Indistinguishability and the origins of contextuality in physics

Abstract

In this work we discuss a formal way of dealing with properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz's principle of identity of indiscernibles. This allows us to consider a new ontology in order to study properties of quantum systems.

Indistinguishability and Negative Probabilities

“…Some authors have proposed that and should be considered different whenever a system manifests a strong degree of contextuality [ 16 , 17 ]. In previous works [ 7 , 18 ], we have proposed an alternative solution to the dichotomy vs . Using a formal framework that allows dealing with collections of indistinguishable objects (see Section 4 of this work), we have proposed that and can be thought of as indistinguishable (denoted by ).…”

“…This point of view allows us to connect with contextuality one of the most fundamental features of quantum theory: quantum systems of the same kind are indistinguishable. More specifically, we show in [ 7 , 18 ] that the indistinguishability of particles leads to the indistinguishability of propositions and that this, in turn, gives place to contextuality. In the rest of this work, we elaborate on these ideas further and show a strong connection between the indistinguishability of testable propositions (or observables) and negative probabilities.…”

“…In [ 18 ], we have shown that the possibility of identifying particles in different contexts lies at the core of the Kochen-Specker contradiction. In [ 7 ], we studied how the assumption of the indistinguishability of properties allows one to understand the occurrence of contextual random variables.…”

“…It is instructive to illustrate the connection between quantum indistinguishability and the identification of propositions with the same content, but in different contexts, by considering a quasi-pair concept in quasi-set theory. The quasi-pair can be used to describe one quanta possessing the property (see also the discussion presented in [ 7 ]), where the is the collection of all possible indistinguishable elements from x . Thus, , can be interpreted as: “a quantum object satisfies that the value of A lies in ”.…”

“…The other focus of this article is on quantum indistinguishability. In previous works, we have discussed the connection between particle and property indistinguishability as related to contexts [ 7 ]. Here we show that property indistinguishability leads to the no-signaling condition.…”