Approximate Decoherence of Histories and 't Hooft's Deterministic Quantum Theory

Abstract

This paper explores the possibility that an exactly decoherent set of histories may be constructed from an approximately decoherent set by small distortions of the operators characterizing the histories. In particular, for the case of histories of positions and momenta, this is achieved by doubling the set of operators and then finding, amongst this enlarged set, new position and momentum operators which commute, so decohere exactly, and which are ``close'' to the original operators. The enlarged, exactly decoherent, theory has the same classical dynamics as the original one, and coincides with the so-called deterministic quantum theories of the type recently studied by 't Hooft. These results suggest that the comparison of standard and deterministic quantum theories may provide an alternative method of characterizing emergent classicality. A side-product is the surprising result that histories of momenta in the quantum Brownian motion model (for the free particle in the high-temperature limit) are exactly decoherent.

41 pages, plain Tex

References in corpus (3)

• Quantum Gravity as a Dissipative Deterministic System
• Decoherent Histories and the Emergent Classicality of Local Densities
• Classical Dynamics of the Quantum Harmonic Chain

Cited by in corpus (16)

• Disentanglement and Decoherence by Open System Dynamics
• Uncertainty Relation on World Crystal and its Applications to Micro Black Holes
• Can we predict $\Lambda$ for the Non-SUSY sector of the Landscape ?
• Bateman's dual system revisited: I. Quantization, geometric phase and relation with the ground-state energy of the linear harmonic oscillator
• Path Integral Approach to 't Hooft's Derivation of Quantum from Classical Physics
• Dissipation and quantization for composite systems
• Birth of the Universe from the Landscape of String Theory
• First Principles Numerical Demonstration of Emergent Decoherent Histories
• Quantum Behavior of Deterministic Systems with Information Loss. Path Integral Approach
• A Fly in the SOUP
• Commuting Position and Momentum Operators, Exact Decoherence and Emergent Classicality
• Quantum linear Boltzmann equation with finite intercollision time
• Exact Phase Space Localized Projectors from Energy Eigenstates
• Decoherence of Histories: Chaotic Versus Integrable Systems
• Emergent Classicality via Commuting Position and Momentum Operators
• Emergence of non-Markovian Decoherent Histories in Integrable Environment: A "Tape Recorder" Model for Local Quantum Observables