Bell's inequalities and the reduction of statistical theories

verfasst von

R. F. Werner

Abstract

A framework for the description of statistical correlation experiments is introduced in which the hypotheses underlying Bell's inequalities can be analysed. The locality condition is presented as a two-way version of Ludwig's principle of directed interaction, which excludes axiomatically the transmission of signals from the measuring device back to the preparation device. Bell's inequalities follow, when the observed correlation data admit a hypothetical extension to an infinite set of correlation data, which still satisfies this locality condition, and which is classical in the sense that any two observables can be measured jointly. The relation between the observed data, and the observable data encoded in a theoretical description is generalized to the relation of embedding (or reduction) between statistical theories. It is shown that the quantum theories over real, complex, or quaternionic Hilbert spaces can mutually be reduced to each other. As a consequence, it is shown that these theories cannot be distinguished by correlation experiments of the Aspect type.

Organisationseinheit(en)

Institut für Theoretische Physik

Typ

Beitrag in Buch/Sammelwerk

Seiten

419-442

Anzahl der Seiten

24

Publikationsdatum

1984

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja