An Arrow of Time Operator for Standard Quantum Mechanics

Details An Arrow of Time Operator for Standard Quantum Mechanics An Arrow of Time Operator for Standard Quantum Mechanics

2008-02-18

arxiv.org/abs/0802.2448v1

Physics

Quantum Physics

5 pages, 2 figures

Scientific paper

We introduce a self-adjoint operator that indicates the direction of time within the framework of standard quantum mechanics. That is, as a function of time its expectation value decreases monotonically for any initial state. This operator can be defined for any system governed by a Hamiltonian with a uniformly finitely degenerate, absolutely continuous and semibounded spectrum. We study some of the operator's properties and illustrate them for a large equivalence class of scattering problems. We also discuss some previous attempts to construct such an operator, and show that the no-go theorems developed in this context are not applicable to our construction.

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