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A Note to the Reader David Z Albert
Published Sep 28, 2023 • 0 citations
Abstract One way of reading this book is as an epilogue-or (more precisely) as a denouement-to a book I wrote more than thirty years ago, which was called Quantum Mechanics and Experience.That earlier book was meant to do two things:1) To introduce its readers to the elementary nuts and bolts of the foundations of quantum mechanics-the idea of superposition, the basics of the standard mathematical formalism of quantum mechanics, the argument of Einstein and Podolsky and Rosen to the effect that that formalism, considered as a description of the fundamental real ity of the world, must be somehow incomplete, Bell's extension of that argument into a general and power ful theorem about locality, the elaboration (by figures like Erwin Schrödinger, and John von Neumann, and Eugene Wigner) of the quantum-mechanical mea surement prob lem, and vari ous proposals (theories of the spontaneous collapse of the wave-function, Bohmian mechanics, the so-called many-worlds interpretations of quantum mechanics, and so on) for solving it.2) To show how the above-mentioned proposals for solving the mea sure ment prob lem, taken together, amount to a
DOI 10.4159/9780674294837-001 Related papers Readers offer their own magic moments with John Bell
Robert B. Griffiths
Physics Today • Nov 30, 2015• 0 citations
Sheldon Goldstein
Cambridge University Press eBooks • Aug 31, 2016• 0 citations
Angelo Bassi, Tullio Weber, Detlef Dürr
Physics Today • Oct 1, 2018• 0 citations
One way of reading this book is as an epilogue-or (more precisely) as a denouement-to a book I wrote more than thirty years ago, which was called Quantum Mechanics and Experience.That earlier book was meant to do two things:1) To introduce its readers to the elementary nuts and bolts of the foundations of quantum mechanics-the idea of superposition, the basics of the standard mathematical formalism of quantum mechanics, the argument of Einstein and Podolsky and Rosen to the effect that that formalism, considered as a description of the fundamental real ity of the world, must be somehow incomplete, Bell's extension of that argument into a general and power ful theorem about locality, the elaboration (by figures like Erwin Schrödinger, and John von Neumann, and Eugene Wigner) of the quantum-mechanical mea surement prob lem, and vari ous proposals (theories of the spontaneous collapse of the wave-function, Bohmian mechanics, the so-called many-worlds interpretations of quantum mechanics, and so on) for solving it.2) To show how the above-mentioned proposals for solving the mea sure ment prob lem, taken together, amount to a
Reinhold Bertlmann’s article “Magic moments with John Bell” was a pleasure to read. I add a note concerning some later developments that are significant for understanding the implications of Bell’s quantum foundations work.The crucial point is that under the Bell locality hypothesis for a joint measurement as given in the article,E(a,b)=∫dλρ(λ)A(a,λ)·B(b,λ)the quantity λ that represents the hidden variable(s) is a classical, not a quantum, object, and ρ(λ) is a classical probability distribution. Such expressions only make sense in the context of quantum theory when the operators of interest commute with each other, but that is not the case when this expression is used to derive a Bell inequality.Many years ago Arthur Fine pointed out that hidden variables and Bell inequalities were “imposing requirements to make well defined precisely those probability distributions for noncommuting observables whose rejection is the very essence of quantum mechanics.”11. A. Fine, Phys. Rev. Lett. 48, 291 (1982). https://doi.org/10.1103/PhysRevLett.48.291 Thus the real issue is not one of locality but, instead, the proper use of probabilities in quantum theory.Fine’s point has been confirmed by the later development of a fully consistent way of introducing probabilities in quantum mechanics.22. R. B. Griffiths, Stanford Encyclopedia of Philosophy (2014); http://plato.stanford.edu/entries/qm-consistent-histories. That approach has shown that when quantum mechanics is interpreted using subspaces of the Hilbert space rather than classical hidden variables to represent physical properties, it is local: There are no ghostly nonlocal influences.We cannot know how Bell would have responded to those new developments, which only came to full fruition after his untimely death. The reader willing to dig into my somewhat tedious discussion33. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press (2002), sec. 23.4. of the Einstein-Podolsky-Rosen and Bohm situation will find an explicit proof that a measurement by Alice has not the slightest effect on the spin on Bob’s side. More recent is a general argument that quantum mechanics satisfies a principle of Einstein locality: What is done to system A has no effect on system B as long as there is no interaction between the two.44. R. B. Griffiths, Found. Phys. 41, 705 (2011). https://doi.org/10.1007/s10701-010-9512-5Those proofs of quantum locality begin by taking very seriously John von Neumann’s proposal that quantum properties correspond to Hilbert subspaces, whose projectors do not, in general, commute with one another.55. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton U. Press (1955), sec. 3.5. Bell, though, assumed that such properties can be represented by classical hidden variables, which always commute. Thus Bell’s theorem teaches that if one uses classical hidden variables in place of quantum properties, the result will contradict quantum theory and disagree with experiment. Indeed, while Bell started off by pointing out deficiencies in von Neumann’s argument against hidden variables, the end result of his work is an even better and much more conclusive argument, backed by experiment, for rejecting classical hidden variables.REFERENCESSection:ChooseTop of pageREFERENCES <<1. A. Fine, Phys. Rev. Lett. 48, 291 (1982). https://doi.org/10.1103/PhysRevLett.48.291, Google ScholarCrossref2. R. B. Griffiths, Stanford Encyclopedia of Philosophy (2014); http://plato.stanford.edu/entries/qm-consistent-histories. Google Scholar3. R. B. Griffiths, Consistent Quantum Theory, Cambridge U. Press (2002), sec. 23.4. Google Scholar4. R. B. Griffiths, Found. Phys. 41, 705 (2011). https://doi.org/10.1007/s10701-010-9512-5, Google ScholarCrossref5. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton U. Press (1955), sec. 3.5. Google Scholar© 2015 American Institute of Physics.
Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory.The book is intended primarily as a graduate level textbook, but it will also be of interest to physicists and philosophers who study the foundations of QM. Parts of it could be used by senior undergraduates too.
Since this book is closely connected to quantum mechanics, these introductory words will briefly and informally recall some postulates of this theory. Interested readers are urged to consult traditional books on quantum mechanics to complement the discussion ahead and for descriptions of experimental evidence that give rise to the postulates. In physics there are several “equivalent formulations” of quantum mechanics, and a catalogue of the most important appears in [StyO2]. The discussion here is restricted to the nonrelativistic case.
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.
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.
This novel text directly addresses common claims and misconceptions around quantum mechanics and presents a fresh and modern understanding of this fundamental and essential physical theory. It begins with a non-mathematical introduction to some of the more controversial topics in the foundations of quantum mechanics. For those more familiar with the theoretical framework of quantum mechanics, the text moves on to a general introduction to quantum field theory, followed by a detailed discussion of cutting-edge topics in this area such as decoherence and spontaneous coherence. Several important philosophical problems in quantum mechanics are considered, and their interpretations are compared, notably the Copenhagen and many-worlds interpretations. The inclusion of frequent real-world examples, such as superconductors and superfluids, ensures the book remains grounded in modern research. This book will be a valuable resource for students and researchers in both physics and the philosophy of science interested in the foundations of quantum mechanics.