Sunday, August 18, 2019

A visit to Baden-Baden

I participated a symposium held in Baden-Baden (31st International Conference on Systems Research, Informatics and Cybernetics – InterSymp 2019: Symposium on Causal and Anticipative Systems in Living Science, Biophysics, Quantum Mechanics, Relativity). The visit was pleasant: Baden-Baden is small town which has preserved its personal warm character.

I wrote a slightly extended version of the related article mentioning the recent experimental finding of Minev et al supporting zero energy ontology crucial for the approach. The following is the abstract of the article.

Topological Geometro-Dynamics (TGD) proposes a unification of fundamental interactions by identifying space-times as 4-surfaces in 8-D space H=M4× CP2, whose geometry codes for standard model symmetries and geometrizes known fields. Point-like particle is replaced with 3-surface (3-space). One ends up with the notions of many-sheeted space-time and magnetic body (MB) central in TGD inspired quantum biology. p-Adic and adelic physics follows from the extension of physics to describe also the correlates of cognition and imagination. Adelic physics predicts a hierarchy of Planck constants labelling phases of ordinary matter interpreted as dark matter: the predicted quantum coherence in arbitrarily long scales is crucial for quantum biology. Quantum TGD replaces standard ontology with "zero energy ontology" (ZEO) replacing quantum state as time=constant snapshot with zero energy state (ZES) identified as a superposition of deterministic classical time evolutions - kind of quantum program.

See the article TGD inspired theory of consciousness and living systems.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

Saturday, August 17, 2019

Could metaplectic group have some role in TGD framework?

Metaplectic group appears as a covering group of linear symplectic group Sp(2n,F) for any number field and its representations can be regarded as analogs of spinor representations of the rotation group. Since infinite-D symplectic group of δ M4+× CP2, where δ M4+ is light-cone boundary, appears as an excellent candidate for the isometries of the "world of classical worlds" in zero energy ontology (ZEO), one can ask whether and how the notion of metaplectic group could generalize to TGD framework.

The condition for the existence of metaplectic structure is same as of the spinor structure and not met in the case of CP2. One however expects that also the modified metaplectic structure exists if one couples spinors to an odd integer multiple of Kähler gauge potential. For triality 1 representation assignable to quarks one has n=1. The fact that the center of SU(3) is Z3 suggests that metaplectic group for CP2 is 3- or 6-fold covering of symplectic group instead of 2-fold covering.

Besides the ordinary representations of SL(2,C) also the possibly existing analogs of metaplectic representations of SL(2,C) = Sp(2,C) acting on wave functions in hyperbolic space H3 represented as a2=t2-r2 hyperbololoid of M4+ are cosmologically interesting since the many-sheeted space-time in number theoretic vision allows quantum coherence in even cosmological scales and there are indications for periodic redshift suggests tesselations of H3 analogous to lattices in E3 and defined by discrete subgroup of Sl(2,C). In this case one could require that only the subgroup SU(2) is represented projectively so that one would have an analogy with modular functions for discrete subgroup of SL(2,Z) would be represented in this manner.

See the chapter Recent View about K\"ahler Geometry and Spin Structure of WCW.

Wednesday, August 07, 2019

Phase transitions generating dark phases and sensory perception

The TGD based model for biological self-organization relies on the hierarchy heff=nh0 of effective Planck constants labelling dark phases of ordinary particles residing at magnetic flux quanta. This model generalizes and suggests the replacement of non-equilibrium thermodynamics as basis of self-organization with its quantum variant based on dark matter hierarchy. The challenge is to formulate basic thermodynamical notions like work in terms TGD based quantum theory relying on zero energy ontology (ZEO).

The basic mechanism would be a phase transition creating dark matter phase as a Bose-Einstein condensate like state with particles having identical conserved quantum numbers. Conservation laws would force the ordinary matter to have opposite total charges. For instance, in the case of work one has momentum or angular momentum as a conserved charge. In the case of charge separation and high Tc superconductivity it would be em charge. Even color charges can correspond to conserved charges in TGD framework allowing scaled variants of strong interaction physics.

Basic biological functions involving the notion of work and also the formation of sensory percepts would rely on this mechanism. Also the ZEO based theory of consciousness predicting the change the arrow of time in ordinary state function reduction plays a central role and a model of nerve pulse is discussed as an example.

