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Bell’s Theorem and Its Experiments

Alex Mo

Published Aug 25, 2025• 0 citations
Publisher

Abstract

Quantum mechanics makes surprising predictions that defy our classical understanding of the world.Experiments done on entangled particles-particles with linked properties-prove that actions on one particle can affect the other one no matter the distance.In response, physicists came up with local hidden variable theories in an attempt to understand this quantum phenomena through a classical lens.John Bell formulated a way to test whether nature is dictated by local hidden variable theories or quantum mechanics, and since then it has been the goal of numerous physicists to experimentally test the theorem and improve upon the results.This paper describes the history of these experiments, their pros and cons, their advancements, and the potential applications that they will enable.

DOI
10.58445/rars.2981

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Quantum mechanics makes surprising predictions that defy our classical understanding of the world.Experiments done on entangled particles-particles with linked properties-prove that actions on one particle can affect the other one no matter the distance.In response, physicists came up with local hidden variable theories in an attempt to understand this quantum phenomena through a classical lens.John Bell formulated a way to test whether nature is dictated by local hidden variable theories or quantum mechanics, and since then it has been the goal of numerous physicists to experimentally test the theorem and improve upon the results.This paper describes the history of these experiments, their pros and cons, their advancements, and the potential applications that they will enable.
Hidden variable theories, as encouraged by the EPR paper, that proliferated in the 1950s, were taken quite seriously in some academic quarters, despite the existence of the 1932 von Neumann ‘proof’ that supposedly showed that these hidden theories were incompatible with the stochasticity of quantum mechanics. In 1964, John Bell, a particle theorist, reexamined the von Neumann proof, found it ‘wanting’, and offered his own proof that reaffirmed that hidden variable theories were incompatible with quantum mechanics. Bell added a twist: his proof was in the form a neat inequality theorem that was easy to comprehend and became an instant success. Bell's theorem led to a new generation of experimentalists to rediscover quantum entanglement, and to conduct these experiments in the visible spectrum, to test for evidence of hidden variable theories. The results were negative thus reaffirming the validity of quantum mechanics and its indeterminacy. In this chapter the premises of Bell's theorem are explained as well as its link to the probabilities of quantum entanglement.
In our terms, this is Bell's 1964 theorem, ‘No local hidden-variable theory can reproduce exactly the quantum mechanical predictions.' Against this, and bound by what Bell takes to be Einstein's definition of locality, we refute Bell's theorem and reveal his error. We show that Einstein was right: the physical world is local; and we advance Einstein's quest to make quantum mechanics intelligible in a classical way. With respect to understanding, and taking mathematics to be the best logic, the author is as close as an email: eprb@me.com
Quantum physics, which describes the strange behavior of light and matter at the smallest scales, is one of the most successful descriptions of reality, yet it is notoriously inaccessible. Here we provide an approachable explanation of quantum physics using simple thought experiments. We derive all relevant quantum predictions using minimal mathematics, without introducing the advanced calculations that are typically used to describe quantum physics. We focus on the two key surprises of quantum physics, namely wave-particle duality, a term that was introduced to capture the fact that single quantum particles in some respects behave like waves and in other respects like particles, and entanglement, which applies to two or more quantum particles and brings out the inherent contradiction between quantum physics and seemingly obvious assumptions regarding the nature of reality. Following arguments originally made by John Bell and Lucien Hardy, we show that the so-called local hidden variables are inadequate at explaining the behavior of entangled quantum particles. This means that one either has to give up on hidden variables, i.e., the idea that the outcomes of measurements on quantum particles are determined before an experiment is actually carried out, or one has to relinquish the principle of locality, which requires that no causal influences should be faster than the speed of light and is a cornerstone of Einstein's theory of relativity. Finally, we describe how these remarkable predictions of quantum physics have been confirmed in experiments. We have successfully used the present approach in a course that is open to all undergraduate students at the University of Calgary, without any prerequisites in mathematics or physics.
Bell's inequalities(1964) provides a quantitative criterion to test the local hidden variable theory(LHVT) versus quantum mechanics(QM).For the first time,it leads to the possibility to experimentally distinguish LHVT and QM.So far,there have been tens of experiments ever since the first experiment by Clauser et al(1972).An overwhelming majority of these experiments are in good agreement with the predictions of QM yet violate those of LHVT.Some loopholes in these experiments are discussed in Section I,followed by a respective summary to 12 experiments between 1972 to 1982 and 31 experiments from 1985 and on in Sections II and III.It is finally pointed out that so far there is not a single experiment to close both the locality loophole and the detection loophole at the same time,but the experimental outcomes are irreversible.Accordingly,theoretical physicists must admit that the present physics foundation is broken,i.e.quantum mechanics is contradiction with special relativity.
In 1964 John Bell proved a theorem2 allowing the experimental test of whether what Einstein derided as “spooky actions at a distance” actually exist. We will see that they do. Bell's theorem can be displayed with a simple, nonmathematical thought experiment suitable for a physics course at any level. And a simple, semi-classical derivation of the quantum theory result can be given for physics students. These entanglement phenomena are today applied in industrial laboratories and are increasingly discussed in the popular literature. Unfortunately, they are also misappropriated by the purveyors of pseudoscience, something physicists have a responsibility to address.3 Students can be intrigued by the quantum strangeness physics has encountered at a boundary of our discipline.