The Arrow of Time in Rigged Hilbert Space Quantum Mechanics

Bishop, Robert C. (2002) The Arrow of Time in Rigged Hilbert Space Quantum Mechanics.

Abstract

Arno Bohm and Ilya Prigogine's Brussels-Austin Group have been working on the quantum mechanical arrow of time and irreversibility in rigged Hilbert space quantum mechanics. A crucial notion in Bohm's approach is the so-called preparation/registration arrow. An analysis of this arrow and its role in Bohm's theory of scattering is given. Similarly, the Brussels-Austin Group uses an excitation/de-excitation arrow for ordering events, which is also analyzed. The relationship between the two approaches is discussed focusing on their semi-group operators and time arrows. Finally a possible realist interpretation of the rigged Hilbert space formulation of quantum mechanics is considered.