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.
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.
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.
Abstract In 1957, Bohm and Yakir Aharonov alighted on experiments on correlated photons performed some years earlier. Although the experimenters had not looked for EPR-type correlations, Bohm and Aharonov found no contradictions with quantum theory, concluding that entanglement is a real property of matter. Inspired by Bohm, in 1964 John Bell first dispatched von Neumann’s impossibility proof, readmitting the possibility of local hidden variables, and showed how experiment could decide if they existed. Many physicists later misunderstood this as a challenge to Copenhagen. But, as Bohm and Aharonov explained: ‘ . . . there is no inconsistency in the quantum-mechanical conclusion that such correlations exist, but there is, in [Bohr’s] point of view, no way even to raise the question of what is their origin’. If the particles cannot be considered as separable, Einstein’s gaping explanatory hole returns. Interested experimenters had first to disinter the question, which Bell had buried in an obscure journal.
In the early 1960s, John Bell decided to look once again at the hidden variable problem in quantum mechanics, through an examination of the A. Einstein, with B. Podolsky and N. Rosen (EPR) paradox. Proposals for proofs against the possibility of hidden variables had been advanced both before and after EPR. Bell developed both a “theorem” and an inequality, but this may be overstating the case. Most interpretations are that Bell is ruling out any “action-at-a-distance” type of interactions or variables, but would accept that such forces could violate the inequality. By triple of random variables, mentioned by A. Yu. Krennikov, one has to think once again about the experiment suggested by the Bell inequality. Bell has assumed that the set of hidden variables, and more importantly the probability function of the hidden variables, is unchanging. K. Hess and Walter Philipp began to worry about this assumption, because it has some implicit assumptions of its own.
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.
It is proved that Bell's inequality can be traced back to a classical probabilistic formula that is invalid clearly, while the spin correlation formula in quantum mechanics to a formula that has confirmed both by facts and quantum mechanics. Two misunderstandings about Bell's theorem are pointed out: Firstly, the hidden variable theory Bell's used is a special one, but it is regarded as a general form of such theories. Secondly, there are two outcomes obtainable from Bell's hypotheses: one is compatible with quantum mechanics and the other leads to Bell's inequality. Unfortunately, the former is regarded as a property of local hidden variable theory, while the latter as self-evident. G. Lochak has revealed the first misunderstanding, and thereby he pointed out that Bell's inequality has nothing to do with locality, but he did not find the second one, so that he still analyzed this problem starting from hidden variable theory, which is actually irrelative to Bell's inequality. (The Journal of American Science. 2005;1(2):42-50).
Abstract Chapter 14 examines entangled quantum systems, hidden variable theories and Bell’s inequality. In 1935, Einstein and collaborators, postulating the existence of elements of reality, analyzed an entangled system and concluded that quantum theory was incomplete. Their analysis is described using spin singlets, which are entangled states of two spin ½ particles. A possible avoidance of their conclusion is by using hidden variable theories. In analyzing a class of local hidden variable theories, John Bell derived an equality that could test them. This was done by experiments using entangled photons; their results violated the inequality, thereby establishing that quantum mechanics, not local hidden variable theories, is the correct description. Later theoretical analysis, and relevant experimental results, strongly supported this. A further theoretical analysis, involving just a single measurement, led to a pronounced conclusion: farewell to the elements of reality. Ditto as well to the spooky-action-at-a-distance problem that had so bothered Einstein.