The problem of contextuality and the impossibility of experimental metaphysics thereof

Abstract

Recently a new impulse has been given to the experimental investigation of contextuality. In this paper we show that for a widely used definition of contextuality there can be no decisive experiment on the existence of contextuality. To this end, we give a clear presentation of the hidden variable models due to Meyer, Kent and Clifton (MKC), which would supposedly nullify the Kochen-Specker Theorem. Although we disagree with this last statement, the models play a significant role in the discussion on the meaning of contextuality. In fact, we introduce a specific MKC-model of which we show that it is non-contextual and completely in agreement with quantum mechanical predictions. We also investigate the possibility of other definitions of non-contextuality -with an emphasis on operational definitionsand argue that any useful definition relies on the specification of a theoretical framework. It is therefore concluded that no experimental test can yield any conclusions about contextuality on a metaphysical level.It is the general consensus that the Kochen-Specker Theorem excludes the existence of non-contextual hidden variable theories. Naturally this leads to the questions of what is really meant by the notion of contextuality, what the implications are for the future of hidden variable theories, and if experimental proof of this statement is possible. Over the past ten years the discussion on these questions has had an enormous boost but, surprisingly, with mutually opposing outcomes results. On the one hand Meyer, Kent, Clifton and Barrett [5], [18], [23], [31] have advocated the view that non-contextual hidden variable models can be constructed that reproduce the quantum mechanical predictions. On the other hand there have been experiments that claim to prove that nature is contextual, in accordance with quantum mechanical predictions [6], [19], [22], [24], [28], [32], [33], [34], [39]. Thus far, no serious attempt has been made to clarify the paradox at hand.

Understanding quantum mechanics: a review and synthesis in precise language

“…-In another approach, systems again have definite values for all magnitudes, but it is possible that some of those values cannot be revealed by measurements. In this case, the Bell-Kochen-Specker theorem does not imply that the results depend on the context [371]. -A third approach suggests that systems may not have definite values for all magnitudes, and so measurement event outcomes might not be determined in advance: a value-indefinite independent reality [372,373].…”

“…Most approaches involve a form of contextuality [376,377]. Contextuality is generally defined relative to one specific approach to quantum mechanics [371]. Broadly, contextuality suggests that the value assigned to a property depends on the measurement process [306].…”

“…Broadly, contextuality suggests that the value assigned to a property depends on the measurement process [306]. Some suggest that experimental proofs of contextuality are possible but any experiment is likely to be based on one specific definition of contextuality [371], and contextuality is usually only sufficient, not necessary, to explain the relevant results [26]. The Bell-Kochen-Specker theorem itself cannot be directly tested experimentally (as any such test depends on how the assumptions are understood physically) [26,326,378], although this view has been challenged [379].…”

“…6.2 causal generally defined relative to a specific theoretical model [555][556, § 3][557, § 4]; causal notions are not necessarily needed to achieve understanding [38]; even where they are invoked, there is no consensus on how causation is to be defined [327][558, § 2] [559] coherence (for waves) the absence of spatial dispersion; (for superposition states) the existence of interference terms [234]; (for entangled states) statistical balance in collective outcomes, among ensembles for measurements of differing observables on multiple subsystems [235, § 2.3]: see Sects. 3.5 and 3.6 completeness feature of a theory with terms which specify all the properties of a system [53] contextuality generally defined relative to one specific approach to quantum mechanics [328, § V.E] [371]; broadly, assignment of values depends on the relevant measurement process [306]; see Sect. 5.7 counterfactual (formal) a subjunctive conditional sentence, whose antecedent is contrary-to-fact [558]; (informal) relating to circumstances being other than as they are [30]; a complex area [327] decoherence absence of coherence; the disappearance of the interference terms in a density matrix representing a superposition state; see Sect.…”

Conway–Kochen and the Finite Precision Loophole

“…Firstly, in the absence of an Aspect-type experiment using spin-one particles, the former so far has no experimental backing. Secondly, through its use of the Kochen-Specker Theorem as a lemma, the Strong Free Will Theorem is potentially vulnerable to the kind of 'finite precision' challenge discussed (most recently) in [3,5,25]. "…”