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How Stands Collapse I

Philip Pearle

Published Jan 1, 2006• 54 citations
OpenAlex

Abstract

In this volume i.h. of GianCarlo Ghirardi, I discuss my involvement with ideas of dynamical collapse of the state vector. 10 problems are introduced, 9 of which were seen following my initial work. 4 of these problems had a resolution in GianCarlo Ghirardi, Alberto Rimini and Tullio Weber's Spontaneous Localization (SL) model (which added 1 more problem). This stimulated a (somewhat different) resolution of these 5 problems in the Continuous Spontaneous Localization (CSL) model, in which I combined my initial work with SL. In an upcoming volume in h. of Abner Shimony I shall discuss the status of the 5 remaining post-CSL problems.

Related papers

How Stands Collapse I

Philip Pearle

In this volume in honor of GianCarlo Ghirardi, I discuss my involvement with ideas of dynamical collapse of the state vector. 10 problems are introduced, 9 of which were seen following my initial work. 4 of these problems had a resolution in GianCarlo Ghirardi, Alberto Rimini and Tullio Weber's Spontaneous Localization (SL) model (which added 1 more problem). This stimulated a (somewhat different) resolution of these 5 problems in the Continuous Spontaneous Localization (CSL) model, in which I combined my initial work with SL. In an upcoming volume in honor of Abner Shimony I shall discuss the status of the 5 remaining post-CSL problems.

arXiv:quant-ph/0611211•Nov 20, 2006•0 citations

How stands collapse I

Philip Pearle

In this volume in honour of GianCarlo Ghirardi, I discuss my involvement with ideas of dynamical collapse of the state vector. Ten problems are introduced, nine of which were seen following my initial work. Four of these problems had a resolution in GianCarlo Ghirardi, Alberto Rimini and Tullio Weber's spontaneous localization (SL) model (which added one more problem). This stimulated a (somewhat different) resolution of these five problems in the continuous spontaneous localization (CSL) model, in which I combined my initial work with SL. In an upcoming volume in honour of Abner Shimony, I shall discuss the status of the remaining five post-CSL problems.

arXiv:quant-ph/0611212•Journal of Physics A Mathematical and Theoretical•Mar 7, 2007•53 citations

Spontaneous Localization (SL) Theory

Philip Pearle

Abstract Before examining experimental consequences of CSL, this chapter discusses the spontaneous localization (SL) theory of Ghirardi, Rimini and Weber (GRW). As for CSL, the chapter presents the structure of the theory, and then specializes it to a non-relativistic theory. SL does not add a term to Schrodinger’s equation. Instead, the state vector is suddenly altered by a “hit” (GRW’s ‘spontaneous localization’), that is, multiplication by an operator, followed by renormalization. The hits occur at random times. The chapter shows the specific choice of operator made by GRW for their non-relativistic theory. Emphasized are two aspects of SL that helped the journey to CSL. One is that the collapse is always acting (one need not “turn it on.” The other is the “smeared” character of the GRW operator. The chapter then shows how the density matrix is calculated. Finally, it discusses the numerical values, chosen by GRW, of the two parameters of SL theory, λ and a, that are provisionally adopted for CSL.

•Jan 30, 2024•0 citations

In Praise and in Criticism of the Model of Continuous Spontaneous Localization of the Wave-Function

Sofia Wechsler

Different attempts to solve the measurement problem of the quantum me-chanics (QM) by denying the collapse principle, and replacing it with changes in the quantum formalism, failed because the changes in the formalism lead to contradictions with QM predictions. To the difference, Ghirardi, Rimini and Weber took the collapse as a real phenomenon, and proposed a calculus by which the wave-function should undergo a sudden localization. Later on, Ghirardi, Pearle and Rimini came with a change of this calculus into the CSL (continuous spontaneous localization) model of collapse. Both these proposals rely on the experimental fact that the reduction of the wave-function occurs when the microscopic system encounters a macroscopic object and involves a big amount of its particles. Both these proposals also change the quantum formalism by introducing in the Schr?dinger equation additional terms with noisy behavior. However, these terms have practically no influence as long as the studied system contains only one or a few components. Only when the amount of components is very big, these terms become significant and lead to the reduction of the wave-function to one of its components. The present work has two purposes: 1) proving that the collapse postulate is unavoidable; 2) ap-plying the CSL model to the process in a detector and showing step by step the modification of the wave-function, until reduction. As a side detail, it is argued here that the noise cannot originate in some classical field, contrary to the thought/hope of some physicists, because no classical field is tailored by the wave-functions of entanglements.

