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Time-Reversal, Irreversibility and Arrow of Time in Quantum Mechanics

Mario Castagnino, Manuel Gadella, Olímpia Lombardi

Foundations of PhysicsFeb 14, 200616 citations

The time reversal operator for semigroup evolutions

Arno Böhm, Sujeewa Wickramasekara

Foundations of PhysicsJul 1, 199711 citations

Microphysical irreversibility and the time-reversal operation

Arno Böhm

The division of a scattering experiment into the preparation of a state and the registration of an observable in this state defines an obvious but commonly ignored quantum-mechanical arrow of time. This leads to irreversibility on the microphysical level. The time evolution semigroup for exponentially decaying Gamow states is an example of this microphysical irreversibility. A time-reversal operator exists which is compatible with the quantum-mechanical arrow of time.

Physical Review AMar 1, 199523 citations

A quantum mechanical arrow of time and the semigroup time evolution of Gamow vectors

Arno Böhm, Ioannis E. Antoniou, Piotr Kielanowski

The exponential decay (or growth) of resonances provides an arrow of time which is described as the semigroup time evolution of Gamow vector in a new formulation of quantum mechanics. Another direction of time follows from the fact that a state must first be prepared before observables can be measured in it. Applied to scattering experiments, this produces another quantum mechanical arrow of time. The mathematical statements of these two arrows of time are shown to be equivalent. If the semigroup arrow is interpreted as microphysical irreversibility and if the arrow of time from the prepared in-state to its effect on the detector of a scattering experiment is interpreted as causality, then the equivalence of their mathematical statements implies that causality and irreversibility are interrelated.The exponential decay (or growth) of resonances provides an arrow of time which is described as the semigroup time evolution of Gamow vector in a new formulation of quantum mechanics. Another direction of time follows from the fact that a state must first be prepared before observables can be measured in it. Applied to scattering experiments, this produces another quantum mechanical arrow of time. The mathematical statements of these two arrows of time are shown to be equivalent. If the semigroup arrow is interpreted as microphysical irreversibility and if the arrow of time from the prepared in-state to its effect on the detector of a scattering experiment is interpreted as causality, then the equivalence of their mathematical statements implies that causality and irreversibility are interrelated.

Journal of Mathematical PhysicsJun 1, 199546 citations

The Quantum Mechanical Arrows of Time

James B. Hartle

WORLD SCIENTIFIC eBooksDec 9, 20205 citations

Time Asymmetric Quantum Theory — I Modifying an Axiom of Quantum Physics

A. R. Bohm, Mark Loewe, Bryan Van De Ven

A slight modification of one axiom of quantum theory changes a reversible theory into a time asymmetric theory. Whereas the standard Hilbert space axiom does not distinguish mathematically between the space of states (in-states of scattering theory) and the space of observables (out-“states ” of scattering theory) the new axiom associates states and observables to two different Hardy subspaces which are dense in the same Hilbert space and analytic in the lower and upper complex energy plane, respectively. As a consequence of this new axiom the dynamical equations (Schrödinger or Heisenberg) integrate to a semigroup evolution. Extending this new Hardy space axiom to a relativistic theory provides a relativistic theory of resonance scattering and decay with Born probablilities that fulfill Einstein causality and the exponential decay law. 1 Introduction—Time Asymmetry Time asymmetry, irreversibility, time reversal non-invariance are different concepts and they are (probably) not (all) related to each other [1], [2], [3]. These concepts are usually called arrows-of-time. Time asymmetry comes from time asymmetric boundary conditions of time symmetric equations; its most prominent consequence is causality. The radiation arrow of time is its example from classical physics. IrreversibilityA slight modification of one axiom of quantum theory changes a reversible theory into a time asymmetric theory. Whereas the standard Hilbert space axiom does not distinguish mathematically between the space of states (in-states of scattering theory) and the space of observables (out-“states ” of scattering theory) the new axiom associates states and observables to two different Hardy subspaces which are dense in the same Hilbert space and analytic in the lower and upper complex energy plane, respectively. As a consequence of this new axiom the dynamical equations (Schrödinger or Heisenberg) integrate to a semigroup evolution. Extending this new Hardy space axiom to a relativistic theory provides a relativistic theory of resonance scattering and decay with Born probablilities that fulfill Einstein causality and the exponential decay law. 1 Introduction—Time Asymmetry Time asymmetry, irreversibility, time reversal non-invariance are different concepts and they are (probably) not (all) related to each other [1], [2], [3]. These concepts are usually called arrows-of-time. Time asymmetry comes from time asymmetric boundary conditions of time symmetric equations; its most prominent consequence is causality. The radiation arrow of time is its example from classical physics. Irreversibility

Jan 1, 200823 citations

Quantum Time Arrows, Semigroups and Time-Reversal in Scattering

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