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arXiv:0901.4071

Comment on "Dynamical reduction models" by A. Bassi and G.C. Ghirardi (arXiv:quant-ph/0302164)

Fred H. Thaheld

Published Jan 26, 2009• 7 citations
arXivHTMLPDF

Abstract

Bassi and Ghirardi have developed a new theory to address the measurement problem based upon non-linear and stochastic modifications of the Schroedinger equation, which has been given the name Quantum Mechanical Spontaneous Localization or QMSL, with one of the emphasis dealing with reduction or wavefunction collapse within the nervous system. Analysis of this portion of their theory reveals that it faces several problems.

DOI
10.48550/arxiv.0901.4071

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Bassi and Ghirardi have developed a new theory to address the measurement problem based upon non-linear and stochastic modifications of the Schroedinger equation, which has been given the name Quantum Mechanical Spontaneous Localization or QMSL, with one of the emphasis dealing with reduction or wavefunction collapse within the nervous system. Analysis of this portion of their theory reveals that it faces several problems.
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.
The dynamical elimination or reduction of macroscopic superpositions has long been of interest, particularly with regard to the quantum theory of measurement. A number of models have demonstrated this for the reduced density matrix of a system interacting with an environment. Alternatively, Ghirardi, Rhimini, and Weber [Phys. Rev. D 34, 470 (1986)] have proposed a fundamental modification of the Schr\"odinger equation, quantum mechanics with spontaneous localization (QMSL), which provides a master equation similar in mathematical form. In this paper we consider an isotropic environment that is elastically scattered by the system of interest with negligible momentum transfer, extending a previous result of Joos and Zeh [Z. Phys. B. 59, 223 (1985)] from small length scales to all length scales. We discuss the physical nature and relevance of the differences between our result and similar open systems calculations. We describe the mathematical similarity between our extended environmental model and the QMSL dynamics determining the QMSL parameters that allow calculations using QMSL to be used as a model for the effect of the environment. That gives us access to a number of interesting results obtained for the QMSL master equation. Finally, we discuss some experimental considerations for the purposes of detecting effective nonunitary evolution of this form.
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.
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.
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.
Several modifications of the Schr\"odinger equation that dynamically reduce the off-diagonal elements of the density operator in the position representation (localization) have received recent attention in the literature. Models of quantum open systems provide localization for the system of interest by considering the effects of an environment on the effective master equation that describes the dynamics of the reduced density operator for the system of interest. In contrast, localization is introduced as a fundamental modification to the Schr\"odinger equation in quantum mechanics with spontaneous localization (QMSL) [G. C. Ghirardi, A. Rhimini, and T. Weber, Phys. Rev. D 34, 470 (1986)]. We compare several environment models and discuss some of the anomalous features of the effective master equations noted by Ballentine [L. E. Ballentine, Phys. Rev. A 43, 9 (1991)] by examining the Ehrenfest relations for position, energy, and momentum. Insight is provided into the relative importance of various terms in the effective master equations for several environment models. We also briefly discuss the implications of similar anomalous features present in the QMSL master equation in light of our analysis of the open-system models.