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Oxford University Press eBooks

The 1980s

Andrew Charles Whitaker

Published Jun 16, 2016• 0 citations
Publisher

Abstract

The results of Aspect’s experiments, in which the directions of the polarizers in the two wings of the experiment were decided so fast that there could be no interaction, still agreed with quantum theory. Bell continued to refine his ideas and gathered steadily increasing interest. He was intrigued by the Greenberger–Horne–Zeilinger, or GHZ, argument, which, without using inequalities, showed a clash between quantum theory and local realism, and also by the Ghirardi–Rimini–Weber, or GRW, paper, which considered the collapse of wave function rigorously. He worked on quark–antiquark (or quarkonium) systems with Reinhold Bertlmann, with the Bells and the Bertlmanns becoming close, and he also returned to the theory of accelerators, working with Mary Bell on some papers. Bell became friendly with eminent particle physicist Jum John Sakurai but, sadly, both men were to die suddenly during the decade—Bell’s death taking place in October 1990.

DOI
10.1093/acprof:oso/9780198742999.003.0005

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Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi–Rimini–Weber (GRW) model of spon-taneous wavefunction collapse. The GRW model was proposed as a solution of the measurement problem of quantum mechanics and involves a stochastic and nonlinear modification of the Schrödinger equation. It deviates very little from the Schrödinger equation for microscopic systems but efficiently suppresses, for macroscopic systems, superpositions of macroscopically different states. As sug-gested by Bell, we take the primitive ontology, or local beables, of our model to be a discrete set of space-time points, at which the collapses are centered. This set is random with distribution determined by the initial wavefunction. Our model is nonlocal and violates Bell’s inequality though it does not make use of a preferred slicing of space-time or any other sort of synchronization of spacelike separated points. Like the GRW model, it reproduces the quantum probabilities in all cases presently testable, though it entails deviations from the quantum formalism that are in principle testable. Our model works in Minkowski space-time as well as in (well-behaved) curved background space-times. PACS numbers: 03.65.Ta; 03.65.Ud; 03.30.+p. Key words: spontaneous wave-function collapse; relativity; quantum theory without observers. 1

