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QP-PQ, quantum probability and white noise analysis

A macroscopical classical laboratory situation with only macroscopical classical entities giving rise to a quantum mechanical description

Diederik Aerts

Published Oct 1, 1991• 5 citations
Publisher
DOI
10.1142/9789814360203_0004

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We present a macroscopical mechanistic classical laboratory situation, and a classical macroscopical entity, and coincidence measurements on this entity, that lead to a violation of the Bell inequalities corresponding to these coincidence measurements. The violation that we obtain with these coincidence measurements is exactly the same as the violation of the Bell inequalities by the well known coincidence measurements of the quantum entity of two spin 1/2 particles in a singlet spin state. With this we mean that it gives rise to the same numerical values for the expectation values and the same numerical value 2•√2 for the expression used in the Bell inequalities.
In this paper, the quantum logical ‘or ’ is analyzed from a physical perspective. We show that it is the existence of EPR-like correlation states for the quantum mechanical entity under consideration that make it nonequivalent to the classical situation. Specifically, the presence of potentiality in these correlation states gives rise to the quantum deviation from the classical logical ‘or’. We show how this arises not only in the microworld, but also in macroscopic situations where EPR-like correlation states are present. We investigate how application of this analysis to concepts could alleviate some well known problems in cognitive science. Dedication: We dedicate this paper to Marisa Dalla Chiara, one of the founding figures of quantum logic. The ideas expressed in this article have been influenced by her ground-breeaking work in this field. 1