Monday, July 19, 2021

Connection with parity breaking, massivation, and PCAC hypothesis

Conserved vector current hypothesis (CVC) and partially conserved axial current hypothesis (PCAC) are essential elements of old-fashioned hadron physics and hold true also in the standard model.
  1. The ansatz, which realizes the Beltrami hypothesis, states that the vectorial Kähler current J equals apart from sign c=+/- 1 to instanton current I, which is axial current:

    J=+/- I .

    The condition states that only the left or right handed current chiral defined as

    LL/R= J+/- I

    is non-vanishing. For c≠ 1, both JL and JR are non-vanishing. Since both right- and left-handed weak currents exist, c≠ 1 seems to be a plausible option.

    By quantum classical correspondence, these currents serve as space-time correlates for the left- and right-handed fermion currents of the standard model. Note however that induced gamma matrices differ from those of M4: for instance, they are not covariantly constant but defines a current with divergence which vanishes by field equations.

  2. A more general condition would allow c to depend on space-time coordinates. The conservation of J forces conservation of I if the condition ∂αcIα=0 is true. This gives a non-trivial condition only in regions with 4-D CP2 and M4 projections.
  3. The twistor lift of TGD requires that also M4 has Kähler structure. Therefore J and I and corresponding Kähler gauge potential A have both M4 part and CP2 parts and Kähler action K, JK, J and I are sums of M4 and CP2 parts:

    AK= A(M4)+A(CP2),
    JK=JK(M4)+JK(CP2) ,
    K = K(M4)+K(CP2) ,
    J =J(M4)+J(CP2) ,
    I= I(M4)+I(CP2) .

    Only the divergence for the sum I of M4 and CP2 parts of the instanton currents must vanish:

    αIα=0 .

    A possible interpretation is in terms of the 8-D variant of twistorialization by twistor lift requiring masslessness in an 8-D sense.

    PCAC states that the divergence of the axial current is non-vanishing. This is not in conflict with the conservation of the total instanton current I. PCAC corresponds to the non-conservation I(CP2), whose non-conservation is compensated by that of I(M4).

  4. For regions with at most 3-D M4- and CP2 projections, the M4- and CP2 instanton currents have identically vanishing divergence. In these regions the conservation of I is not lost if c has both signs. c could be also position dependent and even differ for I(M4) and I(CP2) in these regions.

    DαIα=0 is true for the known extremals. For the simplest CP2 type extremals and for extremals with 2-D CP2 projection, I itself vanishes. Therefore parity violation is not possible in these regions. This would suggest that these regions correspond to a massless phase.

  5. DαIα≠ 0 is possible only if both M4 and CP2 projections are 4-D. This phase is interpreted as a chaotic phase and by the non-conservation of electroweak axial currents could correspond to a massive phase.

    CP2 type extremals have 4-D projection and for them Kähler current and instanton current vanish identically so that also they correspond to massless phase (M4 projection is light-like). Could CP2 type extremals allow deformations with 4-D M4 projection (DEs)?

    The wormhole throat between space-time region with Minkowskian signature of the induced metric and CP2 type extremal (wormhole contact) with Euclidian signature is light-like and the 4-metric is effectively 3-D. It is not clear whether this allows 4-D M4 projection in the interior of DE.

  6. The geometric model for massivation based on zitterbewegung of DE provides additional insight. M8-H duality allows to assign a light-like curve also to DE. For space-time surfaces determined by polynomials (cosmological constant Λ>0), this curve consists of pieces which are light-like geodesics.

    Also real analytic functions (Λ=0) can be considered and they would allow a continuous light-like curve, whose definition boils down to Virasoro conditions. In both cases, the zigzag motion with light-velocity would give rise to velocity v<c in long length scales having interpretation in terms of massivation.

    The interaction with J(M4) would be essential for the generation of momentum due to the M4 Chern-Simons term assigned with the 3-D light-like partonic orbit. M4 Chern-Simons term can be interpreted as a boundary term due to the non-vanishing divergence of I(M4) so that a connection with two views about massivation is obtained. Does the Chern-Simons term come from the Euclidean or Minkowskian region?

I have proposed two models for the generation of matter-antimatter asymmetry. In both models, CP breaking by M4 Kähler form is essential. Classical electric field induces CP breaking. CP takes self-dual (E,B) to anti-self-dual (-E,B) and self-duality of J(M4) does not allow CP as a symmetry.
  1. In the first model the electric part of J(M4) would induce a small CP breaking inside cosmic strings thickened to flux tubes inducing in turn small matter-antimatter asymmetry outside cosmic strings. After annihilation this would leave only matter outside the cosmic strings.
  2. In the simplest variant of TGD only quarks are fundamental particles and leptons are their local composites in CP2 scale. Both quarks and antiquarks are possible but antiquarks would combine leptons as almost local 3-quark composites and presumably realized CP2 type extremals with the 3 antiquarks associated with the partonic orbit. I should vanish identically for the DEs representing quarks and leptons but not for antiquarks and antileptons.

    Could the number of DEs with vanishing I be smaller for antiquarks than for quarks by CP breaking and could this induce leptonization of antiquarks and favor baryons instead of antileptons? Could matter-antimatter asymmetry be induced by the interior of DE alone or by its interaction with the Minkowskian space-time region outside DE.

In the standard model also charged weak currents are allowed. Does TGD allow their space-time counterparts? CP2 allows quaternionic structure in the sense that the conformally invariant Weyl tensor has besides W3=J(CP2) also charged components W+/-, which are however not covariantly constant. One can assign to W+/- analogs of Kähler currents as covariant divergences and also the analogs of instanton currents. These currents could realize a classical space-time analog of current algebra.

See the article Comparing the Berry phase model of super-conductivity with the TGD based model or the chapter with the same title.

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

Articles and other material related to TGD.

Possible implications of the TGD based model of superconductivity

The universality of the TGD based model of superconductivity provides support for rather far-reaching earlier speculations.
  1. The TGD inspired model suggests that SC could be possible also above Tc by using energy feed providing the energy needed to increase the value of heff. This would be the basic role of metabolism. This could have far reaching technological consequences and also profound implications concerning the creation of artificial life.

    Furthermore, the TGD based model for "cold fusion" \cite{cfagain,krivit,proposal} led to a reformulation of nuclear physics \cite{darkcore} in which phase transition to dark phase of nuclei has a key role also in the ordinary nuclear reactions as a description of tunnelling phenomenon.

  2. In the TGD inspired quantum biology, the cell membrane is identified as a generalized Josephson junction between superconductors assignable to lipid layers of the cell membrane (actually decomposing in a better resolution to membrane proteins acting as Josephson junctions). One can ask what a straightforward application of the basic formulas gives in the case of neuronal membrane.

    One can estimate the gap energy \Delta from the formula \Delta = ℏ ωD using the already discussed formula ωD = kn cs/a, where kn depends on the effective dimension of the lattice like system and has values kn ∈ {3.14,3.54,2.66} for n=1,2,3. Sound velocity cs can be replaced with the conduction velocity v of nerve pulses varying in the range v/c\in[.1,1]\times 106. The formula would give for n=2 and maximal value v/c=10-6 ED= .044 eV which is in the range of neuronal membrane potentials.

  3. The role of ℏgr and Bend in the model would suggest that the SC observed in laboratories is not a mere local condensed matter phenomenon. What happens to SC on Mars? Is the Earth mass replaced with that of Mars and the monopole part Bend with its value in Mars? There is evidence that Bend is non-vanishing: for instance, Mars has auroras.
  4. If the monopole flux tube indeed mediates graviton exchanges, one can wonder whether SC itself is an essentially quantum gravitational phenomenon. Could the attractive interaction between electrons of the Cooper pair be somehow due to gravitation?

    The extremely weak direct gravitational interaction between electrons and nucleons cannot be responsible for the formation of Cooper pairs. One can however argue that Earth takes the role of atomic nuclei in the proposed description. Earth attracts the electrons and causes an effective attraction between them. Could this interaction force the wave functions of the electrons of the Cooper pair with wavelength \Lambdagr= rS=2GM\simeq 9 mm to overlap and form a quantum coherent state. For Sun one has \Lambdagr= 1 Mm, which is slightly below Earth radius. Could Sun's gravitation make the macroscopic quantum phase in the Earth's scale?

    The proposed duality between gauge theories and gravitation, in particular AdS/CFT duality, has a TGD counterpart. The dynamics for the orbits of partonic 2-surfaces and lower-dimensional surface defining a frame for the space-time surface as an analog of soap film \cite{minimal} would be dual to the dynamics in the interior of the space-time surfaces.

    Could the descriptions in terms of cyclotron photon exchanges and graviton exchanges be dual to each other? Note also that at the fundamental level classical TGD are expressible using only 4 classical field-like variables as a selected subset of imbedding space coordinates. This implies extremely strong constraints between fundamental interactions.

See the article Comparing the Berry phase model of super-conductivity with the TGD based model or the chapter with the same title.

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

Articles and other material related to TGD.

