Saturday, July 04, 2015

Deconstruction and reconstruction in quantum physics and conscious experience

Deconstruction means roughly putting something into pieces. Often deconstruction is thought to involve also the reconstruction. This process is applied in deconstructivistic architecture as one can learn by going to Wikipedia and also cubism brings in mind this kind of approach. Reconstruction organizes typical features of existing styles in new - one might even say "crazy" manner. There can be even a kind of "social interaction" between buildings: as if they were communicating by exchanging features. Similar recombination of elements from various styles have appeared also in music - neoclassicism comes in mind immediately.

Postmodernism is a closely related movement and claims that truths are social constructs: great narratives are dead. Nothing could irritate more the physicist who has learned how much mistakes, wrong tracks, and hard work are needed to distill the truth! Everything does not go! On the other hand, one can argue that the recent state of stagnation in the frontier of theoretical physics suggests that postmodernists are right. Superstrings and multiverse are definitely highly social constructs: superstrings were the only game in the town for decades but now American Mathematical Society is worried that super string theoreticians are spoiling the public image of science. Multiverse was in fashion only few years. Certainly one great narrative - the story or reductionism and materialism thought to find its final culmination as M-theory - is dead. It is however nonsense to claim that all great narratives are dead. That telling alternative great narratives in respected journals is impossible does not mean that they are dead!

But the association of deconstruction with postmodernism does not justify throwing away the ideas of deconstruction and reconstruction. Rather, one can ask whether they could be made part of a new great narrative about physical world and consciousness.

1. Deconstruction and reconstruction in perception, condensed matter physics and in TGD inspired theory of consciousness

Deconstruction and reconstruction appear in the construction of percepts, in condensed matter physics, and are also part of TGD inspired theory of consciousness.

1.1 Perception

The very idea of deconstruction in architectural sense is highly interesting from the perspective of both quantum physics and consciousness.

I was astonished as I learned for about 35 years ago that the buildup of our perception involves very concretely what I would now call deconstruction and reconstruction and I could not understand why this. First the sensory input is decomposed into features. Edges, corners, positions, motions analyzed to direction and velocity, colors,... Objects are replaced with collections of attributes: position, motion, shape, surface texture, color,.... Deconstruction occurs at lower cortical layers. After this reconstruction takes place: various kinds of features are combined together through a mysterious looking process of binding - and the outcome is a percept.

Reconstruction can occur also in "wrong" manner. This occurs in hallucinations, delusions, and dreams. Humour is based on association of "wrong" things together, making intentional category errors. Synesthesia involves association between different sensory modalities: note with a given pitch has characteristic color or numbers correspond to colors or shapes. I remember an article telling about how subject persons in hypnosis can experience what circle with four corners looks like. Some attribute can be lacking from the reconstruction: person can perceive the car as object but not its motion. The car is there now and a moment later it is here. Nothing between.

Also non - standard reconstructions are possible. Could these non-standard reconstructions define a key aspect of creativity? Could reconstruction create in some lucky situations new idea rather than hallucination or delusion?

For few years ago I listened a radio document about a professional, who builds soundscapes to movies and learned that the construction of soundscape is deconstruction followed by reconstruction. One starts from natural sounds but as such they are not very impressive: driving by car over some-one does not create any dramatic sound effect - just "splat" - nothing else. This is so non-dramatic that it has been be used to create black humour. In order to cure the situation the real sounds are analyzed to features and then reconstructed by amplifying some features and by throwing away the unessential ones. The fictive output sounds much more real than the real input. Actors are masters of this technique and this is why videos about ordinary people doing something funny is like looking autistic ghosts. And if you look at the collection of modules of video game you see modules with name "Aargh", "Auch", "Bangggg", etc..

Association is the neuroscientist's key notion allowing to get an idea about what happens in reconstruction. Reconstruction involves association of various features to form percepts. First this process occurs for various sensory modalities. These intermediate sensory percepts are then combined to full percept in association regions.

But what associations are at deeper level? What features are? Heretic could ask whether they could correspond to conscious experiences not conscious to us but conscious at lower sub-conscious level. Reader perhaps noticed that deconstruction and reconstruction took place here: the student is not supposed to ask this question since most theories of consciousness for some funny reason - maybe a pure accident - make the assumption that consciousness has no structure - no selves with subselves with sub-selves with... For physicist this kind deconstruction of consciousness is very natural. How do these features bind to our conscious percepts? Neuroscience alone cannot tell much about this since it is based on physicalism: "hard problem" articulates this dead end.

