Representation of the contextual statistical model by hyperbolic amplitudes

Abstract

We continue the development of a so called contextual statistical model (here context has the meaning of a complex of physical conditions). It is shown that, besides contexts producing the conventional trigonometric $\cos$-interference, there exist contexts producing the hyperbolic $\cos$-interference. Starting with the corresponding interference formula of total probability we represent such contexts by hyperbolic probabilistic amplitudes or in the abstract formalism by normalized vectors of a hyperbolic analogue of the Hilbert space. There is obtained a hyperbolic Born's rule. Incompatible observables are represented by noncommutative operators.

We discuss possible applications of hyperbolic quantum mechnaics (in particular, in string theory and cosmology as well as cognitive sciences); there is also given a general scheme of experimental verification of hyperbolic quantum mechanics through statistical verification of hyperbolic interference

Cited by in corpus (5)

• Bicomplex Quantum Mechanics: II. The Hilbert Space
• On consistency of the quantum-like representation algorithm
• Quantum fractals on n-spheres. Clifford Algebra approach
• On hyperbolic interferences in the quantum--like representation algorithm for the case of triple-valued observables
• On the consistency of the quantum-like representation algorithm for hyperbolic interference