The 4 anomalies of BCS model of superconductivity in TGD framework

The article of Koizumi \cite{BerrySC} mentions 4 anomalies of the BCS model of superconductivity (SC) (no generally accepted model of high-Tc SC exists). Besides the absence of the difference of chemical potentials in the condition defining Josephson frequencies, 3 other anomalies are mentioned. These anomalies do not plague the TGD based model. The basic reason is that Cooper pairs reside at the magnetic flux tubes.
  1. There is only one transition temperature in the BCS model of SC whereas high-Tc superconductivity involves 2 transition temperatures. Above critial temperature would be that the gap energy is negative above critical temperature so that the energy liberated in the formation of Cooper pairs cannot provide the energy needed to increase heff.

    In the TGD framework the first transition temperature leads to a superconductivity but in spatial and time scales (proportional to heff), which are so short that macroscopic super-conductivity is not possible. In the lower transition temperature heff increases and the flux tubes reconnect in a stable manner to longer flux tubes. The instability of this phase at critical temperature would be due to the geometric instability of the flux tubes.

  2. London moment depends on the real electron mass me rather than the effective mass me* of the electron. This effect relates to a rotating magnet. There is a supra current in the boundary region creating the magnetic moment. The explanation is that the electrons resulting from the splitting of Cooper pairs at the flux tubes of magnetic field do not interact with the ordinary condensed matter so that the mass is me.
  3. For SCs of type I, the reversible phase transition from SC to ordinary phase in an external magnetic field does not cause dissipation. One would expect that the splitting of Cooper pairs produces electrons, which continue to flow and dissipate in collisions with the ordinary condensed matter. The reversibility of the phase transition can be understood if the electrons continue to flow at the flux tubes as supracurrents.
  4. Magnetic flux tubes also solve the anomaly related to chemical potential: chemical potentials are present but not at the level of magnetic flux tubes so that the erratic calculation gives a correct result in the standard approach.
See the article Comparing the Berry phase model of super-conductivity with the TGD based model or the chapter with the same title.

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

Articles and other material related to TGD.

Beltrami flow as space-time correlate for non-dissipative flow

In the standard model of superconductivity SC is characterized by a complex order parameter for which the Berry phase would serves as an analog in BPM. Berry phase is a consequence of adiabaticity and characterizes collective phase. One can assign to the Berry phase effective U(1) gauge field which reduces to magnetic field in a static situation. What are the TGD counterparts of these notions?

TGD provides the geometrization of classical physics in terms of space-time surfaces carrying gravitational and standard model fields as induced fields so that both the supra current and the phase should have geometric intepretation. This serves as a powerful constraint on the model.

  1. Supra current must correspond to a flow. The flow must be integrable in the sense that the coordinate defined along flow lines defines a global coordinate at flux tubes. One can indeed argue that an operational defition of a coordinate system requires that coordinates correspond to coordinates varying along flow lines of some physical flow. The exponential of the coordinate would define the phase factor of the complex order parameter such that its gradient defines the direction of the supracurrent.

    If the motion of particles is random one cannot talk of a hydrodynamic flow but something analogous to the motion of gas particles or Brownian motion. In the TGD framework this situation corresponds to disjoint space-time sheets as a representation of particle orbits. The flow property could however hold true inside the "pieces" of space-time. The coherence scales of flow would become short.

  2. One must make it clear that here an approximation is made. Elementary particles have as building bricks wormhole contacts defining light-like partonic orbits to which one can assign light-like curves as M4 projections. For a vanishing value \Lambda=0 of cosmological constant (real analytic functions at M8 level), these curves are light-like (light-likeness condition reduces to Virasoro conditions) whereas for \Lambda>0 (real polynomials) at M8 level the projections consist of pieces which are light-like geodesics somewhat like in the twistor diagrams \cite{minimal}. Smooth curve is replaced with its approximation.

    For massive particles, this orbit would be analogous to zitterbewegung orbit and the motion in the long scales would occur with velocity v<c: this provides a geometric description of particle massiation. The supracurrent would not actually correspond to the flow as such but to CP2 type extremals along the flow lines.

  3. The 4-D generalization of so called Beltrami flow \cite{Beltrami,Beltramia,Beltramib,Beltramic}, which defines an integrable flow in terms of flow lines of magnetic field, could be central in TGD. Superfluid flows and supra currents could be along flux lines of Beltrami flows defined by the Kähler magnetic field \cite{class,prext}.

    If the Beltrami property is universal, one must ask whether even the ordinary hydrodynamics flow could represent Beltrami flow with flow lines interpreted in terms of flow lines Kähler magnetic field appearing as a a part of classical Z0 field. Could hydrodynamical flow be stabilized by a superfluid made of neutrino Cooper pairs. heff hierarchy of dark matters in turn inspires the question whether weak length scale could be scaled up to say cellular length scales (neutrino mass corresponds to a length scale of a large neuron).

  4. The integrability condition

    j∧ dj=0

    of the Beltrami flow states that the flow is of form

    j= Ψ dΦ ,

    where Φ and Ψ are scalar functions, which means that Ψ defines a global coordinate varying along the flow lines.

  5. Beltrami property means that the classical dissipation characterized by the contraction of the Kähler current


    with Kähler form Jαβ is absent:

    jβJαβ=0 .

    In absence of Kähler electric field (stationary situation), this condition states the 3-D current is parallel with the magnetic field that it creates.

    In 4-D case, the orthogonality condition guarantees the vanishing of the covariant divergence of the energy momentum tensor associated with the Kähler form. This condition is automatically true for the volume part of the energy momentum tensor but not for the Kähler part, which is essentially energy momentum tensor for Maxwell's field in the induced metric. As far as energetics is considered, the system would be similar to Maxwell's equations.

    The vanishing of the divergence of the energy momentum tensor would support Einstein's equations expected at QFT limit of TGD when many-sheeted space-time is approximated with a slightly curved region of M4 and gauge and gravitational fields are defined as the sums of correspond induced fields (experienced by test particles touching all space-time sheets).

  6. An interesting question is whether Beltrami condition holds true for all preferred extremals \cite{prext} \cite{minimal}, which have been conjectured to be minimal surfaces analogous to soap films outside the dynamically generated analogs of frames at which the minimal surface property fails but the divergences of isometry currents for volume term and Kähler action have delta function divergences cancelling each other. The Beltrami conditions would be satisfied for the minimal surfaces.

    If the preferred extremals are minimal surfaces and simultaneous extremals of both the volume term and the Kähler action, one expects that they possess a 4-D analog of complex structure \cite{minimal}: the identification of this structure would be as Hamilton-Jacobi structure \cite{prext} to be discussed below.

  7. Earlier I have also proposed that preferred extremals involving light-like local direction as direction of the Kähler current and orthogonal local polarization direction. This conforms with the fact that Kähler action is a non-linear generalization of Maxwell action and minimal surface equations generalize massless field equations. Locally the solutions would look like photon like entities.

    This inspires the question whether all preferred extremals except CP2 type extremals defining basic building bricks of space-time surfaces in H have a 2-D or 3-D CP2 projection and allow interpretation as thickening of flux tubes? CP2 type extremals have 4-D CP2 projection and light-like M4 projection and an induced metric with an Euclidean signature.

    See the article Comparing the Berry phase model of superconductivity with the TGD based model or the chapter with the same title.

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

    Articles and other material related to TGD.

Sunday, July 18, 2021

Non-dissipative waves in excitonic insulators: a connection with superconductivity?

This comment was inspired by a popular article, which tells that in excitonic insulators, very fast waves with velocity about v∼ .01c, are detected. What caught my attention is that these waves do not dissipate. The theoretical challenge is to explain why this the case. The absence of dissipation means an analogy with superconductors.

I have just worked out the newest version of the TGD based model of superconductivity (see this) with an inspiration coming from the Berry phases model, in particular the anomalies of the BCS model mentioned in the article describing the model.

  1. The model suggests a universal framework applying not only to super-conductivity but also to super-fluidity and various phenomena involving absence of dissipative effects.
  2. The model predicts that also electrons rather than only Cooper pairs can propagate without dissipation at magnetic flux tubes at which $heff> h$ electrons and their Cooper behaving effectively like dark matter are. Also the Berry phase model predicts this.
  3. Second prediction is that by external energy feed it is possible to have superconductivity also above Tc: this mechanism (metabolic energy feed) is the basic mechanism of TGD inspired quantum biology making possible high Tc superconductivity.
  4. An attractive assumption is that the flux tubes mediated gravitational interaction: in this case one would have h<eff =hgr= GMm/v0, where M is Earth mass, m is the mass of charge carrier, and v0 is velocity parameter with at Earth surface has value v0=c/2 giving for the universal gravitational Compton length the value λgr= 2GM =rs, the Scwartshild radius, which is .9 cm for Earth. This would predict universality for various supraphases. Intriguingly, for Sun and inner planets one has v0= about 2-11 and λgr is very near to the radius of Earth!
Excitonic insulators are described in a second popular article telling about their discovery (see this . They exist in a phase transition region between insulator and conductor as the gap between valence band and conduction band becomes zero. In the TGD framework this means quantum criticality and the presence of heff> h phases are associated with the long range correlations and fluctuations at criticality quite generally.

