Origin of the Arrow of Time in Quantum Mechanics

Abstract

We point out that time's arrow is naturally induced by quantum mechanical evolution, whenever the systems have a very large number $\mathcal{N}$ of non-degenerate states and a Hamiltonian bounded from below. When $\mathcal{N}$ is finite, the arrow is imperfect, since evolution can resurrect past states. In the limit $\mathcal{N}\to \infty$ the arrow is fixed by the "tooth of time": the decay of excited states induced by {\it spontaneous emission} to the ground state, mediated by interactions and a large number of decay products which carry energy and information to infinity. This applies to individual isolated atoms, and does not require a coupling to a separate large heath bath.

arXiv comment13 pages XeLaTeX, 2 .png figures; expanded discussion, typos fixed, references added, accepted in IJMPD

References in corpus (11)

• The Dynamics of General Relativity
• Quantum mechanical evolution towards thermal equilibrium
• Foundation of Statistical Mechanics under experimentally realistic conditions
• Disturbing Implications of a Cosmological Constant
• Recycling universe
• Coherent States for the Hydrogen Atom
• The arrow of time in operational formulations of quantum theory
• Quantum causality and the arrows of time and thermodynamics
• Irreversibility of Time for Quasi-Isolated Systems
• A Quantum-Mechanical Mechanism for Reducing the Cosmological Constant
• Hidden Variables of Gravity and Geometry and the Cosmological Constant Problem