A QUANTUM MECHANICAL MODEL OF EVOLUTION AND CONSCIOUSNESS

                    P. J. Marcer, BSc, DPhil, FBCS.

ABSTRACT

Quantum mechanics is chosen as the starting point to define a science
of Evolution and consciousness, because it is now science's most
established accurate, tried and tested theory and because the
transactional interpretation is explicitly non-local and thereby
consistent with recent tests of Bell's inequality, yet it is
relativistically invariant, fully causal and allows a long sought
after visualization of quantum phenomena denied not by the abstract
quantum mechanical formalism but by the Copenhagen interpretation.

This visualization in the format of a 3 dimensional movie defined
through the emission/absorption model of quantum holography then not
only provides a mathematical specified, physical realizable and
potentially experimentally validatable model of Evolution as a process
of phase conjugate adaptive resonance, but as a fundamental physical
model of image and signal processing applicable to the brain/mind as a
non-classical machine phase conjugately mirroring that Evolution, it
generates the stream of conscious perception and cognition we all
experience.  And thus in the context of the brain/mind - itself a
product of that Evolution - the brain is enabled through the processes
of quantum holography to transduce representations of knowledge as
suggested by the Copenhagen interpretation within the mind, so that
neural events and processes give rise to mental events and processes.
The converse process is thought where mental events and processes give
rise to neural events and processes.  This particular emergent ability
of the mind to learn to control the brain through phase conjugate
adaptive resonance characterizes human behaviour and defines
consciousness as we experience it.

And thus the model of quantum mechanics described maps on to reality
as we consciously experience it as indeed it must if we are to survive
in an evolving Universe.


INTRODUCTION

The basis of the model of Evolution to be considered is quantum
holographic phase conjugate adaptive resonance. (1)

It concerns an emitter/absorber model of quantum holography defined by
means of harmonic analysis on the Heisenberg nilpotent Lie group G,
algebra g and nilmanifold (2).  That is G represents the non
commutative group of symmetries to analyze and synthesize in terms of
the unitary dual of G, the convolution structure of the wavelets
generated from the mother wavelet for the case of phase coherence
under Fourier transform action F.

Thus the case of the three dimensional Heisenberg group representation

          1    x    z
  Matrix  0    1    y    :    =    (x,y,z)
          0    0    1

group parameters x,y,z, models the conditions appropriate to
macroscopic quantum field theory for the phase coherence/
synchronization necessary for the holography where G implements in an
appropriate gauge the symmetries of phase conjugate based adaptive
resonance at the quantum level appropriate to any geometric scale.
(1,2)  Furthermore, when holography is performed by excitation of
stationary modes inside a wave-propagating medium with reflecting
boundaries, phase conjugation occurs spontaneously and both virtual
and real images of recorded information are elicited by wave
diffraction3, and so the model proposed is one of adaptive self-
organization appropriate to all geometric scales when x,y,z are given
their usual meaning.

This emitter/absorber model is therefore a holomovement such that each
phase conjugate resonant emission or process of holographic decoding
is a frame of a 3+1 dimensional space-time movie where there is
adaptive change from frame to frame.  This change is a consequence of
the absorption or process of holographic encoding of each frame into a
stationary quantum interference pattern and the subsequent emission
see figure I.

Thus this provides not only a mathematically specified, physically
realizable model of Evolution4 where there is an arrow of time, but as
a fundamental physical model of image and signal processing applied to
the brain/mind phase conjugately mirroring that Evolution, such
adaptive resonance generates the stream of conscious perception and
cognition such as we all experience (see the companion paper -
"Getting Quantum Theory Off The Rocks").  That is, the properties of
the model and therefore of both Evolution and the brain/mind's
perception of it, exhibit

a)   an arrow of time,
b)   correspond to a present advancing in the
     direction of that arrow,
c)   a fixed unalterable past,
d)   a present filled with three dimensional objects
     where the relativistic invariance of the model
     says that space-time is the universal property of
     those objects in relative motion to one another.
     Furthermore since the Lie derivative LX concerns
     the vectorfield

