Locality, probability and quantum mechanics

W. Michael Dickson

Claudio Garola, Sandro Sozzo

Most physicists uphold that the tests of the Bell-Clauser, Horne, Shimony and Holt (BCHSH) inequalities confirm quantum mechanics (QM) and refute local realism. Some scholars, however, criticize this conviction, yet maintaining that QM conflicts with local realism. At variance with both viewpoints one of the authors has recently worked out an extended semantic realism (ESR) model which shows that, if quantum probabilities are interpreted as conditional rather than absolute probabilities, a picture of the microworld can be constructed that is simultaneously consistent with local realism and QM. We show here that the BCHSH inequalities must be replaced, within the ESR model, by more general inequalities. These depend on parameters (detection probabilities) which may be such that the inequalities are never violated by quantum expectation values. The condition that no violation occurs implies the existence of upper bounds on detection probabilities, which makes the ESR model falsifiable. These results admit an intuitive explanation in terms of unfair sampling but basically differ from the seemingly similar results obtained by other approaches in which the efficiency problem is discussed in order to vindicate some kind of local realism.

Gregg S. Jaeger

J. Leite Lopes, Michel Paty

Include the Observer in the Wave Function?.- On the Possible Connections between Quantum Mechanics and Gravitation.- The Quantum Probability Calculus.- Quantum Logics and Ideal Measurements of the First Kind.- A First Lecture on Quantum Mechanics.- Essay on the Development of the Statistical Theory of the Calculus of Probability.- The Quantum Mechanical One-System Formalism, Joint Probabilities and Locality.- On Propositions and Physical Systems.- Towards a Proper Quantum Theory.- On the Intuitive Understanding of Non-Locality as Implied by Quantum Theory.- Four Ideas of David Bohm on the Relationship between Quantum Mechanics and Relativity.- The Role of Quantum Mechanics in the Set-up of a Mathematical Government among Molecular Populations.- Hidden Parameters, Hidden Probabilities.- The Recent Attempts to Verify Quantum Mechanics.- Spin Correlation Measurement in Proton-Proton Scattering and Comparison with the Theories of the Local Hidden Variables.

Detlev Buchholz A, Stephen J. Summers

Simon W. Saunders

Abstract Probability is distinguished into two kinds: physical and epistemic, also, but less accurately, called objective and subjective. Simple postulates are given for physical probability, the only novel one being a locality condition. Translated into no-collapse quantum mechanics, without hidden variables, the postulates imply that the elements in any equiamplitude expansion of the quantum state are equiprobable. Such expansions therefore provide ensembles of microstates that can be used to define probabilities in the manner of frequentism, in von Mises’ sense (where the probability of P is the frequency of occurrence of P in a suitable ensemble). The result is the Born rule. Since satisfying our postulates, and in particular the locality condition (meaning no action-at-a-distance), these probabilities for no-collapse quantum mechanics are perfectly local, even though they violate Bell inequalities. The latter can be traced to a violation of outcome independence, used to derive the inequalities. But in no-collapse theory it is not a locality condition; it is a criterion for entanglement, not locality.