What is Bell's theorem: Definition and 98 Discussions

Bell's theorem proves that quantum physics is incompatible with local hidden-variable theories. It was introduced by physicist John Stewart Bell in a 1964 paper titled "On the Einstein Podolsky Rosen Paradox", referring to a 1935 thought experiment that Albert Einstein, Boris Podolsky and Nathan Rosen used to argue that quantum physics is an "incomplete" theory. By 1935, it was already recognized that the predictions of quantum physics are probabilistic. Einstein, Podolsky and Rosen presented a scenario that, in their view, indicated that quantum particles, like electrons and photons, must carry physical properties or attributes not included in quantum theory, and the uncertainties in quantum theory's predictions were due to ignorance of these properties, later termed "hidden variables". Their scenario involves a pair of widely separated physical objects, prepared in such a way that the quantum state of the pair is entangled.
Bell carried the analysis of quantum entanglement much further. He deduced that if measurements are performed independently on the two separated halves of a pair, then the assumption that the outcomes depend upon hidden variables within each half implies a constraint on how the outcomes on the two halves are correlated. This constraint would later be named the Bell inequality. Bell then showed that quantum physics predicts correlations that violate this inequality. Consequently, the only way that hidden variables could explain the predictions of quantum physics is if they are "nonlocal", somehow associated with both halves of the pair and able to carry influences instantly between them no matter how widely the two halves are separated. As Bell wrote later, "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."Multiple variations on Bell's theorem were proved in the following years, introducing other closely related conditions generally known as Bell (or "Bell-type") inequalities. These have been tested experimentally in physics laboratories many times since 1972. Often, these experiments have had the goal of ameliorating problems of experimental design or set-up that could in principle affect the validity of the findings of earlier Bell tests. This is known as "closing loopholes in Bell test experiments". To date, Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems do, in fact, behave.The exact nature of the assumptions required to prove a Bell-type constraint on correlations has been debated by physicists and by philosophers. While the significance of Bell's theorem is not in doubt, its full implications for the interpretation of quantum mechanics remain unresolved.

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  1. cianfa72

    I Understanding Bell Inequality Proof: Explained from a Probability Perspective

    Starting from this link my understanding of Bell inequality proof goes as follows: Suppose we have a model of local pre-determinate hidden variables for QM. This amounts to say QM objects are in pre-determinate given states even if we do not measure it. Locality just means that spacelike...
  2. bhobba

    I Could Tim Maudlin's Views on Bell and QM Be Flawed?

    Hi All I have never been particularly impressed with Tim Mauldin's general take on Bell and QM. I am reading an article of his at the moment. Here is an excerpt (lightly edited by Grammarly to have correct punctuation, etc). Start Quote But for expository purposes, the point is most...
  3. Lynch101

    I Looking For Help Understanding Bell's Theorem, Hidden Variables & QM

    I was revisiting @DrChinese 's Bell's Theorem with Easy Math which sparked a few questions, which I am hoping might offer a potential path to a deeper understanding of Bell's Theorem and Quantum Mechanics (QM) in general. The explanation uses light polarisation experiments to explain how we...
  4. golya

    I Bell’s Theorem for dummies

    Hi everyone, I need some help getting the gist of Bell’s theorem and his notion of inequalities. How would you explain it to someone with limited knowledge of mathematics? What are the potential implications?
  5. Jarvis323

    A Hidden Assumptions in Bell's Theorem?

    There has been a lot of discussion on Bell's theorem here lately. Superdeterminism as a Bell's theorem loophole has been discussed extensively. But I have not seen discussion about Karl Hess, Hans De Raedt, and Kristel Michielsen's ideas, which essentially suggest that there are several hidden...
  6. P

    A Bell's theorem vs Kochen–Specker theorem

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  7. N

    I In Bell's Theorem, communication

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  8. Quantum Entanglement & Spooky Action at a Distance!

    Quantum Entanglement & Spooky Action at a Distance!

    Quantum Entanglement & Spooky Action at a Distance! Bell's theorem.
  9. N

    I Frontiers in Physics had 2 papers quest. Bell's theorem, any othrs?

    One is fr. worker at U. Karlsruhe, another fr. Israeli res. The latter argued findings can be integrated into classical physics.
  10. plmustard

    B Bell Test Configuration Question

    Qutools makes quantum physics kits for educational purposes. Its quED kit is designed to help students learn about entanglement by performing Bell tests. In the manual section 5.1 it describes "the simplest test to verify entanglement of photon pairs." My question is if the entangled photons...
  11. Strilanc

    I A tool for checking claims of violating Bell's theorem

    I just wanted to point out a resource useful for dealing with claims of violating Bell's theorems. You can point the claimant at https://algassert.com/quantum/2015/10/11/Bell-Tests-vs-No-Communication.html and say "I won't believe you unless you can make the 'Write Your Own Classical CHSH...
  12. M

    I Model used to refute Bell's theorem

    I’m looking over a recent paper mentioned in another thread. It claims to refute Bell’s theorem. At first glance, the model presented in the paper doesn’t appear consistent with QM. Here’s a simple example. Suppose we set both polarizers to the same angle ##\alpha = \pi /4##. In the model...
  13. E

    I Bell's theorem claimed to be refuted - paper published by EPL

    The Paper “On a contextual model refuting Bell’s theorem” has now been published by the journal EPL (Europhysics Letters) and is available under https://iopscience.iop.org/article/10.1209/0295-5075/134/10004 In this paper a contextual realistic model is presented which correctly predicts...
  14. Lunct

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    So I have often heard it argued that "super-determinism" is a loophole to Bell's theorem, that allows a local hidden variable theory. Bell himself alluded to it in a 1980s BBC interview. But why is this the case? And how is super-determinism different to regular determinism. And the many-world's...
  15. S

    I Bell's Theorem - why product of (2)spins can be +1 (Griffith's text)

    Hello, Within Griffith's text - chap 12 section 12.2 page 423 - this is a brief summary of Bell's Theorem and description of Bell's 1964 work. There is a table on page 423 showing the spin of the electron and positron (from pi meson decay) - these would be in the singlet state, one would be...
  16. Lynch101

    B Bell's theorem, QFT, and the Relativity of Simultaneity

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  17. jk22

    I Bell's theorem : pre- and post-digitization

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  18. jk22

    I Does Bell's theorem imply other Lorentz transformations?

