Planning to move to Mars?: have you asked the opinion of your magnetic body?

There has been a lot of talk about the colonization of Mars. I was asked about possible problems involved. In the following I consider the question only from TGD point of view about life.

The new element of TGD based quantum biology is the notion of magnetic body carrying dark matter as phases of ordinary matter labelled by the effective value h_eff =nh₀ of Planck constant (h= 6h₀ is a good guess). MB is the boss controlling ordinary matter by using dark photons transforming to ordinary photon and vice versa. Actually one has hierarchy of values of h_eff and master slave hierarchy.

Cyclotron frequencies and generalize Josephson frequencies are in a central roles in the communications between MB and biological body relying on frequency and energy resonance if the values of h_eff are identical or only energy resonance if they are not same.

Frequencies are thus fundamental for the control level of life and the question is whether MB can adapt and change its frequency spectrum. Also Schumann frequency is known to be important for life and in Mars its scae 2 times that in Earth. These problems might make already the travel to Mars dangerous to say nothing about living there.

1. Cyclotron frequencies and Schumann frequencies

On basis of findings done already at seventies about unexpected effects of ELF em fields on vertebrate brain, EEG resonances seem correspond to cyclotron frequencies in endogeneous magnetic field of B_end=.2 Gauss which is 2/5 of the nominal value B_E=.5 Gauss of Earth's magnetic field. A possible interpretation is that B_end corresponds to field strength for the monopole flux part of B_E. It is stable against dissipation since no current is needed to create it unlike ordinary Maxwellian magnetic field. This explains why B_E has not decayed away long time ago by the decay of the current creating it.

Cyclotron frequencies are in a key role in TGD based quantum biology. The value spectrum of h_eff determining bio-photon energies is in central role: dark photon energies are given by E=h_eff×f.

The cyclotron energy spectrum in Earth would be in bio-photon range (visible and UV) and same for all charged particles - there is no dependence on mass of charged particle since one has hbar_eff= hbar_gr= GMm/v₀ at gravitational flux tubes. hbar_gr= GMm/v₀ is gravitational Planck constant fundamental introduced first by Nottale. v₀ is velocity parameter with value about v₀/c= 2^-11 in the case of Sun. It might relate to the parameters of the system but could be also almost universal parameter (it is near electron proton mass ratio).

The cyclotron energy spectrum in Earth would be in bio-photon range and same for all charged partcles - there is no dependence on mass since one has hbar_eff= hbar_gr= GMm/v₀ at what I call gravitational flux tubes. This would make possible the control of molecular transitions by transforming dark photons to visible and UV photons first. MB could control molecular transitions and act as "boss". Quite generally, the layers of MB with different values of h_eff would form a master slave hierarchy with ordinary biomatter at bottom.

Schumann resonances correspond to resonance frequencies for the radiation fields of Earth. In the approximation that the conductivity of the medium is infinite, the wavelengths depend on the radius R_E of Earth only. Lowest wavelength corresponds in good approximation to lambda= 2πR_E. Lowest Schumann frequency has nominal value 7.8 Hz. These frequencies are in EEG range.

Remark: I remember having read in some source that 10 Hz frequency corresponding to alpha band in brain is needed in space and is produced artificially. I could not find the original source.

2. Coupling between Schumann frequencies and cyclotron frequencies

1. Schumann frequencies are is in the range of EEG frequencies, which strongly suggests resonant coupling with the cyclotron transitions corresponding to frequencies near to Schumann frequencies.
2. For instance, the cyclotron frequency 7.5 Hz for K⁺ ions is near to the nominal value 7.8 Hz of the lowest Schumann frequency. K⁺ currents through K⁺ channels cell membrane are known to be important for what happens in anesthesia and when organism falls asleep and thus for consciousness.

   What happens when organism falls asleep is of course not quite clear. The membrane voltage increases and nerve pulse generation becomes improbable. Metabolism continues and this means consciousness in TG framework but not sensory and motor consciousness. Could the apparent loss of consciousness mean fusion of self with higher level self representing the collecting consciousness of magnetic Mother Gaia? Could it be that during sleep we could form a larger collective consciousness representing "human condition" (see this) .

3. Irradiaton by frequency around 7 Hz is also necessary in the experiments of HIV Nobelist Montagnier involve remote DNA replication (see this) and this) .
4. Irradiation by Schumann frequency around 60 Hz appears leads to healing of cancer cell population in lab (see this) .
5. Also higher Schumann resonances could represent resonant coupling between Mother Gaia and brains of vertebrates allowing realization of levels of collective consciousness. Coherent collective gene expression in various scales (organ, organism, group, population,...) is one of the possible testable implication.

3. Possible problems related to different values of magnetic fields in Earth and Mars

The first problem relates to the magnetic field of Mars. Martian magnetic field has been believed to be weak but the recent findings suggests that it might be present and order of magnitude as in Earth (see this) .

1. TGD based view about life requires B_end which could be monopole part of B_E. Flux tubes can carry monopole flux or not - the latter option is realized in the case of ordinary Maxwellian magnetic field. Monopole flux would be biologically important and it would be in Earth 2/5 of total flux. It could be of course different in Mars. Different value of B_end in Mars could lead to severe difficulties since cyclotron frequencies are in a key role in TGD based quantum biology.
2. Also the value spectrum of hbar_gr= GMm/v₀ determining biophoton energies is in central role: one has for energies E=h_eff×f. In Mars the mass parameter M and velocity parameter v₀ in h_gr could be different and this could have fatal consequences for bio-control by the magnetic body of earthly biosystems.
   1. In the case of Earth M seems to correspond to the mass of "inner inner core" of Earth. If M is same for Mars (planets would be like atoms having varying number of identical "shells"), then it would be enough to have same value B/v₀ to keep the spectrum same. The value of B is under control by varying the flux tube thickness and this control mechanism would be used in terrestial biology.
   2. The optimistic guess is that v₀ has universal spectrum and the value is same in Mars and Earth. A not necessarily good guess is that the velocity v₀ scales like the rotation frequency of planet. Here we would have good luck! The Martian day has essentially the same length as day in Earth. The value of v₀ would be same! In this case hbar_gr could be the same! Sounds too optimistic!
   3. One can imagine also second option. The strength of monopole flux magnetic field B_end =.2 Gauss at flux tubes is free parameter and magnetic bodies could vary its value by varying thickness of flux tubes: this would be a basic biological control mechanism for instance in water and allow water to develop antennas sensitive to the cyclotron frequencies of invader molecules and detect them: this would be water memory and basis of the immune system.

   4. Problems related to different Schumann frequencies

   Schumann frequency scale in Mars is roughly twice that in Earth since radius is about 2 times smaller: around 15.6 Hz instead of 7.8 Hz for lowest Schumann frequency. Schumann frequency is known to be important for us although this is not well-understood. This might cause severe problems.

   The scaling of Schumann frequencies by 2 might cause bad complications but we do not really understand their effect even in Earth.

   We of course do not have thorough knowledge about B in Mars. There are auroras but earlier it was believed that magnetic field in large scales is very small.The latest findings suggest in TGD framework that there is monopole flux tube part of order B_end (see this).

   One can consider a possible solution to Schumann frequency doubling problem. Scale also the cyclotron frequencies by factor 2!

   1. At Earth the lowest Schumann frequency 7.8 Hz corresponds to cyclotron frequency 7.5 Hz of K⁺ ion quite well and this might make possible resonant coupling between Mother Gaia and magnetic bodies of living system. If the B_end=.2 Gauss is scaled by factor 2 in Mars to about .4 Gauss, cyclotron frequency scale doubles and one would have 15 Hz cyclotron frequency for K⁺ not far from Schumann.
   2. Could human MB scale up the cyclotron frequencies by factor 2? Note that TGD based model for Cambrian explosion (see this) predicts that Schumann frequency doubled in geologically short time scale (extremely long from human perspective). The lifeforms that would have bursted from underground oceans to the surface survived this transition. One could test what happens if artificially produced counterpart of Schumann frequency is doubled in artificial conditions using Faraday cage.

