Chronometry-Based Approach to Consciousness
Alex Levichev, levit@math.bu.edu
The goal of this message is to indicate new possibilities to model consciousness. They arise due to the Chronometric Theory which has been developed by Irving Segal (MIT, he passed away in 1998).
In my survey article "On mathematical foundations and physical applications of chronometry" (see Semigroups in Algebra, Geometry and Analysis, Eds.: Hofmann/Lawson/Vinberg; Walter de Gruyter & Co., 1995, pp.77-103) I was justifying the claim that "Segal's chronometric theory is the crowning accomplishment of special relativity". The above publication is later referred to as [Le-95]. Its URL is http: //math.bu.edu/people/levit
Being recently enrolled into a "Science, Philosophy, and Religion" graduate program at the Boston University Division of Religious and Theological Studies, I have suggested a few possibilities to apply chronometry-based field theory to the study of Consciousness.
Accordingly to quantum mechanics each object is described by its wave function. In general, the latter is neither numerical- nor vector-valued. Rather, it is a section of an induced vector bundle. The respective Hilbert space is thus determined (essentially, uniquely) since the very notion of an induced bundle pre-supposes the action of the symmetry group. The entire construction will be below referred to as a representation; each object is described by a certain representation. It is an aknowledged way of modern theoretical physics to describe elementary particles and their interactions in terms of induced representations. Here I only mention about three distinctions between conventional quantum mechanics (QM) and its chronometric counterpart CQM: 1) the "underlying" spacetime (the Minkowski world M) of QM can be canonically embedded into Einsteinian E of CQM; 2) the symmetry group of M is a subgroup of that of E; 3) chronometric energy of an object is always greater than (or equal to) its conventional energy.
The characteristic feature of a typical chronometric representation is its indecomposability. As a consequence, one has to distinguish (see [Le-95, Sect. 6.1]) between an exact particle which is represented by a section (= state) of a respective induced bundle, and a reduced particle, a theoretical entity obtained by formation of quotient representations. The latter correspond to conventional representations. The "consciousness of a photon", say, can be described by its state in the upper level, whereas its "physical arena" is the space of the factor-representation. Another possibility is presence of unstable components on the upper level. They disappear after formation of the quotient representation. Such a feature might explain precognition more naturally than it is done under a conventional approach to the notion of a particle. (Unstable, or tachionic representations, are mathematically quite common; there is no bound on possible speeds; such a property on that "higher level" does not directly contradict to the causality in special and general relativity).
The "superluminal" approach to describe consciousness has been already suggested by R.Dutheil in "L'Homme supra-lumineux", ed.Sand, 1990 (in French). A less radical suggestion is to preserve causality on each level but bounds on possible speeds on higher levels might be larger than the speed of light.