A Quantum Mechanical Model of Evolution and Consciousness

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


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.


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)


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


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 1. Schempp W, J of Math. Imaging and Vision, 2,279-326, 1992, Quantum Holography and Neurocomputer Architectures.

  1. Schempp W, Harmonic Analysis on the Heisenberg Group with Applications in Signal Theory. Pitman Research Notes in Mathematics series 147, Longman Scientific and Technical, London 1986.
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  3. Marcer P J, World Futures, 44, 1-11, 1995 (in press), A Proposal for a Mathematical Specification of Evolution and the Psi Field.
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  6. Hoffman W C, Mathematical Biosciences, 6, 437-471, 1970, Higher Visual Perception as Prolongation of the Basic Lie Transformation Group.
  7. Schempp W, Phase Coherent Wavelets, Fourier Transform Magnetic Resonance Imaging and temporally encoded synchronized neural networks, Pitman Research Notes in Mathematics Series 303, Longman Scientific and Technical London 1994.
  8. Leith E and Cunha A, Optical Engineering, 28, 6, 574-579 June 1989, Holographic Methods for Imaging through Inhomogenity.
  9. Fatmi H A and Young R W, Nature 228,3 Oct., 97, 1970; A Definition of Intelligence.
  10. Wilson K G, Rev of Mod. Phys, 55,3, 583-600, July 1983, The Renormalization Group and Critical Phenomena.
  11. Anandan J, Nature, 360, 26, Nov, 307-313, 1992, The Geometric Phase.
  12. Berry M V, Quantum Chaos and Statistical Nuclear Physics (Springer Lecture Notes in Physics No.263) Springer Berlin, 1-17, 1986, ed. Seliman T H and Nishioka H: Riemann's Zeta Function: a Model for Quantum Chaos?
  13. Pierce A, Dahleh M and Rabitz H, Phys.Rev.A 423, 1065-1079, 1st August 1990, Optimal Control of Uncertain Quantum Systems. 15. Judson S R and Rabitz H, Phys.Rev.Letts., 68(10), 1500-1503 9 March 1992, Teaching Lasers to Control Molecules. 16. Miller Stanley, Professor University of California at San Diego, USA.


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 amp; 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

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