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

   Articles and other material related to TGD.

Schumann resonances and consciousness

The role of Schumann resonances for consciousness is highly interesting in TGD framework, where the notion of magnetic body (MB) carrying dark matter as h_eff=n*h₀ phases is in key role. MB would control biological body by dark photons - probably at cyclotron frequencies - and receive information as dark generalized Josephson radiation from cell membrane with the modulation of membrane potential inducing frequency modulation coding for the sensory data (see this ) .

On basis of findings done already at seventies about unexpected effects of ELF em fields on vertebrate brain, EEG resonances seem correspond to cyclotron frequencies in endogeneous magnetic field of B_end=.2 Gauss which is 2/5 of the nominal value B_E=.5 Gauss of Earth's magnetic field. A possible interpretation is that B_end corresponds to field strength for the monopole flux part of B_E. It is stable against dissipation since no current is needed to create it unlike ordinary Maxwellian magnetic field. This explains why B_E has not decayed away long time ago by the decay of the current creating it.

Cyclotron frequencies are in a key role in TGD based quantum biology. The value spectrum of h_eff determining bio-photon energies is in central role: dark photon energies are given by E=h_eff*f. The cyclotron energy spectrum in Earth would be in bio-photon range (visible and UV) and same for all charged particles - no dependence on mass since one has hbar_eff= hbar_gr= GMm/v₀ at what I call gravitational flux tubes. This would make possible for MB to control molecular transitions and act as "boss". Quite generally, the layers of MB with different values of h_eff would form a master slave hierarchy with ordinary biomatter at bottom.

1. Schumann frequencies are is in the range of EEG frequencies, which strongly suggests resonant coupling with the cyclotron transitions corresponding to frequencies near to Schumann frequencies.
2. For instance, the cyclotron frequency 7.5 Hz for K⁺ ions is near to the nominal value 7.8 Hz of the lowest Schumann frequency. K⁺ currents through K⁺ channels cell membrane are known to be important for what happens in anesthesia and when organism falls asleep and thus for consciousness.

   What happens when organism falls asleep is of course not quite clear. The membrane voltage increases and nerve pulse generation becomes improbable. Metabolism continues and this means consciousness in TG framework but not sensory and motor consciousness. Could the apparent loss of consciousness mean fusion of self with higher level self representing the collecting consciousness of magnetic Mother Gaia? Could it be that during sleep we could form a larger collective consciousness representing "human condition" (see this) .

3. Irradiaton by frequency around 7 Hz is also necessary in the experiments of HIV Nobelist Montagnier involve remote DNA replication. See (see this and this) .
4. Irradiation by Schumann frequency around 60 Hz appears leads to healing of cancer cell population in lab (see this) .
5. Also higher Schumann resonances could represent resonant coupling between Mother Gaia and brains of vertebrates allowing realization of levels of collective consciousness. Coherent collective gene expression in various scales (organ, organism, group, population,...) is one of the possible testable implications.

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

   Articles and other material related to TGD.

Has Pluto experienced a period of fast expansion?

The surprise of this morning was that Pluto seems to have experienced a rapid expansion and might have had underground oceans.

Actually not a surprise if one lives in TGD Universe. TGD predicts that all astrophysical objects, including planets, might have experienced this kind of periods. In general relativity these periods would correspond smooth cosmological expansion of this objects: the absence this smooth expansion is indeed an enigma - astrophysical objects co-move with expanion in large scale but do not expand themselves. Earth would have experienced this expansion during Cambrian explosion.

The underground oceans would make possible evolution of life without problems from cosmic rays and meteorites and radioactivity (for instance) could provide the metabolic energy.

This would solve Fermi's paradox: most planets could be carriers of intraplanetary invisible-to-outsider life waiting the next fast expansion and burst to the surface of the planet.

See http://tgdtheory.fi/public_html/articles/expearth.pdf .

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

Articles and other material related to TGD.

New evidence for two values of Hubble constant

Sabine Hossenfelder tells about a further evidence for the Hubble constant discrepancy and refers to this popular article discussing new kind of local measurements independent of other measurements also giving 10 per cent higher value than the value deduce from CMB measurements in much longer scales.

In the many-sheeted cosmology of TGD the cosmic parameters are length scale dependent. The natural guess is that the two measurements could correspond to sHubble constant in different p-adic length scales. The naive dimensional guess based inspired by the p-adic length scale hypothesis would suggest that Hubble constant could come as half octaves. The ratio of the two values is however around .1 much nearer to unity than 2^-1/2≈.71.

Some time there was a popular article about a possible explanation of Hubble constant discrepancy (see this). The article told about a proposal of Lucas Lombriser discussed in the article Consistency of the local Hubble constant with the cosmic microwave background (see this) for an explanation of this discrepancy. The proposal is that the local region around our galaxy having size of order few hundred Mly - this is the scale of the large voids forming a honeycomb like structure containing galaxies at their boundaries - has average density of the matter 1/2 of that elsewhere.

This would fit nicely with the TGD picture. I do not bother to repeat the argument given in the earlier blog posting. The point is that in TGD the string tension of magnetic flux tubes comes by p-adic length scale hypothesis in powers of 2. The density of matter is generated by the decay of matter and energy of cosmic string like objects to ordinary matter as they thicken to flux tubes. If the string tension of local void is by a factor 1/2 smaller than for a typical void, the density of ordinary matter would be smaller by this factor. One could say that local void would be a forerunner in cosmic evolution. This is of cousre highly interesting from the persperctive of biological evolution, in particular Fermi paradox).

To sum up, this model would rely on the prediction that there are two kinds of flux tubes and that the cosmic evolution proceeds by phase transitions increasing p-adic length scale by half octave reducing the energy density by factor 1/2 at flux tubes. The local void would be one step further in cosmic evolution as compared to a typical void.

See the article The problem of two Hubble constants or the chapter More about TGD and Cosmology.

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

Articles and other material related to TGD.

How are the space-time surfaces assignable to the opposite boundaries of CD glued together?

How do the solutions assignable to the opposite boundaries of CD relate to each other?

Causal diamond identified basically as intersection of future and past directed light-cones is basic notion in zero energy ontology. It has 4-D variant cd₄, 8-D Minkowski variant cd₈, and H=M⁴× CP₂-variant CD= cd₄× CP₂.

Space-time surfaces in M picture are defined as roots for "real" or "imaginary" part of complexified octonion valued polynomial obtained by algebraically continuing first real valued polynomial with rational coefficients to complex valued polynomial by replacing real argument with complex argument $z$ commuting with octonions and then perfoming continuation to complexified octonion valued polynomial. One can continue at first step to a polynomial of z or of z** and complex conjugation has interpretation as particle- antiparticle conjugation.

To construct the solutions to the polynomial equations one must consider the equations near both boundaries of CD and glue them together smoothly. I have not consider this problem earlier. In principle, the polynomials associated with them could be different in the general formulation discussed in but they could be also same (see this and this). How are the solutions associated with opposite boundaries of CD glued together in a continuous manner?

1. The polynomials assignable to the opposite boundaries of CD are allowed to be polynomials of o resp. (o-T): here T is the distance between the tips of CD.
2. CD brings in mind the realization of conformal invariance at sphere: the two hemispheres correspond to powers of z and 1/z: the condition z*= 1/z at unit circle is essential and there is no real conjugation. How the sphere is replaced with 8-D CD which is also complexified. The absence of conjugation looks natural also now: could CD contain a 3-surface analogous to the unit circle of sphere at which the analog of z*= 1/z holds true? If so, one has P(o,z)=P(1/o,z) and the solutions representing roots fo P(o,z) and P(1/o,z) can be glued together.

   Note that 1/o can be expressed as o*/oo* when the Minkowskian norm squared oo* is non-vanishing and one has polynomial equation also now. This condition is true outside the boundary of 8-D light-cone, in particular near the upper boundary of CD.

