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AIP conference proceedings

Spontaneous Decoherence as a Result of a Random Course of Time

Lev I. Rozonoer

Published Jan 1, 2006• 0 citations
Publisher

Abstract

A possibility of spontaneous, not environment‐induced, decoherence is considered. A hypothesis on a random course of time is proposed. According to the hypothesis a “microscopic” time is a random process with independent increments in the “macroscopic”, averaged, time. A scale of the random process is defined by a scale time constant. If the scale constant tends to zero, then the course of time becomes not random but deterministic. It is demonstrated that the random course of time destroys phase relations between oscillations and, therefore, stationary states lose their coherence. Modifications of quantum and classical dynamics for random time are considered. All main principles of quantum or classical theory hold in these modifications. The modifications consist of averaging of physical quantities with respect to random microscopical time and going over to macroscopical time. Modified equations of a system evolution in the macroscopical time are irreversible and entropy of an isolated system increases. When the macroscopical time increases, nondiagonal elements of an averaged density matrix in the energy representation tend to zero. Thus, the hypothesis of a random course of time introduces irreversibility into systems dynamics (in macroscopic time) without violating of the main principles of classical or quantum mechanics. Experiments for checking the possibility of spontaneous decoherence and for evaluating of the scale constant are discussed. The stimulus for the considering of the spontaneous decoherence is the intention to explain the transformation of a pure state to a mix in quantum measurement and my hope to overcome difficulties (underlined by N.S.Krylov) of co‐ordinating of micromechanics with randomness. I hope that the spontaneous decoherence can provide a basis for statistical physics principles. It is possible that randomness of time is a trace on the classical space‐time imprinting by space‐time foam.

