Hidden variable theories, ‘the hidden parameter’ as von Neumann called them, entered the quantum scene soon after the formalization of quantum mechanics as we know it today. That formalization was led by front-line physicists like Born, Dirac, Heisenberg, Jordan, and Schrödinger. Attention to hidden variable theories garnered strength following the criticisms towards quantum mechanics formulated by Einstein and colleagues in 1935. That criticism, stating that quantum mechanics was ‘not complete,’ as a theory, led Bohm, in the 1950s, to formulate hidden variable theories. In turn, Bell in 1964 introduced his famed Bell theorem that provided a test for the existence of hidden variable theories. This chapter examines the history of the futile search, for experimental proof, for the existence of these theories.
Hidden variable theories, ‘the hidden parameter’ as von Neumann called them, entered the quantum scene soon after the formalization of quantum mechanics as we know it today. That formalization was led by front-line physicists like Born, Dirac, Heisenberg, Jordan, and Schrödinger. Attention to hidden variable theories garnered strength following the criticisms towards quantum mechanics formulated by Einstein and colleagues in 1935. That criticism, stating that quantum mechanics was ‘not complete,’ as a theory, led Bohm, in the 1950s, to formulate hidden variable theories. In turn, Bell in 1964 introduced his famed Bell theorem that provided a test for the existence of hidden variable theories. This chapter examines the history of the futile search, for experimental proof, for the existence of these theories.
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.
This article reviews the history of J. von Neumann’s analysis of hidden variables in quantum mechanics and the subsequent analysis by others. In his book The Mathematical Foundations of Quantum Mechanics, published in 1932, von Neumann performed an analysis of the consequences of introducing hidden parameters (hidden variables) into quantum mechanics. He arrived at two principal conclusions: first, hidden variables cannot be incorporated into the existing theory of quantum mechanics without major modifications, and second, if they did exist, the theory would have already failed in situations where it has been successfully applied. This analysis has been taken as an “incorrect proof” against the existence of hidden variables, possibly due to a mistranslation of the German word prufen. von Neumann’s so-called proof isn’t even wrong as such a proof does not exist, but it is an examination of the limitations imposed by internal consistency of the Hilbert space formulation of the theory. One of the earliest attempts to eliminate uncertainty, by D. Bohm, requires a major modification of quantum mechanics (observables are not represented by Hermitian operators), which supports von Neumann’s first principal conclusion. However, testing the Bohm theory requires constructing a physically impossible initial state. As such, the theory has no experimental consequences, so W. Pauli referred to it as an “uncashable check”. As there are no observable consequences, the Bohm theory is possibly a counterexample to von Neumann’s second conclusion that hidden variables in particular would have already led to a failure of the theory.
In his book \textit{The Mathematical Foundations of Quantum Mechanics}, published in 1932, J. von Neumann performed an analysis of the consequences of introducing hidden parameters (hidden variables) into quantum mechanics. He showed that hidden variables cannot be incorporated into the existing theory of quantum mechanics without major modifications, and concluded that if they did exist, the theory would have already failed in situations where it has been successfully applied. von Neumann left open the possibility that the theory is not complete, and his analysis for internal consistency is the best that can be done for a self-referenced logical system (Gödel's theorem). This analysis had been taken as an ``incorrect proof" against the existence of hidden variables. von Neumann's so-called proof isn't even wrong as such a proof does not exist. One of the earliest attempts at a hidden variable theory was by D. Bohm, and because there were no experimental consequences, W. Pauli referred to it as an ``uncashable check." To our knowledge, a successful hidden variable extension to quantum mechanics with testable consequences has not yet been produced, suggesting that von Neumann's analysis is worthy of rehabilitation, which we attempt to provide in a straightforward manner.
Abstract In chapter 12 we give an overview of the historical development of hidden-variable theories aiming to attribute ‘hidden’ definite outcomes to any potential measurement on a quantum system. We start with a discussion of von Neumann’s assumption on hidden-variable models, which was later realized not to hold by Hermann, Kochen, Specker, and Bell, going into detail on Bell’s refutation of von Neumann’s arguments. We then turn to the notion of contextuality, which severely restricts hidden-variable models: we discuss Gleason’s theorem before stating and proving the famous Kochen-Specker theorem, as well as the simpler versions of Peres’ nonet and Mermin’s pentagram. These results show that quantum mechanics is not compatible with the assignment of definite measurement outcomes to all possible measurements, and such assignments can hence only be made once a restricted set of observables, a context, is selected
Prologue A memorial conference for John Bell, open to the public, was held at Rutgers University around 20 years ago. I gave a short talk there on Bell's views about David Bohm's “hidden variables” formulation of quantum mechanics, a version of quantum mechanics often called the de Broglie–Bohm theory or Bohmian mechanics. This theory was in fact discovered by Louis de Broglie in 1927. In 1952, it was rediscovered and developed by Bohm, who was the first to appreciate its connection to the predictions of standard quantum mechanics. I did not publish the talk. I have decided that it would be appropriate to publish a very lightly edited version of it here, in this volume devoted to the work of Bell on the foundation of quantum mechanics. One reason for doing so is that the connection between Bell and Bohm continues to be somewhat underplayed, with the strength of his advocacy of Bohmian mechanics not properly appreciated. For example, about half of the papers in Bell's collected works on the foundations of quantum mechanics deal with Bohmian mechanics. But in his fine introduction to the revised edition of this great book [1], Alain Aspect mentions this theory in only a single sentence, and parenthetically at that. For several decades after Bell proved his nonlocality theorem, based in part on Bell's inequality, it was widely claimed that Bell had shown that hidden variables – and Bohmian mechanics in particular – were impossible, that they were incompatible with the predictions of quantum mechanics. For example, the great physicist Eugene Wigner, who, unlike most of his contemporaries, was profoundly concerned with the conceptual foundations of quantum mechanics and usually wrote on the subject with great clarity and insight, has written that This [hidden variables] is an interesting idea and even though few of us were ready to accept it, it must be admitted that the truly telling argument against it was produced as late as 1965, by J. S. Bell … This appears to give a convincing argument against the hidden variables theory.
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.