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arXiv:1311.6050 · Journal of Mathematical Psychology

A quantum probability explanation in Fock space for borderline contradictions

Sandro Sozzo

Published Dec 5, 2013• 42 citations
arXivHTMLPDF
DOI
10.1016/j.jmp.2013.11.001

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The term "vagueness" describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno's sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib's and Pelletier's () theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful as this classical perspective is, we show that it falls short of providing an adequate coverage of the relevant empirical results. In the final part, we will argue that a substantial modification of the analysis put forward by Alxatib and Pelletier and its probabilistic pendant is needed. The proposed modification replaces the standard notion of probabilities by quantum probabilities. The crucial phenomenon of borderline contradictions can be explained then as a quantum interference phenomenon.
Purpose The standard terms of time and space lead to logical contradictions near the borderline of physics. Therefore, we suggest a new term for time and space, which enlarges the understanding but takes the actual knowledge of quantum mechanics into account. Design/methodology/approach The procedure to define a broader and basic term of time and space is based on the relation between the information stored inside a system, the decision which is to be connected with it and the interaction with other systems. Findings Fundamental to this new understanding is a definition and an explanation of the terms system, decision and information. Based on these three terms we developed a new understanding of time and space. In which case, it involves a specifying and extension of the present understandings. A meaningful point is that these three terms determine each other as they are open terms. Thus, they must be used in the interactive description before and during their own definition. Originality/value Produces a new understanding and viewpoint which is enlarged by taking into account the knowledge of quantum mechanics.
Quantum systems in Fock states do not have a phase. When two or more Bose-Einstein condensates are sent into interferometers, they nevertheless acquire a relative phase under the effect of quantum measurements. The usual explanation relies on spontaneous symmetry breaking, where phases are ascribed to all condensates and treated as unknown classical quantities. However, this image is not always sufficient: when all particles are measured, quantum mechanics predicts probabilities that are sometimes in contradiction with it, as illustrated by quantum violations of local realism. In this letter, we show that interferometers can be used to demonstrate a large variety of violations with an arbitrarily large number of particles. With two independent condensates, we find violations of the BCHSH inequalities, as well as new N-body Hardy impossibilities. With three condensates, we obtain new GHZ (Greenberger, Horne and Zeilinger) type contradictions.