The following considerations represent deconstructions and reconstructions, and I will not explicitly mention when this happens - just warning.

1.2 Condensed matter physics

One must bring in some basic notions of quantum theory if one wants to reduce de- and reconstruction to quantum physics. The key mathematical fact is that in quantum theory each particle in many-particle state corresponds to a tensor factor of state space of the entire system. This notion is very difficult to explain without actually having a lecture series about quantum theory and I prove in the following that this is indeed the case.

  1. The space of quantum states of system is the basic notion: technically it is known as Hilbert space, which can have finite or even infinite dimension and also infinite dimension (and this in many senses!).

    The basic idea is that one can build bigger Hilbert spaces as their tensor products. If you have Hilbert spaces of dimensions n1 and n2, the tensor product has dimension n1× n2. This is algebraically like multiplying numbers and one can indeed identify prime Hilbert spaces as those with prime dimension. Also direct sums of Hilbert spaces are possible.

    Hilbert spaces represent physical systems: say electron and proton. To describe a world consisting of proton and electron one forms the tensor product of electron and proton Hilbert spaces. This is somewhat like playing with legos.

    I was cheating a little bit. Life is not quite so simple. One can also form bound states of two systems - say hydrogen atom from proton and electron, and the bound states of hydrogen atom represent only a sub-space of the tensor product. Connes tensor product is more exotic example: only certain kind of entangled states in tensor product for which the composites are strongly correlated are allowed. As a matter of fact, also the gluing the legos together creates strong correlations between them so that it serves as a good analogy for Connes tensor product and tensor product assignable to bound states.

  2. Even elementary particles have several degrees of freedom - say spin and charge - to which one can assign Hilbert spaces decomposing formally into tensor product of Hilbert spaces associated with these degrees of freedom. Sub-space of the full tensor product is allowed, and one can purely formally say that elementary particle is a bound state of even more elementary particles. Somewhat like written word having meaning to us consists of letters, which as such represent nothing to us (but could represent something to lower level conscious entities). Could it be possible to apply deconstruction to elementary particles?

Now comes the surprise: condensed matter physicists have discovered deconstruction long time ago)! Condensed matter electron can be deconstructed under some circumstances.

  1. Electron in the valence band of conductor has three kinds of degrees of freedom labelled by spin, charge and orbital state - state of electron in atom - characterizing the valence band. The state of electron decomposes in purely formal sense to a bound state of spinon, chargon, and holon carrying spin, charge, and phase of electron wave function. Could one deconstruct this bound state to its composites? If so, one would have effectively three particles - three quantum waves moving with different velocities. For free electrons obeying Dirac equation this is certainly impossible. But this might be (and is!) possible in condensed matter.

    Instead of single wave motion there can be three free wave motions occurring with different velocities (wave vectors) corresponding to spinon, chargon and holon. In popular articles this process is called "splitting" of electron. The term is optimal choice if the purpose is to create profound mis-understandings in the layman reader associating naturally splitting with a geometric process of putting tiny ball into pieces. As already explained, it is Hilbert space, which is split into tensor factors, not the tiny ball. The correlations between factors forced by bound state property are broken in this divorce of degrees of freedom.

  2. What condensed matter theorist propose is roughly following. The consideration is restricted to effectively one-dimensional systems - wires. Electron has spin, charge, and orbital degrees of freedom if in conduction band and delocalized and thus shared by the atoms. Usually these degrees of freedom are bound to single entity.

    The holy trinity of charge, spin, and orbital degrees of freedom can be however split under some circumstances prevailing in condensed matter. The phase of the spinor representing electron can vary along wire and defines wave motion with some velocity/wave vector assignable with the ordinary electric current. The spin of electron can rotate at each point and the phase of this rotation can vary along wire so that a quantum wave moving along wire with velocity different from that for charge: this is spin wave having as classical analog the rotation of bicycle pedals. If the wire is a linear lattice of atoms, the orbital excitation can also vary along the wire and a third quantum wave moving with its own velocity is possible. One has three particle like entities moving with different velocities! This kind of waves are certainly not possible for the solutions of Dirac equation representing freely moving fermions and particle physicists do not encounter them.

