When Are Two Wave Functions Distinguishable: A New Answer to Pauli’s Question, with Potential Application to Quantum Cosmology

• Published in: International journal of theoretical physics Vol. 47; no. 3; pp. 814 - 831
• Main Authors: Longpré, Luc, Kreinovich, Vladik
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01-03-2008
• Subjects: Elementary Particles; Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum Field Theory; Quantum Physics; Theoretical; Poss; Probability Measure; Wave Function; Quantum State; Hilbert Space
• ISSN: 0020-7748; 1572-9575
• DOI: 10.1007/s10773-007-9505-0

Traditional quantum mechanics (QM) predicts probabilities of different events. If we describe an elementary particle, then, experimentally, these probabilities mean that if we repeat the same measurement procedure with multiple particles in the same state, the resulting sequence of measurement results will be random w.r.t. the corresponding probability measure. In quantum cosmology, QM is used to describe the world as a whole; we have only one copy of the world, so multiple measurements are impossible. How to interpret these probabilities?
In this paper, we use the approach of the algorithmic information theory to come up with a reasonable interpretation. This interpretation is in good accordance with the arguments presented by several physicists (such as D. Finkelstein) that a wave function is not always a physically reasonable description of a quantum state.