The physical picture looks very similar to that in super-conductivity.

  1. Instead of Cooper pairs, one could have bound states of electron and hole bound by Coulomb interaction. The gap energy approaches zero at critical temperature in both cases. For a superconductor the gap energy corresponds to the energy needed to kick out an electron or Cooper pair formed at the level of ordinary matter to the magnetic flux tube with heff> h (increase of heff increases the energy of the state). The liberated binding energy - gap energy - allows the kicking. The gap energy is negative above Tc and superconductivity is not possible.

    The same would apply also in the case of excitonic insulators. The formation of the bound states of heff> helectrons and holes would liberate the binding energy allowing kicking of something to the magnetic flux with heff> h.

  2. What is this something? The high velocity v ∼ 10-2c non-dissipating charge neutral waves are observed. v is much higher than sound velocity (or order 10-4c roughly). The Fermi velocity for electrons for EF< 10 eV gives a correct order of magnitude so that some kind of charge density waves of this something at flux tubes could be in question. Could this something be Cooper pairs and/or electrons? One would have something resembling superconductivity as a quantum coherent state phase of Cooper pairs.

    The experimentalists believe that the non-dissipating waves are charge neutral - probably because one has an insulator. Is charge neutrality necessary if flux tubes can serve as carriers of dark currents?

For background, see the article Comparing the Berry phase model of super-conductivity with the TGD based model or the chapter with the same title.

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

Articles and other material related to TGD. 

Thursday, July 15, 2021

Comparing the Berry phase model of super-conductivity with the TGD based model

Hiroyasu Koizumi (see this) has proposed a new theory of superconductivity (SC) based on the notion of Berry phase related with an effective magnetic field assignable to adiabatically evolving systems. The model shares similarities with the TGD inspired view about SC. The article also mentioned anomalies that were new to me. This motivated a fresh look in the TGD inspired model. The outcome was an integration of two separate ideas about supraphases.
  1. Space-time surfaces as preferred extremals with CP2 projection of dimension D=2 or D=3 would naturally correspond to 4-D generalizations of so called Beltrami flows, which are integrable flows defined by the flow lines of the induced K\"ahler field. The existence of a global coordinate z varying along flow lines requires the integrability of the flow. Classical dissipation is absent so that these surfaces are excellent candidates for the space-time correlates of supra flows. The exponential of z gives a phase factor associated with the complex order parameter of a coherent state of Cooper pairs as a counterpart of the Berry phase. K\"ahler magnetic monopole flux defines the TGD counterpart of "novel" magnetic field.
  2. The identification of supra phases as dark matter as heff>h phases at magnetic flux quanta (tubes and sheets) implies that Cooper pairs correspond to dark fermions associated with the members of flux tube pair, which actually combine to form a closed flux tube. Also single electrons can define supraflow.
  3. The Cooper pairs must be created by bosonic oscillator operators constructed from fermionic oscillator operators by bosonization. This is possible only in 1+1-dimensional situations. Thanks to the Beltrami flow the situation is effectively 1+1-dimensional. Bosonization makes it possible to identify SU(2) Kac-Moody algebra, which has an interpretation in the TGD framework.
The assumption that Cooper pairs reside at the magnetic flux quanta solves the 4 problems of standard framework mentioned by Koizumi: high-Tc SCs have two transition temperatures; electron mass me instead of its effective mass me* appears in Thomson moment; the reversible phase transition in an external magnetic field inducing a splitting of Cooper pairs does not involve dissipation; why the erratic calculation of the Josephson frequencies in standard model neglecting the chemical potentials gives a correct result?.

The formation of the Cooper pairs appears as a condition stabilizing the space-time sheets carrying dark matter and all preferred extremals could satisfy the conditions guaranteeing integrable flow and existence of a phase factor varying along flow lines. Could supra phases exist in all scales? Could the breaking of supra phases be only due to the finite size of the space-time sheets? Could even hydrodynamic flow involve super-fluidity of some kind - perhaps based on neutrino Cooper pairs as speculated earlier?

See the article Comparing the Berry phase model of super-conductivity with the TGD based model or the chapter with the same title.

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

Articles and other material related to TGD. 

Saturday, July 10, 2021

Galois groups and genetic code

Galois groups are realized as number theoretic symmetry groups realized physically in TGD a symmetries of space-time surfaces. Galois confinement as an analog of color confinement is proposed in TGD inspired quantum biology .

Galois groups, in particular simple Galois groups, play a fundamental role in the TGD view of cognition. The TGD based model of the genetic code involves in an essential manner the groups A5 (icosahedron), which is the smallest non-abelian simple group, and A4 (tetrahedron). The identification of these groups as Galois groups leads to a more precise view about genetic code. The question  why the genetic code is a fusion of 3 icosahedral codes and of only a  single tetrahedral code  remained however poorly understood. 

  The identification of the symmetry groups  of  the I, O, and T  as Galois groups  makes it possible  to  answer this question. Icosa-tetrahedral tesselation of 3-D hyperbolic space H3, playing centrl role in TGD, can be replaced with its 3-fold covering replacing  I/O/T with the corresponding symmetry group acting as a Galois group.  T has only  only a single Hamiltonian cycle and  its 3-fold covering  behaves effectively as a  single cycle. Octahedral codons can be regarded as icosahedral and tetrahedral codons so they do not contribute to the code.

See the article Galois groups and genetic code.

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

Articles and other material related to TGD.

Thursday, July 08, 2021

About the role of Galois groups in TGD framework

The inverse problem of Galois theory is highly interesting from TGD viewpoint. Galois groups are realized as number theoretic symmetry groups realized physically in TGD a symmetries of space-time surfaces. Galois confinement is as analog of color confinement is proposed in TGD inspired quantum biology .

Two instances of the inverse Galois problem, which are especially interesting in TGD, are following:

Q1: Can a given finite group appear as Galois group over Q? The answer is not known.

Q2: Can a given finite group G appear as a Galois group over some EQ? Answer to Q2 is positive as will be found and the extensions for a given G can be explicitly constructed.

The TGD based formulation based on M8-H duality in which space-time surface in complexified M8 are coded by polynomials with rational coefficients involves the following open question.

Q: Can one allow only polynomials with coefficients in Q or should one allow also coefficients in EQs?

The idea allowing to answer this question is the requirement that TGD adelic physics is able to represent all finite groups as Galois groups of Q or some EQ acting physical symmetry group.

If the answer to Q1 is positive, it is enough to have polynomials with coefficients in Q. It not, then also EQs are needed as coefficient fields for polynomials to get all Galois groups. The first option would be the more elegant one.

The inverse problem is highly interesting from the perspective of TGD. Galois groups, in particular simple Galois groups, play a fundamental role in the TGD view of cognition. The TGD based model of the genetic code involves in an essential manner the groups A5 (icosahedron), which is the smallest simple and non-commutative group, and A4 (tetrahedron). The identification of these groups as Galois groups leads to a more precise view about genetic code and answers to a key open question of the model in its recent form.

About the role of Galois groups in TGD framework or the chapter with the same title.

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

Articles and other material related to TGD.

Friday, June 25, 2021

What could 2-D minimal surfaces teach about TGD?

In the TGD Universe space-time surfaces within causal diamonds (CDs) are fundamental objects.
  1. M8-H duality means that one can interpret the space-time surfaces in two manners: either as an algebraic surface in complexified M8 or as minimal surfaces in H=M4× CP2. M8-H duality maps these surfaces to each other.
  2. Minimal surface property holds true outside the frame spanning minimal surface as 4-D soap film and since also extremal of Kähler action is in question, the surface is analog of complex surface. The frame is fixed at the boundaries of the CD and dynamically generated in its interior. At frame the isometry currents of volume term and Kähler action have infinite divergences which however cancel so that conservation laws coded by field equations are true. The frames serve as seats of non-determinism.
  3. At the level of M8 the frames correspond to singularities of the space-time surface. The quaternionic normal space is not unique at the points of a d-dimensional singularity and their union defines a surface of CP2 of dimension dc=4-D<d defining in H a blow up of dimension dc.
In this article, the inspiration provided by 2-D minimal surfaces is used to deepen the TGD view about space-time as a minimal surface and also about M8-H duality and TGD itself.
  1. The properties of 2-D minimal surfaces encourage the inclusion of the phase with a vanishing cosmological constant Λ phase. This forces the extension of the category of real polynomials determining the space-time surface at the level of M8 to that of real analytic functions. The interpretation in the framework of consciousness theory would be as a kind of mathematical enlightenment, transcendence also in the mathematical sense.
  2. Λ>0 phases associated with real polynomials as approximations of real analytic functions would correspond to a hierarchy of inclusions of hyperfinite-factors of type II1 realized as physical systems and giving rise to finite cognition based on finite-D extensions of rationals and corresponding extensions of p-adic number fields.
  3. The construction of 2-D periodic minimal surfaces inspires a construction of minimal surfaces with a temporal periodicity. For Λ>0 this happens by gluing copies of minimal surface and its mirror image together and for Λ=0 by using a periodic frame.