 X =(X1(x,y,z,t),X2(x,y,z,t),X3(x,y,z,t),X4(x,y,z,t) )

     the invariant pathcurves specifying the motion of
     objects are those of the associated Lie
     transformation group and may be found by solving
     the Pfaffian system

          dx/X1   =    dy/X2   =    dz/X3   =    dX4

       ie they are the straight lines in space-time or
     geodesics of general relativity.5  That is, this
     model resolves the dichotomy between quantum
     mechanics and general relativity for macroscopic
     objects in relative motion in a Universe as a
     quantum coherent whole.  Thus it can be
     postulated that gravitational object images
     concern the inertial properties of objects in
     motion as the result of adaptive change from
     frame to framein the same way acoustic or
     electromagnetic object images concernthe acoustic
     or electromagnetic properties of objects respectively,
     and Mach's postulate of inertial non-locality that
     the mass or inertia of any object is a consequence of
     the mass or inertia of all other masses is simply a
     consequence of quantum non-locality as it applies to
     the gravitational field and would constitute quantum
     gravity,

e)   (Exhibit) perception and cognition where the images the
     brain/mind creates are coincident ie phase conjugate with
     the objects themselves outside the brain/mind so that the
     sensory information the brain/mind encodes incrementally
     can be inferred to contain geometric information about the
     objects perceived including their morphology in the three
     dimensional Cartesian theatre they define.

This model shows that the formalism of quantum mechanics need not lead
to models of the physical world at variance with that world as
consciously perceived so putting reality on the rocks.  It has the
advantage of allowing the brain/mind to use non-local quantum
interference to achieve the massive parallelism it requires without
the use of co-ordinating signals between geometrically separated
active brain segments, and to affect a change of mind by
instantaneously shutting down such activity and replacing it by that
in another set of segments without the use of signals needed in a
classical machine from a central control or switching centre.  That
is, the brain/mind will be a fully distributed, synchronously
partitioned massively parallel processor, where the perceptual
constancies, shape constancy, size constancy, etc are the
spatiotemporal Lie group invariances6 and the Lie group prolongations
generate the differential invariances characterizing higher form
perception.7

It is worthwhile emphasizing that functional magnetic resonance
imaging (fMRI) is already a most impressive way of realizing a model
of the image and signal processing based on the Heisenberg group G.8
Such imaging is currently the hottest topic in cognitive neuroscience
for what experimentally it reveals non-invasively about the living
brain, where for example complex areas such as the visual cortex, the
motor strip and the silent speech area are being mapped.  These
mappings show a morphology and dynamics in accordance with the
temporal coding principle of biological neural networks as discovered
by Eckhorn, Singer and collaborators, von der Malsburg and others;
that is that timing/synchroncity is everything as it is in fMRI
itself.  The application of these new image processing principles to
the brain's own workings as postulated here is therefore a natural
progression.

                    _______________________________

Figure I - the emitter/absorber model of quantum holography
(REFER TO AUTHOR IF FIGURE IS NEEDED)
                         set of 3 dimensional object images


Movie of a set of
3 dimensional object
images in motion
relative to one another
                                   adaption       adaption


OBJECTIONS

Now it may be objected that

1)   the brain/mind does not employ phase conjugation but this
     is erroneous since the survival of the imagemaker or
     brain/mind is completely dependent on detecting objects
     where they actually are whether it be by vision, sound,
     touch, etc.  That is on phase conjugation and of sensing
     the world the way it actually is.  If one doubts this, snap
     one's fingers and ask where the brain/mind creates the
     acoustic object image of the snap.  Listen, it is outside
     the head coincident with the snap as a phase conjugate
     image must be, similarly, reach out for a nearby object and
     verify by doing this that not only do the visual and
     tactile object images the brain/mind creates coincide, but
     this coincidence is also with the object itself, ie it is
     phase conjugate with object in every geometric particular
     with reference to the scale of resolution of which the
     senses are capable and which defines the human scale.

2)   Holography and/or quantum coherence cannot be the mechanism
     of Evolution or of the workings of the brain/mind because
     of increasing thermodynamic disorder and excessive noise
     respectively.  In fact holographic imaging through
     increasing inhomogeneity called superresolution imaging
     employing phase conjugation only serves to sharpen images9
     and so counterintuitively increasing thermodynamic disorder
     and noise will be essential to the process of adaption
     taking place in Evolution and the brain/mind so that new
     order is created and existing order perfected.
     Intelligence may therefore be defined as the perception of
     order where none was previously perceived,10 and Evolution
     as the creation of order where none previously existed and
     in particular from the point prior to the very first
     coherent emission.  That is, this is an Evolution of
     Everything from Nothing beginning with an initial resonance
     or Big Bang.4

