On superselection rules in Bohm–Bell theories
- 30 November 2006
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 39 (50), 15403-15419
- https://doi.org/10.1088/0305-4470/39/50/008
Abstract
The meaning of superselection rules in Bohm-Bell theories (i.e., quantum theories with particle trajectories) is different from that in orthodox quantum theory. More precisely, there are two concepts of superselection rule, a weak and a strong one. Weak superselection rules exist both in orthodox quantum theory and in Bohm-Bell theories and represent the conventional understanding of superselection rules. We introduce the concept of strong superselection rule, which does not exist in orthodox quantum theory. It relies on the clear ontology of Bohm-Bell theories and is a sharper and, in the Bohm-Bell context, more fundamental notion. A strong superselection rule for the observable G asserts that one can replace every state vector by a suitable statistical mixture of eigenvectors of G without changing the particle trajectories or their probabilities. A weak superselection rule asserts that every state vector is empirically indistinguishable from a suitable statistical mixture of eigenvectors of G. We establish conditions on G for both kinds of superselection. For comparison, we also consider both kinds of superselection in theories of spontaneous wave function collapse.Keywords
Other Versions
This publication has 14 references indexed in Scilit:
- Bell-type quantum field theoriesJournal of Physics A: General Physics, 2005
- Bohmian Mechanics and Quantum Field TheoryPhysical Review Letters, 2004
- Entanglement Constrained by Superselection RulesPhysical Review Letters, 2003
- Dynamical reduction modelsPhysics Reports, 2003
- Trajectories and particle creation and annihilation in quantum field theoryJournal of Physics A: General Physics, 2003
- A survey of Bohmian mechanicsIl Nuovo Cimento B (1971-1996), 1995
- Quantum equilibrium and the origin of absolute uncertaintyJournal of Statistical Physics, 1992
- Unified dynamics for microscopic and macroscopic systemsPhysical Review D, 1986
- Quantum field theory of without observersPhysics Reports, 1986
- A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. IPhysical Review B, 1952