Sensory perception (time reversal of motor action could involve generation of coherent phases of dark matter carrying collective quantum numbers in 1-1 corresponds with the sensory qualia. This would represent a general charge separation process.

Consider first sensory capacitor model for color qualia.

  1. The notion of QCD color as analog of ordinary visual colors was originally introduced as a joke since the algebra of color summation resembles that for the summation of QCD colors in tensor product. In TGD however the dark hierarchy (heff) and p-adic length scale hierarchy predict that scaled variants of QCD type physics are possible for arbitrarily large length scales. In cellular scales scaled up QCDs are predicted. In the length scale range between cell membrane thickness and nucleus size there are as many as 4 Gaussian Mersennes, which is a number theoretical miracle. They could label copies of QCDs with size scale for the analogs of hadrons given by the corresponding p-adic length scales. QCD type colors could correspond to perceived colors.

  2. Gluons or quarks labelled by color charge characterizing particular color quale would flow between the plates of "capacitor" associated with the sensory receptor. The amount of particular color charge increases at the other plate giving rise to sensation of this particular color quale and its complement at the other plate - by color confinement also the same plate could also contain regions with complementary colors. This would explain why we see around a region of particular color a narrow boundary with complementary color.

  3. The model for sensory perception as sequences of analogs of weak measurements suggest that the flow of color charges could induce color qualia. The prediction emerging from the structure of SU(3) color algebra would be four pairs of basic color and complement color: 3 ordinary pairs and white-black pair. They could correspond to particular changes of color quantum numbers and color quantum numbers of gluons. Also color mixing could be understood.

  4. Photons are not coloured but gluons (and also quarks) are, and the latter and could be responsible for color sensation. How photon flux can generate a flow of color quantum numbers? The notion of induced gauge field -classical color gauge potentials would be projections of SU(3) Killing vectors - explains this.

    In TGD classical em field is sum of two terms induced Kähler form and neutral vectorial component of spinor curvature. Classical gluon field has components proportional to classical color Hamiltonian (function in CP2 which can be said to have quantum numbers of gluon) and induced Kähler form. In general case any classical em field is accompanied by a classical color field.

    Photons are accompanied by classical em fields and therefore also by classical gluon fields at the fundamental level: this correspondence disappears at QFT limit unable to describe biology and sensory experience. The flow of photons to retina would be accompanied by classical em and color fields and therefore a flow of gluons. Also quark flow between the plates of sensory capacitor could generate the color qualia.

  5. A simple model for the visual qualia is in terms of a phase transition transforming gluons of a scaled copy of QCD to ordinary gluons. Dark gluons would form a BE condensate and force a formation its shadow at the level of ordinary matter. This is a variant of sensory receptor as quantum capacitor. The plates of capacitor correspond to dark and ordinary phase and the analog of electric breakdown means formation of the dark phase. Cooper pairs of quarks with quantum numbers of gluon would be second option but gluons in TGD framework are actually this kind of pairs!!

See the article Quantum self-organization by heff changing phase transitions or the chapter General theory of qualia.

Zero energy ontology and quantum model for nerve pulse

In TGD based model of nerve pulse axonal membrane is generalized cylindrical Josephson junction defined by axonal membrane consisting of smaller Josephson junctions defined by membrane proteins.

  1. A sequence of mathematical penduli along axon in rotation in the same direction is the mechanical analog. Oscillation frequency Ω transforming to a rotation frequency above critical value is proportional to the resting potential V. When V is overcritical, the pendulum starts to rotate instead of oscillating. The system should be near quantum criticality for the transformation of rotation to oscillation or vice versa.

  2. During nerve pulse membrane potential and therefore also rotation frequency is reduced and changes sign and then returns back to the original value. The first guess is that at criticality there is a kick reducing the rotation frequency Ω and continuing to change its sign and then return it to original.

The basic condition is that resting state becomes critical at critical hyper-polarization. There are two options for the resting state.
  1. According to the original model resting state can be regarded as a soliton sequence associated with the phase difference over the membrane. More concretely, the mathematical penduli rotate in same direction with phase difference between determining the propagation velocity of solitons. The rotation frequency is slightly above that for oscillation. There is a preferred direction along axon. This conforms with the reduction and change of sign of potential and thus of Ω.