arXiv:2010.03392•Journal of Quantum Information Science•Jan 1, 2020•10 citations

Parameter diagrams of the GRW and CSL theories of wavefunction collapse

William Feldmann, Roderich Tumulka

It has been hypothesized that the time evolution of wavefunctions might include collapses, rather than being governed by the Schrödinger equation. The leading models of such an evolution, Ghirardi–Rimini–Weber (GRW) and continuous spontaneous localization (CSL), have two parameters (or new constants of nature): the collapse width σ and the collapse rate λ. We draw a diagram of the σλ-plane showing the region that is empirically refuted and the region that is philosophically unsatisfactory.

arXiv:1109.6579•Journal of Physics A Mathematical and Theoretical•Jan 26, 2012•93 citations

Spontaneous collapse: A solution to the measurement problem and a source of the decay in mesonic systems

Kyrylo Simonov, Beatrix C. Hiesmayr

Dynamical reduction models propose a solution to the measurement problem in quantum mechanics: the collapse of the wave function becomes a physical process. We compute the predictions to decaying and flavor-oscillating neutral mesons for the two most promising collapse models, the QMUPL (quantum mechanics with universal position localization) model and the mass-proportional CSL (continuous spontaneous localization) model. Our results are showing (i) a strong sensitivity to the very assumptions of the noise field underlying those two collapse models and (ii) under particular assumptions the CSL case allows one even to recover the decay dynamics. This in turn allows one to predict the effective collapse rates solely based on the measured values for the oscillation (mass differences) and the measured values of the decay constants. The four types of neutral mesons ($K$ meson, $D$ meson, ${B}_{d}$ meson, and ${B}_{s}$ meson) lead surprisingly to ranges comparable to those put forward by Adler [J. Phys. A: Math. Theor. 40, 2935 (2007)] and Ghirardi, Rimini, and Weber [Phys. Rev. D 34, 470 (1986)]. Our results show that these systems at high energies are very sensitive to possible modifications of the standard quantum theory, making them a very powerful laboratory to rule out certain collapse scenarios and study the detailed physical processes solving the measurement problem.