  3. These wave motions are different from the wave motions associated with phonons and magnons. For sound it is periodic oscillation for the position of atom, which propagates in sound wave. For magnon it is change of spin value, which propagates and defines a spin 1 collective excitation. Spinon as a quasiparticle has spin 1/2 so that spinon and magnon are different things. Spinon is formal constituent of electron made visible by the condensed matter environment. Magnon is collective excitation of condensed matter system.

    Spin currents provide an example of a situation in which spin and charge currents can flow at different speeds and are becoming important in a new technology known as spintronics. Spin currents have very low resistance and the speculation is that they might relate to high Tc super conductivity.

From the articles that I have seen one might conclude that deconstruction is in practice possible only for effectively 1-dimensional systems. I do not see any obvious mathematical reason why the deconstruction could not occur also in higher-dimensional systems.

It is however true that 1-dimensional systems are very special physically. Braid statistics replaces ordinary statistics bringing in a lot of new effects. Furthermore, 2-D integrable gauge theories allow to model interactions as permutations of quantum numbers and lead to elegant models describing deconstructed degrees of fields as quantum fields in 2-D Minkowski space with interactions reducing to 2-particle interactions decribable in terms of R-matrix satisfying the Yang-Baxter equations. It is difficult to say how much the association of deconstruction to 1-D systems is due the fact that they are mathematically easier to handle than higher-D ones and there is existing machinery.

The rise of superstring models certainly was to a high degree due to this technical easiness. As I tried to tell about 3-surfaces replacing strings as fundamental dynamical objects, the almost reflect like debunking of this idea was to say that super-conformal invariance of super-string models is lost and the theory is not calculable and does not even exist - period. It took indeed a long time to realize that super-conformal symmetry allows a huge generalization, when space-time is 4-D and imbedding space has Minkowski space as its Cartesian factor. Twistorial considerations fixed the imbedding space uniquely to M4× CP2. The lesson is clear: theoretician should be patient and realize that theory building is much more than going to math library and digging the needed mathematics. Maybe colleagues are mature to learn this lesson some day.

1.3 TGD inspired theory of consciousness

The believer in quantum consciousness of course wonders what could be the quantum counterparts of de- and reconstruction as mechanism of perception. It would seem that analysis and synthesis of the sensory input deconstructs the mental image associated with it to features - perhaps simpler fundamental mental images - and reconstruct from these the percept as mental image. What does this correspond at the level of physics?

Before one can really answer one must understand what the quantum physical correlates of mental image are. How mental images die and are born? What features are as mental images? What their binding to sensory percepts does mean physically?

Here I can answer only on my own behalf and to do it I must introduce the basic notions and ideas of TGD inspired theory of consciousness. I will not go into details here because I have done this so many times and just suggest that the reading of some basic stuff about TGD inspired theory of consciousness. Suffice it to list just the basic ideas and notions.

  1. Zero energy ontology (ZEO), the closely related causal diamonds (CDs), and hierarchy of Planck constants assignable to quantum criticality are basic notions. Number theoretic vision is also central. In particular, adelic physics fusing real physics and various p-adic physics as correlates for cognition is also a basic building brick.

  2. TGD inspired theory of consciousness theory can be seen as a generalization of quantum measurement theory constructed to solve the basic problems of ordinary quantum measurement theory: observer becomes "self" - conscious entity - described by physics and part of physical system rather than being an outsider. Consciousness does not cause state function reduction: consciousness is state function reduction. Consciousness is therefore not in the world but between two worlds. This resolves the basic paradox of quantum measurement theory since there are two causalities: causality of consciousness and causality of field equations.

    Negentropy Maximization Principle (NMP) defines the basic variational principle. Strong form of NMP states that the negentropy gain in state function reduction is maximal. Weak form of NMP leaves for self free will in that self can choose also non-maximal negentropy gain. This makes possible universe with ethics and moral with good defined as something which increases negentropy resources of the Universe.

    Self hierarchy is the basic notion of TGD inspired theory of consciousness. Self experiences sub-selves as mental images. Self corresponds to a state function reduction sequence to the same boundary of causal diamond (CD). In standard quantum measurement theory this sequence does not change the state but in TGD framework the state at the opposite boundary of CD and even opposite boundary changes. This gives rise to the experience flow of time having the increases of the temporal distance between the tips of CD as a geometric correlate. Self dies as the first reduction to the opposite boundary takes place and re-incarnates at the opposite boundary as its time reversal. Negentropy Maximization Principle forces it to occur sooner or later. The continual birth and death of mental images supports this view if one accepts the idea about hierarchy. One can also consider a concrete identification for what the change of the arrow of time means for mental image (see this).