    Problem: Hypo- rather than hyper-polarization should cause the nerve pulse as a transformation of rotation to oscillation. Something goes wrong.

  2. Alternatively, the penduli almost rotate being near criticality for the rotation: the penduli almost reaches the vertical position at each oscillation as required by criticality. That hyper-polarization would cause the nerve pulse as propagating soliton conforms with this idea.

    Problem: Ω and thus V should increase rather than reduce and even change sign temporarily.

Neither option seems to work as such but the first option is more plausible as a starting point of an improved model.

The membrane potential changes sign suggesting quantum jump. Could zero energy ontology (ZEO) based view about quantum jump as "big" (ordinary) state function reduction (BSFR) help? Could nerve pulse correspond to BSFR?

  1. Could BSFR occur changing temporarily the arrow of time in ZEO and induce nerve pulse. Could opposite BSFR take place after this in millisecond scale and establish the original arrow of time. Using the language of TGD inspired theory of consciousness a conscious entity, sub-self or mental image, would die and reincarnate with an opposite arrow of time, live for the duration of nerve pulse and then die and reincarnate with the original arrow of time. Nerve pulse would be a propagation of a temporary neuron death along the axon and would occur as neuron becomes hyper-polarized.

  2. In the article about the recent findings of Minev et al related to quantum jump in atomic physics are discussed. ZEO predicting that the arrow of time is changed in BSFR. This would create the illusion that discontinuous quantum jumps correspond to a classical time evolution leading smoothly and deterministically to the final state.

    This because BSFR leads to a state with reversed arrow of time, which corresponds to a superposition of classical time evolutions leading from the final state to the geometric past and it this, which is observed.
    This would also explain why the removal of the irradiation inducing quantum jumps has no effect during the transition process and why a stimulation inducing opposite quantum jump can stop the process. Also the findings of Libet related to the active aspects of consciousness showing that neural activity seems to preceded volitional act can be understood in this framework without giving up the notion of free will.

    The first half of the nerve pulse would correspond to this apparent evolution to the time reversed final state with opposite membrane potential but actually being time reversed evolution from the final state. The second half of nerve pulse would correspond to opposite state function reduction establishing the original arrow of time. This model looks attractive but many details remain to be checked.

Why hyper-polarization should cause the temporary death of neuron or its subself?
  1. Metabolic energy feed is needed to preserve the polarization of neuron since membrane potential tends to get reduced by second law stating that all gradients are bound to decrease. There should be some maximal polarization possible to preserve using the existing metabolic energy resources.

  2. Does quantum jump to a state with opposite arrow of time happen as this limit is reached? Why? Could the metabolic energy feed stop causing the neuron to die to starvation? Why the death of neuron should happen so fast? Could the quantum criticality against the change of rotation to oscillation be the reason. When neuron cannot rotate anymore it would die immediately: the mental image "I am rotating" would die and reincarnate as its time reversal. Does the neuron feeded by metabolic energy become a provider metabolic energy during this period somewhat like dead organisms after their death. Can one conclude that this energy goes to some purpose inside neuron?

See the article Quantum self-organization by heff changing phase transitions or the chapter Quantum model for nerve pulse.

Quantum self-organization by heff changing phase transitions

The TGD based model for biological self-organization relies on the hierarchy heff=nh0 of effective Planck constants labelling dark phases of ordinary particles residing at magnetic flux quanta. This model generalizes and suggests the replacement of non-equilibrium thermodynamics as basis of self-organization with its quantum variant based on dark matter hierarchy. The challenge is to formulate basic thermodynamical notions like work in terms TGD based quantum theory.

The basic mechanism would be a phase transition creating dark matter phase as a Bose-Einstein condensate like state with particles having identical conserved quantum numbers. Conservation laws would force the ordinary matter to have opposite total charges. For instance, in the case of work one has momentum or angular momentum as a conserved charge. In the case of charge separation and high Tc superconductivity it would be em charge. Even color charges can correspond to conserved charges in TGD framework allowing scaled variants of strong interaction physics.

Basic biological functions involving the notion of work and also the formation of sensory percepts would rely on this mechanism. Also the ZEO based theory of consciousness predicting the change the arrow of time in ordinary state function reduction plays a central role and a model of nerve pulse is discussed as an example.

See the article Quantum self-organization by heff changing phase transitions or the chapter Quantum Theory of Self-Organization.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.