   The counter part for the length squared of octonion in Minkowskian signature is light-one proper time coordinate a²=t²-r² for M⁸₊. Replacing o which scaled dimensionless variable o₁= o/(T/2) the gluing take place along a=T/2 hyperboloid.

One has algebraic holomorphy with respect to o but also anti-holomorphy with respect to o is possible. What could these two options correspond to? Could the space-time surfaces assignable to self and its time-reversal relate by octonionic conjugation o→o* relating two Fock vacuums annihilated by fermionic annihilation resp. creation operators?

See the article About M⁸-H-duality, p-adic length scale hypothesis and dark matter hierarchy or the chapter Zero energy ontology and matrices.

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

Articles and other material related to TGD.

Indications for an axionlike state in mass range 1-7 keV from XENON

There was a popular article about bump claimed by XENON group and suggesting the existence of an axion-like state with mass in the range 1-7 keV. Also Jester discusses the evidence for the claimed bump.

Originally XENON searched evidence for WIMPs - weak interacting very massive particles. They would have made themselves visible via scattering from ZENON nuclei. Nothing was found.

Second candidate for dark matter particles are very light axions, which could be produced copiously in Sun. They would not have any detectable effect on heavy XENON atom but they could scatter from electrons and ionize XENON atom. The figure in the posting of Jester summarizes the energy spectrum of the observed ionization events. The figure shows approximately constant backgroud below 30 keV down to 1 keV below which it drops abruptly suggesting threshold. There are also indications for a peak around 1-2 keV. There is 3.5 sigma excess of events in the range 1-7 keV.

The mass of the dark particle candidate is in the range 1-7 keV. TGD allows to imagine several options but for all of them one would have analog of pion as dark matter candidate.

1. TGD Universe is fractal and this predicts p-adically scaled variants of hadron physics and electroweak physics. Mass squared scales would come as powers of 2. Mersenne primes and Gaussian Mersennes define especially promising candidates.
   1. M₈₉ hadron physics (see this) would be scaled up variant of ordinary hadron physics (M₁₀₇) and would make itself visible at LHC. The masses of M₈₉ hadrons would be scaled up by factor 512 from those of ordinary hadrons. There is evidence for bumps with predicted masses and the original proposal as Higgs did not work and they were forgotten. The mesons of this physics would be dark with h_eff/h₀=n≈ 512 so that the Compton lengths would be those of ordinary mesons and they would appear at quantum criticality for what was expected to be de-confiment phase transition.
   2. There are indications for the particles of these physics having mass scaled by a power of 2 from that for say ordinary meson. Could the particle be a scaled down pion of some kind. There are actually several candidates for scaled variants of pion. There is evidence for so called X boson with mass around 16-17 MeV proposed to be spin 1 bosonof a fifth force (see this). In TGD framework the identification as pion-like state is more natural and provides new insights on the relation between weak and strong interactions (see this). There is also quite recent evidence for pionlike exotic particle with mass not far from that of pion showing itself in the decays of long-lived kaon: there is actually evidence for scaled variants of pion also from earlier experiments. These pieces of evidence are discussed from TGD point of view in (see this) (see this).
   3. In biologically important length scales there are as many as 4 Gaussian Mersenne M_G,n=(1+i)ⁿ-1 with n=151, 157, 163, 167 defining p-adic length scales in the range 10 nm (cell membrane thickness) and 2.5 μm (cell nucleus size) and might involve scaled variants of hadron and electroweak physics.
   p-Adic length scale hypothesis also allows the possibility of p-adically scaled variants of leptons and quarks with mass scaled down or up by a power of 2 and there are some indications for this kind of states. For instance, the claimed axion-like state could be a scaled down pion as bound state of scaled down quarks.
2. Heavy ion collisions near Coulomb wall gave already around seventies indicatons for a pion-like state of mass 1 MeV decaying to electron positron pair. TGD inspred interpretation (see this) was in terms of electropion identified as bound state of color octet electrons. TGD view about color indeed allows colored excitation of leptons since color is not spin-like but angular momentum like quantum number assignable to CP₂ color partial waves. Later evidence for muon and tau analogs of this state has emerged. The decay widths of weak bosons do not allow color octet ptons in MeV scale and this forced the interpretation that they are dark in some sense and appear ony at quantum criticality - now at collision energies around Coulomb wall.

   Leptopion could also be color bound state of quark and antiquark. As noticed, there is evidence for several bound states of this kind.

3. The TGD based model for "cold fusion" (see this, this), and this) led to a new view about nuclear physics (see this) in which dark nuclei appear also as intermediate states of ordinary nuclear reactions. Dark nuclei as nuclear string with distance of about electron Compton length would be crucial for "cold fusion" and would have dark nuclear binding energies in few keV range.

   Remarkably, they would have scaled down dark nuclear binding energies in few keV range. This because the binding energy scale of ordinary nuclear physics about 7 MeV would be scaled down by the ratio 2^-10≈ 10^-3 of the p-adic length scales of proton and electron labelled by k=107 and k=127 to a value about 7 keV, which represents the upper end of the range 1-7 keV. There is also evidence that X ray emission with energies of this order of magnitude from Sun affects nuclear decay rates at Earth.

   The pion-like particles could be indeed dark in TGD sense (ordinary particle but with h_eff=n× h₀>h). Could the axion candidate be scaled down variant of electro-pion with mass 1 MeV with k=127: if the mass of electro-pion scales down like the nuclear binding energy, the scaling k=107 → 127 would take the mass of electro-pion to 1 keV. Also scaled down pion formed by quarks could be in question.

To sum up, the recent axion-like state would add only one item to the increasing list of pion-like states allowed by p-adic fractality of TGD Universe. One might hope that despite their high specialization colleagues could eventually wake-up to see the big picture behind the anomalies.

See the article Exotic pion like states as "infra-red" Regge Trajectories and a new view about nuclear physics or the chapter New Physics Predicted by TGD: Part I.

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

Articles and other material related to TGD.

Skyrmions in TGD

I received a link to an article telling about research carried out for condensed matter skyrmions, which are very general condensed matter quasiparticles. They were found to replicate like DNA and cells. I realized that I have not clarified myself the possibility of skyrmions on TGD world and decided to clarify my thoughts.

What skyrmions are?

Consider first what skyrmions are.

1. Skyrmions are topological entities. One has some order parameter having values in some compact space S. This parameter is defined in say 3-ball such that the parameter is constant at the boundary meaning that one has effectively 3-sphere. If the 3rd homotopy group of S characterizing topology equivalence classes of maps from 3-sphere to S is non-trivial, you get soliton-llike entities, stable field configurations not deformable to trivial ones (constant value). Skyrmions can be assigned to space S which is coset space SU(2)_L× SU(2)_R/SU(2)_V, essentially S³ and are labelled by conserved integer-valued topological quantum number.

   One can imagine variants of this. For instance, one can replace 3-ball with disk. SO(3)=S³ with 2-sphere S². The example considered in the article corresponds to discretized situation in which one has magnetic dipoles/spins at points of say discretized disk such that spins have same direction about boundary circle. The distribution of directions of spin can give rise to skyrmion-like entity. Second option is distribution of molecules which do not have symmetry axis so that as rigid bodies the space of their orientations is discretized version of SO(3). The field would be the orientation of a molecule of lattice and one has also now discrete analogs of skyrmions.

2. More generally, skyrmions emerge naturally in old-fashioned hadron physics, where SU(2)_L× SU(2)_R/SU(2)_V involves left-handed, right-handed and vectorial (diagonal) subgroups of SO(4)=SU(2)_L× SU(2)_R. The realization would be in terms of 4-component field (π,σ), where π is charged pion with 3 components - axial vector - and σ which is scalar. The additional constraint π•π +σ²= constant defines 3-sphere so that one has field with values in S³. There are models assigning this kind of skyrmion with nucleon, atomic nuclei, and also in the bag model of hadrons bag can be thought of as a hole inside skyrmion. These models seem to have something to do with reality so that a natural question is whether skyrmions might appear in TGD.

