Uncertainty relations and possible experience
type: Item
instance of: scholarly article
title: Uncertainty relations and possible experience
zbMATH Open document ID: 1360.81037
published in: Mathematics
publication date: 2017-03-16T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 81P15
Mathematics Subject Classification ID: 62J10
Mathematics Subject Classification ID: 81P13
zbMATH DE Number: 6695460
zbMATH Keywords: quantum logic
zbMATH Keywords: complementarity mechanics
zbMATH Keywords: uncertainty relations
zbMATH Keywords: Boolean
author: Gregg Jaeger
MaRDI profile type: Publication
full work available at URL: math4020040
OpenAlex ID: W2417791574
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DOI: 10.3390/MATH4020040
description: scientific article; zbMATH DE number 6695460