JNLRMI Vol. II Nr. 1 February 2003

Macrotemporal quantum coherence, quantum
spin glass degeneracy and number theoretic
information concept

Matti Pitkanen 

 Department of Physical Sciences, High Energy Physics Division,
PL 64, FIN-00014, University of Helsinki, Finland.
E-mail: matpitka@rock.helsinki.fi
http://www.physics.helsinki.fi/~matpitka
Recent address: Kadermonkatu 16, 10900, Hanko, Finland

Full article:  www.emergentmind.org/PDF_files.htm/qcohe12.PDF

 Appendix: Two-dimensional illustrations related to the many-sheeted space-time concept
URL: www.emergentmind.org/PitkanenII(1)c.htm

Contents

Abstract:  The basic objection against quantum consciousness theories is that decoherence times for macroscopic quantum states are quite too short. This argument has been put in quantitative form by Max Tegmark [1]. These counter arguments are however problematic. First of all, the notions of quantum coherence and decoherence are problematic in standard physics framework since the non-determinism of the state function reduction is in conflict with the determinism of Schrodinger equation. The intuitive idea is however that one can estimate the decoherence times as essentially lifetimes of quantum states. Secondly, the estimates for decoherence times are based on standard physics, and it is quite possible that new physics is essential for understanding living matter.

Topological Geometrodynamics (TGD) inspired theory of consciousness leads to a first principle theory of state function reduction free of the logical paradoxes, allows precise definitions for the notions of quantum coherence and decoherence, and predicts a mechanism making the lifetimes of macroscopic bound states much longer than predicted by the standard physics. The basic distinction between TGD and standard physics is quantum spin glass degeneracy, which among other things implies that quantum bound states of, say, two molecules have enormous spin glass degeneracy absent in the free state. This in turn means that the system spends much longer time in bound states than in free states and this implies much longer decoherence time than expected otherwise. The almost degenerate spin glass states differ only by their classical gravitational energy so that gravitation is indeed important. 

In the p-adic context one must modify Shannon's definition of entropy by replacing the ordinary logarithm based on p-adic norm. This definition gives rise to a real valued entropy in both real and p-adic contexts if entanglement coefficients are algebraic numbers. For non-algebraic entanglement standard Shannon formula and its p-adic variant must be used and gives rise to non-negative entropy. Unlike Shannon entropy, the p-adic entropies (one for each p) can be also negative so that the entanglement entropy defines a genuine information measure whose sign tells whether the system contains information or dis-information. For the p-adic entropies Negentropy Maximization Principle tends to preserve the quantum coherence. Thus the states with algebraic entanglement can be regarded as bound states, which are not at all fragile like the states with non-algebraic entanglement are. This leads to a purely number-theoretic characterization of life: life corresponds to islands of algebraic numbers in the seas of real and p-adic continua. A more restrictive definition would be based on rational entanglement and even rational entanglement probabilities. The new views about quantum coherence and information have testable implications at the level of fundamental physics, quantum computation, biology, and consciousness.

Keywords: macroscopic quantum coherence, decoherence, spin glass, p-adic numbers, number theoretic entropy, quantum computation.