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Abstract
In this paper, we propose a new interpretation of quantum mechanics according to which Born probabilities are interpreted as many-valued truth values of statements concerning results of not-yet-performed experiments on quantum objects, or equivalently [0,1]-valued degrees to which quantum objects possess all their properties prior to measurements. The interpretation is based on mathematical results already published by the author, according to which any Birkhoff–von Neumann quantum logic can be isomorphically represented as a family of fuzzy sets or, equivalently, many-valued propositional functions.
Acknowledgements
This work was supported by the University of Gdańsk grant BW/5100-5-0468-8. The main part of the work was completed when the Author visited the University of Salento in September 2008 being supported by Istituto Nazionale di Fisica Nucleare. The Author is specially indebted to Prof. Claudio Garola and Dr Sandro Sozzo for the hospitality extended to him during this visit. Special thanks are due to Dr M. Góra for his assistance, continuous support and improvement of the Author's poor English.
Notes
1. see, e.g., an exhaustive exposition of various interpretations of quantum mechanics at par http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics.