Helpful · 1

Other answers

  1. Emeka Anyaoha

    Fellow

    For teaching I use a simpler line that seems to stick: before Bell, Einstein and Bohr disagreed about what was real and nobody could test it. After Bell, nature was asked, and it ruled out one of Einstein's two hopes. It did not tell us which story about reality to put in its place. That last part is why the philosophy is still going.

    Helpful · 2
  2. Ethan Mercer

    Fellow

    This is really helpful. So the result constrains the metaphysics without settling it, and the slogans each pick one interpretation and pretend it's the theorem. I'll take that back to the three people.

    Helpful · 3