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arXiv:gr-qc/9807085

Decoherence and time emergence

Abel Camacho

Published Jul 30, 1998• 3 citations
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Abstract

In this work the possible role that Decoherence Model could play in the emergence of the classical concept of time is analyzed. We take the case of a Mixmaster universe with small anisotropy and construct its Halliwell propagator. Afterwards we introduce in our system terms that comprise the effects of Decoherence Model. This is done by means of the so called Restricted Path Integral Formalism. We obtain Halliwell's modified propagator and find that a gauge invariant physical time emerges as consequence of this process.

DOI
10.48550/arxiv.gr-qc/9807085

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In this work the possible role that Decoherence Model could play in the emergence of the classical concept of time is analyzed. We take the case of a Mixmaster universe with small anisotropy and construct its Halliwell propagator. Afterwards we introduce in our system terms that comprise the effects of Decoherence Model. This is done by means of the so called Restricted Path Integral Formalism. We obtain Halliwell's modified propagator and find that a gauge invariant physical time emerges as consequence of this process.
We begin this work calculating Halliwell's propagator in the case of a Mixmaster universe with small anisotropy. Afterwards in the context of the Decoherence Model we introduce in our system terms that comprise the self-measurement of the universe of this model by higher multipoles of matter. Analyzing self-measurement with the Restricted Path Integral Formalism we obtain Halliwell's modified propagator and find that a gauge invariant physical time emerges as consequence of this process. The conditions leading to Wheeler-DeWitt dynamics are also obtained. The comparison of our results with those of the isotropic case will enable us to conclude that the number of conditions to be satisfied in order to have Halliwell's regime is in the anisotropic situation bigger than in an isotropic universe. We obtain also in terms of the parameters of the measurement process an expression for the threshold in time beyond which the scale factors of this model are meaningless.
We show that the emergence of time evolution in an otherwise timeless nonrelativistic closed quantum system -- viewed as a poor man's model of generally covariant quantum theory -- can be understood from the perspective of the path integral representation. As often happens in the functional integral approach, this viewpoint offers a more intuitive account of features that become cumbersome in the operator/Hilbert-space formulation. We show how Schrödinger evolution emerges once a clock degree of freedom is identified and placed in a suitable semiclassical `good-clock state'. Our analysis has a consequence that extends to path integral formulations of generally covariant systems with action SSS (including gravity). In such theories certain transition amplitudes take the form exp⁡(iS/ℏ)+exp⁡(−iS/ℏ)\exp(iS/\hbar)+\exp(-iS/\hbar)exp(iS/ℏ)+exp(−iS/ℏ) rather than the expected `forward propagating' exp⁡(iS/ℏ)\exp(iS/\hbar)exp(iS/ℏ). This feature, known as the {\em cosine problem}, appears in concrete regularizations of the path integral, for example in the spin foam representation defining the physical inner product between spin network states in loop quantum gravity. Both formally and in explicit regularizations, this apparent difficulty has led some authors to seek modifications of the basic amplitudes to eliminate backward propagation. Our model shows that the cosine problem is instead a natural consequence of time-reversal invariance of the fundamental dynamics together with the time-neutral boundary states commonly used in transition amplitudes. When a suitable clock system is identified and placed in a semiclassical `good-clock state', it introduces a time arrow selecting the `forward propagating' exp⁡(iS/ℏ)\exp(iS/\hbar)exp(iS/ℏ), without modifying the fundamental dynamics. The analysis clarifies how time emerges under suitable conditions and emphasizes that, in the canonical formulation, quantum gravity is fundamentally timeless.
The dynamics of the quantum universe under self-measurement is investigated in the framework of the path-integral approach to quantum theory of continuous measurements. The corresponding amplitude (propagator) is evaluated explicitly for a simple superspace model. It is shown that the picture of time evolution of the quantum universe naturally emerges as a result of its self-measurement. The Wheeler-DeWitt dynamics holds for small times when the effect of measurement can be neglected and time dependence disappears.
The dynamics of the quantum universe under self-measurement is investigated in the framework of the path-integral approach to quantum theory of continuous measurements. The corresponding amplitude (propagator) is evaluated explicitly for a simple superspace model. It is shown that the picture of time evolution of the quantum universe naturally emerges as a result of its self-measurement. The Wheeler-DeWitt dynamics holds for small times when the effect of measurement can be neglected and time dependence disappears.
The concept of time presents a profound challenge at the intersection of quantum mechanics and thermodynamics. While fundamental microscopic laws are largely time-symmetric, macroscopic phenomena universally exhibit a distinct thermodynamic arrow of time, characterized by increasing entropy. This paper explores the hypothesis that quantum entanglement plays a crucial role in the emergence of this thermodynamic arrow. We review how the entanglement between a quantum system and its environment leads to decoherence, effectively driving the system towards a state of higher entropy and classical-like behavior. By analyzing concepts such as von Neumann entropy, entanglement entropy, and the Page-Wootters mechanism, we propose a theoretical framework where the degradation and spreading of entanglement act as the underlying mechanism for the perceived unidirectional flow of time. This approach offers a potential resolution to the "problem of time" in quantum gravity and provides a unified perspective on the genesis of irreversibility from the inherently reversible laws of quantum mechanics. We discuss the implications of this entanglement-driven temporal emergence for our understanding of the universe's initial low-entropy state and the fundamental nature of reality.
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete states is introduced, which presently is still treated as decoupled from the system. This is motivated by the recent discussion of ``timeless'' reparametrization invariant models, where discrete physical time has been constructed based on quasi-local observables. Employing the path-integral formulation of classical mechanics developed by Gozzi et al., we show that these deterministic classical systems can be naturally described as unitary quantum mechanical models. We derive the emergent quantum Hamiltonian in terms of the underlying classical one. Such Hamiltonians typically need a regularization - here performed by discretization - in order to arrive at models with a stable groundstate in the continuum limit. This is demonstrated in several examples, recovering and generalizing a model advanced by 't Hooft.