    A more general engineering construction using different basic pieces fitting together like legos gives rise to a model of logical thinking with thoughts as legos. This also allows an improved understanding of how M8-H duality manages to be consistent with the Uncertainty Principle.

  4. At the physical level, one gains a deeper understanding of the space-time correlates of particle massivation and of the TGD counterparts of twistor diagrams. Twistor lift predicts M4 Kähler action and its Chern-Simons implying CP breaking. This part is necessary in order to have particles with non-vanishing momentum in the Λ=0 phase.
See the article What could 2-D minimal surfaces teach about TGD?.

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

Articles and other material related to TGD. 

Saturday, June 19, 2021

Cosmic spinning filaments that are too long

The inspiration for writing this posting came from a highly interesting popular article (see this) providing new information about the cosmic filaments (thanks to Jebin Larosh for the link). The popular article tells about the article published in Nature (see this) and telling about the work of a team led by Noam Libeskind.

1. Findings

What has been studied is a long filament with length of order 108 ly characterizing the sizes of large cosmic voids. The filament consists of galaxies and the surprising finding is that besides moving along the filament, the galaxies associated with the filaments spin around the filament axis.

This finding suggests a network of filaments of length of order 108 ly and thickness of order 106 ly intersecting at nodes formed by large galaxy clusters. The larger the masses at the ends of the filament are, the larger the spin is.

How angular momentum is generated is the problem. The problem is quite general and is shared by both Newtonian and General Relativistic Universes. The natural assumption is that angular momentum vanishes in the original situation. Angular momentum conservation requires a generation of compensating angular momentum. This should happen in the case of all rotating structures. Already the case of galaxies is problematic but if the length scale of the structure is 108 ly, the situation becomes really difficult.

Gravitationally bound states have as a rule angular momentum preventing gravitational collapse but how the angular momentum is generated in a process believed to be a concentration of a homogeneous matter density to astrophysical objects? The basic problem is that the Newtonian description relies on scalar potential so that the field lines of the Newtonian gravitational field are never closed. It is difficult to imagine mechanisms for the generation of angular momentum by rotation. In the GRT based description gravi-magnetic fields, which are rotational, emerge but they are extremely weak. The proposal is that tidal forces could generate angular momentum but the generation of angular momentum remains poorly understood.

2. TGD view about the angular momentum generation

Could one understand the recent finding, and more generally, the generation of angular momentum, in the TGD framework? What raises hope is that in the TGD framework K\"ahler magnetic fields, whose flux tubes can be regarded as space-time quanta, are key players of dynamics in all scales besides gravitation.

2.1 Cosmic strings as carriers of dark matter and energy

The basic difference between GRT and TGD are cosmic strings and flux tubes resulting from their thickening. Cosmic strings are preferred extremals which are space-time surfaces with 2-D string world sheet as M4 projection and complex surface of CP2 as CP2 projection.

  1. The presence of the long filaments is one of the many pieces of support for the fractal web of cosmic strings thickened to flux tubes predicted by TGD. The scale is the scale of large voids 108 ly forming a kind of honeycomb like structure. The density of matter would be fractal in the TGD Universe (see this and this).
  2. Long cosmic string has a gravitational potential proportional to 1/\rho, \rho the transverse distance. This predicts a flat velocity spectrum for the stars rotating around the galaxy. No dark matter halo is needed. The model contains only a single parameter, string tension, and also this can be understood in terms of the energy density of the cosmic string. The motion along the string is essentially free motion which allows to distinguish the model from the halo model. In fact, the article reports linear motion along the filament.

    Amusingly, the same day that I learned about the spinning filaments, I learned about a new evidence for the absence of the galactic halo from a popular article (see this) telling about the article by Shen et al (see this).

2.2 Compensating angular moment as angular momentum of dark matter at cosmic string

Consider now the problem of how the compensating angular momentum is generated as visible matter starts to rotate.

In the TGD framework the picture is just the opposite.

  1. The basic assumption of the Newtonian and GRT based models for the generation of angular momentum is that all astrophysical objects are formed by a condensation of matter along perturbations of the mass density. The flow of mass occurs from long scales to short scales.
  2. Cosmic strings are the basic objects present already in primordial cosmology. Long cosmic strings form tangles along them in a local thickening, which gives rise to flux tubes. This involves the decay of dark energy and matter at cosmic string to ordinary matter around them as the string tension is reduced in a phase transition decreasing the coefficient of the volume term present in the action besides K\"ahler action as predicted by twistor lift of TGD. This parameter corresponds to length scale dependent cosmological constant Λ.

    Λ depends on p-adic length scale Lp∝ p1/2, p≈eq 2k and satisfies Λ(k)∝ 1/L2(k)2. Λ(k) approaches zero in long p-adic length scales characterizing the transversal size of flux tubes. This solves the cosmological constant problem. The thickness d≈ L(k) of the flux tube, which is rather small, determines the string tension. To L(k) there is associated a long p-adic length scale which is of order size of observed cosmology if d≈ L(k) is of order of 10-4 meters, which happens to be the size of a large neuron.

  3. The phase transitions reducing Λ reduce string tension are analogous to the decay of the inflaton field vacuum energy to ordinary matter. Now inflaton field vacuum energy is replaced with the dark energy and matter associated with the thickening cosmic string. Each phase transition is accompanied by an accelerated expansion. The period known as inflation in stanaard cosmology is the first phase transition of this kind. The recent accelerated expansion would correspond to a particular period of this kind and will eventually slow down.
What could happen in the decay of the energy of a flux tube tangle of a cosmic string to visible matter?
  1. The visible matter resulting in the decay of the cosmic string must start to rotate around the cosmic string since otherwise it would fall back to the cosmic string like matter into a blackhole. The cosmic string must somehow generate a spin compensating the angular momentum of the visible matter.
  2. One should understand angular momentum conservation. Generation of visible matter with angular momentum is possible only if the dark cosmic string is helical or becomes (increasingly) helical in the phase transitions. The angular momentum would be accompanied by the longitudinal motion along the string: this motion has been observed for the filaments.

    The helical structure could be present from the beginning or be generated during the decay of energy of the cosmic string leading to the local thickenings to flux tube giving rise to galaxies as tangles along a long cosmic string. Also the dark matter and energy at the cosmic string already have angular momentum so that the dark matter that transforms to visible matter would inherit this angular momentum.

    The reported correlation between the masses at the ends of the filament and the spin of the filament could be understood if the masses at the ends are formed from the dark energy and mass of the filament having angular momentum. The amount of spin and mass at the ends would be the larger, the longer the decay process has lasted.

  3. The identification of the galaxies as tangles along long cosmic strings explains the flatness of the galactic velocity spectrum. Galaxy rotates and also now the angular momentum conservation is the problem. The simplest solution is that the cosmic string portions between the tangles generate the angular momentum opposite to that of the visible matter.

    This would happen not only for the portions of cosmic string between galaxies but also those between stars in the galactic tangle. Stars would be flux tube spaghettis and the angular momentum of the star would be compensated by the angular momentum associated with the helical cosmic string continuing outside the star and connecting it to other stars.

The illustration of the popular article brings in mind a DNA double strand and inspires a consideration of an alternative, perhaps unnecessarily complex, model.
  1. Suppose one has a double helix of cosmic strings, call them Alice and Bob. Two stellar objects can form a gravitationally stable state only if relative rotation is present. This would be true also for a cosmic double strand to prevent gravitational collapse in 2-D sense.
  2. Alice could remain a cosmic string and thus dark so that we would not see it. Bob would thicken to a flux tube and produce ordinary matter as galaxies as ordinary matter realized tangles along it. The matter would inherit the angular momentum the dark matter and energy producing it already has. The string tension of Bob would be reduced in this process. Of course, both Alice and Bob could have tangles along them. The experiments however support the view that spin direction is the same along the filament.
  3. If the helical pair of cosmic strings is actually a closed loop in which the second strand is a piece of the same string, the motion of matter along strands is automatically in opposite directions and spins are opposite. The rotational motion as a stabilizer of a gravitationally bound state is transformed to a helical motion. The problem is however why only the other strand decays to ordinary matter (in the case of ordinary DNA there is an analogous problem due to the passivity of the second strand).
2.3 Is quantum gravitation in cosmic scales involved?

There is an interesting connection to atomic physics suggesting that quantum effects are associated with gravitationally bound dark matter even in astrophysical scales.

  1. The basic problem was that the electron should radiate its energy and fall into the atomic nucleus. The Bohr model of the atom solved the problem and non-radiating stationary states prevented the infrared catastrophe. Also in the gravitational case something similar is expected to happen for gravitational interaction.
  2. The Bohr model of solar system, originally introduced by Nottale, relies on the notion of gravitational Planck constant ℏgr= GMm/β0 predicts angular momentum quantization.
  3. Angular momentum quantization as multiples of ℏgr could occur also for the matter rotating around the cosmic string. In the case of the filament, the mass M could be replaced with the mass of the cosmic string (or possibly several of parallel cosmic strings) and m could correspond to the mass of a galaxy rotating around it. The velocity parameter β0=v0/c has a spectrum of values proposed to come as inverse integers.
See the article Cosmic spinning filaments that are too long or the chapter Cosmic string model for the formation of galaxies and stars.

