Linnaeus University, Växjö, SE
Bohmian model outside of physics
Following Bohm-Hiley-Pylkkänen, we apply the mathematical formalism of Bohmian mechanics to model cognition. The process of thinking is mathematically represented as classical dynamics combined with the pilot wave. The latter has the purely information meaning, the active information field. This model is nonlocal, but this is just formal. It can be created by the classical signals (e.g., electromagnetic field) in the brain at the scale which is finer then the scale of conscious processing of information. This viewpoint has the important philosophic consequence: here Bohmian mechanics is not an ontic model, but the epistemic model about the knowledge which consciousness can extract from physical world and unconsciousness. For cognition, the configuration space has the tree like structure generated by the neuronal trees in the brain. Therefore it may be useful to work with Bohmian-like models based on treelike configuration spaces. An important class of such spaces is based on the fields of p-adic numbers. Then we apply this model to finance. Here the financial market can be modeled as a nonlocal information system which parts are coupled via the quantum potential. We apply the equations of Bohmian mechanics (including stochastic generalizations) to model dynamics of the prices of shares.
References:  A. Khrennikov, Classical and quantum mechanics on p-adic trees of ideas. BioSystems, 56, 95-120 (2000).  A. Khrennikov, Information dynamics in cognitive, psychological, social, and anomalous phenomena. Ser.: Fundamental Theories of Physics, Kluwer, Dordrecht, 2004.