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Cambridge University Press eBooks

Desiderata for a modified quantum dynamics

Abner Shimony

Published Feb 26, 1993• 3 citations
Publisher

Abstract

THE MOTIVATION FOR MODIFYING QUANTUM DYNAMICS A cluster of problems – the “quantum mechanical measurement problem,” the “problem of the reduction of the wave packet,” the “problem of the actualization of potentialities,” and the “Schrödinger cat problem” – is raised by standard quantum dynamics when certain assumptions are made about the interpretation of the quantum mechanical formalism. Investigators who are unwilling to abandon these assumptions will be motivated to propose modifications of the quantum formalism. Among these, many (including Professor Ghirardi and Professor Pearle) have felt that the most promising locus of modification is quantum dynamics, and they have suggested stochastic modifications of the standard deterministic and linear evolution of the quantum state ( PSA 1990 , A. Fine, M. Forbes, and L. Wessels (eds.), East Lansing, Michigan: Philosophy of Science Association, 1991). Others who have followed this avenue of investigation are F. Károlyházy, A. Frenkel, and B. Lukács (Károlyházy et al. 1982), N. Gisin (1984, 1989), A. Rimini and T. Weber (in Ghirardi et al. 1986), L. Diósi (1988, 1989), and J. S. Bell (1987, pp. 201–12). At a workshop at Amherst College in June 1990 Bell remarked that the stochastic modification of quantum dynamics is the most important new idea in the field of foundations of quantum mechanics during his professional lifetime. My own attitude is somewhat cautious and exploratory.

DOI
10.1017/cbo9781139172196.004

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Desiderata for a Modified Quantum Dynamics

Abner Shimony

A cluster of problems — the “quantum mechanical measurement problem”, the “problem of the reduction of the wave packet”, the “problem of the actualization of potentialities,” and the “Schrödinger Cat problem” — are raised by standard quantum dynamics when certain assumptions are made about the interpretation of the quantum mechanical formalism. Investigators who are unwilling to abandon these assumptions will be motivated to propose modifications of the quantum formalism. Among these, many (including Professor Ghirardi and Professor Pearle) have felt that the most promising locus of modification is quantum dynamics, and in their presentations (this Volume) they have suggested stochastic modifications of the standard deterministic and linear evolution of the quantum state.

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The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of nonlinear and stochastic modifications of the Schroedinger equation. The proposed new dynamics is characterized by the feature of not contradicting any known fact about microsystems and of accounting, on the basis of a unique, universal dynamical principle, for wavepacket reduction and for the classical behavior of macroscopic systems. We recall the motivations for the new approach and we briefly review the other proposals to circumvent the above mentioned difficulties which appeared in the literature. In this way we make clear the conceptual and historical context characterizing the new approach. After having reviewed the mathematical techniques (stochastic differential calculus) which are essential for the rigorous and precise formulation of the new dynamics, we discuss in great detail its implications and we stress its relevant conceptual achievements. The new proposal requires also to work out an appropriate interpretation; a procedure which leads us to a reconsideration of many important issues about the conceptual status of theories based on a genuinely Hilbert space description of natural processes. We also discuss the possibility and the problems one meets in trying to develop an analogous formalism for the relativistic case. Finally we discuss the experimental implications of the new dynamics for various physical processes which should allow, in principle, to test it against quantum mechanics.

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The measurement problem in quantum mechanics

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In most textbooks, measurement does not receive the full attention it deserves and sometimes is even not treated at all, apart a brief and cryptic mention of the “reduction of the wave packet.” However, in the last decades, the situation has profoundly changed and it is time to consider measurement a fundamental part of quantum mechanics, even, to a certain extent, an important generalization of the traditional theory (see also Chs. 14–15). This chapter consists of three major parts. In the first block (Secs. 9.1–9.4) we develop the main physical features of the measurement process: the heart of the argument is here represented by the aspects related to the interpretation. In the second part (Secs. 9.5–9.8) we discuss several special (and partly interdependent) topics of measurement: the heart here is represented by experimental aspects. In the third part (Secs. 9.9–9.12) we deal with the measurement process on a more formal plane, making use, in particular, of the generalization represented by the concepts of effect and positive operator valued measure (POVM). As we have said, the measurement problem is one of the most fundamental issues in the conceptual structure of quantum mechanics (as described in Sec. 9.1) and has a long history that will be examined in Sec. 9.2. In this context, the existence of apparently paradoxical quantum states comes about: the so-called Schrödinger cat states (see Sec. 9.3).

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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.

Physics Today•Oct 1, 2018•0 citations

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In order to address the measurement problem of quantum theory we make the assumption that quantum state reduction should be regarded as a genuine physical process deserving of a dynamical description. Generalizing the nonrelativistic spontaneous localization models of Ghirardi, Rimini, Weber, and Pearle, a relativistic state reduction mechanism is proposed. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a mediating field to facilitate smearing of quantum field interactions.