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

Articles and other material related to TGD.

Thursday, June 17, 2021

Questions related to coupling constant evolution

There are several open questions related to the hierarchy of Planck constants and p-adic coupling constant evolution in the TGD framework.
  1. p-Adic length scale (PLS) hypothesis states Lp =p1/2R(CP2), Is this hypothesis correct in this recent form and can one deduce this hypothesis or its generalization from the basic physics of TGD defined by Kähler function of the "world of classical worlds" (WCW)? The fact, that the scaling of the roots of polynomial does not affect the algebraic properties of the extension forcesn to conlude that p-adic prime does not depend on purely algebraic properties of EQ. In particular, the proposed identification of p as a ramified prime of EQ must be given up.

    Number theoretical universality suggests the formula exp(Δ K)= pn, where Δ K is the contribution to Kähler function of WCW for a given space-time surface inside causal diamond (CD).

  2. The understanding of p-adic length scale evolution is also a problem. The "dark" coupling constant evolution would be αK = gK2/2heff = gK2/2nh0, and the PLS evolution gK2(k)=gK2(max)/k should define independent evolutions since scalings commute with number theory. The total evolution αK= αK(max)/nk would induce also the evolution of other coupling strengths if the coupling strenghts are related to αK by Möbius transformation as suggested.
  3. Nottale hypothesis predicts gravitational Planck constant ℏgr= GMm/β00=v0/c is velocity parameter), which has gigantic values. Gravitational fine structure constant is given by αgr= β0/4π. Kepler's law β2=GM/r=rS/2r suggests length scale evolution β2=xrS/2LN = β20,max/N2, where x is proportionality constant, which can be fixed.

    Phase transitions changing β0 are possible at LN/agr=N2 and these scales correspond to radii for the gravitational analogs of the Bohr orbits of hydrogen. p-Adic length scale hierarchy is replaced by that for the radii of Bohr orbits. The simplest option is that β0 obeys a coupling constant evolution induced by αK.

    This picture conforms with the existing applications and makes it possible to understand the value of β0 for the solar system, and is consistent with the application to the superfluid fountain effect.

  4. The formula heff=nh0 involves the minimal value h0. The simplest explanation for the findings of Randell Mills is that one has h=6h0. h0 could be also smaller. The natural guess is h0= gK2(max)/2, where gK is Kähler coupling constant which is the only fundamental coupling parameter in TGD. It turns out that this formula is implied by the number theoretic vision about coupling constant evolution. Gauge coupling strengths are predicted to be practically zero at gravitational flux tubes so that only gravitational interaction is effectively present. This conforms with the view about dark matter.
See the article Questions about coupling constant evolution or the chapter TGD View about Coupling Constant Evolution.

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

Articles and other material related to TGD.

Saturday, June 12, 2021

Sensory hubs in the brain are shifting although they should not

Sensory hubs (see this ) of sensory cortex responsible for integrated brain function are found to behave in an unexpected manner (see this. According to the textbook wisdom, sensory hubs responsible for sensory percepts should be static structures. Sensory hubers are however drifting in time scale of months. The phenomenon is called representational drift.

Sensory hubs are groups of highly connected neurons believed to be responsible for the integration of sensory experiences. They are present already from childhood and shift during childhood from the primary sensory areas receiving the sensory input from thalamus to the association areas. The connectivity strengthens, especially at frontal areas, from birth to adulthood. Note that also this shifting can be interpreted as a representational drift but in longer scale. Could this kind of evolution of sensory hubs be present also in time scale of months and make the drift necessary?

The findings

The popular article describes some examples of representational drift. The odor specific sensory hubs found by Carl Schoonover and Andrew Fink to drift around the piriform cortex is the first example.

  1. It is odor specificity that drifts. Sensory hub is clearly like a moving vortex in a flow - moving self-organization pattern of water flow rather than moving water. The connection structure between neurons essential for the formation of associations as learning is drifting. The drift seems to involve learning, which cannot be induced by the ordinary sensory input. Could there be a "teacher" that provides virtual sensory input? Learning analogous to that encountered in AI comes first in mind.
  2. In the case of odor perception studied for mice, daily sniffing slows down the drift. Why would the sensory input slow down or even prevent the virtual learning that seems to be present? Could the real sensory input interfere with the virtual sensory input?
  3. Experiments using weak electric shocks to induce conditioning of neurons of the hub, show that the conditioning is preserved in the drift. Is it really neurons that are conditioned at the fundamental level? Could the conditioning takes place at some other, in some sense higher level? Emotions are involved with conditioning. Who is the experiencer of these emotions? Does this higher level entity, kind of Mr. X, teach also the conditioning to the recruited neurons of the drifted sensory hub.

    Interestingly, the analogy with dark matter is noticed by Schoonover and Fink. Maybe they suggestt that something analogous to dark matter might be involved with living matter.

Also other examples are discussed.
  1. Hippocampal place cells are mentioned as a second example. Motion of an organism from position A to B is represented by certain place cells of the hippocampus, which are firing during the movement. The locus of firing place cells drifts slowly. Standard neuroscience interpretation would be as an overwriting of memories. Mice moving in a T-shaped maze are mentioned as an example. The neuronal groups in the posterior parietal cortex involved with spatial reasoning are drifting.
  2. Representational drift in the visual cortex is slower or not present. Could the slowness and possible absence be due to the more complex and precise organization? Or could it be due to the presence of a continual visual input interfering with the virtual sensory input needed for the drift? However, for the mouse that watched the same movies over many days, the drift took place. Pan-psychist might imagine that the neurons or something else related to the sensory hub got tired or bored while seeing the same movie from day to day and became a poor perceiver so that fresh neurons had to be recruited?


These findings just describe raise the following questions:

  1. How the representational drift is possible? The new neurons must learn associations and become conditioned. Ordinary sensory input cannot take care of this. Is there some kind of virtual sensory input from mysterious Mr. X present, which teaches the conditionings giving rise to specific sensory perceptions?

    How can the conditionings be preserved in the drift? Does this Mr. X also teach the conditionings to the recruited neurons by using virtual sensory input inducing them.

  2. Why does the drift occur and what would cause it? Could the neurons of the sensory hub get "bored" and become non-alert perceivers so that new neurons must be recruited? Or could one think that serving as a hub neuron or its MB is hard work and also neurons or their MBs must have "vacation" and rest.
  3. Why sensory input slows down the drift? Does it interfere with or prevent the learning process of the recruited neurons?
  4. Could the analogy of drifting sensory hub with a moving vortex, self-organization pattern of flow, serve as a guideline? Note that incompressible hydrodynamical flow is mathematically highly analogous to a magnetic field. Could one see neurons as particles of an analog of hydrodynamic flow or perhaps its counterpart at the level of magnetic field?
These purposefully leading questions should make it easy for any-one familiar with the TGD based view about neuroscience to guess the TGD inspired model for the representational drift. Before introducing the model, some basic ideas about the brain in the TGD Universe are discussed.

TGD view about sensory perception and emotions

The representational drift provides a new challenge for the standard dogma that sensory qualia are somehow constructed at neuronal level in the brain. There is also the problem that the neuronal stuff looks the same in all sensory areas: how could this give rise to so different sensory qualia.

Magnetic body (MB) defines the basic notion.

  1. Magnetic body (MB) carrying heff=g×h0 behaving like dark matter has IQ characterized by n, which is identifiable as a measure of complexity of an n-D extension of rationals associated with the polynomial defining a region of space-time surface assignable to MB. n characterizes also the scale of quantum coherence at MB and this quantum coherence induces the ordinary (non-quantal)vcoherence of biomatter. By its higher IQ MB serves as a boss for layers of MB with smaller IQ and at the bottom of hierarchy is the ordinary matter with heff=h.

    MB has both "small" parts with size scale of brain structure and "large" parts having size scale even larger than scale of Earth which corresponds to EEG frequencies around alpha band. Also highly neuron groups have both small MB and larger part of MB. Small MB would have flux tubes parallel to axons and these flux tubes could induce the self-organization leading to the formation of axons and synaptic contacts.

  2. The primary sensory qualia are at the level of sensory organs and the brain builds only cognitive representations (also secondary sensory representations not directly conscious to us are possible) and pattern recognition by receiving the input from the sensory organs and providing feedback as a virtual sensory input to sensory organs (see this). REM dreams and hallucinations are a good example of an sensory experience due to mere virtual sensory input. Also imagination can be understood. The picture generalizes to the level of motor actions.

    Phantom limb serves as an obvious objection: if the sensation is sensory memory this objection can be circumvented. Sensory memories can be produced by electrical stimulation of temporal lobes artificially.

