Details
| Original language | English |
|---|---|
| Title of host publication | Reduction in science |
| Editors | W. Balzer, D.A. Pearce, H.-J. Schmidt |
| Place of Publication | Dordrecht |
| Pages | 419-442 |
| Number of pages | 24 |
| Publication status | Published - 1984 |
Abstract
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Reduction in science. ed. / W. Balzer; D.A. Pearce; H.-J. Schmidt. Dordrecht, 1984. p. 419-442.
Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review
}
TY - CHAP
T1 - Bell's inequalities and the reduction of statistical theories
AU - Werner, R. F.
PY - 1984
Y1 - 1984
N2 - 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.
AB - 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.
M3 - Contribution to book/anthology
SP - 419
EP - 442
BT - Reduction in science
A2 - Balzer, W.
A2 - Pearce, D.A.
A2 - Schmidt, H.-J.
CY - Dordrecht
ER -