DOI
10.1063/1.2158753

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Physical Review A•Jul 1, 1990•1,135 citations
A possibility of spontaneous, not environment‐induced, decoherence is considered. A hypothesis on a random course of time is proposed. According to the hypothesis a “microscopic” time is a random process with independent increments in the “macroscopic”, averaged, time. A scale of the random process is defined by a scale time constant. If the scale constant tends to zero, then the course of time becomes not random but deterministic. It is demonstrated that the random course of time destroys phase relations between oscillations and, therefore, stationary states lose their coherence. Modifications of quantum and classical dynamics for random time are considered. All main principles of quantum or classical theory hold in these modifications. The modifications consist of averaging of physical quantities with respect to random microscopical time and going over to macroscopical time. Modified equations of a system evolution in the macroscopical time are irreversible and entropy of an isolated system increases. When the macroscopical time increases, nondiagonal elements of an averaged density matrix in the energy representation tend to zero. Thus, the hypothesis of a random course of time introduces irreversibility into systems dynamics (in macroscopic time) without violating of the main principles of classical or quantum mechanics. Experiments for checking the possibility of spontaneous decoherence and for evaluating of the scale constant are discussed. The stimulus for the considering of the spontaneous decoherence is the intention to explain the transformation of a pure state to a mix in quantum measurement and my hope to overcome difficulties (underlined by N.S.Krylov) of co‐ordinating of micromechanics with randomness. I hope that the spontaneous decoherence can provide a basis for statistical physics principles. It is possible that randomness of time is a trace on the classical space‐time imprinting by space‐time foam.
The problem of time’s arrow is (roughly) to understand why macroscopic physical processes typically evolve in a specific direction (the one we call “the future”) even though the underlying laws of physics describing the individual microscopic systems are time-reversal invariant. The standard answer to this problem is given by Boltzmann’s explanation of the II law of thermodynamics: a classical system starting in a non-equilibrium state spontaneously (i.e. with a high level of probability) tends towards equilibrium, thus implementing an irreversible process. However, this explanation has two drawbacks: 1. it needs a further assumption on the entropy of the initial state of the universe (past hypothesis); 2. microscopic systems (e.g. molecules in a box) should be represented as quantum states and not classical states. In this talk, I want to propose a different hypothesis to explain the origin of time’s arrow, based on quantum mechanics, specifically on decoherence theory. Differently from isolated systems, open quantum systems described by decoherence theory showirreversible behavior, as they evolve towards decoherence and von Neumann entropy increase. Is this behavior a sign of genuine irreversibility? And, if so, can this be linked to thermodynamic irreversibility?
The hypothesis of the random flow of time is considered. To do this, the concepts of microscopic random time and macroscopic mean time, as well as random modular time are introduced. The possibilities of experimental verification of the hypothesis of the random flow of time are discussed. The possibility of interpreting the time-like fifth coordinate (introduced by V.A. Fock) as absolute time is considered and the question of the reality of absolute time is discussed. The absolute time, which manifests itself as the proper time of the particles, is assumed to be random.
Abstract The deterministic and time-reversal symmetric dynamics of isolated quantum systems is at odds with irreversible equilibration observed in generic thermodynamic systems. Standard approaches at a reconciliation employ subjective restrictions on the space of observables or states and do not explain how a single macroscopic quantum system achieves equilibrium dynamically. We instead argue that quantum theory is an effective theory and requires corrections to accurately describe systems approaching the thermodynamic limit. We construct a stochastic extension of quantum theory which is practically identical to quantum mechanics for microscopic systems, yet allows individual macroscopic and isolated systems to objectively thermalize, generically. A fluctuation–dissipation relation guarantees physical consistency including norm preservation, energy conservation, no superluminal signalling and the emergence of microcanonical equilibrium. We further discuss the inclusion of objective collapse, thereby realizing a falsifiable theory of spontaneous universal irreversibility which describes the quantum-to-classical crossover dynamics of macroscopic quantum systems. The dynamics of the model describe spontaneous symmetry breaking, quantum state reduction and objective quantum thermalization for individual systems, while realizing emergent hybrid statistics for ensembles that integrate Born’s rule and microcanonical equilibrium.
Abstract Quantum mechanics is the foundation of modern physics that is thought to be applicable to all physical phenomena, at least in principle. However, when applied to macroscopic bodies, the theory seems to be inconsistent. Wigner's friend and related thought experiments demonstrate that accounts by different observers described by the rules of quantum mechanics may be contradictory. Although still highly debated, such experiments seem to demonstrate an incompatibility of quantum mechanics with the usual rules of logic. Alternatively, one of the hidden assumptions in the thought experiments must be wrong. For instance, the argument is invalidated if macroscopic observers cannot be considered as physical systems described by the rules of quantum theory. Here we prove that there is a way to apply the rules of quantum mechanics to macroscopic observers while avoiding contradictory accounts of measurement by the observers. The key to this is the random noise that is ever present in nature and that represents the uncontrollable part of interaction between measured system and the surroundings in classical and quantum physics. By exploring the effect of the noise on microscopic and macroscopic bodies, we demonstrate that accounts of Wigner, the friend and other agents all become consistent. Our result suggests that the existing attempts to modify the Schrodinger equation to account for measurement results may be misguided. More broadly, the proposed mechanism for modeling measurements underlies the phenomenon of decoherence and is shown to be sufficient to explain the transition to Newtonian physics in quantum theory.
We propose a novel approach to intrinsic decoherence without adding new assumptions to standard Quantum Mechanics. We generalize the Liouville equation just by requiring the dynamical semigroup property of time evolution and dropping the unitarity requirement. With no approximations and specific statistical assumptions we find a generalized Liouville equation which depends on two characteristic time t1 and t2 and reduces to the usual equation in the limit t1 = t2 --> 0. However, for t1 and t2 arbitrarily small but finite, our equation can be written as a finite difference equation which predicts state reduction to the diagonal form in the energy representation. The rate of decoherence becomes faster at the macroscopic limit as the energy scale of the system increases. In our approach the evolution time appears, a posteriori, as a statistical variable as if time evolution would take place randomly at average intervals t2, each evolution having a time width t1. A generalized Tam Mandelstam inequality is derived. The relation with previous work by Milburn is discussed. The agreement with recent experiments on damped Rabi oscillations is described.
Stochastic differential equations describing the Markovian evolution of state vectors in the quantum Hilbert space are studied as possible expressions of a universal dynamical principle. The general features of the considered class of equations as well as their dynamical consequences are investigated in detail. The stochastic evolution is proved to induce continuous dynamical reduction of the state vector onto mutually orthogonal subspaces. A specific choice, expressed in terms of creation and annihilation operators, of the operators defining the Markov process is then proved to be appropriate to describe continuous spontaneous localization of systems of identical particles. The dynamics obtained in such a way leaves practically unaffected the standard quantum evolution of microscopic systems and induces a very rapid suppression of coherence among macroscopically distinguishable states. The classical behavior of macroscopic objects as well as the reduction of the wave packet in a quantum measurement process can be consistently derived from the postulated universal dynamical principle.