Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for interactions so that they are empirically traceable, and that observations necessarily go with such an interaction with the observed system. We investigate consequences of this assumption: The unfolding language game, inspired by "quantum logic," leads to a class of contextual and probabilistic theories. Contextuality becomes a means to render interactions, thus also measurements, empirically tangible. The measurement "problem" arises in all such theories, not only quantum mechanics: It is a consequence of the need for empirical evidence of interactions. And a consequence of the converse need for an interaction when obtaining that empirical evidence.
Results of measurements give legitimacy to a physical theory. What if acquiring these results in the first place necessitates what the same theory considers to be an interaction? In this note, we assume that theories account for interactions so that they are empirically traceable, and that observations necessarily go with such an interaction with the observed system. We investigate consequences of this assumption: The unfolding language game, inspired by "quantum logic," leads to a class of contextual and probabilistic theories. Contextuality becomes a means to render interactions, thus also measurements, empirically tangible. The measurement "problem" arises in all such theories, not only quantum mechanics: It is a consequence of the need for empirical evidence of interactions. And a consequence of the converse need for an interaction when obtaining that empirical evidence.
Measurements play a crucial role in doing physics: Their results provide the basis on which we adopt or reject physical theories. In this note, we examine the effect of subjecting measurements themselves to our experience. We require that our contact with the world is empirically warranted. Therefore, we study theories that satisfy the following assumption: Interactions are accounted for so that they are empirically traceable, and observations necessarily go with such an interaction with the observed system. Examining, with regard to these assumptions, an abstract representation of measurements with tools from quantum logic leads us to contextual theories. Contextuality becomes a means to render interactions, thus also measurements, empirically tangible. The measurement becomes problematic---also beyond quantum mechanics---if one tries to commensurate the assumption of tangible interactions with the notion of a spectator theory, i.e., with the idea that measurement results are read off without effect. The problem, thus, presents itself as the collision of different epistemological stances with repercussions beyond quantum mechanics.
The circumstances of measurement have more direct significance in quantum than in classical physics, where they can be neglected for well-performed measurements. In quantum mechanics, the dispositions of the measuring apparatus-plus-environment of the system measured for a property are a non-trivial part of its formalization as the quantum observable. A straightforward formalization of context, via equivalence classes of measurements corresponding to sets of sharp target observables, was recently given for sharp quantum observables. Here, we show that quantum contextuality, the dependence of measurement outcomes on circumstances external to the measured quantum system, can be manifested not only as the strict exclusivity of different measurements of sharp observables or valuations but via quantitative differences in the property statistics across simultaneous measurements of generalized quantum observables, by formalizing quantum context via coexistent generalized observables rather than only its subset of compatible sharp observables. Here, the question of whether such quantum contextuality follows from basic quantum principles is then addressed, and it is shown that the Principle of Indeterminacy is sufficient for at least one form of non-trivial contextuality. Contextuality is thus seen to be a natural feature of quantum mechanics rather than something arising only from the consideration of impossible measurements, abstract philosophical issues, hidden-variables theories, or other alternative, classical models of quantum behavior.
Recent research on quantum contextuality has been strongly centered on device-independent frameworks, such as the many graph approaches to contextuality and the celebrated sheaf-theoretical approach. Contextuality is described in these frameworks as a property of data only, making it possible to characterize and quantify the phenomena regardless of the reasons why it occurs. In this paper we look beyond the data and focus on possible explanations for this experimental fact. We show that a classical system generating contextual data can easily be found if the following conditions are satisfied (1) We only have access to a specific collection of epistemic measurements (which, all things considered, is basically Bohr's view on quantum measurements) and (2) There is a limitation on which of these measurements can be jointly performed. The way we see it, this example indicates that contextuality may be a consequence of the type of measurement taken into account, instead of an intrinsic feature of the system upon which these measurements are performed; if this is correct, the widespread idea that quantum contextuality is a non-classical feature can be avoided.
The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements could not be viewed as deterministically revealing pre-existing properties of the system. More precisely, no model can assign deterministic outcomes to the projectors of a quantum measurement in a way that depends only on the projector and not the context (the full set of projectors) in which it appeared, despite the fact that the Born rule probabilities associated with projectors are independent of the context. A more general, operational definition of contextuality introduced by Spekkens, which we will term 'probabilistic contextuality', drops the assumption of determinism and allows for operations other than measurements to be considered contextual. Even two-dimensional quantum mechanics can be shown to be contextual under this generalised notion. Probabilistic noncontextuality represents the postulate that elements of an operational theory that cannot be distinguished from each other based on the statistics of arbitrarily many repeated experiments (they give rise to the same operational probabilities) are ontologically identical. In this paper, we introduce a framework that enables us to distinguish between different noncontextuality assumptions in terms of the relationships between the ontological representations of objects in the theory given a certain relation between their operational representations. This framework can be used to motivate and define a 'possibilistic' analogue, encapsulating the idea that elements of an operational theory that cannot be unambiguously distinguished operationally can also not be unambiguously distinguished ontologically. We then prove that possibilistic noncontextuality is equivalent to an alternative notion of noncontextuality proposed by Hardy. Finally, we demonstrate that these weaker noncontextuality assumptions are sufficient to prove alternative versions of known 'no-go' theorems that constrain ψ -epistemic models for quantum mechanics.
The context-sensitivity of cognition has been demonstrated across a wide range of cognitive functions such as perception, memory, judgement and decision making. A related term, 'contextuality', has appeared from the field of quantum cognition, with mounting empirical evidence demonstrating that cognitive phenomena are sometimes contextual. Contextuality is a subtle notion that influences how we must view the properties of the cognitive phenomenon being studied. This article addresses the questions: What does it mean for a cognitive phenomenon to be contextual? What are the implications of contextuality for probabilistic models of cognition? How does contextuality differ from context-sensitivity? Starting from George Boole's "conditions of possible experience", we argue that a probabilistic model of a cognitive phenomenon is necessarily subject to an assumption of realism. By this we mean that the phenomenon being studied is assumed to have cognitive properties with a definite value independent of observation. In contrast, quantum cognition holds that a cognitive property maybe indeterminate, i.e., its properties do not have well established values prior to observation. We argue that indeterminacy is sufficient for incompatibility between cognitive properties. In turn, incompatibility is necessary for their contextuality. The significance of this argument for cognitive psychology is the following:if a cognitive phenomenon is found to be contextual, then there is reason to believe it may be indeterminate. We illustrate by means of two crowdsourced experiments how context-sensitivity and contextuality of cognitive properties in the form of facial trait judgements can be characterized from empirical data. Finally, we conceptually and formally contrast contextuality with context-sensitivity. We propose that both involve a form of context dependence, with causality being the differentiating factor: the context dependence in context-sensitivity has a causal basis, whereas the context dependence in contextuality is acausal. The resulting implications for probabilistic models of cognition are discussed.