Skyrmion number as winding number

In TGD framework one can regard space-time as 4-surface in either octonionic M⁸_c - "c" refers here to complexification by an imaginary unit i commuting with octonions- or in M⁴× CP₂. For the solution surfaces M⁸ has natural decomposition M⁸=M²× E⁶ and E⁶ has SO(6) as isometry group containing subgroup SU(3) having automorphisms of octonions as subgroup leaving M² invariant. SO(6)=SU(4) contains SU(3) as subgroup, which has interpretation as isometries of CP₂ and counterpart of color gauge group. This supports M⁸-H duality, whose most recent form is discussed here.

The map S³→ S³ defining skyrmion could be taken as a phenomenological consequence of M⁸-H duality implying the old-fashioned description of hadrons involving broken SO(4) symmetry (PCAC) and unbroken symmetry for diagonal group SO(3)_V (CCV). The analog of (π,σ) field could correspond to a B-E condensate of pions (π,σ).

The obvious question is whether the map S³→ S³ defining skyrmion could have a deeper interpretation in TGD framework. I failed to find any elegant formulation. One could however generalize and ask whether skyrmion like entities characterize by winding number are predicted by basic TGD.

1. In the models of nucleon and nuclei the interpretation of conserved topological skyrmion number is as baryon number. This number should correspond to the homotopy class of the map in question, essentially winding number. For polynomials of complex number degree corresponds to winding number. Could the degree n=h_eff/h₀ of polynomial P having interpretation as effective Planck constant and measure of complexity - kind of number theoretic IQ - be identifiable as skyrmion number? Could it be interpreted as baryon number too?
2. For leptons regarded as local 3 anti-quark composites in TGD based view about SUSY \citesusyTGD the same interpretation would make sense. It seems however that the winding number must have both signs. Degree is n is however non-negative.

   Here complexification of M⁸ to M⁸_c is essential. One an allow both holomorphic and anti-holomorphic continuations of real polynomials P (with rational coefficients) using complexification defined by commutative imaginary unit i in M⁸_c so that one has polynomials P(z) resp. P(z*) in turn algebraically continued to complexified octonionic polynomials P(z,o) resp. P(z*,o).

   Particles resp. antiparticles would correspond to the roots of octonionic polynomial P(z,o) resp. P(z*,o) meaning space-time geometrization of the particle-antiparticle dichotomy and would be conjugates of each other. This could give a nice physical interpretation to the somewhat mysterious complex roots of P.

More detailed formulation

To make this formulation more detailed on must ask how 4-D space-time surfaces correspond to 8-D "roots" for the "imaginary" ("real") part of complexified octonionic polynomial as surfaces in M⁸_c.

1. Equations state the simultaneous vanishing of the 4 components of complexified quaternion valued polynomial having degree n and with coefficients depending on the components of O_c, which are regarded as complex numbers x+iy, where i commutes with octonionic units. The coefficients of polynomials depend on complex coordinates associated with non-vanishing "real" ("imaginary") part of the O_c valued polynomial.
2. To get perspective, one can compare the situation with that in catastrophe theory in which one considers roots for the gradient of potential function of behavior variables xⁱ. Potential function is polynomial having control variables as parameters. Now behavior variable correspond "imaginary" ("real") part and control variables to "real" ("imaginary") of octonionic polynomial.

   For a polynomial with real coefficients the solution divides to regions in which some roots are real and some roots are complex. In the case of cusp catastrophe one has cusp region with 3-D region of the parameter defined by behavior variable x and 2 control parameters with 3 real roots, the region in which one has one real root. The boundaries for the projection of 3-sheeted cusp to the plane defined by control variables correspond to degeneration of two complex roots to one real root.

   In the recent case it is not clear whether one cannot require the M⁸_c coordinates for space-time surface to be real but to be in M⁸=M¹+iE⁷ .

3. Allowing complex roots gives 8-D space-time surfaces. How to obtain real 4-D space-time surfaces?
   1. One could project space-time surfaces to real M⁸=M¹+iE⁷ to obtain 4-D real space-time surfaces. In time direction the real part of root is accepted and is same for the root and its conjugate. For E⁷ this would mean that imaginary part is picked up.
   2. If one allows only real roots, the complex conjugation proposed to relate fermions and anti-fermions would be lost.
4. One can select for 4 complex M⁸_c coordinates X^k of the surface and the remaining 4 coordinates Y^k can be formally solved as roots of n:th degree polynomial with dynamical coefficients depending on X^k and the remaining Y^k. This is expected to give rise to preferred extremals with varying dimension of M⁴ and CP₂ projections.
5. It seems that all roots must be complex.
   1. The holomorphy of the polynomials with respect to the complex M⁸_c coordinates implies that the coefficients are complex in the generic point M⁸_c. If so, all 4 roots are in general complex but do not appear as conjugate pairs. The naive guess is that the maximal number of solutions would be n⁴ for a given choice of M⁸ coordinates solved as roots. An open question is whether one can select subset of roots and what happens at t=r_n surfaces: could different solutions be glued together at them.
   2. Just for completeness one can consider also the case that the dynamical coefficients are real - this is true in the E⁸ sector and whether it has physical meaning is not clear. In this case the roots come as real roots and pairs formed by complex root and its conjugate. The solution surface can be divided into regions depending on the character of 4 roots. The n roots consist of complex root pairs and real roots. The members or complex root pairs are mapped to same point in E⁸.

Could skyrmions in TGD sense replicate?

What about the observation that condensed matter skyrmions replicate? Could this have analog at fundamental level?

1. The assignment of conserved topological quantum number to the skyrmion is not consistent with replication unless the skyrmion numbers of outgoing states sum up to that of the initial state. If the system is open one can circumvent this objection. The replication would be like replication of DNA in which nucleotides of new DNA strands are brought to the system to form new strands.
2. It would be fascinating if all skyrmions would correspond to space-time surfaces at fundamental M⁸ level. If so, skyrmion property also in magnetic sense would be induced by from a deeper geometric skyrmion property of the MB of the system. The openness of the system would be essential to guarantee conservation of baryon number. Here the fact that leptons and baryons have opposite baryon numbers helps in TGD framework. Note also ordinary DNA replication could correspond to replication of MB and thus of skyrmion sequences.

See the article About M⁸-H-duality, p-adic length scale hypothesis and dark matter hierarchy or the chapter Zero energy ontology and matrices.

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

Articles and other material related to TGD.

Basic organic molecules appear much before they should

Nikolina Benedikovic gave a link to an interesting article about the appearance of pre-biotic molecules in stellar nurseries at time when star formation had not yet begun. The article told about the work of astrophysicists Yancy Shirley and Samantha Scibelli published in Astrophysical Journal with the title "Prevalence of Complex Organic Molecules in Starless and Prestellar Cores within the Taurus Molecular Cloud".

The stellar nursery studied consisted of 31 starless cores scattered throughout a star-forming region in Taurus molecular cloud located about 440 ly from Earth. The molecules studied were methanol (CH3OH) and acetaldehyde (CH3CHO). These molecules serving as building bricks for chemical life were found to be much more ubiquitous than expected and present hundreds of thousands of years before star formation actually began.

The molecular evolution producing complex organic molecules requires the analog of metabolic energy feed: the temperature should be quite high - measured using molecular binding energies as scale - about few eV typically. The existing theories assume that proto-stars - stars in the process of formation produced the heating necessary for the formation of these molecules. But in regions without proto-stars the temperature of gas has been quite to provide the heating. Where did the energy needed for local heating come from?

TGD based view about "cold fusion" - which during last years has been getting rid of the label of pseudoscience - is that it is induced by what I call dark nuclear fusion possible at low temperatures (see this). Dark matter corresponds in TGD Universe to ordinary particles but with non-standard value of Planck constant (or cautiously effective Planck constant) h_eff=nh₀ larger than h.

