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arXiv:1205.6390

Predecoherence: before Decoherence and Collapse

Roland L. Omnes

Published May 29, 2012• 0 citations
arXivHTMLPDF

Abstract

Predecoherence, as its name indicates, is the same physical effect as decoherence, originating in the same interactions with an environment, injecting also incoherence and breaking unitarity. But whereas decoherence acts immediately after a measurement, predecoherence is acting long before. It is also a very strong effect and its main properties are established in this paper, including generation, transport, damping, and stationary level. A mechanism for objectification, or wave function collapse, is also proposed as consisting in a perturbation by predecoherence of the intricacy between a measuring system and a measured one. The theory is made explicit on a special example and the quantitative results are found sensible.

DOI
10.48550/arxiv.1205.6390

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Predecoherence, as its name indicates, is the same physical effect as decoherence, originating in the same interactions with an environment, injecting also incoherence and breaking unitarity. But whereas decoherence acts immediately after a measurement, predecoherence is acting long before. It is also a very strong effect and its main properties are established in this paper, including generation, transport, damping, and stationary level. A mechanism for objectification, or wave function collapse, is also proposed as consisting in a perturbation by predecoherence of the intricacy between a measuring system and a measured one. The theory is made explicit on a special example and the quantitative results are found sensible.
Two categories of results regarding quantum measurements are derived in this work and applied to the problem of collapse. The first category is concerned with local and transient features of the entanglement between a macroscopic measuring system and a measured one. These properties result directly from the Schrödinger equation. They cannot be formulated in terms of observables, do not affect the wave functions themselves but express their history in an irreversible way. They carry a specific new kind of local probabilities, which evolve with a finite velocity under nonlinear wave equations. The second category of results extends these local properties to the case of a macroscopic system and its environment. Fluctuations in their interaction are predicted then and generate a specific incoherence in the quantum state of the system. These two kinds of effects act together when a macroscopic measuring system interacts with a measured system and with an environment. Their combination yields then an explicit and effective mechanism of collapse, with a random behavior resulting from random incoherence. Born's basic probability rule for the results of measurements turns out then simply a consequence of quantum dynamics. Some conjectures still enter into the derivation of these effects, which one may recognize to look hardly credible at first sight. They fit however so well together that one proposes a more thorough investigation of their approach as a promising strategy for a self-contained explanation of collapse.
Abstract Moving to more subtle experiments, we consider how the standard formulation of quantum mechanics predicts and explains interference phenomena. Tracking the conditions under which one observes interference phenomena leads to the notion of quantum decoherence. We see why one must sharply distinguish between collapse phenomena and decoherence phenomena on the standard formulation of quantum mechanics. While collapses explain determinate measurement records, environmental decoherence just produces more complex, entangled states where the physical systems involved lack ordinary physical properties. We characterize the quantum-mechanical wave function as both an element of a Hilbert space and a complex-valued function over a configuration space. We also discuss how the wave function is interpreted in the standard theory.
Entanglement of a macroscopic system with a microscopic one is shown to begin by a topological property of histories in the Feynman formulation of quantum mechanics. This property can also be expressed algebraically on the Schrödinger equation through a convenient extension of the Hilbert space formalism. Entanglement shows then properties of growth and transport, the corresponding local and temporary character of entanglement being called here "intricacy" when it occurs. When applied to the continuous interaction of a macroscopic system with a random environment, intricacy implies a "predecoherence" effect, which can generate and transport permanently incoherence within the system. The possible relevance of these results for a theory of wave function collapse is also indicated.
We show that it is possible to explain the quantum measurement process within the framework of quantum mechanics without any additional postulates. The key concept of the theory is decoherence, which appears as an inherent characteristic of quantum mechanics and results from the uncertainty relation. In contrast to environment-induced decoherence, this decoherence exists prior to a measurement being made. To clarify our idea, we examine three elemental experiments: a Stern-Gerlach-like experiment, the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) experiment, and the double-slit experiment. By considering the first experiment, we explain how the uncertainty relation between position and momentum introduces decoherence prior to measurement. Consideration of the EPR-Bohm experiment leads us to conclude that the correlation of the EPR pair is not a consequence of what is known as the collapse of the wave function. Our theory of decoherence can also be applied to experiments with continuous eigenvalues, such as the double-slit experiment. Consideration of the double-slit experiment leads us to understand how pure quantum mechanics describes the fact that quanta behave as interfering particles.