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THE MOTIVATION FOR MODIFYING QUANTUM DYNAMICS A cluster of problems – the “quantum mechanical measurement problem,” the “problem of the reduction of the wave packet,” the “problem of the actualization of potentialities,” and the “Schrödinger cat problem” – is raised by standard quantum dynamics when certain assumptions are made about the interpretation of the quantum mechanical formalism. Investigators who are unwilling to abandon these assumptions will be motivated to propose modifications of the quantum formalism. Among these, many (including Professor Ghirardi and Professor Pearle) have felt that the most promising locus of modification is quantum dynamics, and they have suggested stochastic modifications of the standard deterministic and linear evolution of the quantum state ( PSA 1990 , A. Fine, M. Forbes, and L. Wessels (eds.), East Lansing, Michigan: Philosophy of Science Association, 1991). Others who have followed this avenue of investigation are F. Károlyházy, A. Frenkel, and B. Lukács (Károlyházy et al. 1982), N. Gisin (1984, 1989), A. Rimini and T. Weber (in Ghirardi et al. 1986), L. Diósi (1988, 1989), and J. S. Bell (1987, pp. 201–12). At a workshop at Amherst College in June 1990 Bell remarked that the stochastic modification of quantum dynamics is the most important new idea in the field of foundations of quantum mechanics during his professional lifetime. My own attitude is somewhat cautious and exploratory.
A cluster of problems — the “quantum mechanical measurement problem”, the “problem of the reduction of the wave packet”, the “problem of the actualization of potentialities,” and the “Schrödinger Cat problem” — are raised by standard quantum dynamics when certain assumptions are made about the interpretation of the quantum mechanical formalism. Investigators who are unwilling to abandon these assumptions will be motivated to propose modifications of the quantum formalism. Among these, many (including Professor Ghirardi and Professor Pearle) have felt that the most promising locus of modification is quantum dynamics, and in their presentations (this Volume) they have suggested stochastic modifications of the standard deterministic and linear evolution of the quantum state.
The report presents an exhaustive review of the recent attempt to overcome the difficulties that standard quantum mechanics meets in accounting for the measurement (or macro-objectification) problem, an attempt based on the consideration of nonlinear and stochastic modifications of the Schroedinger equation. The proposed new dynamics is characterized by the feature of not contradicting any known fact about microsystems and of accounting, on the basis of a unique, universal dynamical principle, for wavepacket reduction and for the classical behavior of macroscopic systems. We recall the motivations for the new approach and we briefly review the other proposals to circumvent the above mentioned difficulties which appeared in the literature. In this way we make clear the conceptual and historical context characterizing the new approach. After having reviewed the mathematical techniques (stochastic differential calculus) which are essential for the rigorous and precise formulation of the new dynamics, we discuss in great detail its implications and we stress its relevant conceptual achievements. The new proposal requires also to work out an appropriate interpretation; a procedure which leads us to a reconsideration of many important issues about the conceptual status of theories based on a genuinely Hilbert space description of natural processes. We also discuss the possibility and the problems one meets in trying to develop an analogous formalism for the relativistic case. Finally we discuss the experimental implications of the new dynamics for various physical processes which should allow, in principle, to test it against quantum mechanics.
In most textbooks, measurement does not receive the full attention it deserves and sometimes is even not treated at all, apart a brief and cryptic mention of the “reduction of the wave packet.” However, in the last decades, the situation has profoundly changed and it is time to consider measurement a fundamental part of quantum mechanics, even, to a certain extent, an important generalization of the traditional theory (see also Chs. 14–15). This chapter consists of three major parts. In the first block (Secs. 9.1–9.4) we develop the main physical features of the measurement process: the heart of the argument is here represented by the aspects related to the interpretation. In the second part (Secs. 9.5–9.8) we discuss several special (and partly interdependent) topics of measurement: the heart here is represented by experimental aspects. In the third part (Secs. 9.9–9.12) we deal with the measurement process on a more formal plane, making use, in particular, of the generalization represented by the concepts of effect and positive operator valued measure (POVM). As we have said, the measurement problem is one of the most fundamental issues in the conceptual structure of quantum mechanics (as described in Sec. 9.1) and has a long history that will be examined in Sec. 9.2. In this context, the existence of apparently paradoxical quantum states comes about: the so-called Schrödinger cat states (see Sec. 9.3).
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.
In order to address the measurement problem of quantum theory we make the assumption that quantum state reduction should be regarded as a genuine physical process deserving of a dynamical description. Generalizing the nonrelativistic spontaneous localization models of Ghirardi, Rimini, Weber, and Pearle, a relativistic state reduction mechanism is proposed. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a mediating field to facilitate smearing of quantum field interactions.