# Contextual Approach to Quantum Formalism

Part of the Fundamental Theories of Physics book series (FTPH, volume 160)

Part of the Fundamental Theories of Physics book series (FTPH, volume 160)

The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems: the impossibility to establish a finer description of micro-phenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bell’s theorem (including quantum non-locality). Also, possible applications of the contextual probabilistic model and its quantum-like representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed.

Bell's Inequality Contextual Probabilistic Model Contextual Probability Foundation of Physics Interference of Probabilities Observable Probability distribution Probability space Quantum Formalism Quantum Physics Quantum Probability quantum mechanics statistical model

- DOI https://doi.org/10.1007/978-1-4020-9593-1
- Copyright Information Springer Netherlands 2009
- Publisher Name Springer, Dordrecht
- eBook Packages Physics and Astronomy
- Print ISBN 978-1-4020-9592-4
- Online ISBN 978-1-4020-9593-1
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