CRITICAL PHENOMENA

Classical physics therefore corresponds to the case where microscopic
fluctuations average out when larger scales are considered and the
averaged quantities satisfy classical continuum equations for example
hydrodynamics when the classical hydrodynamic equations emerge.
Quantum holography is however allied to the much more difficult class
of problems that of critical points where microscopic fluctuations
persist out to macroscopic wavelengths and where fluctuations on
intermediate length scales are important too.  A critical point is a
special case of a phase transition;  consider for example the water-
steam transition where at the critical point bubbles of steam and
drops of water co-exist at all size scales from the macroscopic
visible sizes down to atomic scales so constituting a water-steam
quantum hologram.  That is the phenomemology of the postulated
Evolution will involve the appearance of new physical or 'order'
parameters such as the magnetization or superfluid density and the
concept formalized in the 3 dimensional Heisenberg group
representation that there is a dominant scale on which fluctuations
are important ie the resonant scale so that shorter range fluctuations
may for the purposes of calculation be averaged out with impunity and
one deals with a block or cell variable averaged on the resonant
scale. (3)  K G Wilson's11 complete solution to this problem of
critical phenomena for which he received the 1982 Nobel Prize
concerned the key idea of mapping the Hamiltonian or energy space onto
itself - namely the idea of stable and unstable fixed points,
attractors and so on, so that the mapping leads eventually to one or
another stable fixed point.  But this is exactly the nature of the
model of Evolution proposed here where this proceeds through an
unending sequence of phase transitions or unstable fixed or saddle
points between two different stable fixed points.  Furthermore in
agreement with Wilson's findings this model with its mapping on to the
integers ie the number of emissions and absorptions constitutes a
universality class dependent only on dimensionality and the symmetry
of the order parameter or Lie group.  This last point is of great
importance because it shows that this quantum mechanical model of
Evolution suffers from none of the problems of infinities that plague
standard quantum models.

The phenomonology of critical points however says that the Evolution
proposed must correspond to a Hamiltonian and the existence of such a
Hamiltonian can be postulated from the fact that the holographic
encoding and decoding process of the emitter/absorber model
corresponds to an embedding of the complex plane C co-ordinates z = x
+ iy in the Heisenberg group G (8).  This is in excellent accord with
Berry's Hypothesis concerning the Berry or geometric phase (13) which
is the quantity of physical significance in this quantum holographic
model of Evolution. Berry's hypothesis (13) says that this Hamiltonian
concerns that of an unknown dynamical system without time reversal
symmetry of which the phase space trajectories are chaotic and the
eigenvalues of which are the imaginary parts E(Suffix m) m = 1, 2 ...
of the zeros of the Riemann Zeta function

     (Zeta)(z)  =   Sigma over n of   l/n**z

where n is taken here to be the number of emissions/absorptions. This
well-known function by the Riemann hypothesis has its zeros on the
line 1/2 so that (zeta) (1/2 + iE(suffix m)) = 0 and thus can be
interpreted here as defining every fermionic state of the Evolution.
That is every object and object image of this Evolution is by the
Pauli exclusion principle unique.

A Possible Explanation of the Origin of Life

Equally important is the realization that the adaptive self-
organization described above must involve an optimum control of an
uncertain quantum system14 following the recent discovery that quantum
coherence is the key to demonstrating such a control in the
laboratory.  Such demonstrations concern spectral irradiation of a
chemical soup via a laser under computer control of a genetic
algorithm so as to be able to optimize the desired chemical output
from the soup. (15)  This process constitutes a real time solution of
the Schrodinger equation describing the chemistry and suggests this is
how self-organized living systems carry out their electrochemistry
where their DNA supplies the necessary sequence of optimum controls.
That is DNA encodes holographically the morphologies and dynamics of
the organism on every scale so providing an entirely satisfactory
explanation as to how for example anything as complex as the human
organism can develop in the womb so efficiently and effectively on so
many scales simultaneously.  It is a testable hypothesis which in
principle could be performed by repeating the original Miller
experiment16 under the new set of conditions set out above.

REFERENCES

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Additional reading: Cramer J G, Rev.Mod.Phys. 58,3,647-687, July 1986.
The Transactional Interpretation of  Quantum Mechanics.

This research is a continuation of that published at the last Namur
Congress under the titles "An Outline Model, Cosmological Evolution",
authors D. Dubois & P. J. Marcer, pages 157-160 and "A Specification
of the Unified Field", author P. J. Marcer, pages 161-164.

Copyright, P. J. Marcer, all rights reserved

Refer queries to:-

                            Peter J Marcer,
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                 Keynsham, Avon, England  BS18 2DH, UK