  3. In the TGD framework the sensory data are communicated to MB by EEG and its fractally scaled variants, where the fundamental representations reside. Neurons are analogous to RAM memory which is organized at the MB. The selection of neurons responsible for the construction of the sensory perceptions as kinds of artworks and for the communication of data to MB can be dynamical.

    There is indeed evidence that neurons in the brain obey an effective hyperbolic geometric determined statistically (see this). Neurons functionally close to each other are near to each other in this geometry. Their images at MB would indeed be near to each other and this geometry would be hyperbolic as a geometry of hyperboloid of Minkowski space. One weird finding conforming with this picture is that salamander survives in a process reshuffling of its neurons.

  4. Sensory perceptions correspond to standardized mental images created bu a combination of a real sensory input communicated to MB and inducing as a response virtual sensory input from MB via brain to sensory organs as dark photons signals.

The TGD inspired model model for representational drift

  1. Sensory hub is a higher level structure having MB controlling it. It is MB that experiences emotions as higher level sensory experiences by entangling with sensory organs and receiving sensory input also as dark photon signals. The highly connected flux tube structure of MB induces the neuronal connections of the sensory hub. Structural hubs are present from birth.
  2. Either the small MB or its big brother would control the sensory hub by sending control signals and virtual sensory input. MB could even teach neuronal groups various associations and conditionings. This would be somewhat like teaching of a neural network in AI.
  3. Emotions are associated with conditionings and they would represent higher level sensory perceptions of MB and be essential for the conditioning. The "big" part of MB would be responsible for higher level emotions and "small" part for more primitive emotions like hunger and first essential for conditioning of neurons.
  4. The fact that sensory hubs are present already in childhood suggests that standardized sensory mental images could be genetically determined and therefore inherited. One can wonder whether this could relate to the inheritance of long term moods. Could also moods and emotional patterns be genetically coded and also inherited to some degree?

    The TGD based model for the genetic code indeed leads to this picture. The key element of ZEO is that not only structures but also temporal patterns (functions, behaviors) are inherited.

  5. Representational drift requires that the connection structure for the neurons of a new hub is recreated by learning. Ordinary sensory input cannot generate the hubs with standardized sensory mental images at neuronal level.

    Does MB as a boss teach standardized mental to neurons by using virtual sensory input just at it would do to induce standardized mental images? This would be analogous to teaching in associative learning and in AI.

  6. Why does the drift occur? Why would MB recruit new neurons and teach them to produce standardized mental images?

    Does something happen to the neurons of the hub. Do they get bored or tired and lose their alertness after experiencing the same mental images again and again? The notion of aging is a universal phenomenon in TGD view about life and consciousness (see this): could the the neurons of the sensory hub begin to suffer from problems caused by aging?

    The sensory hubs shift from primary areas to the associative cortex during childhood and their connectivity increases. Could this mean some kind of personal evolution at the level of the sensory hub, analogous to professional at the level of human society.

To sum up, MB might be doing for the brain the same as we are now doing for robots, that is teaching them. Could our AI technology be an externalization of what MB is doing for the biological body?

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

Articles and other material related to TGD.

Wednesday, June 09, 2021

Some questions concerning zero energy ontology

The article Some comments related to Zero Energy Ontology (ZEO) written for few years ago challenged the basic assumptions of ZEO. One tends to forget the unpleasant questions but now it was clear that it is better to face the fear that there might be something badly wrong. ZEO however survived and several ad hoc assumptions were eliminated.

Progress at the level of basic TGD

The basic goal is to improve the understanding about quantum-classical correspondence. The dynamics of soap films serves as an intuitive starting point.

  1. In TGD frame 3-surfaces at the boundaries of CD define the analog of frame for a 4-D soap film as a minimal surface outside frame. This minimal surface would be an analog of a holomorphic minimal surface and simultaneous exremal of Kähler action except at the frame where one would have delta function singularities analogous to sources for massless d'Alembert equation.
  2. There is also a dynamically generated part of the frame since the action contains also Kähler action. The dynamically generated parts of the frame would mean a failure of mimimal surface property at frame and also the failure of complete determinism localized at these frames.
  3. At frame only the equations for the entire action containing both volume term and Kähler term would be satisfied. This guarantees conservation laws and gives very strong constraints to what can happen at frames.

    The frame portions with various dimensions are analogous to the singularities of analytic functions at which the analyticity fails: cuts and poles are replaced with 3-, 2-, and 1-D singularities acting effectively as sources for volume term or equvavelently Kähler term. The sum of volume and Kähler singularities vanish by field equations. This gives rise to the interaction between volume and Kähler term at the loci of non-determinism.

  4. H-picture suggests that the frames as singularities correspond to 1-D core for the deformations of CP2 type extremals with light-like geodesic as M4 projection, at partonic 2-surfaces and string world sheets, and at 3-D t=tn balls of CD as "very special moments in the life of self" which integrate to an analog of catastrophe.

    Deformations of Euclidian CP2 type extremals, the light-like 3-surfaces as partonic orbits at which the signature of the induced metric changes, string world sheets, and partonic 2-surfaces at r=tn balls taking the role of vertices give rise to an analog of Feynman (or twistor -) diagram. The external particles arriving the vertex correspond to different roots of the polynomial in M8 picture co-inciding at the vertex.

The proposed picture at the level of H=M4 × CP2 has dual at the level of (complexified) M8 identifiable as complexified octonions. The parts of frame correspond to loci at which the space-time as a covering space with sheet defined by the roots of a polynomial becomes degenerate, i.e. touch each other.

There is a nice analogy with the catastrophe theory of Thom. The catastrophe graph for cusp catastrophe serves as an intuitive guide line. Imbedding space coordinates serve as behaviour variables and space-time coordinates as control variables. One obtains a decomposition of space-time surface to regions of various dimension characterized by the degeneracy of the root.

Progress in the understanding of TGD inspired theory of consciousness

The improved view about ZEO makes it possible to define the basic notions like self, sub-self, BSFR and SSFR at the level of WCW. Also the WCW correlates for various aspects of consciousness like attention, volition, memory, memory recall, anticipation are proposed. Attention is the basic process: attention creates sub-CD and subself by a localization in WCW and projects WCW spinor field to a subset of WCW. This process is completely analogous to position measurement at the level of H. At the level of M8 it is analogous to momentum measurement.

One can distinguish between the Boolean aspects of cognition assignable to WCW spinors as fermionic Fock states (WCW spinor field restricted to given 3-surface). Fermionic consciousness is present even in absence of non-determinism. The non-determinism makes possible sensory perceptions and spatial consciousness.

A precise definition of sub-CD as a correlate of perceptive field at WCW level implies that the space-time surfaces associated with sub-CDs continue outside it. This gives powerful boundary conditions on the dynamics. For the largest CD in the hierarchy of CDs of a given self, this constraint is absent, and it is a God-like entity in ZEO. This leads to a connection between the western and eastern views about consciousness.

A connection with the minimal surface dynamics emerges. The sub-CDs to which mental image as subselves are assigned would be naturally associated with portions of dynamically generated frames as loci of non-determinism. If one identifies partonic 2-surfaces as vertices, one can interpret the collection of possible space-time surfaces for a fixed 3-surface at PB as a tree. All paths along the tree are possible time-evolutions of subself. The dynamics of consciousness for fixed 3-surface at PB becomes discrete and provides discrete correlate for a volitional action as selection of a path or a subset of paths in the tree. The reduction of dynamics of mental imagines to discrete dynamics would mean a huge simplification and conforms with the discreteness of cognitive representations.


There are many challenges to be faced. The discreteness dynamics of sub-self consciousness certainly correlates with the notion of cognitive representation based on adelic physics and implying a discretization at both space-time level and WCW level. The Galois group for the extension of rationals acting on the roots of the polynomial plays a key role in this dynamics.

One teaser question remains. Localization requires energy quite generally and this conforms with the fact that mental images demand metabolic energy feed. It is possible to redirect attention and remain unclear whether the mental image disappears totally or suffers BSFR.

See the article Some questions concerning zero energy ontology.

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

Articles and other material related to TGD.

Wednesday, June 02, 2021

Water oxidation and photosynthesis in TGD framework

Water oxidation in which water splits into 4 electrons, 4 protons and oxygen molecule O2 is the first step of photosynthesis.  The catalytic mechanism behind water oxidation remains rather  poorly understood. The total binding energy of H2O is about 75 eV and the catalyst should  provide this energy to temporarily overcome this barrier. Zero energy ontology (ZEO), which is behind the TGD based quantum measurement theory,   predicts that "big" (ordinary) state function reductions (BSFRs) involve time reversal. The time reversal of water oxidation occurs spontaneously in a  reversed time direction and second BSFR establishing the original arrow of time  makes it possible  to achieve water oxidation.  This mechanism involving two BSFRs applies quite generally to  catalysis.

 The  function of the  catalyst is to make possible the BSFR and the natural expectation is that the description of catalysis as a process with apparently standard arrow of time is possible.  The reduction of the value of $h_{eff}$ for cyclotron states of dark  particles at magnetic flux tube liberates energy assignable to cyclotron states of dark particles and could kick the reactants over the potential wall making the reaction extremely slow otherwise.

