Titlebook: Contextual Approach to Quantum Formalism; Andrei Khrennikov Book 2009 Springer Science+Business Media B.V. 2009 Bell‘s Inequality.Contextu

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https://doi.org/10.1007/978-3-031-61044-8The interference of probabilities (and consequently the representation of them by complex probability amplitudes and Born’s rule) can be obtained even in the Kolmogorov measure-theoretic (but contextual!) approach, i.e., by representing contexts by some elements of the Kolmogorov’s .-algebra.

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Vietnamese Higher Education at a CrossroadsIn this chapter we show that quantum probabilistic description can naturally appear in classical statistical mechanics for disordered systems.

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Arne Ernst,Dietmar Basta,Klaus JahnThe Schrödinger equation plays the fundamental role in quantum theory. Therefore it would be interesting to investigate the possibility to derive this equation in the contextual framework. We show that it is really possible to obtain the Schrödinger equation by starting with classical stochastic dynamics.

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Quantum Mechanics: Postulates and InterpretationsWe start this chapter with a brief presentation of the quantum formalism and discussion on the two main interpretations of quantum mechanics: Copenhagen Interpretation and Ensemble Interpretation.

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Contextual Probability and InterferenceIn this chapter we present our basic model—contextual probabilistic model—providing a general description of probabilistic data (classical as well as quantum).

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Quantum-Like Representation of Contextual Probabilistic ModelBy starting with the formula of total probability with an interference term, we obtain Born’s rule and representation of the observables by (noncommutative) self-adjoint operators. Thus the quantum probabilistic formalism can be derived from the contextual probabilistic model.

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Ensemble Representation of Contextual Statistical ModelIn this chapter we consider the representation of contexts (e.g., physical) by ensembles of systems.

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Interference of Probabilities from Law of Large NumbersIn previous chapters we derived the interference of probabilities in frequency (von Mises) and measure-theoretic (Kolmogorov) frameworks. In this chapter we would like to combine previous considerations and derive interference by using the . in the Kolmogorov model.