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Contextual Approach to Quantum Formalism

Part of the Fundamental Theories of Physics Book Series (volume 160)

DOI: 10.1007/978-1-4020-9593-1

ISBN: 978-1-4020-9592-4

Publisher: Springer Netherlands - Springer Journals

Jan 1, 2009

1 - 10 of 16 Chapters

LitStream

Quantum Mechanics: Postulates and Interpretations

Khrennikov, Andrei

Pages: 3 –26

[We 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.]
LitStream

Classical Probability Theories

Khrennikov, Andrei

Pages: 27 –43

[In this chapter we present a brief introductions to Kolmogorov’s measure-theoretic and von Mises’ frequency probability theories. These are classical probability theories. A rather common opinion is that classical probability can not describe the probabilistic structure of quantum mechanics....
LitStream

Contextual Probability and Interference

Khrennikov, Andrei

Pages: 47 –79

[In this chapter we present our basic model—contextual probabilistic model—providing a general description of probabilistic data (classical as well as quantum).]
LitStream

Quantum-Like Representation of Contextual Probabilistic Model

Khrennikov, Andrei

Pages: 81 –114

[By 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.]
LitStream

Ensemble Representation of Contextual Statistical Model

Khrennikov, Andrei

Pages: 115 –130

[In this chapter we consider the representation of contexts (e.g., physical) by ensembles of systems.]
LitStream

Latent Quantum-Like Structure in the Kolmogorov Model

Khrennikov, Andrei

Pages: 131 –158

[The 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 σ-algebra.]
LitStream

Interference of Probabilities from Law of Large Numbers

Khrennikov, Andrei

Pages: 159 –167

[In 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 law of large numbers in the Kolmogorov model.]
LitStream

Probabilistic Analysis of Bell’s Argument

Khrennikov, Andrei

Pages: 171 –191

[Bell’s inequality really beats all records on publications, citations, discussions and controversies. As an organizer of a few international conferences on foundations of quantum theory I was really disappointed by stormy debates on Bell’s inequality. I could not find any problem in quantum...
LitStream

Bell’s Inequality for Conditional Probabilities

Khrennikov, Andrei

Pages: 193 –203

[In Bell’s “classical probability model” there is no any definition of conditional probabilities. The only thing which is evident from Bell’s works is that conditional probability in his model cannot be defined by Bayes’ formula. We show this in this chapter. To prove this, we use the approach...
LitStream

Frequency Probabilistic Analysis of Bell-Type Considerations

Khrennikov, Andrei

Pages: 205 –222

[As we have seen in two previous chapters, the derivation of Bell’s inequality (and its generalizations) is based on a number of assumptions on probability distributions. However, such assumptions are always formulated in the standard measure-theoretical framework. In this chapter we perform the...

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