Dark nuclei formed as dark proton sequences at magnetic flux tubes with protons having distance about electron Compton length and scaled down nuclear binding energy in eV scale would have formed at temperatures of order eV or even lower. They would have spontaneously decayed to ordinary nuclei liberating energy of order nuclear binding energy, which is in MeV scale. The dark nuclei can actually occur in several scales but could transform sequentially to ordinary nuclei. The liberated nuclear binding energy would have heated the gas locally. This kind of regions would have served as pre-stellar objects leading to protostars and eventually stellar cores as ordinary nuclear reactions would have started.

TGD predicts that also ordinary nuclear reactions are initiated by phase transitions generating dark nuclei as intermediate states: this would be the counterpart for quantum tunnelling assumed to take place in ordinary nuclear reactions and allow them to already occur at collision energies about 1/100 lower than classical considerations would allow (see for instance this and this).

See the article Solar Metallicity Problem from TGD Perspective 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.

TGD interpretation of new experimental results about the mechanism of anesthesia

I received a link to a highly interesting popular article with title Century-Old Scientific Debate Settled: Anesthesia’s Effect on Consciousness Solved). The article tells about a study from Scripps Research published in the Proceedings of the National Academies of Sciences (PNAS) . The paper Studies on the mechanism of general anesthesia has appeared in PNAS. In addition to Lerner and Hansen, the authors are Mahmud Arif Pavel, E. Nicholas Petersen and Hao Wang, all of Scripps Research.

I have pondered possible mechanism of anesthesia in TGD framework several times earlier (see this and this) and it is interesting to see whether the findings allow to make earlier insights more detailed or even develop new ones.

What was observed

According to the popular article the discovery by chemist Richard Lerner, MD, and molecular biologist Scott Hansen, PhD, settles a century-old scientific debate about whether anesthetics act directly on cell-membrane gates called ion channels, or do they somehow act on the membrane to signal cell changes in a new and unexpected way. The conclusion of the researcheres is that anesthetic action is a two-step process that begins in the membrane. The anesthetics perturb ordered lipid clusters within the cell membrane known as "lipid rafts" to initiate the signal. There are two kinds of clusters involved and known with names GM1 and PIP2.

What was observed was following.

• A shift in the GM1 cluster’s organization, a shift from a tightly packed ball to a disrupted mess occurred first As GM1 grew disordered, it spilled its contents, among them, an enzyme called phospholipase D2 (PLD2). Melting is a good analog for what happens. Gel-to-sol transition in cytoplasm is second analogy.
• PLD2 moved like a billiard ball away from its GM1 home and over to a different, less-preferred lipid cluster called PIP2.
• This activates key molecules within PIP2 clusters, TREK1 potassium ion channels and their lipid activator, phosphatidic acid (PA) are among them. The activation of TREK1 potassium channels releases potassium hyper-polarizing the nerve and it makes it more difficult to fire. Nerve pulse generation rate becomes low and leads to a loss of consciousness - at least in clinical sense. Something analogous to this could happen when one falls in sleep.

In the article I try to understand in the framework provided by TGD inspired model of cell membrane and nerve pulse (see this), compare these findings to TGD inspired views about anesthesia based on hyperpolarization, and also try to build a bridge from TGD description provided by a generalization of thermodynamics forced by zero energy ontology (ZEO) predicting that in ordinary state function reduction the arrow of time changes (see this and this).

See the article TGD interpretation of new experimental results about the mechanism of anesthesia or the chapter TGD Inspired Model for Nerve Pulse.

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

Articles and other material related to TGD.

How the life cycle of self could corresponds to a transition to chaos as iteration of polynomial?

I have discussed how the evolution of self by BSFRs could correspond to a transition to chaos as iteration of the polynomial defining the space-time surface. The proposed picture was that the evolution by SSFRs corresponds to iteration of a polynomial P assignable to the active boundary of CD. This would predict a continual increase of the degree of the polynomial involved. This is however only one possibility to interpret the evolution of self as iteration leading to chaos.

1. One could argue that the polynomial P_nk= P_n∘....∘ P_n associated with the active boundary remains the same during SSFRs as long as possible. This because the increase of degree from nk to n(k+1) in P_nk→ P_nk∘ P_n increases h_eff by factor (k+1)/k so that the metabolic feed needed to preserve the value of h_eff increases.

   Rather, when all roots of the polynomials P assignable to the active boundary of CD are revealed in the gradual increase of CD preserving P_nk, the transition P_nk→ P_nk∘ P_n could occur provided the metabolic resources allow this. Otherwise BSFR occurs and self dies and re-incarnates. The idea that BSFR occurs when metabolic resources are not available is very natural for this option.

2. Could P_nk→ P_nk∘ P_n occur only in BSFRs so that the degree n of P would be preserved during single life cycle of self - that n can increase only in BSFRs was indeed the original guess.

See the articles Could quantum randomness have something to do with classical chaos? and When does "big" state function reduction as universal death and re-incarnation with reversed arrow of time take place?.

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

Articles and other material related to TGD.

Conscious problem solving and quantum counterpart of computationalism in TGD

This posting was inspired by discussion with Bruno Marchal about his article with title "Do the laws of physics apply to the mind?".

I do not go to the discussion itself here. Bruno Marchal is a representative of computationalism, which might be called idealistic and Bruno believes that physics follows from computationalism. The somewhat mystical and certainly inspiring notion of self-reference is believed to lead to consciousness.

I do not share this view. I do not share this view. The gist of the posting comes towards end where I describe how computationalism generalizes to quantum computationalism in TGD generalizing also the notion of quantum computation. What conscious problem solving is? This is the question to be discussed.

Start from a problem

The basic problem in consciousness theories is that people do not have ability to leave this division to idealistic, materialistic and dualistic camps. Each of these approaches fails but people put themelves into one of these big and safe boxes. One should be able to see the biggest picture but this is surprisingly difficult.

To get out of the box, one should start from the problems rather than text book wisdom.

1. Idealism and materialism are only mirror images of each other and their problems mirror each other: for materialism mind as illusion and for idealism matter is illusion. Computationalism must select between these options two.
2. If dualist wants to cope with what we know, he ends up with materialism or idealism. In dualism the identification of mind and matter as separate substances is in conflict with the fact that mind is about something, it is does just exist as matter. Substance aspect of mind has however analog in TGD: p-adic space-time sheets serve as correlates for cognition, as thought bubbles but are not conscious thoughts.

To make progress, one must have some ideas about what conscious experience rather than deciding what it is in terms of something already known. One must identify the differences between conscious existence and physical existence in the classical sense.

Some of them are the "aboutness" property, the division of the world to me and external world in conscious experience, and experience (at least) of free will. How to realize free will without regarding laws of physics as illusion created by mind or denying it? Here the physical mystery of state function reduction comes in rescue. From this one must begin. When one does this one eventually ends up with what I call zero energy ontology, ZEO.

TGD view about life and consciousness

First my view about the relationship of physics and conscious experience.

1. In TGD Universe minds do not reduce to the properties of physical system. Nor is the reduction of physics to dynamics of mind possible. As a matter of fact, there are no minds as logical or any other kind of entities - entities are not about something as conscious experience is: the belief to mind as entity is the failure leading to the problems with free will and extremes the denial of mind or matter except as illusion. Mountains of literature has been written in order to put this problem under the rug. But in vain: black remains black and does not transform to white.

   Denialism is never a solution of a problem, it is essentially an attempt to get rid of cognitive dissonance. It is better to start from a problem or rather - paradox in the recent case. Nor can physics in its recent form explain conscious mind.

   State function reduction (SFR) is the black sheep of quantum theory and by its non-determinism rather obvious candidate for moment of consciousness and act of free will.

2. Conscious experience could therefore be in quantum jump between quantum states - SFR. The occurrence of SFR is a physical fact and with proper generalization of ontology to what I call zero energy ontology (ZEO) one can solve the problem of free will and basic paradox of quantum measurement theory.

