The 3-fold Way and Consciousness Studies
K. Korotkov, A. Levichev
Contents
Part I. Biological fields and Quantum Mechanical representations
I.1. Conventional Quantum Mechanical representations.
I.2. Chronometric development of QM and the DLF-perspective.
I.3. Fields of biological subjects.
Part II. Penrose-Hameroff approach to quantum mechanics as the
foundation for a theory of consciousness
II.1. Discussion of some quantum-mechanical topics involved
II.2. Quantum coherence, quantum computation, and where to seek the
physical basis of mind
II.3. The Penrose-Hameroff Orchestrated Objective Reduction model
II.4. DLF-approach implanted into Penrose-Hameroff model
Part III. Segal’s Chronometry and its LF-development
III.1. Segal’s Chronometric Theory: a brief overview.
III.2. Space-times L, F are on equal footing with D; the list is now
complete
III.3. Can the New Science be based on the DLF-triad?
Part IV. Emergence of New Science and the GDV Bioelectrography
IV.1. The three worlds have been known to humanity since ancient
times
IV.2. Is Direct Vision an example of L-phenomenon?
I.1. Conventional Quantum Mechanical representations.
Accordingly to quantum mechanics, each object is described by its state, or wave function. We prefer to use “state”, since (initially, at least) it is neither numerical-, nor vector-valued. Rather, it is a section of an induced vector bundle over spacetime.
It can be converted into a function (with values in a prescribed “spin space”) but one needs to go through the “parallelization” procedure (see our III.2, III.3 for more details). When dealing with an elementary particle, the respective Hilbert space is determined (as part of the induction procedure, see below). It has become an acknowledged way of modern theoretical physics to describe elementary particles and their interactions in terms of induced representations of the (respective) symmetry group. To say a little bit more, “the main philosophical point of these developments is perhaps the importance of induced representations, not purely as representations, but as actions on the homogeneous vector bundles that naturally emerge from the induction process. This additional structure provides a spatiotemporal labelling of the vectors (or states, KL) in the group representation space that is absolutely essential for the formation of local nonlinear interactions, and relatedly, for causality considerations. Although a few decades ago, practical physics resisted and abominated the “Gruppenpest”, in recent times it has surrendered…”
([Se-86, p.133]).
Conventional Quantum Mechanics uses representations of the Poincare group which are induced from its Lorentz subgroup as in Wigner’s seminal work, [Wi-39] .
The underlying space-time is the Minkowski world M (the one of Special
Relativity).
Let us refer to the entire construction (which we do not specify more) as to a representation; each (microscopic or macroscopic) object is described by a certain representation. Let us now turn to chronometric representations.
I.2. Chronometric development of Quantum Mechanics and the
DLF-perspective.
The reader is referred to III.1 to learn more details on Segal’s Chronometry. In this paragraph, we only indicate some of the features which distinguish the “chronometric quantum mechanics” (or the “D-generalization” of QM) from the conventional theory.
The underlying space-time D is “larger” here: the Minkowski world M can be canonically embedded into D. The latter might be viewed as a modified version of the Einstein static universe, if to use terminology from the General Relativity Theory.