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arXiv:quant-ph/9908019

Dualist interpretation of quantum mechanics

Guy Potvin

Published Aug 4, 1999• 0 citations
arXivHTMLPDF

Abstract

An interpretation of quantum mechanics is proposed which augments the stochastic pilot-wave model, introduced by Nelson [E. Nelson, Phys. Rev., 150, 1079 (1966)], with a dual guidance condition. Namely, in addition to the stochastic guidance condition which describes how the wave controls the particle (wave-to-particle guidance condition), we introduce another stochastic guidance condition describing how the particle guides the wave (particle-to-wave guidance condition). We therefore introduce an action-reaction principle in the pilot-wave formulation of quantum mechanics. The particle-to-wave guidance condition takes the form of spontaneous transitions of the wavefunction that are Poisson distributed in time. The wavefunction selected by the transition is influenced by its likelyhood with respect to the particle position, as well as certain conservation constraints. It is shown that the stochastic particle-to-wave guidance condition reproduces certain aspects of the spontaneous localization model of Ghirardi, Rimini and Weber [G. C. Ghirardi, A. Rimini and T. Weber, Phys. Rev. D, 34, 470 (1986)], and of Milburn's intrinsic decoherence model [G. J. Milburn, Phys. Rev. A, 44, 5401 (1991)], while avoiding some of the difficulties associated with them. The macroscopic limit of the dualist interpretation is analyzed for the case of a free body. Possible improvements of this interpretation are discussed.

