Contextuality and Indistinguishability

Abstract

Abstract:It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities. In this paper, we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we assume the ontological thesis that quantum particles or properties can be indistinguishable yet different, no contradiction arising from a Kochen-Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same. We will discuss how the consequences of this move may help us understand quantum contextuality.

Understanding quantum mechanics: a review and synthesis in precise language

“…6.3 result collective outcomes of a measurement Schrödinger equation an equation specifying how the quantum state evolves in time [25, § 6.4] selection using single run outcomes to split an ensemble into subensembles, each with one value of the relevant observable [193] self-identity feature of an entity for which different instances of it can be distinguished, like currency coins (and unlike currency in a bank account) [567, § 8]; the extent to which quanta have self-identity is unresolved [17] [56, ch. 3] [374,376,384,388,565,568] single run (in measurement): one system (from an ensemble) interacting with an apparatus, followed by reading of an outcome [193]; see Sect. 4.1 state mathematical term which prescribes, generally in terms of probability distributions, aspects of expected future events relating to a statistical ensemble of systems in a range of possible situations; see Sect.…”

Indistinguishability and the origins of contextuality in physics

“…To do so, we use quasi-set theory [27], which is a logical formalism developed to deal with collections of truly indistinguishable entities. Quasi-sets have been applied to quantum mechanics before, in order to describe quantum non-individuality [11,12,13], and as above mentioned, to avoid Kochen-Specker-type contradictions [9]. We see our approach as having two advantages over the more general one of [14].…”

“…This paper examines contextuality in physics by extending a point of view put forth on references [9] and [28], namely that quantum indistinguishability is connected to contextuality. In [9], we argued that the indistinguishability of particles, expressed mathematically by a set-theoretical construct where the law of identity of indiscernibles is violated, invalidates the contradiction argument put forth by Kochen and Specker (KS) in [22] (see Section 2 for a sketch of the KS argument).…”

“…This paper examines contextuality in physics by extending a point of view put forth on references [9] and [28], namely that quantum indistinguishability is connected to contextuality. In [9], we argued that the indistinguishability of particles, expressed mathematically by a set-theoretical construct where the law of identity of indiscernibles is violated, invalidates the contradiction argument put forth by Kochen and Specker (KS) in [22] (see Section 2 for a sketch of the KS argument). In their paper, KS discuss the concept of quantum properties, represented by self-adjoint operators in a Hilbert space [39], and show that attempts to assign truth values to those properties in different experimental contexts fail if we assume that such properties are context-independent.…”

Non-Deterministic Semantics for Quantum States

“…As an example, negative probabilities have been applied to the study of inconsistent judgments [17]. Our extension could be useful for studying contextuality [18][19][20][21][22] in quantum mechanics and generalized probabilistic models from a novel logical perspective.…”