The pilot wave function and its uses outside of quantum mechanics

Let us recall our discussion on Bohmian mechanics in Chapter 6. The idea of using Bohmian mechanics outside of quantum mechanics is not new anymore. Khrennikov [1] provides for an overview on how this model can contribute in precise terms to areas such as economics and finance.1 Historically, the work by Bohm and Hiley [2] and also Hiley and Pylkkanen [3] brought forward the idea that the pilot wave function could be seen as a wave function containing information. In Khrennikov [4], Choustova [5], and Haven [6], the idea of using pilot wave theory to finance was investigated. Khrennikov [1] (p. 160) remarks that “the force induced by the pilot wave field does not depend on the amplitude of the wave.” He cites the argument made by Bohm and Hiley [2] that because of this property the pilot wave is an information wave.

The various interpretations (with applications) of the wave function will be covered in detail in Chapter 13.

Here are some of the key features which can be of use in an financial/economics setting. When the wave function is not factorized, then a change in the price of a stock i will affect the prices of stocks, j, with j ≠ i. See Khrennikov [1] (p. 161). The Bohmian theory, as we remarked already in Chapters 1 and 6, is non-local.