See the article Water oxidation and photosynthesis in TGD framework or the chapter Quantum criticality in TGD Universe: part III

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

Articles and other material related to TGD.

Saturday, May 22, 2021

Chemistry revolution

Thanks for Moore Thaung for a very interesting article of new chemistry. Unfortunately, a subscription to New Scientist is required. One can however find in the web several popular articles telling about the changing views of chemical bonds.

This weird chemical bond acts like a mash-up of hydrogen and covalent bonds tells about hybrids of hydrogen and and covalent bonds. For short bond lengths these bonds become strong valence bonds and for long bond lengths weak hydrogen bonds which can even have length of 3 Angstrom.

Strange bonds entirely new to chemists predicted in ammonia hydrides tells that ammonium NH3 can form in the presence of hydrogen in very high pressure an exotic compound NH7, which can decay to NH4+ + H2+ H. NH4+ is also exotic.

Sticking together: Another look at chemical bonds and bonding discusses the theory of chemical bonds proposed by Prof. David Brown, which has turned out to be very successful. His article Another look at bonds and bonding is published in Structural Chemistry 31(1), 2019.

The bond theory of David Brown

The bond theory of David Brown is of special interest.

  1. The theory involves the notion of electric flux as a purely classical element. The delocalization of valence electrons is of course a non-classical element and one can argue that this aspect is not well-understood in standard chemistry.

    In the TGD framework, the counterpart of electric flux is a flux tube carrying magnetic flux, which can be monopole flux. Thetube can also carry an electric flux and a simple modification of purely magneticflux tubes gives tubes carrying also an electric flux.

  2. The key concept besides the notions of valence defined as the number Nv of valence electrons belonging to bonds, and the number of valence bonds Nb, is valence strength defined as Nv/Nb. The total electric flux is the sum of fluxes assignable to the bonds and equals to the total electric charge -Nve of valence electrons.

    By flux conservation, the electric fluxes at the ends of a given bond are opposite and this gives a strong constraint on the model. This condition is new from the point of standard bond theory and is purely classical.

  3. The configurations with minimum energy are expected to be symmetric. In this case, the electric fluxes for the bonds are expected to be identical and proportional to the common bond strength.
    1. An important implication of flux conservation in the symmetric case is that the valence strengths must be the same for bonded atoms. This condition excludes a large number of candidates.
    2. If Nb is larger than Nv the flux is fractional. This would represent an exotic situation. An interesting question, is whether the flux could correspond to a quark pair or two quark pairs possible in TGD framework in long scales: in this case the flux would be 1/3:rd or 2/3:rd of the flux associated with a single valence electron.
  4. The model works for many kinds of bonds, and is claimed to work even for hydrogen bonds, and can be used to predict possible bonding structures. What is remarkable, that the notion of conserved electric flux assignable to chemical bonds resonates with the TGD view that non-trivial space-time topology behind the notion of flux tube is directly visible at the level of chemistry.

TGD view about chemical bonds

I remember the time when I realized that TGD suggests a description of the chemical bond in terms of the space-time topology. Could chemistry books be wrong, was the question, which I barely dared to articulate.

Gradually I learned that chemistry books do not really allow any deeper understanding of chemical bonds. One just says that they follow from Schodinger equation but computational complexity prevents proving this.

TGD indeed implies a revolution in chemistry. Some chemical bonds are accompanied by flux tubes carrying dark particles with effective Planck constant heff>h=6h0. Valence electrons of the less electronegative atom would get to the flux tube and become dark. This leads to a model of valence bonds and the value of heff/h0= n increases as one moves to the right along the row of the periodic table. This implies delocalization of the valence electrons to longer scale scaling like heff2 for the Bohr model and this is essential for the delocalization. This delocalization would be essential for chemistry of valence bonds and for biochemistry in particular.

The article also mentions bonds without electrons. Hydrogen bond is of course an example of such: now it would be a proton that becomes dark and has heff>h. In water one could have a spectrum of heff values with various bond lengths and this would give water its very special properties. Even flux tubes without any particles but creating correlations and correlates of entanglement between atoms involved are possible.

Also heff<h bonds are possible. Randell Mills has found evidence for a variant of hydrogenfor which energies are scaled by factor 1/4: this would mean heff=h/2.

An interesting possibility is that in the past scaled down atoms with heff= h/2 have existed. Could they correspond to most of the dark matter, the primordial dark matter? The strange disappearance ofthe valence electrons of some transition metals in heating has been also known for decades: heating would provide the energy needed to increase he<>ff for valence electrons so that they become dark relative to us?

In biology metabolic energy would be used to increase heff, which serves as a kind of universal IQ as a measure of algebraic complexity.

For background, see this, this, and this .

For the topics discussed, see the article Revolution in chemistry.

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

Articles and other material related to TGD.

Thursday, May 13, 2021

Has AI hit a dead end?

95 per cent of brain activity has been found to be fluctuations seemingly unrelated to conscious activities involving sensory perception, motor actions and cognition. In the neuroscience framework they are interpreted as noise. Since fluctuations are poison for deterministic computation, the finding poses a serious problem for model of the brain as a deterministic classical computer.

In this article the TGD based interpretation of the long range fluctuations as quantum fluctuations characterized by the value of the effective Planck constant heff=nh0 labelling the phases of ordinary matter identified as dark matter and residing at magnetic body (MB) of the system is discussed. n has number theoretic interpretation and can be regarded as a universal IQ so that fluctuations are a prerequisite for intelligence. According to the TGD based view about neuroscience primary sensory percepts reside at the sensory organs which requires back and forth communications between brain and sensory organs to build sensory perceptions as standardized mental images. These communications must be fast and the proposal is that they use dark photon signals.

In this view nerve pulses do not represent signals inside the brain but act as neural relays at synaptic junctions making possible long range dark photon communications inside the brain. Part of the metabolic energy associated with the fluctuations could be used to the building of mental images in the proposed manner. Nerve pulse patterns generate Josephson radiation communicating sensory information to MB and also require metabolic energy. Dark cyclotron radiation from MB represents control signals to the brain. In both cases, long range fluctuations at brain level are involved.

See the article Has AI hit a dead end? or the chapter Artificial Intelligence, Natural Intelligence, and TGD

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

Articles and other material related to TGD.

Updated version of Expanding Earth Model

I wrote an updated version of the Expanding Earth Model (EEM)based on the assumption that during the Cambrian Explosion (CE) for about .5 billion years ago, the radius of Earth increased by factor 2.

The recent findings demonstrating that the Earth's mantle contains water and even pockets of fluid water plus a detailed discussion of various objections against EEM lead to an updated version of the model. The new key element is that the value of heff was heff=3h0=h/2 at the atomic level before CE for Earth. Earth consisted of matter which would be dark relative to us. In CE the transition heff=3h0=6h0= h took place and induced scaling by a factor 2. This transition also initiated biological evolution.

The finding that Earth was already billions of years ago covered by water suggests that this water had heff=h so that it could leak almost freely into the interior of Earth and because of its darkness could have much lower temperature and pressure than the heff=h/2 matter around it. Therefore life could evolve in Mother Gaia's womb shielded from cosmic rays and meteoric bombardment.

See the article Updated version of Expanding Earth model or the chapter Expanding Earth Model and Pre-Cambrian Evolution of Continents, Climate, and Life.

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

Articles and other material related to TGD.

Friday, May 07, 2021

A chordate able to regenerate copies of it when dissected into 3 parts

The popular article Polycarpa mytiligera can regrow all of its organs if dissected into three pieces tells about  an extraordinary biological discovery.

The creature known as  Polycarpa mytiligera  is a marine animal commonly found in   Gulf of Eilat that is capable of regenerating its organs. The surprising discovery was that  the animal can regenerate all of its organs even when dissected into three fragments.

Such a high regenerative capacity has not been detected earlier  in a chordate animal that reproduces only by sexual reproduction. In the experiment, the researchers dissected specimens in a method that left part of the body without a nerve center, heart, and part of the digestive system. Not only did each part of the creature survive the dissection on its own, all of the organs regenerated in each of the three sections.

This is highly interesting challenge for TGD.  The information about the  full animal body  was needed for a full generation. How it was preserved in dissection? Was genetic information, as it is understood in standard biology, really enough to achieve  this? 

  1.  In TGD inspired quantum biology magnetic body (MB) carrying dark matter as h_eff/h_0=n phases is the  key notion. h_eff is an effective Planck constant defining the scale of quantum coherence. n is dimension of extension of rationals defined by a polynomial defining space-time region,  and serves  as a measure for algebraic complexity and serves as a kind of IQ. MB with high IQ defined by n serves as  the master of the biological body (BB)  controlling it and receiving information from it. The layers of MB also define  abstracted representations of BB. 
  2. If BB suffers damage, the information about BB is not lost at MB and  MB, which carries abstracted representations about BB and able to control BB, could  restore BB partially. Healing of wounds would be the basic example.  A more dramatic example about healing was discovered by Peoch:  the neurons of the  salamander brain can be shuffled like cards in a package but the animal recovers. 

