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11 - Contextual Structuring of Classical and Quantum Physics
from Part III - Contextuality: Mathematical Modeling and Interpretation
Andrei Khrennikov, Linnaeus University
Book:

Contextual Reinterpretation of Quantum Nonlocality

Published online:

28 November 2024

Print publication:

05 December 2024, pp 127-139
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Summary

In this chapter the contextual measurement model (CMM) is employed forprobabilistic structuring of classical and quantum physics. We start with CMM framing of classical probability theory (Kolmogorov 1933) servingas the basis of classical statistical physics and thermodynamics. Then weconsider the von Neumann quantum measurement theory with observablesgiven by Hermitian operators and the state update of the projective typeand represent it as CMM. The quantum instrument theory is a generalizationof the von Neumann theory permitting state updates of the non-projectivetype and it also can be represented as CMM. We also show connectionof the generalized probability theory with the space of probability measureswith CMM. Finally, linear space representation for contextual probabilityspace is constructed by using the construction going back to Mackey.