    Could it be that the transformations keeping the wave equation invariant have other solutions than the usual Lorentz ones ?
  19. jk22

    I Influence on world's number and Bell's theorem

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  20. A

    A Does Bell's theorem imply nonlocality using a false assumption

    In https://arxiv.org/ftp/arxiv/papers/1409/1409.5158.pdf, the author (Donald A. Graft) concludes that Bell tests cannot refute local realism, because they employ a wrong analysis. He says: "The quantum joint prediction cannot be recovered in an experiment with separated (marginal) measurements...
  21. facenian

    I Is Superdeterminism a Plausible Explanation for Quantum Mechanics?

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  22. E

    I Is Bell's Theorem Inconsistent with Quantum Mechanics?

    I've published a paper on local hidden variables with surprising consequences for Bells Theorem. It is available on https://doi.org/10.1515/phys-2017-0106 The journal Open Physics is listed in T/R. To the background of Bell's argument, the following comments: Since Bell published his theorem...
  23. whitsona

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  24. R

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  25. B

    I How do you understand EPR & Bell's Theorem?

    This is related to vanhees71 statements (see bottom). I'll explain. First. The idea is very simple. As summary: Einstein showed that if reality was objective and quantum theory complete, then there had to be nonlocal effects. But since nonlocal effects can violate relativity, then there had to...
  26. P

    B Some questions about "superdeterminism" and Bell's Theorem

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  27. U

    I Bell's theorem and Superdeterminism

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  28. R

    Bell's theorem mathematical content

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  29. N

    I What is the physical significance of Bell's math?

    Bell (1964) http://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf has 3 unnumbered equations following his equation (14). Let them be (14a)-(14c). Bell then uses his equation (1) to move from (14a)-(14b). It seems to me that he uses this: [A(b,λ)]2 = 1. (X)...
  30. A. Neumaier

    I Classicality in Bell's original reasoning

    Please give a reference to Bell's original papers (if possible in a free online version) that demonstrates this, so that we can discuss it.
  31. jk22

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    I just suppose the Bell's Ansatz for the result of measurement to be $$A (\theta,\lambda) $$ Now the parameter lambda could be anything : -a physical quantity like the polarization angle of the incoming photon -the coordinate of a 'world' - the whole wavefunction. ... In the case of the...
  32. J

    B Simple proof of Bell's theorem

    The thread I wanted to post my question on got closed. Recapitulating: The best (simplest) account I have found to date for the Bell inequality (SPOT stands for Single Photon Orientation Tester): Imagine that each random sequence that comes out of the SPOT detectors is a coded message. When...
  33. petrushkagoogol

    I Imposition of relativistic constraints on Bell's theorem

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  34. S

    I Quantum Entanglement-Susskind-lecture 4&5

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  35. Tony Weston

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  36. J

    A Shocker: PR Box is logically inconsistent

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  37. J

    B Bell's Theorem basic question on contextuality & locality

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  38. ShayanJ

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  39. entropy1

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    There's something I don't quite get about most illustrations about Bell's inequality theorem. I will explain what: Consider a pair of entangled photons fired at two arbitrarily oriented polarizers. I most explications, it seems the author suggests that the hidden variable represents the binary...
  40. DrChinese

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  41. G

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  42. M

    I Bell's Theorem: more general interactions with detector?

    [Mentor's note: split off from the thread https://www.physicsforums.com/threads/first-loophole-free-bell-test.829586/ as this is a general question about Bell's Theorem, not the specific experiment discussed in that thread] It says in the paper ... ... and the 'CHSH-Bell inequality' all...
  43. atyy

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  44. Jilang

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    I read with interest the thread here https://www.physicsforums.com/threads/bells-theorem-and-negative-probabilities.59163/ and was trying to find out more about how a negative probability might be interpreted. I came across this and wondered if anyone could shed more light on it. "Let us...
  45. G

    Hidden variables & partial correlations

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  46. L

    Does Measuring Two Entangled Photons at the Same Time Break the Laws of Physics?

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  47. D

    A variation of the Bell experiment

    If we start with a Bell state 1/Sqrt(2)(|00>+|11>) and (after moving the second qbit a significant distance away) apply the interferometer transformation |0> -> 0.5(|0>+|1>) |1> -> 0.5(|0>-|1>) to the first qbit, we get 0.5/Sqrt(2)((|0>+|1>)|0>+(|0>-|1>)|1>) =0.5/Sqrt(2)(|00>+|10>+|01>-|11>)...
  48. bohm2

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  49. Gary Boothe

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  50. MikeGomez

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    Quote from this recently posted article. http://www.nature.com/news/physics-bell-s-theorem-still-reverberates-1.15435 “Quantum theory does not predict the outcomes of a single experiment, but rather the statistics of possible outcomes.” My question is not in regards to the statistics of...