TY - JOUR

T1 - Resonance and decay phenomena lead to quantum mechanical time asymmetry

AU - Bohm, A.

AU - Bui, H. V.

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2013

Y1 - 2013

N2 - The states (Schrödinger picture) and observables (Heisenberg picture) in the standard quantum theory evolve symmetrically in time, given by the unitary group with time extending over - < t < +. This time evolution is a mathematical consequence of the Hilbert space boundary condition for the dynamical differential equations. However, this unitary group evolution violates causality. Moreover, it does not solve an old puzzle of Wigner: How does one describe excited states of atoms which decay exponentially, and how is their lifetime τ related to the Lorentzian width Γ? These question can be answered if one replaces the Hilbert space boundary condition by new, Hardy space boundary conditions. These Hardy space boundary conditions allow for a distinction between states (prepared by a preparation apparatus) and observables (detected by a registration apparatus). The new Hardy space quantum theory is time asymmetric, i.e, the time evolution is given by the semigroup with t0 ≤ t < +, which predicts a finite «beginning of time» t0, where t0 is the ensemble of time at which each individual system has been prepared. The Hardy space axiom also leads to the new prediction: the width Γ and the lifetime τ are exactly related by τ/γ.

AB - The states (Schrödinger picture) and observables (Heisenberg picture) in the standard quantum theory evolve symmetrically in time, given by the unitary group with time extending over - < t < +. This time evolution is a mathematical consequence of the Hilbert space boundary condition for the dynamical differential equations. However, this unitary group evolution violates causality. Moreover, it does not solve an old puzzle of Wigner: How does one describe excited states of atoms which decay exponentially, and how is their lifetime τ related to the Lorentzian width Γ? These question can be answered if one replaces the Hilbert space boundary condition by new, Hardy space boundary conditions. These Hardy space boundary conditions allow for a distinction between states (prepared by a preparation apparatus) and observables (detected by a registration apparatus). The new Hardy space quantum theory is time asymmetric, i.e, the time evolution is given by the semigroup with t0 ≤ t < +, which predicts a finite «beginning of time» t0, where t0 is the ensemble of time at which each individual system has been prepared. The Hardy space axiom also leads to the new prediction: the width Γ and the lifetime τ are exactly related by τ/γ.

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U2 - 10.1088/1742-6596/428/1/012016

DO - 10.1088/1742-6596/428/1/012016

M3 - Conference article

AN - SCOPUS:84876521913

VL - 428

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012016

T2 - 21st International Symposium on the Jahn-Teller Effect 2012

Y2 - 26 August 2012 through 31 August 2012

ER -