•Jan 1, 2004•233 citations
The results of Aspect’s experiments, in which the directions of the polarizers in the two wings of the experiment were decided so fast that there could be no interaction, still agreed with quantum theory. Bell continued to refine his ideas and gathered steadily increasing interest. He was intrigued by the Greenberger–Horne–Zeilinger, or GHZ, argument, which, without using inequalities, showed a clash between quantum theory and local realism, and also by the Ghirardi–Rimini–Weber, or GRW, paper, which considered the collapse of wave function rigorously. He worked on quark–antiquark (or quarkonium) systems with Reinhold Bertlmann, with the Bells and the Bertlmanns becoming close, and he also returned to the theory of accelerators, working with Mary Bell on some papers. Bell became friendly with eminent particle physicist Jum John Sakurai but, sadly, both men were to die suddenly during the decade—Bell’s death taking place in October 1990.
On 1 June 2018, theoretical physicist GianCarlo Ghirardi, known for his work on the foundations of quantum mechanics, died unexpectedly in his summer resort home in Grado, Italy. GianCarlo Ghirardi MASSIMO SILVANO, ICTP PHOTO ARCHIVES, 2005PPT|High resolutionGhirardi was born in Milan on 28 October 1935. A few years after his 1959 graduation from the University of Milan with a PhD in physics, he moved to Trieste. In 1964 he met Alberto Rimini and one of us (Weber), and they worked on scattering theory. They parted after a brief period but remained in touch. In 1973 they wrote a paper that gave a new interpretation of the decay process and for the first time advanced a consistent explanation of the exponential decay law.Meanwhile, Ghirardi became more and more attracted to the foundations of quantum mechanics. The catalyst for him had been the 1970 International School of Physics conference, Foundations of Quantum Mechanics, in Varenna, Italy. Also fueling his interest was the 1971 book Conceptual Foundations of Quantum Mechanics by Bernard D’Espagnat. He was fascinated by the depth of the subject, and he suggested to Rimini and Weber that they join him in working on it. They accepted, with some hesitation. During the next roughly 15 years, Ghirardi, Rimini, and Weber succeeded in establishing a unique and enthusiastic collaboration.The main issue was the measurement problem: Quantum mechanics cannot explain the reduction of the wavepacket produced by a measurement; it must be appended ad hoc. Since collapse is not consistent with the dynamics of the linear Schrödinger equation, Ghirardi, Rimini, and Weber considered making the Schrödinger equation nonlinear. In 1984 they came up with an idea that works: Observing that all measurements involve measurements of the position of some sort of indicator, they imposed on the wavefunction a spatial localization that affects any particle, isolated or constituent, of any physical system.They wrote the desired wave equation effortlessly. It was stochastic and nonlinear, with the stochastic noise acting as a series of localizations occurring in time according to a Poisson distribution with some mean frequency. The nature and origin of the stochasticity were left undetermined. The remaining problem was to understand the equation’s physical import: What happens for a system of N particles? They found that the frequency of localizations becomes N times larger, meaning that the new dynamics mimics that of the Schrödinger equation for a small number of particles and that of the classical world for a large number. They called the modification quantum mechanics with spontaneous localization.Ghirardi, Rimini, and Weber submitted an abridged version of their paper for a 1984 workshop on quantum probability and applications held in Heidelberg, Germany. The proceedings were published in 1985; the final version appeared in Physical Review D in July 1986.The preprint, which came out in 1985, achieved wide circulation. In February 1986 Ghirardi, Rimini, and Weber, to their great surprise, received a letter from John Bell that began, “I read with very great interest and admiration your paper,” and informed them that he was preparing a review talk based on their work. Bell presented it at Imperial College London the following year, at a conference celebrating the centenary of the birth of Erwin Schrödinger. It was then that he named the theory GRW, an acronym that has been in use ever since.The GRW theory solves the quantum mechanics measurement problem by eliminating the need to appeal to an observer. But before GRW, two other quantum theories solved the same problem: Bohmian mechanics and many worlds, both from the 1950s. Nevertheless, GRW had a huge effect on physics, mainly for two reasons. First, Bohmian mechanics and many worlds were considered to be interpretations of quantum theory that offered no new predictions, but GRW was not. It was by all standards a new theory that made new predictions. After all, it destroyed one of the pillars of quantum theory: the linearity of wavefunction evolution. For the majority of physicists who acknowledged the measurement problem, GRW was a serious proposal with experimental implications, even if the technology was not yet in place to test them.Second, and more on the theoretical side, the theory seemed to ease some of the tension between relativity and quantum physics. Quoting Bell, from his Schrödinger centenary contribution, “I am particularly struck by the fact that the model is as Lorentz invariant as it could be in the nonrelativistic version. It takes away the ground of my fear that any exact formulation of quantum mechanics must conflict with fundamental invariance.” Indeed, a fully Lorentz invariant version of GRW had been constructed in 2006.Research on GRW is still vibrant, and the experimental community is now hunting its spontaneous collapses, which might explain why the microscopic quantum world seems not to reach the human scale.In addition to his journal editorial work, Ghirardi wrote a well-received popular book on quantum physics and had just finished a voluminous book on symmetries in nature, a subject that intrigued him throughout his scientific life. A theoretical physics professor at the University of Trieste for 42 years, Ghirardi will be remembered for his mentorship, sharp intellect, and inspiring passion for science.© 2018 American Institute of Physics.
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.
Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi–Rimini–Weber (GRW) model of spon-taneous wavefunction collapse. The GRW model was proposed as a solution of the measurement problem of quantum mechanics and involves a stochastic and nonlinear modification of the Schrödinger equation. It deviates very little from the Schrödinger equation for microscopic systems but efficiently suppresses, for macroscopic systems, superpositions of macroscopically different states. As sug-gested by Bell, we take the primitive ontology, or local beables, of our model to be a discrete set of space-time points, at which the collapses are centered. This set is random with distribution determined by the initial wavefunction. Our model is nonlocal and violates Bell’s inequality though it does not make use of a preferred slicing of space-time or any other sort of synchronization of spacelike separated points. Like the GRW model, it reproduces the quantum probabilities in all cases presently testable, though it entails deviations from the quantum formalism that are in principle testable. Our model works in Minkowski space-time as well as in (well-behaved) curved background space-times. PACS numbers: 03.65.Ta; 03.65.Ud; 03.30.+p. Key words: spontaneous wave-function collapse; relativity; quantum theory without observers. 1