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

Abstract

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 certain 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 observable A when measured together with B or together with C will necessarily differ in case [A, B] = [A, C] = 0, and [B, C] = 0. 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.

The Logos Categorical Approach to Quantum Mechanics: I. Kochen-Specker Contextuality and Global Intensive Valuations

“…One of us has argued elsewhere [17] that there exist two different notions of quantum contextuality addressed -and often confused-within the foundational literature. This distinction of contextuality will be useful for the purposes of the present article.…”

The Logos Categorical Approach to Quantum Mechanics: II. Quantum Superpositions and Intensive Values

“…In order to be even more clear regarding our explanation, and before concluding, let us recall from [19] the following two very helpful definitions:…”

Epistemological vs. Ontological Relationalism in Quantum Mechanics: Relativism or Realism?

“…Also modal differences don't amount to separations, only to the different modifications inside the one and only substance: "As regards the parts in Nature, we maintain that division, as has also been said before, never takes place in substance, but always and only in the mode of substance" [Short Treatise I, chap. II, [19][20][21][22].…”

“…However, in the case of epistemic relations it becomes meaningless to seek for such joint probability distribution. In such case, relations are intrinsically determined -following Bohr's notion of contextuality [19]-by the choice performed by a subject of the particular experimental set-up with which the object is studied. The problem is that due to the structure of the quantum formalism different choices of contexts determine incompatible local valuations which -according to the Kochen-Specker theoremcannot be embedded into a whole global valuation [19].…”

“…In such case, relations are intrinsically determined -following Bohr's notion of contextuality [19]-by the choice performed by a subject of the particular experimental set-up with which the object is studied. The problem is that due to the structure of the quantum formalism different choices of contexts determine incompatible local valuations which -according to the Kochen-Specker theoremcannot be embedded into a whole global valuation [19]. For example, if we consider a composite system ω = αβγ in a pure state and we take the two subsystems αβ and αγ, these two subsystems have properties which are realized with respect to different relative systems.…”