  3. Magnetic bodies carrying dark matter identified as heff=n× h phases of ordinary matter define quantum correlates for selves. Magnetic body has hierarchical onion-like structure and it communicates with biological body using dark photons propagating along magnetic flux tubes. EEG and its fractal generalizations make possible both communication from/control of biological body to/by magnetic body. Dark matter hierarchy can be reduced to quantum criticality and this in turn has deep roots in the adelic physics. Magnetic body means an extension of the usual organism-environment double to triple involving magnetic body as intentional agent using biological body for its purposes.

What reconstruction could mean in TGD inspired theory of consciousness?
  1. The restriction of deconstruction to the degrees of freedom of elementary particle i s un-necessarily restrictive. One can consider also larger units such a as ..., molecules, cells,... and corresponding magnetic bodies and their representations using tensor products.

  2. Besides bound state formation also negentropic entanglement (NE) allows states which are almost stable with respect to NMP. One can imagine two kinds of NE, which can be metastable with respect to NMP. In the first case density matrix is a projector with n identical eigenvalues of density matrix. This state can be an outcome of a state function reduction since it is an eigenstate of the universal observable defined by the density matrix.

    Density matrix has matrix elements in an algebraic extension algebraic extension of rationals characterizing the system in the evolutionary hierarchy. It can also happen that the eigenvalues of the density matrix (probabilities) do not belong to this extension. One can argue that since diagonalization is not possible inside the extension, also state function reduction is impossible without a phase transition extending the extension and identifiable as a kind of evolutionary step. This is assumed - at least tentatively.

    Both kinds of NEs would have natural place in the world order. The first kind of NE would correspond to a kind of enlightened consciousness since any orthonormal state basis would define an eigenstate basis of density matrix. Schrödinger cat would be exactly half alive and half dead or exactly half of X and half of Y, where X and Y are any orthonormal superpositions of alive and dead. For the second kind of NE there would be a unique state basis. For instance, the cat could be 1/21/2 alive and 1 - 1/21/2 dead. The words dead and alive have meaning. This would correspond to a state of rational mind discriminating between things. If a phase transition bringing into daylight 21/2 takes place, state function reduction makes cat fully alive or fully dead.

  3. In condensed matter example the velocity of quantal wave motion serves as a criterion allowing to tell whether the degrees of freedom bind or not. Velocity/wave fector is obviously too limited criterion for binding or its absence. In neuroscience the coherence of EEG is seen as a signature of binding: maybe oscillation with same EEG frequency could serve the signature of fusion of mental images to a larger one. In TGD inspired theory of consciousness EEG frequencies correspond to differences of generalized Josephson frequencies that is sums of Josephson frequency for the resting potential and of the difference of cyclotron frequencies for ions at different sides of cell membrane (see this, this, and this ).

  4. At the level of magnetic flux tubes binding would correspond to a reconnection of magnetic flux tubes of synchronously firing region to form a larger structure for which the magnetic field strength is same for the composites and therefore also cyclotron frequencies are identical. Reconstruction would have a concrete geometric correlate at the level of magnetic flux tubes as a reconnection. Different parts of brain containing quantum states serving as mental images defining features would connected by flux tubes of the magnetic body and binding of mental images would take place.

  5. In TGD inspired quantum biology dark matter identified as large heff=n× h phases give rise to a deconstruction if one accepts the hypothesis heff=hgr =GMm/v0, where M represents mass of dark matter and m particle mass (see this and this). Here hgr is assigned with a flux tube connecting masses M and m and v0 is a velocity parameter characterizing the system. This hypothesis implies that dark cyclotron energy is given Ec=hgrfc, where fc is cyclotron frequency, is independent of particle mass: universal cyclotron energy spectrum is the outcome. The dark cyclotron photons can transform to ordinary photons identified as biophotons having energy spectrum in visible and UV range, where also the energy spectrum of molecules is. Magnetic body could use dark photons to control bio-chemistry.

    What makes this also so remarkable is that particles with magnetic dipole moment possessing different masses correspond to different values of heff and reside at different magnetic flux tubes. This is mass spectroscopy - or deconstruction of matter by separating charged particles with different masses to their own dark worlds! Dark living matter would not be a random soup of particles: each charged particle (also neutral particles with magnetic dipole moment) would sit neatly at its own shelf labelled by hgr! In TGD inspired theory of consciousness magnetic flux tubes can be associated with magnetic bodies serving as correlates of selves so that deconstruction for mental images would reduce to this process with each charged particle representing one particular combination and perhaps also a quale (see this).

