Contextual Approach to Quantum Formalism

Violation of contextual generalization of the Leggett–Garg inequality for recognition of ambiguous figures

“…However, recently contextuality was also represented with the aid of Bell type inequalities, e.g., [27]. These recent theoretical and experimental results on the Bell type expression of contextuality match well with the contextual approach to the problem of violation of Bell's inequalities developed by one of the authors of this paper [9], [28]- [30], see also [31]- [39]. Originally Bell mixed in one cocktail nonlocality and realism.…”

“…Here, we express the LG's assumptions in terms of context-dependent probabilities [9]. We remark that in general context-dependent probabilities cannot be represented in common Kolmogorov probability space.…”

“…We shall come back to this discussion and extend it to the problem of inter-relation of mental contextuality and mental realism in sections 2.1, 7. (We also remark that T. Nieuwenhuizen invented the terminology Contextuality Loophole summarizing outputs of studies [31], [9], [28]- [30], [32]- [36]. ) We point out that contextual dependent systems (in physics, biology, economics, finances, and social science) and non-Kolmogorov probability theory can be described mathematically [19], [8] by the adaptive dynamics and the operation of lifting (the latter is widely used in quantum information theory [40]).…”

“…We interpret the LG inequality as a kind of contextual probabilistic inequality in which one combines data collected in experiments performed for three different contexts, cf. [9], [6], [10], [15], [8]. In the original version of the inequality these contexts have the temporal nature and they are given by three pairs of instances of time, (t1, t2), (t2, t3), (t3, t4), where t1 < t2 < t3.…”

Event‐by‐event simulation of quantum phenomena

“…The fact that the event-based model reproduces, for instance, the correlations of the singlet state without violating Einstein's local causality criterion suggests that the data {x n,1 , x n,2 } generated by the event-based model cannot be represented by a single Kolmogorov probability space. This complies with the idea that contextual, non-Kolmogorov models can lead to violations of Bell's inequality without appealing to nonlocality or nonobjectivism [73,74].…”