arXiv:1606.01682•Physical Review A•Nov 28, 2016•8 citations
In this volume i.h. of GianCarlo Ghirardi, I discuss my involvement with ideas of dynamical collapse of the state vector. 10 problems are introduced, 9 of which were seen following my initial work. 4 of these problems had a resolution in GianCarlo Ghirardi, Alberto Rimini and Tullio Weber's Spontaneous Localization (SL) model (which added 1 more problem). This stimulated a (somewhat different) resolution of these 5 problems in the Continuous Spontaneous Localization (CSL) model, in which I combined my initial work with SL. In an upcoming volume in h. of Abner Shimony I shall discuss the status of the 5 remaining post-CSL problems.
In this volume in honor of GianCarlo Ghirardi, I discuss my involvement with ideas of dynamical collapse of the state vector. 10 problems are introduced, 9 of which were seen following my initial work. 4 of these problems had a resolution in GianCarlo Ghirardi, Alberto Rimini and Tullio Weber's Spontaneous Localization (SL) model (which added 1 more problem). This stimulated a (somewhat different) resolution of these 5 problems in the Continuous Spontaneous Localization (CSL) model, in which I combined my initial work with SL. In an upcoming volume in honor of Abner Shimony I shall discuss the status of the 5 remaining post-CSL problems.
In this volume in honour of GianCarlo Ghirardi, I discuss my involvement with ideas of dynamical collapse of the state vector. Ten problems are introduced, nine of which were seen following my initial work. Four of these problems had a resolution in GianCarlo Ghirardi, Alberto Rimini and Tullio Weber's spontaneous localization (SL) model (which added one more problem). This stimulated a (somewhat different) resolution of these five problems in the continuous spontaneous localization (CSL) model, in which I combined my initial work with SL. In an upcoming volume in honour of Abner Shimony, I shall discuss the status of the remaining five post-CSL problems.
Abstract Before examining experimental consequences of CSL, this chapter discusses the spontaneous localization (SL) theory of Ghirardi, Rimini and Weber (GRW). As for CSL, the chapter presents the structure of the theory, and then specializes it to a non-relativistic theory. SL does not add a term to Schrodinger’s equation. Instead, the state vector is suddenly altered by a “hit” (GRW’s ‘spontaneous localization’), that is, multiplication by an operator, followed by renormalization. The hits occur at random times. The chapter shows the specific choice of operator made by GRW for their non-relativistic theory. Emphasized are two aspects of SL that helped the journey to CSL. One is that the collapse is always acting (one need not “turn it on.” The other is the “smeared” character of the GRW operator. The chapter then shows how the density matrix is calculated. Finally, it discusses the numerical values, chosen by GRW, of the two parameters of SL theory, λ and a, that are provisionally adopted for CSL.
Different attempts to solve the measurement problem of the quantum me-chanics (QM) by denying the collapse principle, and replacing it with changes in the quantum formalism, failed because the changes in the formalism lead to contradictions with QM predictions. To the difference, Ghirardi, Rimini and Weber took the collapse as a real phenomenon, and proposed a calculus by which the wave-function should undergo a sudden localization. Later on, Ghirardi, Pearle and Rimini came with a change of this calculus into the CSL (continuous spontaneous localization) model of collapse. Both these proposals rely on the experimental fact that the reduction of the wave-function occurs when the microscopic system encounters a macroscopic object and involves a big amount of its particles. Both these proposals also change the quantum formalism by introducing in the Schr?dinger equation additional terms with noisy behavior. However, these terms have practically no influence as long as the studied system contains only one or a few components. Only when the amount of components is very big, these terms become significant and lead to the reduction of the wave-function to one of its components. The present work has two purposes: 1) proving that the collapse postulate is unavoidable; 2) ap-plying the CSL model to the process in a detector and showing step by step the modification of the wave-function, until reduction. As a side detail, it is argued here that the noise cannot originate in some classical field, contrary to the thought/hope of some physicists, because no classical field is tailored by the wave-functions of entanglements.
It has been hypothesized that the time evolution of wavefunctions might include collapses, rather than being governed by the Schrödinger equation. The leading models of such an evolution, Ghirardi–Rimini–Weber (GRW) and continuous spontaneous localization (CSL), have two parameters (or new constants of nature): the collapse width σ and the collapse rate λ. We draw a diagram of the σλ-plane showing the region that is empirically refuted and the region that is philosophically unsatisfactory.
Dynamical reduction models propose a solution to the measurement problem in quantum mechanics: the collapse of the wave function becomes a physical process. We compute the predictions to decaying and flavor-oscillating neutral mesons for the two most promising collapse models, the QMUPL (quantum mechanics with universal position localization) model and the mass-proportional CSL (continuous spontaneous localization) model. Our results are showing (i) a strong sensitivity to the very assumptions of the noise field underlying those two collapse models and (ii) under particular assumptions the CSL case allows one even to recover the decay dynamics. This in turn allows one to predict the effective collapse rates solely based on the measured values for the oscillation (mass differences) and the measured values of the decay constants. The four types of neutral mesons (KKK meson, DDD meson, Bd{B}_{d}Bd​ meson, and Bs{B}_{s}Bs​ meson) lead surprisingly to ranges comparable to those put forward by Adler [J. Phys. A: Math. Theor. 40, 2935 (2007)] and Ghirardi, Rimini, and Weber [Phys. Rev. D 34, 470 (1986)]. Our results show that these systems at high energies are very sensitive to possible modifications of the standard quantum theory, making them a very powerful laboratory to rule out certain collapse scenarios and study the detailed physical processes solving the measurement problem.