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AIP conference proceedings

Facets of contextual realism in quantum mechanics

A. K. Pan, Dipankar Home, Dipankar Home, Guruprasad Kar, Archan S. Majumda

Published Jan 1, 2011• 0 citations
Publisher

Abstract

In recent times, there is an upsurge of interest in demonstrating the quantum contextuality. In this proceedings, we explore the two different forms of arguments that have been used for showing the contextual character of quantum mechanics. First line of study concerns the violations of the noncontextual realist models by quantum mechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantum mechanics.

DOI
10.1063/1.3635842

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In recent times, there is an upsurge of interest in demonstrating the quantum contextuality. In this proceedings, we explore the two different forms of arguments that have been used for showing the contextual character of quantum mechanics. First line of study concerns the violations of the noncontextual realist models by quantum mechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantum mechanics.
The belief that quantum mechanics (QM) does not admit a realistic interpretation is widespread. According to some scholars concerned with the foundations of QM all existing interpretations of this theory (except for the statistical interpretation) presuppose instead a form of realism which consists in assuming that QM deals with individual objects and their properties. We uphold in the present paper that the arguments supporting the contextuality and the nonlocality of QM are a significant clue to the implicit adoption of stronger forms of realism (realism of theoretical entities and realism of theories). If these kinds of realism are substituted by a simpler and more intuitive semantic realism one can contrive a noncontextual and local interpretation of the formalism of QM (SR interpretation). Moreover one can provide a model for such an interpretation (ESR model) in which local realism and QM do not conflict and some fundamental problems of the standard interpretation of QM are avoided.
Our everyday experiences support the hypothesis that physical systems exist independently of the act of observation. Concordant theories are characterized by the objective realism assumption whereby the act of measurement simply reveals preexisting well-defined elements of reality. In stark contrast quantum mechanics portrays a world in which reality loses its objectivity and is in fact created by observation. Quantum contextuality as first discovered by Bell [1] and Kochen-Specker [2] captures aspects of this philosophical clash between classical and quantum descriptions of the world. Here we briefly summarize some of the more recent advances in the field of quantum contextuality. We approach quantum contextuality through its close relation to Bell type nonlocal scenarios and highlight some of the rapidly developing tests and experimental implementations.
Our everyday experiences support the hypothesis that physical systems exist independently of the act of observation. Concordant theories are characterized by the objective realism assumption whereby the act of measurement simply reveals preexisting well defined elements of reality. In stark contrast quantum mechanics portrays a world in which reality loses its objectivity and is in fact created by observation. Quantum contextuality as first discovered by Bell [Rev. Mod. Phys. 38, 447 (1966)] and Kochen-Specker [J. Math. Mech. 17, 59 (1967)] captures aspects of this philosophical clash between classical and quantum descriptions of the world. Here we briefly summarize some of the more recent advances in the field of quantum contextuality. We approach quantum contextuality through its close relation to Bell type nonlocal scenarios and highlight some of the rapidly developing tests and experimental implementations.
The field of quantum foundations seeks to answer questions such as: What do the elements of the mathematical formalism of quantum theory represent? From what physical principles can the formalism be derived? What are the precise ways in which a quantum world differs from a classical world and other possible worlds? These lectures will cover some important foundational topics which touch upon these questions, in particular, operational and realist interpretations of the formalism, the quantum measurement problem, nonlocality and contextuality.
In this thesis we explore the questions of what should be considered a "classical" theory, and which aspects of quantum theory cannot be captured by any theory that respects our intuition of classicality. This exploration is divided in two parts: in the first we review classical results of the literature, such as the Kochen-Specker theorem, von Neumann's theorem, Gleason's theorem, as well as more recent ideas, such as the distinction between ψψψ-ontic and ψψψ-epistemic ontological models, Spekkens' definition of contextuality, Hardy's ontological excess baggage theorem and the PBR theorem. The second part is concerned with pinning down what should be the "correct" definition of contextuality. We settle down on the definition advocated by Abramsky and Branderburger, motivated by the Fine theorem, and show the connection of this definition with the work of George Boole. This definition allows us to unify the notions of locality and noncontextuality, and use largely the same tools to characterize how quantum mechanics violates these notions of classicality. Exploring this formalism, we find a new family of noncontextuality inequalities. We conclude by reviewing the notion of state-independent contextuality.
In a recent paper Griffiths [38] has argued, based on the consistent histories interpretation, that Hilbert space quantum mechanics (QM) is noncontextual. According to Griffiths the problem of contextuality disappears if the apparatus is "designed and operated by a competent experimentalist" and we accept the Single Framework Rule (SFR). We will argue from a representational realist stance that the conclusion is incorrect due to the misleading understanding provided by Griffiths to the meaning of quantum contextuality and its relation to physical reality and measurements. We will discuss how the quite general incomprehension of contextuality has its origin in the "objective-subjective omelette" created by Heisenberg and Bohr. We will argue that in order to unscramble the omelette we need to disentangle, firstly, representational realism from naive realism, secondly, ontology from epistemology, and thirdly, the different interpretational problems of QM. In this respect, we will analyze what should be considered as Meaningful Physical Statements (MPS) within a theory and will argue that Counterfactual Reasoning (CR) -considered by Griffiths as "tricky"- must be accepted as a necessary condition for any representational realist interpretation of QM. Finally we discuss what should be considered as a problem (and what not) in QM from a representational realist perspective.