During the 1960s, Bell produced his seminal work on the foundations of quantum theory, first showing that, contrary to von Neumann’s argument, hidden variable theories were allowed but then that they had to be non-local. Thus, he showed that quantum theory did not respect local causality, and he outlined experiments that could be used to test whether the assumption of local realism was true in quantum theory: Bell’s theorem, or Bell’s inequality, or Bell’s inequalities. His work was followed up by John Clauser, Abner Shimony, Michael Horne, and Richard Holt, who produced the CHSH inequality. Bell had moved to CERN, where he worked on the theory of neutrino experiments, and on nuclear and elementary particle physics, making crucial suggestions concerning the use of gauge theory for each type of physical force and also producing the Adler–Bell–Jackiw anomaly, or the ABJ anomaly.
During the 1960s, Bell produced his seminal work on the foundations of quantum theory, first showing that, contrary to von Neumann’s argument, hidden variable theories were allowed but then that they had to be non-local. Thus, he showed that quantum theory did not respect local causality, and he outlined experiments that could be used to test whether the assumption of local realism was true in quantum theory: Bell’s theorem, or Bell’s inequality, or Bell’s inequalities. His work was followed up by John Clauser, Abner Shimony, Michael Horne, and Richard Holt, who produced the CHSH inequality. Bell had moved to CERN, where he worked on the theory of neutrino experiments, and on nuclear and elementary particle physics, making crucial suggestions concerning the use of gauge theory for each type of physical force and also producing the Adler–Bell–Jackiw anomaly, or the ABJ anomaly.
Abstract John Stewart Bell was one of the most significant physicists of the twentieth century; his work has led to a much enhanced understanding of quantum theory and what it says about the physical universe, particularly about realism, determinism, and locality. This book describes Bell's relatively humble origins and his struggles to obtain secondary and university education. It then describes his work at Harwell, where he made important theoretical contributions to the development of particle accelerators, in particular with his pioneering work on strong focussing. Later, he proved the extremely important CPT theorem. At CERN, Bell made a range of important theoretical contributions to elementary particle physics; these contributions include the physics of neutrinos, the existence of different types of neutrinos, the suitability of gauge theory for all physical interactions, and the Adler–Bell–Jackiw anomaly, which shows how classical symmetries are lost under quantum theory. In his work on quantum theory, he criticized the orthodox 'Copenhagen' interpretation of quantum theory, which did not allow the actual state of the physical world to be analysed. He showed that the famous von Neumann theorem, which claimed to show that 'hidden variables' were not allowed in quantum theory, was incorrect; his famous Bell's theorem, or Bell's inequality, showed that any such variables much be non-local. Bell's work led to greatly increased freedom in the discussion of quantum theory, and the development of quantum information theory.
Abstract Abner Shimony read a pre-print of Bell’s paper, and realized its brilliance. The old experiments discussed by Bohm and Aharonov were indecisive. New experiments were urgently needed. John Clauser, who as a student had become greatly frustrated by Bohr’s quantum obscurity, reached the same conclusion. Clauser became obsessed, encouraged by support from Bell, Bohm, and de Broglie. Shimony and Clauser agreed to collaborate. They alighted on an experiment in which pairs of entangled photons are produced by atomic cascade emission, and developed a form of Bell’s inequality more suited to laboratory conditions. By 1970, the growing interest in foundations gave birth to a new journal and an international conference at which familiar arguments were aired by the old faithful, and at which newcomers gave fresh perspectives. Clauser published his results in 1972. Quantum mechanics prevails: local hidden variables do not exist. Other results soon followed, one contradictory, most confirmatory.
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.
Abstract This chapter presents a detailed discussion of Bell inequalities and their experimental tests. Starting from the Aharonov-Bohm version of the Einstein-Podolsky-Rosen (EPR) paradox, we review EPR’s criteria for realism and completeness and Bell’s locality condition, before deriving the Clauser-Horne-Shimony-Holt (CHSH) inequality. This is followed by an exposition on Bell’s original inequality and other Bell inequalities by Wigner, as well as Clauser and Horne. We then discuss the milestones in the experimental violation of Bell inequalities, from the experiment of Freedman and Clauser in the 1970s, to the efforts of Aspect et al. in the 1980s, the experiments by the teams of Zeilinger and Gisin in the 1990s, and culminating the loophole-free tests in 2015. Finally we turn to a brief discussion of the interpretations of quantum mechanics, focusing on contrasting the realist views held by, e.g., Einstein and Bell, and the informational views with proponents such as Brukner and Zeilinger
Introduction Since its inception, fifty years ago, Bell's theorem has had a long history not only of experimental tests but also of theoretical developments. Studying pairs of correlated quantummechanical particles separated in space, in a composite “entangled” state, Bell [1] showed that the joint ascription of hidden variables and locality to the system led to an inequality that is violated by the predictions of quantum mechanics. Fifteen years later, experiments confirmed the predictions of quantum mechanics, ruling out a large class of local realist theories. One of the most meaningful theoretical developments that followed Bell's work was the Greenberger–Horne–Zeilinger (GHZ) theorem, also known as Bell's theorem without inequalities. In 1989, the American physicists Daniel Greenberger and Michael Horne, who had been working on Bell's theorem since the late 1960s, together with the Austrian physicist Anton Zeilinger, introduced a novelty into the testing of entanglement, extending Bell's theorem in a different and interesting direction. According to Franck Laloë [2], For many years, everyone thought that Bell had basically exhausted the subject by considering all really interesting situations, and that two-spin systems provided the most spectacular quantum violations of local realism. It therefore came as a surprise to many when in 1989 Greenberger, Horne, and Zeilinger (GHZ) showed that systems containing more than two correlated particles may actually exhibit even more dramatic violations of local realism. The trio analyzed the Einstein, Podolsky, and Rosen 1935 argument once again and were able to write what are now called Greenberger–Horne–Zeilinger (GHZ) entangled states, involving three or four correlated spin-1/2 particles, leading to conflicts between local realist theories and quantum mechanics. However, unlike Bell's theorem, the conflict now was not of a statistical nature, as was the case with Bell's theorem, insofar as measurements on a single GHZ state could lead to conflicting predictions with local realistic models [3–5]. In this paper we present the history of the creation of this theorem and analyze its scope.
Bell's theorem has been described as the most profound discovery of science; one of the few essential discoveries of 20th Century physics; indecipherable to non-mathematicians. However, taking elementary analysis to be an adequate logic here, we refute Bell's theorem, correct his inequality and identify his error. Further, we do this under the principle of true local realism, the union of true locality (or relativistic causality: no influence propagates superluminally) and true realism (or non-naive realism: some existents change interactively). We thus lay the foundation for a more complete physical theory: one in line with Einstein's ideas and Bell's hopes. Let's see.