Quantum-Classical Correspondence in the Brain: Scaling, Action Distances and Predictability behind Neural Signals

Gustav Bernroider¹* and Sisir Roy^2,3

¹Department Organismic Biology, Neuroethology, University of Salzburg, 5020 Salzburg, Austria
²School of Computational Science, George Mason University, Fairfax, VA 22030, U.S.A.
³Indian Statistical Institute, Kolkata, India
*E-mail address: Gustav.Bernroider@sbg.ac.at

(Received February 1, 2004; Accepted March 16, 2004)

Keywords: Action Orders, Action Distance, Quantum-Neurodynamics, Ion Channels, Neural Coding

Abstract. Quantum models of higher level brain functions such as conscious experience, suggest that the neural correlate of mentation requires dynamical properties instantiated at the Planck-scale. Several candidate quantum processes have been suggested, but it remains to be seen how these quantum properties can relate to the established classical signals in the brain involving physical action twenty magnitudes above the quantum domain. In this paper we show the results of a systematic analysis of Lagrangian action order to brain processes at different scales of resolution. The results encompass processes at the macroscopic single cell level to processes at the sub-molecular and concerted molecular population level. It is shown that the state of ions in the permeation filter of channel proteins, as for example indicated by the MacKinnon KcsA K⁺ channel model, is a quantum phenomenon involving a Lagrangian in the order of 10^-34 Js. Further, we show that the brain spans at least 20 orders of magnitudes of physical action with physiologically significant signal properties. We suggest that the quantum-classical correspondence in the brain is resolved by the spread of quantum-witness states that correlate with the gating states of voltage sensitive ion channels.