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Mathematics 2016, 4(2), 40; doi:10.3390/math4020040

Uncertainty Relations and Possible Experience

Quantum Communication and Measurement Laboratory, Department of Electrical and Computer Engineering and Division of Natural Science and Mathematics, Boston University, Boston, MA 02215, USA
Academic Editors: Paul Busch, Takayuki Miyadera and Teiko Heinosaari
Received: 13 April 2016 / Revised: 24 May 2016 / Accepted: 27 May 2016 / Published: 3 June 2016
(This article belongs to the Special Issue Mathematics of Quantum Uncertainty)
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Abstract

The uncertainty principle can be understood as a condition of joint indeterminacy of classes of properties in quantum theory. The mathematical expressions most closely associated with this principle have been the uncertainty relations, various inequalities exemplified by the well known expression regarding position and momentum introduced by Heisenberg. Here, recent work involving a new sort of “logical” indeterminacy principle and associated relations introduced by Pitowsky, expressable directly in terms of probabilities of outcomes of measurements of sharp quantum observables, is reviewed and its quantum nature is discussed. These novel relations are derivable from Boolean “conditions of possible experience” of the quantum realm and have been considered both as fundamentally logical and as fundamentally geometrical. This work focuses on the relationship of indeterminacy to the propositions regarding the values of discrete, sharp observables of quantum systems. Here, reasons for favoring each of these two positions are considered. Finally, with an eye toward future research related to indeterminacy relations, further novel approaches grounded in category theory and intended to capture and reconceptualize the complementarity characteristics of quantum propositions are discussed in relation to the former. View Full-Text
Keywords: quantum mechanics; uncertainty relations; quantum logic; boolean logic; complementarity quantum mechanics; uncertainty relations; quantum logic; boolean logic; complementarity
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Jaeger, G. Uncertainty Relations and Possible Experience. Mathematics 2016, 4, 40.

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