   The realization of this simple modification of ontology to ZEO - conscious existence is in change as physiologists realized long time ago - seems to be extremely difficult for both physicists and philosophers. They cannot overcome the boundaries posed by the dogmatism taught to them - be it materialism, idealism or dualism. Again and agan I find that the proposals proposing a new brave theory of conciousness remain in one of these three boxes.

3. TGD based physics involves several dynamics. The deterministic of classical dynamics as field equations for space-time surfaces is exact part of quantum theory in ZEO. The deterministic dynamics of second quantized induced spinor fields at space-time surfaces. Quantum states in ZEO are just superpositions of these deterministic time evolutions. And also that of spinor fields of "world of classical worlds" (WCW) describing the quantum states of the Universe.

   There is also the dynamics of conscious experience. Sequence of unitary time evolutions and "small" SFRs following each of them defines sensory experience and all that accompanies it. There are also "big" (ordinary) SFRs (BSFRs) meaning the death of conscious entity and its re-incarnation with opposite arrow of time: this in universal sense - not only biologically. ZEO gives also rise to self-organization forced by generalization of second law assuming that the hierarchy of effective Planck constants predicted by number theoretical TGD is accepted.

4. Boolean logic, which is often raised by comptationalistic to a fundamental role, can be understood in terms of fermions: this is a further new element provided by TGD and provides interpretation for anti-commutation relations of fermions having also purely geometric interpretation at the level WCW in terms of the spinor structure of WCW. The truth preserving dynamics of logic is determined by modified Dirac equation at space-time level and means infinite number of conservations laws representing physics laws. ZEO is essential again: state pairs as zero energy states correspond to initial and final state connected by the dynamics described.
5. In TGD framework correlates of cognition become part of what physics described using p-adic number fields and adelic physics. Number theoretical universality is the basic principle and formally p-adic physics obeys same field equations as real number based physics correlates for for sensory perception. Cognition is universal and present already for elementary particles and has deep implications for physics itself: the success of p-adic mass calculations is one example of this.

   p-Adic space-time sheets as correlates of cognition are "thought bubbles" - the mind stuff of Descartes but not conscious as such.

   The intersection of sensory and cognitive - cognitive representation - consists of the points of space-time surface with imbedding space coordinates in the extension of rationals defining the adele in question. This hierarchy corresponds to evolutionary hierarchy with increasing algebraic complexity characterized partially by the dimension n of extension having interpretation in terms of effective Planck constant and labelling ordinary phases of matter behaving like dark matter.

   Cognitive representations are unique and in the generic case finite and basic stuff in number theory, which becomes part of quantum physics in TGD.

6. At deeper level p-adic physics and hierarchy of effective Planck constants h_eff= nh₀ labelling phases of ordinary matter behaving like dark matter follow both from number theoretic vision and servng as macroscopically quantum coherent masters controlling ordinary matter and explaining its coherence as induced coherence. n corresponds to the degree of polynomial determining space-time region as algebraic surface in octonionic M⁸ and mapped to H=M⁴× CP₂ by M⁸-H duality. Dark matter in this sense is absolutely essential for understanding of living matter in TGD framework.

   ZEO gives also the dynamics self-organization in ZEO implied by dissipation in reverse arrow of time solely so that nothing new is needed besides generalized thermodynamics. It also explains the necessity of energy feed: it is required to increase the value of h_eff (meaning increase of algebraic complexity as "IQ") and is implied by dissipation with reversed arrow of time. The laws of self-organization essentially analogs of traffic rules based on useful conventions obeyed only in statistical sese. This dynamics Wolfram fatally confuses with the fundamental dynamics.

   See this .

The relationship of TGD view about consciousness to computationalism

Computationalism is one of the failed approaches to consciousness - it cannot cope with free will for instance. It however contains an essential aspect which is correct: the idea of deterministic program leading from A to B.

Problem solving can regarded as attempt to find this program. You fix A as initial data and try to find a program leading from A to a final state characterized by data B. The program has duration T and can be very long and it is not clear whether it exists at all. You try again and again and eventually you might find it. In the real conscious problem solving this process means making guesses so that the process cannot be deterministic.

What does this view about problem solving correspond to in ZEO? We have states A and B represented as quantum states and we try to find quantum analog of classical program leading from A to B in some time T which can be varied.

1. A and B are realized as superpositions of 3-surfaces and fermionic states at them - located at time values t=0 and t=T. T can vary. Can we find by varying T a (superposition of) deterministic time evolution(s) - preferred extremal(s) (PE) - connecting A and B?

   In ZEO and for fixed A and T PE in general does not exist. In ideal situation (infinite measurement resolution) and for given A and T, B is unique if it exists at all. One has analog of Bohr orbit and the quantum analog of classical program as the superposition of Bohr orbits starting from A and hopefully leading to B as a solution of the problem.

   Remark: These superpositions can be regarded as counterparts of functions in biology and behaviors in neuroscience. The big difference to standard physics is that time=constant snapshot in time evolution of say bio-system is replaced with quantum superposition of very special time evolutions - PEs. Darwinian selection of also behaviors in biology correlates strongly with this.

2. So: given A and B, we try to find a value of T for which superposition of PEs from A to B exists. This would be the quantum program leading from A to B, and solving our problem.

   Actually, not only ours, universe is full of conscious entities solving problems at various levels of self hierarchy. This takes place by a sequences of "small" SFRs (SSFRs, weak measurements) increasing T in statistical sense and replacing the state at B with a new one determined by state A for given value of T. At the level of conscious experience this is sensory perception and all that which is associated with it.

   Finding the solution is analogous to the halting of quantum Turing machine by ordinary state function reduction, which corresponds in ZEO to a "big" (ordinary) SFR (BSFR). This would mean death in universal sense and reincarnation with reversed arrow of time in ZEO? Or is BSFR and death failure to solve the problem? I cannot answer. Remark: The notion of self-reference is replaced with much more concrete notion of becoming conscious of what one was conscious of before SSFR. SSFR indeed gives rise to conscious eperience and one avoids the infinite regress associated with genuine self-reference. As an additional bonus one obtains evolution since the extension of rationals characterizing space-time surfaces can increase meaning higher level of consciousness. At the limit algebraic numbers the cognitive representation is a dense subset of space-time surface.

3. Also finite measurement resolution and discreteness characterizing computation emerge from number theory. To be a solution classically means that the 3-surface(s) representing B to have fixed discrete cognitive representation given by finite number of imbedding space points in the extension of rationals defining the adele. Quantally, quantum superpositions of these points with fixed quantum numbers represent the desired final state. Also Boolean logic emerges at fundamental level as square root of Kähler geometry one might say. Many-fermion state basis defines a Boolean algebra and time evolution for induced spinors is analogous to truth preserving Boolean map in which truths code for infinite number of conservation laws associated with symmetries of WCW.
4. How to find the possibly existing solution at given step (unitary evolution plus SSFR) with t=T? One performs cognitive quantum measurements at each step represented by SSFR. They reduce to cascades of quantum measurements for the states in the group algebra of Galois group - call it Gal - of Galois extension considered.

   Gal has hierarchical decomposition to inclusion hierarchy of normal subgroups implying the representation of states in group algebra of Gal as entangled states in the tensor product of the group algebras of normal sub-groups of Gal. The hope is that this Galois cascade of SFRs produces desired state as an outcome and one can shout "Eureka!".

   See the article The dynamics of SSFRs as quantum measurement cascades in the group algebra of Galois group or the chapter Zero Energy Ontology and Matrices .

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

   Articles and other material related to TGD.

New resuls on M8-H duality

M⁸-H duality (H=M⁴× CP₂) has taken a central role in TGD framework. M⁸-H duality allows to identify space-time regions as "roots" of octonionic polynomials P in complexified M⁸ - M⁸_c - or as minimal surfaces in H=M⁴× CP₂ having 2-D singularities.

Remark:O_c,H_c,C_c,R_c will be used in the sequel for complexifications of octonions, quaternions, etc.. number fields using commuting imaginary unit i appearing naturally via the roots of real polynomials.

