Roots and (Re)sources of Value (In)definiteness Versus Contextuality

Svozil, Karl

doi:10.1007/978-3-030-34316-3_24

Cited by 6 publications

(4 citation statements)

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“…They are also critical to appealing to JMC, and not only because it is based on counterfactuals (cf. [ 151 , 152 , 153 ]). Here is a good place to recall that Svozil [ 154 , 155 ] and Griffiths [ 63 , 156 , 157 , 158 ] have a different viewpoint, and they suggested experimental tests for JMC.…”

Section: Discussionmentioning

confidence: 99%

Contextuality, Complementarity, Signaling, and Bell Tests

Khrennikov

2022

Entropy

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This is a review devoted to the complementarity–contextuality interplay with connection to the Bell inequalities. Starting the discussion with complementarity, I point to contextuality as its seed. Bohr contextuality is the dependence of an observable’s outcome on the experimental context; on the system–apparatus interaction. Probabilistically, complementarity means that the joint probability distribution (JPD) does not exist. Instead of the JPD, one has to operate with contextual probabilities. The Bell inequalities are interpreted as the statistical tests of contextuality, and hence, incompatibility. For context-dependent probabilities, these inequalities may be violated. I stress that contextuality tested by the Bell inequalities is the so-called joint measurement contextuality (JMC), the special case of Bohr’s contextuality. Then, I examine the role of signaling (marginal inconsistency). In QM, signaling can be considered as an experimental artifact. However, often, experimental data have signaling patterns. I discuss possible sources of signaling—for example, dependence of the state preparation on measurement settings. In principle, one can extract the measure of “pure contextuality” from data shadowed by signaling. This theory is known as contextuality by default (CbD). It leads to inequalities with an additional term quantifying signaling: Bell–Dzhafarov–Kujala inequalities.

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Section: Discussionmentioning

confidence: 99%

Contextuality, Complementarity, Signaling, and Bell Tests

Khrennikov

2022

Entropy

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“…And this paper is not directed to such foundational issues. We mention just the nonlocal interpretation [ 1 , 2 , 3 , 4 , 9 ] (and one must differ Einsteinian and Bell nonlocalities [ 90 , 91 , 92 , 93 ]), the contextual interpretation [ 2 , 8 , 11 , 94 , 95 , 96 , 97 , 98 , 99 , 100 , 101 , 102 , 103 , 104 , 105 , 106 , 107 , 108 , 109 , 110 , 111 , 112 , 113 , 114 ], and the observables incompatibility interpretation [ 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 115 , 116 ].…”

Section: Interpretations For the Violation Of The Bell Inequalitiesmentioning

confidence: 99%

On Applicability of Quantum Formalism to Model Decision Making: Can Cognitive Signaling Be Compatible with Quantum Theory?

Khrennikov

2022

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This note is devoted to the problem of signaling (marginal inconsistency) in the Bell-type experiments with physical and cognitive systems. It seems that in quantum physics, this problem is still not taken seriously. Only recently have experimenters started to check the signaling hypothesis for their data. For cognitive systems, signaling was statistically significant in all experiments (typically for decision making) performed up to today. Here, one cannot simply ignore this problem. Since signaling contradicts the quantum theory of measurement for compatible observables, its statistical significance in experiments with humans can be considered as an objection for quantum-like modeling—applications of quantum theory to cognition, decision making, psychology, economics and finance, social and political science. In this paper, we point to two possible sources of signaling generation that are consistent with quantum measurement theory. Thus, the signaling objection for quantum-like modeling is not catastrophic. One of these sources is the direct physical signaling about selection of experimental settings, questions or tasks in quantum-like studies. Another possible source is a state modification dependent on experimental settings. The latter was a rather common source of signaling in quantum physics. Since the physical size of the brain is very small comparing with the light velocity, it seems to be impossible to prevent the direct physical signaling (with electromagnetic waves) between the brain’s areas processing two questions a and b. However, if, for these questions, not the electromagnetic waves, but electrochemical communication plays the crucial role, the experimenter may hope to make signaling weaker by answering the questions faster. The problem of question-dependent mental state modification seems to be solvable via smarter experimental design. This paper can be useful both for physicists interested in quantum foundations and for researchers working in quantum-like studies, e.g., applying the quantum theory to model decision making or psychological effects. This paper is solely about quantum theory. Thus, we do not consider general contextual probabilistic models.

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“…However, these views come at a price: value indefiniteness. (Value indefiniteness is often expressed as contextuality, but this view is distractive, as it suggests some existing entity which is changing its value; depending on how—that is, along which context—it is measured [ 259 ].) It might also come as no surprise that by artificially forcing classical relations build on subset relations on Hilbert space entities yields indeterminacies: the standard relation and set theoretical operations on subsets may simply not an adequate framework to investigate vector-worlds.…”

Section: Epistemologic Deceptionsmentioning

confidence: 99%