Contextual viewpoint to quantum stochastics

Details Contextual viewpoint to quantum stochastics Contextual viewpoint to quantum stochastics

2001-12-10

arxiv.org/abs/hep-th/0112076v1

J.Math.Phys. 44 (2003) 2471-2478

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1063/1.1570952

We study the role of context, complex of physical conditions, in quantum as well as classical experiments. It is shown that by taking into account contextual dependence of experimental probabilities we can derive the quantum rule for the addition of probabilities of alternatives. Thus we obtain quantum interference without applying to wave or Hilbert space approach. The Hilbert space representation of contextual probabilities is obtained as a consequence of the elementary geometric fact: $\cos$-theorem. By using another fact from elementary algebra we obtain complex-amplitude representation of probabilities. Finally, we found contextual origin of noncommutativity of incompatible observables.

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