DOI
10.48550/arxiv.quant-ph/9908019

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An interpretation of quantum mechanics is proposed which augments the stochastic pilot-wave model, introduced by Nelson [E. Nelson, Phys. Rev., 150, 1079 (1966)], with a dual guidance condition. Namely, in addition to the stochastic guidance condition which describes how the wave controls the particle (wave-to-particle guidance condition), we introduce another stochastic guidance condition describing how the particle guides the wave (particle-to-wave guidance condition). We therefore introduce an action-reaction principle in the pilot-wave formulation of quantum mechanics. The particle-to-wave guidance condition takes the form of spontaneous transitions of the wavefunction that are Poisson distributed in time. The wavefunction selected by the transition is influenced by its likelyhood with respect to the particle position, as well as certain conservation constraints. It is shown that the stochastic particle-to-wave guidance condition reproduces certain aspects of the spontaneous localization model of Ghirardi, Rimini and Weber [G. C. Ghirardi, A. Rimini and T. Weber, Phys. Rev. D, 34, 470 (1986)], and of Milburn's intrinsic decoherence model [G. J. Milburn, Phys. Rev. A, 44, 5401 (1991)], while avoiding some of the difficulties associated with them. The macroscopic limit of the dualist interpretation is analyzed for the case of a free body. Possible improvements of this interpretation are discussed.
An interpretation of non-relativistic quantum mechanics is presented in the spirit of Erwin Madelung's hydrodynamic formulation of QM and Louis de Broglie's and David Bohm's pilot wave models. The aims of the approach are as follows: 1) to have a clear ontology for QM, 2) to describe QM in a causal way, 3) to get rid of the wave-particle dualism in pilot wave theories, 4) to provide a theoretical framework for describing creation and annihilation of particles, and 5) to provide a possible connection between particle QM and virtual particles in QFT. These goals are achieved, if the wave function is replaced by a fluid of so called virtual particles. It is also assumed that in this fluid of virtual particles exist a few real particles and that only these real particles can be directly observed. This has relevance for the measurement problem in QM and it is found that quantum probabilities arise in a very natural way from the structure of the theory. The model presented here is very similar to a recent computational model of quantum physics and recent Bohmian models of QFT.
This paper and a following one develop a Hamiltonian formulation of the de Broglie-Bohm (deBB) interpretation of quantum mechanics. Drawing upon a unified Hamiltonian treatment of a classical particle and its associated ensemble, it is shown how the interaction of a particle and a spin-0 quantum wave can be consistently expressed in a canonical framework. A formulation is found in which the particle is acted upon by a force determined by the quantum potential but the particle does not react on the Schrodinger field. This requires the introduction of an additional field which the particle does act upon, and allows the deBB theory to be expressed in Hamiltonian terms. An ensemble theory for the wave-particle system based on Liouville's equation is developed, and it is shown that for a pure quantum state the particle obeys its own Liouville equation. The general particle phase space distribution that is compatible with ‖ψ‖ 2 is derived. A special case of this corresponds to the relation p = ∂S/∂q (and thus the guidance law of the deBB theory) but more general distributions, and hence non-deBB motions, are possible. This relation is interpreted as a constraint on the phase space of the composite system. Using the theory of Hamiltonian constraints it is shown that the first-order guidance law and Hamilton's second-order particle equations are dynamically equivalent.
This thesis is an attempt to reconstruct the conceptual foundations of quantum mechanics. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown to be consistent with existing experiments and our macroscopic experience. In addition, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and dynamical collapse theories, and briefly analyze the problem of the incompatibility between quantum mechanics and special relativity.
A weakness which has previously seemed unavoidable in particle interpretations of quantum mechanics (such as in the de Broglie-Bohm model) is addressed here and a resolution proposed. The weakness in question is the lack of action and reaction occurring between the model's field (or "pilot wave") and the particle. Although the field acts on the particle, the particle does not act back on the field. It is shown here that this rather artificial feature is, in fact, not necessary and can be fully eliminated while remaining consistent with the usual quantum predictions. Mathematically this amounts to demonstrating that there exists a suitable Lagrangian density function which generates equations coinciding with quantum mechanics yet incorporates the desired action and reaction. As a by-product, an appealing explanation emerges to another long-standing question, namely why the mathematical formalism of quantum mechanics seems only to be describing fields when measurements generally detect localised particles. A further bonus is that the hitherto unrelated concept of a gauge transformation is found to arise naturally as an essential part of the formalism. In particular, the phase S of the gauge transformation is seen to be the action function describing the hidden motion of the particle.
We have revisited the Ghirardi-Rimini-Weber-Pearle (GRWP) approach for continuous dynamical evolution of the state vector for a macroscopic object. Our main concern is to recover the decoupling of the state vector dynamics for the center-of-mass (CM) and internal motion, as in the GRWP model, but within the framework of the standard cosmology. In this connection we have taken the opposite direction of the GRWP argument that the cosmic background radiation (CBR) has originated from a fundamental stochastic hitting process. We assume the CBR to be a clue of the Big Bang, playing a main role in the decoupling of the state vector dynamics of the CM and internal motion. In our model, instead of describing a continuous spontaneous localization (CSL) of a system of massive particles as proposed by Ghirardi, Pearle, and Rimini [Phys. Rev. A 42, 78 (1990)] the It\^o stochastic equation accounts for the intervention of the CBR on the system of particles. Essentially, this approach leads to a precursor of the master equation for both the CBR and particle degrees of freedom. The violation of the principle of energy conservation characteristic of the CSL model is avoided as well as the additional assumption on the size of the GRWP's localization width necessary to reach the decoupling between the collective and internal motions. Moreover, realistic estimation for the decoherence time, exhibiting an interesting dependence on the CBR temperature, is obtained. From the formula for the decoherence time it is possible to analyze the transition from micro- to macrodynamics in both the early hot universe and the nowadays cold one. The entropy of the system under decoherence is analyzed and the emergent ``pointer basis'' is discussed. In spite of not having imposed a privileged basis, in our model the position still emerges as the preferred observable as in the CSL model.
We discuss a model of spontaneous collapse of the quantum state that does not require adding any stochastic processes to the standard dynamics. The additional ingredient with respect to the wave function is a position in the configuration space which drives the collapse in a completely deterministic way. This new variable is equivalent to a set of positions of all the particles, i.e., a set of Bohmian positions, which obey the usual guiding equation of Bohmian theory. Any superposition of quantum states of a macroscopic object occupying different regions of space is projected by a localization process onto the region occupied by the positions. Since the Bohmian positions are well defined in a single realization of the experiment, a space localization into one region is produced. The mechanism is based on the correlations between these positions arising from the cohesive forces inside macroscopic objects. The model introduces two collapse parameters which play a role very similar to those of the Ghirardi-Rimini-Weber (GRW) [Ghirardi et al., Phys. Rev. D 34, 470 (1986)] and continuous spontaneous localization (CSL) [Pearle, Phys. Rev. A 39, 2277 (1989); Ghirardi et al., Phys. Rev. A 42, 78 (1990)] theories. With appropriate values of these parameters, we check that the corresponding dynamics rapidly projects superpositions of macroscopic states localized in different regions of space into a single region, while it maintains a negligible effect in all situations where the predictions of standard quantum dynamics are known to be correct. We briefly speculate about the possible relations with gravity. We then study the evolution of the density operator and a mean-field approximation of the dynamical equations of this model, as well as the change of the evolution of the momentum introduced by the localization process. Possible theoretical interpretations are discussed. Generally speaking, this model introduces a sharper border between the quantum and classical worlds than the GRW and CSL theories and leaves a broader range of acceptable values for the parameters.