What about re-construction in this framework?

  1. In reconstruction flux tube connections between two subsystems representing sub-selves (experienced by self as mental images) would be formed so that they would fuse to single system characterized by the same cyclotron frequency. Flux tube connection would be formed by the reconnection of U-shaped flux tubes to form single pair of connecting flux tubes connecting the systems.

    Resonant exchange of dark cyclotron photons and also dark super-conductivity would accompany this process. This process would represent a correlate for directed attention and would take place already at bio-molecular level. I have proposed that bio-molecules with aromatic rings in which circulating electron pair currents generate magnetic bodies are especially important and in some sense fundamental level of the self hierarchy at molecular level \citeallb/pulse. In brain different brain regions could connect to single coherently firing region in this manner.

  2. The magnetic bodies associated with brain regions representing features could be connected in this manner to larger sub-selves. Negentropic quantum entanglement - a purely TGD based notion - could define a further correlate for the binding. This entanglement could take place in discrete degrees of freedom related to the hierarchy heff=n× h of Planck constants having no correlate in standard physics. The discrete degree of freedom would correspond to n sheets of singular coverings representing space-time surfaces. The sheets would co-incide at the ends of causal diamonds (CDs): one possible interpretation (holography allows many of them) could be that entire closed 3-surfaces formed by the unions of space-like 3-surfaces at the boundaries of CD and light-like 3-surfaces connecting them serve as basic objects.

  3. Reconstruction by negentropic quantum entanglement and flux tube connections inducing resonance could also lead to non-standard composites. Synesthesia could be understood in this manner and even the sensory experience about circle with four corners could be understood. The binding of left and right brain visual experiences to single one could take place through negentropic entanglement and effectively generate the experience of third dimension. The dimensions would not however simply add: 3-D experience instead of 4-D. The dream of a mathematician is to perceive directly higher dimensional objects. Could sensory perception of higher than 3-D objects be possible by a reconstruction fusing several visual percepts - maybe even from different brains - together? Could higher levels of self hierarchy carry out this kind of reconstruction? Could Mother Gaia fuse our experiences to single experience about what it is to be a human kind, species, or bio-sphere?

2. Could condensed matter physics and consciousness theory have something to share?

Magnetic bodies are present in all scales and one can ask whether consciousness theory and condensed matter physics might have something in common. Could the proposed picture of matter as consisting of selves with sub-selves with.... defining analogs of quasiparticles and collective excitations make sense even at the level of condensed matter? Could construction and reconstruction of mental images identifiable as sub-selves take place already at this level and have interpretation in terms of primitive information processing building standardized primitive mental images?

Deconstruction need not be restricted to electron and velocity could be replaced by oscillation frequency for various fields: at quantum level there is not actually real distinction since in quantum theory velocity defines wave vector. Also more complex objects, atoms, molecules, etc. could be deconstructed and the process could occur at the level of magnetic bodies and involve in essential manner reconnection and other "motor actions" of flux tubes. The notions of quasi-particle and collective excitation would generalized dramatically and the general vision about basic mechanism might help to understand this zoo of exotics.

Future condensed matter theorists might also consider the possibility of reconstruction in new manner giving rise to the analogs of synesthesia. Could features from different objects be recombined to form exotic quasi-objects having parts all around. Could dark matter in TGD sense be involved in an essential manner? Could cyclotron resonance or its absence serve as a correlate for the binding? Note that the disjoint regions of space would be in well-defined sense near to each other in the reconstructed state. Topology would be different: effective p-adic topology could provide a natural description for a situation: in p-adic topology systems at infinite distance in real sense can be infinitesimally close to each other p-adically.

See the aritcle Deconstruction and reconstruction in quantum physics and conscious experience

For a summary of earlier postings see Links to the latest progress in TGD.


Leo Vuyk said...

You wrote:
The lesson is clear: theoretician should be patient and realize that theory building is much more than going to math library and digging the needed mathematics. Maybe colleagues are mature to learn this lesson some day.

I would advise write a LuLu book onit its free! said...

Maybe sometime. Now I am busily gathering the fruits. Still some years left;-).

It is really amazing how fast things go. Few years ago I had a science fictive vision that the reductionistic dogma might be some day given up. Now it has happened! This is not due to theoretical advances by simple experimental facts discovered in condensed matter physics.