Incompatible Variables and “Quantal” Phenomena in Psychology

Mindfulness-based cognitive therapy (MBCT) is an area of modern psychology that provides a successful method for preventing the recurrence of depression. The standard theory of MBCT may be interpreted in terms of a simple theoretical model that employs incompatible variables as its fundamental observable quantities. Although the MBCT theory is not related to or derived from quantum theory, the existence of incompatible variables results in “quantal” phenomena, such as interference and the uncertainty principle, which have been widely believed to occur only as a consequence of the laws of quantum mechanics. The predictions of the model are subject to experimental testing and at present the model agrees with all published clinical data. To our knowledge, this work is the first quantitative theoretical treatment of a natural non-quantal system possessing incompatible variables. It confirms the intuition of Bohr and Heisenberg that incompatible variables may exist in human psychology.

Quantal phase factors accompanying adiabatic changes

A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar dynamical phase factor. An explicit general formula for γ(C) is derived in terms of the spectrum and eigenstates of Ĥ(R) over a surface spanning C. If C lies near a degeneracy of Ĥ, γ(C) takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy. As an illustration γ(C) is calculated for spinning particles in slowly-changing magnetic fields; although the sign reversal of spinors on rotation is a special case, the effect is predicted to occur for bosons as well as fermions, and a method for observing it is proposed. It is shown that the Aharonov-Bohm effect can be interpreted as a geometrical phase factor.