Unscrambling the Omelette of Quantum Contextuality (Part I): Preexistent Properties or Measurement Outcomes?

摘要

In this paper we attempt to analyze the physical and philosophical meaning of quantum contextuality. We will argue that there exists a general confusion within the foundational literature arising from the improper “scrambling” of two different meanings of quantum contextuality. While the first one, introduced by Bohr, is related to an epistemic interpretation of contextuality which stresses the incompatibility (or complementarity) of measurement situations described in classical terms; the second meaning of contextuality is related to a purely formal understanding of contextuality as exposed by the Kochen–Specker (KS) theorem which focuses instead on the constraints of the orthodox quantum formalism in order to interpret projection operators as preexistent or actual (definite valued) properties. We will show how these two notions have been scrambled together creating an “omelette of contextuality” which has been fully widespread through a popularized “epistemic explanation” of the KS theorem according to which: The measurement outcome of the observableAwhen measured together withBor together withCwill necessarily differ in case[A,B]=[A,C]=0documentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$[A, B] = [A, C] = 0$$end{document}, and[B,C]≠0documentclass[12pt]{minimal}usepackage{amsmath}usepackage{wasysym}usepackage{amsfonts}usepackage{amssymb}usepackage{amsbsy}usepackage{mathrsfs}usepackage{upgreek}setlength{oddsidemargin}{-69pt}egin{document}$$[B, C] e 0$$end{document}. We will show why this statement is not only improperly scrambling epistemic and formal perspectives, but is also physically and philosophically meaningless. Finally, we analyze the consequences of such widespread epistemic reading of KS theorem as related to statistical statements of measurement outcomes.