Space-time as algebraic surface in M⁸_c regarded complexified octonions

The octonionic polynomial giving rise to space-time surface as its "root" is obtained from ordinary real polynomial P with rational coefficients by algebraic continuation. The conjecture is that the identification in terms of roots of polynomials of even real analytic functions guarantees associativity and one can formulate this as rather convincing argument. Space-time surface X⁴_c is identified as a 4-D root for a H_c-valued "imaginary" or "real" part of O_c valued polynomial obtained as an O_c continuation of a real polynomial P with rational coefficients, which can be chosen to be integers. These options correspond to complexified-quaternionic tangent- or normal spaces. For P(x)= xⁿ+.. ordinary roots are algebraic integers. The real 4-D space-time surface is projection of this surface from M⁸_c to M⁸. One could drop the subscripts "_c" but in the sequel they will be kept.

M⁴_c appears as a special solution for any polynomial P. M⁴_c seems to be like a universal reference solution with which to compare other solutions.

One obtains also brane-like 6-surfaces as 6-spheres as universal solutions. They have M⁴ projection, which is a piece of hyper-surface for which Minkowski time as time coordinate of CD corresponds to a root t=r_n of P. For monic polynomials these time values are algebraic integers and Galois group permutes them.

One cannot exclude rational functions or even real analytic functions in the sense that Taylor coefficients are octonionically real (proportional to octonionic real unit). Number theoretical vision - adelic physics suggests that polynomial coefficients are rational or perhaps in extensions of rationals. The real coefficients could in principle be replaced with complex numbers a+ib, where i commutes with the octonionic units and defines complexifiation of octonions. i appears also in the roots defining complex extensions of rationals.

Brane-like solutions

One obtains also 6-D brane-like solutions to the equations.

1. In general the zero loci for imaginary or real part are 4-D but the 7-D light-cone δ M⁸₊ of M⁸ with tip at the origin of coordinates is an exception. At δ M⁸₊ the octonionic coordinate o is light-like and one can write o= re, where 8-D time coordinate and radial coordinate are related by t=r and one has e=(1+e_r)/\sqrt2 such that one as e²=e.

   Polynomial P(o) can be written at δ M⁸₊ as P(o)=P(r)e and its roots correspond to 6-spheres S⁶ represented as surfaces t_M=t= r_N, r_M= \sqrtr_N²-r_E²≤ r_N, r_E≤ r_N, where the value of Minkowski time t=r=r_N is a root of P(r) and r_M denotes radial Minkowski coordinate. The points with distance r_M from origin of t=r_N ball of M⁴ has as fiber 3-sphere with radius r =\sqrtr_N²-r_E². At the boundary of S³ contracts to a point.

2. These 6-spheres are analogous to 6-D branes in that the 4-D solutions would intersect them in the generic case along 2-D surfaces X². The boundaries r_M=r_N of balls belong to the boundary of M⁴ light-cone. In this case the intersection would be that of 4-D and 3-D surface, and empty in the generic case (it is however quite not clear whether topological notion of "genericity" applies to octonionic polynomials with very special symmetry properties).
3. The 6-spheres t_M=r_N would be very special. At these 6-spheres the 4-D space-time surfaces X⁴ as usual roots of P(o) could meet. Brane picture suggests that the 4-D solutions connect the 6-D branes with different values of r_n.

   The basic assumption has been that particle vertices are 2-D partonic 2-surfaces and light-like 3-D surfaces - partonic orbits identified as boundaries between Minkowskian and Euclidian regions of space-time surface in the induced metric (at least at H level) - meet along their 2-D ends X² at these partonic 2-surfaces. This would generalize the vertices of ordinary Feynman diagrams. Obviously this would make the definition of the generalized vertices mathematically elegant and simple.

   Note that this does not require that space-time surfaces X⁴ meet along 3-D surfaces at S⁶. The interpretation of the times t_n as moments of phase transition like phenomena is suggestive. ZEO based theory of consciousness suggests interpretation as moments for state function reductions analogous to weak measurements ad giving rise to the flow of experienced time.

4. One could perhaps interpret the free selection of 2-D partonic surfaces at the 6-D roots as initial data fixing the 4-D roots of polynomials. This would give precise content to strong form of holography (SH), which is one of the central ideas of TGD and strengthens the 3-D holography coded by ZEO alone in the sense that pairs of 3-surfaces at boundaries of CD define unique preferred extremals. The reduction to 2-D holography would be due to preferred extremal property realizing the huge symplectic symmetries and making M⁸-H duality possible as also classical twistor lift.

   I have also considered the possibility that 2-D string world sheets in M⁸ could correspond to intersections X⁴∩ S⁶? This is not possible since time coordinate t_M constant at the roots and varies at string world sheets.

   Note that the compexification of M⁸ (or equivalently octonionic E⁸) allows to consider also different variants for the signature of the 6-D roots and hyperbolic spaces would appear for (ε₁, ε_i,..,ε₈), epsilon_i=+/- 1 signatures. Their physical interpretation - if any - remains open at this moment.

5. The universal 6-D brane-like solutions S⁶_c have also lower-D counterparts. The condition determining X² states that the C_c-valued "real" or "imaginary" for the non-vanishing Q_c-valued "real" or "imaginary" for P vanishes. This condition allows universal brane-like solution as a restriction of O_c to M⁴_c (that is CD_c) and corresponds to the complexified time=constant hyperplanes defined by the roots t=r_n of P defining "special moments in the life of self" assignable to CD. The condition for reality in R_c sense in turn gives roots of t=r_n a hyper-surfaces in M²_c.

Explicit realization of M⁸-H duality

M⁸-H duality allows to map space-time surfaces in M⁸ to H so that one has two equivalent descriptions for the space-time surfaces as algebraic surfaces in M⁸ and as minimal surfaces with 2-D singularities in H satisfying an infinite number of additional conditions stating vanishing of Noether charges for super-symplectic algebra actings as isometries for the "world of classical worlds" (WCW). Twistor lift allows variants of this duality. M⁸_H duality predicts that space-time surfaces form a hierarchy induced by the hierarchy of extensions of rationals defining an evolutionary hierarchy. This forms the basis for the number theoretical vision about TGD.

M⁸-H duality makes sense under 2 additional assumptions to be considered in the following more explicitly than in earlier discussions.

1. Associativity condition for tangent-/normal space is the first essential condition for the existence of M⁸-H duality and means that tangent - or normal space is quaternionic.
2. Also second condition must be satisfied. The tangent space of space-time surface and thus space-time surface itself must contain a preferred M²_c⊂ M⁴_c or more generally, an integrable distribution of tangent spaces M²_c(x) and similar distribution of their complements E²c(x). The string world sheet like entity defined by this distribution is 2-D surface X²_c⊂ X⁴_c in R_c sense. E²_c(x) would correspond to partonic 2-surface.

   One can imagine two realizations for this condition.

   Option I: Global option states that the distributions M²_c(x) and E²_c(x) define slicing of X⁴_c.

   Option II: Only discrete set of 2-surfaces satisfying the conditions exist, they are mapped to H, and strong form of holography (SH) applied in H allows to deduce space-time surfaces in H. This would be the minimal option.

   How these conditions would be realized?

   1. The basic observation is that X²c can be fixed by posing to the non-vanishing H_c-valued part of octonionic polynomial P condition that the C_c valued "real" or "imaginary" part in C_c sense for P vanishes. M²_c would be the simplest solution but also more general complex sub-manifolds X²_c⊂ M⁴_c are possible. This condition allows only a discrete set of 2-surfaces as its solutions so that it works only for Option II.

      These surfaces would be like the families of curves in complex plane defined by u=0 an v= 0 curves of analytic function f(z)= u+iv. One should have family of polynomials differing by a constant term, which should be real so that v=0 surfaces would form a discrete set.

   2. One can generalize this condition so that it selects 1-D surface in X²_c. By assuming that R_c-valued "real" or "imaginary" part of quaternionic part of P at this 2-surface vanishes. one obtains preferred M¹_c or E¹_c containing octonionic real and preferred imaginary unit or distribution of the imaginary unit having interpretation as complexified string. Together these kind 1-D surfaces in R_c sense would define local quantization axis of energy and spin. The outcome would be a realization of the hierarchy R_c→ C_c→ H_c→ O_c realized as surfaces.

