Can Bell’s Theorem Be Disproved?

Bell’s theorem (BT) was formulated in 1964 as a continuation of the 1935 Einstein, Podolski, Rosen (EPR) criticism on the completeness of quantum mechanics (QM).

Based on the principle of locality, i.e., instantaneous spooky actions at a distance are not allowed, EPR showed through a thought experiment that QM was an incomplete theory in the sense that it fails to describe the underlying reality of the microscopic world.

The complete theory is supposed to be obtained by supplementing QM with hidden variables (HV) that would allow superseding quantum uncertainties with deterministic predictions.

John Stewart Bell in 1964 continued the EPR reasoning and managed to replace the thought experiment by an inequality that this time can be tested by an experiment. In a nutshell, BT postulates a complete theory complying with two hypothesis: locality and realism and from these hypotheses he derived an inequality known as Bell’s inequality (BI) that must be satisfied by any local realistic theory. Since then many experimental tests have been performed with increasing orders of accuracy and in all of them, BI is found to be violated.

These experimental results are widely interpreted as the impossibility of completing QM in order to restore realism and, what is considered even more astonishing, locality. There is, however, controversy with this interpretation since there are many researchers and commentators that view BI violations differently thus refuting the “orthodox” interpretation.

The intentions to disprove Bell’s conclusions, in a sense, resembles the vain attempts to prove what in mathematics is known as Fermat’s last theorem. This theorem was famous for the futile attempts to prove it until it was finally proved in 1995 by the English mathematician Andrew Wiles.

Although some rebuttals of BT are logically correct they are achieved by attacking some necessary implicit hypothesis which denial are widely regarded as implausible, e.g., the free will of the experimenter to choose his device settings. Other rejections are simply based on misinterpretations of various kinds.

Such refutations of Bell’s result appeared soon after publication and Bell himself reacted to this criticisms by relaxing and generalizing the hypothesis of his theorem. One of these generalizations consisted in the abandonment of determinism as a necessary hypothesis for the derivation, another was the inclusion of the issue of contextuality.

As regards the relinquishment of determinism he considered it unnecessary and in fact, it was later explicitly proven by Arthur Fine (Phys. Rev. Lett.1982,48,291–295) that it was a superfluous generalization. On the other hand, the contextuality issue deals with the inclusion of the effect that the measuring devices might have on the measurement results.

One of the misunderstandings regarding BT goes by the name of contextuality loophole alleging that Bell’s derivation is meaningless because it does not properly include the effect of the measuring devices.

This misunderstanding is explained in the article “On Nieuwenhuizen’s Treatment of Contextuality in Bells Theorem” published in Foundations of Physics by J. P. Lambare from the University of FIUNI and FaCEN of Paraguay.

Questions & Answers (5)

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  1. Question

    This article fails to grasp that Fine disproved Bell, but for the sake of politeness does not state this directly. Fine showed that the inequality holds precisely for models corresponding to random variables on a joint probability space and that locality is not needed. A few years later Itamar Pitowsky observed that Bell and Fine had merely rediscovered Boole’s inequality well known outside of physics, which characterizes joint probability spaces regardless of assumptions of locality or non-locality or philosophical assumption about the reality of quantum observables. Rosinger points this out and many others after have done the same including the late Walter Philipp. This is a general problem with so called “no-go theorems”. The philosophical or physical assumptions that they try to prove do not correspond to the mathematics of the the proof.

    1. Answer

      This is nonsense. Fine showed that the 8 Bell-CHSH inequalities are necessary and sufficient for local realism. The inequality is a trivial probabilistic inequality, indeed it figures as an exercise for the reader in Boole’s book. One can see Bell-CHSH as an elementary application of the basic Boole inequality Prob(A union B union C…) is less that or equal to Prob(A) + Prob(B) + …. Bell’s theorem uses the probability inequality as a lemma to prove a theorem of metaphysics: no theory having the properties called nowadays locality, realism, and no-conspiracy can reproduce the predictions of quantum mechanics. One can go further: thanks to so-called “loophole free” experiments, no such theory can even approximately reproduce the results of laboratory experiments.

      Richard David Gill PRO INVESTOR
    2. Answer

      It is fair to vindicate Arthur Fine against the claims that he disproved Bell theorem. That interpretation of Fine’s theorem is not his and it is not a matter of politeness.

      Justo PRO INVESTOR
  2. Question

    See: Simplest refutation of Bell’s inequality © Copyright 2018 by Colin James III All right reserved.

    Colin James III
  3. Question

    Those who wish to delve deeper into these matters are encouraged yo see the following:

    “Matrix models as non-local hidden variables theories”

    ~Lee Smolin

    A theory that yields “maybe” as an answer should be recognized as an inaccurate theory.

    ~ ‘t Hooft

    It seems clear that the present quantum mechanics is not in its final form […] I think it very likely, or at any rate quite possible, that in the long run Einstein will turn out to be correct.


    Can it really be true that Einstein, in any significant sense, was a profoundly “wrong” as the followers of Bohr maintain? I do not believe so. I would, myself, side strongly with Einstein in his belief in a submiscroscopic reality, and with his conviction that present-day quantum mechanics is fundamentally incomplete.


    Whatever the meaning assigned to the term *complete,* the following requirement for a complete theory seems to be a necessary one: every element of the physical reality must have a counterpart in the physical theory.


    If you ask a physicist what is his idea of yellow light, he will tell you that it is transversal electromagnetic waves of wavelength in the neighborhood of 590 millimicrons. If you ask him: But where does yellow come in? he will say: In my picture not at all, but these kinds of vibrations, when they hit the retina of a healthy eye, give the person whose eye it is the sensation of yellow.


    Brian Flanagan

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