    Indeed, since nothing happens to the MB of salamander or Polycarpa Mytilera,  recovery is in principle possible. The  new finding gives additional support for MB as a carrier of the biological information.

One can also make questions about  the recovery process itself. Could recovery be seen as a self-organization process of some kind? 
  1. In the TGD framework, quantum measurement theory relies on zero energy ontology (ZEO)  and solves  its  basic problem. The basic prediction is that in the TGD counterparts of ordinary state function reductions ("big" SFRs or BSFRs) time reversal takes place.  In small SFRs (SSFRs) identifiable as analogs of "weak" measurements, the arrow of time is preserved. ZEO  makes it also  possible to understand why the Universe looks classical in all scales although BSFRs occur in all scales at the dark onion-like layers of MB controlling the lower layers with ordinary biomatter at the bottom of the hierarchy.
  2.  Time reversed dissipation after BSFR looks like self-organization from the perspective of the outsider with a standard arrow of time, called it briefly O,  and would bea  basic self-organization process in living systems. In dissipation gradients disappear but in time-reversed dissipation they appear from the perspective of O.  
  3. This  makes possible also self-organized quantum criticality (SOQC), which is impossible in standard thermodynamics because criticality by definition means instability. The change of the arrow of time changes the situation from the perspective of  O  since the  time reversed  system tends to approach the criticality. Homeostasis would rely  SOQC  rather than on extremely complex  deterministic control programs as in the computerism based picture. Change the arrow of time for a subsystem and let it happen. Very Buddhist approach to healing! 
  4. The change of the arrow of time would be also central in the healing processes and also regeneration.
      For a summary of earlier postings see Latest progress in TGD.

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Sunday, May 02, 2021

AI research may have hit a dead end

I found a link to a very interesting article titled "Artificial intelligence research may have hit a dead end" followed by the comment "Misfired" neurons might be a brain feature, not a bug — and that's something AI research can't take into account" (see this).

Also Philip K. Dick's 1968 sci-fi novel, "Do Androids Dream of Electric Sheep?" is mentioned.  Would an intelligent robot  (if it were still a robot) dream?

AI models the brain as a deterministic computer. Computer does not dream:  it does just what  is needed to solve a highly specialized problem (just what a top  specialist does in his job;  computer is the  idol of every professional highflier). 

Computerism assumes  physicalism denying such things as genuine free will but this is not seen as a problem.  Also the mainstream  neuroscientist believes in physicalism. Some computational imperialists   even claim that physics reduces to computerism.

1. Is 95 per cent of brain activity mere noise?

What might be called neuroscience of fluctuations has however  led to a strange conclusion: 95 per cent of brain's activity and therefore metabolic energy seems to be used  to  generate fluctuations,  which in standard neuroscience represents noise.   Neuroscientists have routinely averaged out this "noise" and concentrated on the study of  what can be regarded as  motor actions and sensory input. These contributions seem to represent only ripples in a vast sea of activity.

[Amusingly, junk DNA corresponds to 95 per cent of DNA in the case of humans, as the article observes.]

By the way,  EEG is  still often regarded  as a mere noise. This  represents a similar puzzle: why the brain would use a lot of metabolic energy to send information to outer space: coding of information about contents of consciousness and brain state indeed requires a lot of metabolic energy.   To sum up, the brain seems to be diametrically opposite to a computer in the sense that spontaneous fluctuations are poison for a computer but food for the brain.

What article suggests  is that this 95 per cent could correspond to "dreaming"  that is  imagination. Ability to imagine  would give rise to intelligence rather than the property of being a dead automaton. Dreams would be freely associating cognitive fluctuations - whatever that might mean physically. Interestingly, it is mentioned that newborns dream twice as much as adults: they must learn. One can learn by imaging, not merely by doing all possible mistakes in the real world.

What can one say about these findings in the TGD framework?

2. Could fluctuations be induced by quantum fluctuations in quantum critical Universe of TGD?

Consider first the TGD interpretation of quantum fluctuations.

  1.  TGD Universe is  quantal  in all scales. Zero energy ontology (ZEO) allows to overcome the basic objection that the universe looks classical in long scales: ZEO view about quantum jumps forces the Universe to look classical for  the outsider. The experiments of Minev et al indeed demonstrated this concretely.
  2. TGD Universe is also quantum critical in all scales. Quantum criticality means that the system is maximally complex  and sensitive  for perturbations. Complexity means that the system is ideal for representing the  external world via sensory inputs. By criticality implying maximal sensitivity it is also an ideal sensory receptor  and motor instrument.
  3. The basic characteristic of criticality are long range fluctuations. They are not random noise but highly correlated.  Could the fluctuation in  the brain correspond to quantum fluctuations. 
 Long range quantum fluctuations are not possible for the ordinary value of  Planck constant.  
  1. Number theoretical view about TGD, generalizing ordinary physics of sensory experience to the physics of both sensory experience and cognition, leads to the prediction that there is infinite hierarchy of phases of ordinary matter  identifiable as dark matter and labelled by the values of effective Planck constant heff= nh0, n is dimension for an extension of rationals defined by a polynomial determining space-time region.
  2. The value of n serves as a measure for complexity and therefore defines a kind of IQ. The longer the scale of quantum fluctuations, the higher the value of n, and the larger the heff, and the longer the scale of quantum coherence. Fluctuations would make  the brain intelligent. Their  absence would make the brain a complete idiot - an ideal computer.
  3. The higher the value of heff, the larger the energy of  the particle when other parameters are kept as constant. This means that intelligence requires metabolic energy feed to increase heff and keep its values the same, since heff tends to be spontaneously reduced.
One can however argue that since the brain consists of ordinary matter,  brain fluctuations cannot be quantal. 
  1. In TGD they would be induced by quantum fluctuations at the level of  the magnetic body (MB) having a hierarchical onion-like structure. The dark matter would be ordinary particles with heff=nh0 at MB and since heff/h0 serves as a measure of IQ it would be higher for dark matter than for ordinary biomatter. MB containing dark matter would be the "boss" controlling the biological body (BB).  
  2. The quantum coherence of MB would force ordinary coherence of ordinary biomatter as a forced coherence. Ordinary matter would be like soldiers  obeying the  orders and in this manner behaving apparently like a larger coherent unit.
MB would receive sensory input from BB and control it by using EEG realizes as dark photons. This would explain EEG and its probably existing scaled  variants.

3. TGD view about sensory perception, motor actions, and dreaming and imagination

The proposal of the article was that most of the brain activity goes to "dreaming". Dreaming, hallucinations,  and imagination are poorly understood notions in neuroscience.  TGD provides a rather detailed view about these notions.

  1. What  distinguishes TGD from neuroscience is that sensory receptors are assumed to serve as carriers of sensory percepts. Zero energy ontology (ZEO)  providing a new view about time and memory makes it possible  to solve the basic objections related to  the phantom limb phenomenon: pain in  the phantom limb would be sensory memory.   
  2. The assumption that sensory percepts are artworks rather than passive records  of sensory input   requires virtual sensory input from brain to sensory organs and build-up of the final  percept by  pattern recognition -  an iterative procedure involving very many forth-and back signals. Nerve pulse transmission is quite too slow a process to allow this and signals propagating with maximal signal velocity are suggestive.
  3.  Nerve pulses and neurotransmitters  would not represent real communication but give rise to  temporary intra-brain communication lines along which communications as dark photon signals would take place with maximal signal velocity using dark photons  (characterized by heff/h0=n) transforming to biophotons in an  energy conserving manner. 

    Neurotransmitters and also other  information molecules (hormones, messengers) attached to receptors would serve as bridges fusing  permanent but disjoint communication lines along axons to a connected temporary communication line for dark photons to propagate.  Nerve pulses would also generate generalized Josephson radiation allowing communications   between biological body (BB) and magnetic body (MB) using EEG.  Meridian system could be a permanently connected system of communication lines.

    This picture leads to a concrete  proposal about the roles of  DMT and pineal gland  concerning imagination and dreams and hallucinations. 

Returning to the original topic,  the natural question is following: How large fraction  of the 95 percent of brain activity goes to  feedback not present in the brain of the standard neuroscience? This would include  the construction of the feedback to sensory organs as  virtual sensory inputs to build standardized mental images. Dreams are a special case of this. There  is  also the virtual sensory input which does not reach sensory organs and gives rise to imagination, in particular internal speech.

 Similar picture applies to virtual  motor input and the construction of motor output as "standardized motor patterns" - this notion makes sense only in ZEO.  Note that the feedback loop could extend from brain to MB. 

There is also an interesting finding related to motor activities. In the experiments made for rats it is found that the spontaneous brain activity increases dramatically as the rat moves. This brings in mind a lecturer who moves forth and back  as he talks. This rhythmic motion could give rise to a brain/body rhythm  coupling the lecturer to a layer of MB with large heff. Its   quantum coherence of MB would induce ordinary coherence of BB in body scale and with large heff and raise the "IQ" of the lecture.  Thinking requires motion!

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

Articles and other material related to TGD.