      This option could be made possible by SH. SH states that preferred extremals are determined by data at 2-D surfaces of X⁴. Even if the conditions defining X²_c have only a discrete set of solutions, SH at the level of H could allow to deduce the preferred extremals from the data provided by the images of these 2-surfaces under M⁸-H duality. Associativity and existence of M²(x) would be required only at the 2-D surfaces.

   3. I have proposed that physical string world sheets and partonic 2-surfaces appear as singularities and correspond to 2-D folds of space-time surfaces at which the dimension of the quaternionic tangent space degenerates from 4 to 2. This interpretation is consistent with a book like structure with 2-pages. Also 1-D real and imaginary manifolds could be interpreted as folds or equivalently books with 2 pages.

      For the singular surfaces the dimension quaternionic tangent or normal space would reduce from 4 to 2 and it is not possible to assign CP₂ point to the tangent space. This does not of course preclude the singular surfaces and they could be analogous to poles of analytic function. Light-like orbits of partonic 2-surfaces would in turn correspond to cuts.

   Does M⁸-H duality relate hadron physics at high and low energies?

   During the writing of this article I realized that M⁸-H duality has very nice interpretation in terms of symmetries. For H=M⁴× CP₂ the isometries correspond to Poincare symmetries and color SU(3) plus electroweak symmetries as holonomies of CP₂. For octonionic M⁸ the subgroup SU(3) ⊂ G₂ is the sub-group of octonionic automorphisms leaving fixed octonionic imaginary unit invariant - this is essential for M⁸-H duality. SU(3) is also subgroup of SO(6)== SU(4) acting as rotation on M⁸= M²× E⁶. The subgroup of the holonomy group of SO(4) for E⁴ factor of M⁸= M⁴× E⁴ is SU(2)× U(1) and corresponds to electroweak symmetries. One can say that at the level of M⁸ one has symmetry breaking from SO(6) to SU(3) and from SO(4)= SU(2)× SO(3) to U(2).

   This interpretation gives a justification for the earlier proposal that the descriptions provided by the old-fashioned low energy hadron physics assuming SU(2)_L× SU(2)_R and acting acting as covering group for isometries SO(4) of E⁴ and by high energy hadron physics relying on color group SU(3) are dual to each other.

   See the article About p-adic length scale hypothesis and dark matter hierarchy or the chapter TGD view about McKay Correspondence, ADE Hierarchy, Inclusions of Hyperfinite Factors, M⁸-H Duality, SUSY, and Twistors.

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

   Articles and other material related to TGD.

About p-adic length scale hypothesis and dark matter hierarchy

The following represents an introduction to an article summarizing my recent understanding of p-adic length scale hypothesis and dark matter hierarchy. These considerations lead to more detailed proposals. In particular, a proposal for explicit form of dark scale is made.

p-Adic length scale hypothesis

In p-adic mass calculations real mass squared is obtained by so called canonical identification from p-adic valued mass squared identified as analog of thermodynamical mass squared using p-adic generelization of thermodynamics assuming super-conformal invariance and Kac-Moody algebras assignable to isometries ad holonomies of H=M⁴× CP₂. This implies that the mass squared is essentially the expectation value of sum of scaling generators associated with various tensor factors of the representations for the direct sum of super-conformal algebras and if the number of factors is 5 one obtains rather predictive scenario since the p-adic temperature T_p must be inverse integer in order that the analogs of Boltzmann factors identified essentially as p^L₀/T_p.

The p-adic mass squared is of form Xp+O(p²) and mapped to X/p+ O(1/p²). For the p-adic primes assignable to elementary particles (M₁₂₇=2¹²⁷-1 for electron) the higher order corrections are in general extremely small unless the coefficient of second order contribution is larger integer of order p so that calculations are practically exact.

Elementary particles seem to correspond to p-adic primes near powers 2^k. Corresponding p-adic length - and time scales would come as half-octaves of basic scale if all integers k are allowed. For odd values of k one would have octaves as analog for period doubling. In chaotic systems also the generalization of period doubling in which prime p=2 is replaced by some other small prime appear and there is indeed evidence for powers of p=3 (period tripling as approach to chaos). Many elementary particles and also hadron physics and electroweak physics seem to correspond to Mersenne primes and Gaussian Mersennes which are maximally near to powers of 2.

For given prime p also higher powers of p define p-adic length scales: for instance, for electron the secondary p-adic time scale is .1 seconds characterizing fundamental bio-rhythm. Quite generally, elementary particles would be accompanied by macroscopic length and time scales perhaps assignable to their magnetic bodies or causal diamonds (CDs) accompanying them.

This inspired p-adic length scale hypothesis stating the size scales of space-time surface correspond to primes near half-octaves of 2. The predictions of p-adic are exponentially sensitive to the value of k and their success gives strong support for p-adic length scale hypothesis. This hypothesis applied not only to elementary particle physics but also to biology and even astrophysics and cosmology. TGD Universe could be p-adic fractal.

Dark matter as phases of ordinary matter with h_eff=nh₀

The identification of dark matter as phases of ordinary matter with effective Planck constant h_eff=nh₀ is second key hypothesis of TGD. To be precise, these phases behave like dark matter and galactic dark matter could correspond to dark energy in TGD sense assignable to cosmic strings thickened to magnetic flux tubes.

There are good arguments in favor of the identification h=6h₀. "Effective" means that the actual value of Planck constant is h₀ but in many-sheeted space-time n counts the number of symmetry related space-time sheets defining space-time surface as a covering. Each sheet gives identical contribution to action and this implies that effective value of Planck constant is nh₀.

M⁸-H duality

M⁸-H duality (H=M⁴× CP₂) has taken a central role in TGD framework. M⁸-H duality allows to identify space-time regions as "roots" of octonionic polynomials in complexified M⁸. The polynomial is obtained from ordinary real polynomial P with rational coefficients by algebraic continuation. One obtains brane-like 6-surfaces as 6-spheres as universal solutions. They have M⁴ projection which is piece of hyper-surface for which Minkowski time as time coordinate of CD corresponds to a root t=r_n of P. For monic polynomials these time values are algebraic integers and Galois group permutes them.

M⁸-H duality allows to map space-time surfaces in M⁸ to H so that one has two equivalent descriptions for the space-time surfaces as algebraic surfaces in M⁸ and as minimal surfaces with 2-D singularities in H satisfying an infinite number of additional conditions stating vanishing of Noether charges for super-symplectic algebra actings as isometries for the "world of classical worlds" (WCW). Twistor lift allows variants of this duality. M⁸_H duality predicts that space-time surfaces form a hierarchy induced by the hierarchy of extensions of rationals defining an evolutionary hierarchy. This forms the basis for the number theoretical vision about TGD.

During the writing of this article I realized that M⁸-H duality has very nice interpretation in terms of symmetries. For H=M⁴× CP₂ the isometries correspond to Poincare symmetries and color SU(3) plus electroweak symmetries as holonomies of CP₂. For octonionic M⁸ the subgroup SU(3) ⊂ G₂ is the sub-group of octonionic automorphisms leaving fixed octonionic imaginary unit invariant - this is essential for M⁸-H duality. SU(3) is also subgroup of SO(6)== SU(4) acting as rotation on M⁸= M²× E⁶. The subgroup of the holonomy group of SO(4) for E⁴ factor of M⁸= M⁴× E⁴ is SU(2)× U(1) and corresponds to electroweak symmetries. One can say that at the level of M⁸ one has symmetry breaking from SO(6) to SU(3) and from SO(4)= SU(2)× SO(3) to U(2).

This interpretation gives a justification for the earlier proposal that the descriptions provided by the old-fashioned low energy hadron physics assuming SU(2)_L× SU(2)_R and acting acting as covering group for isometries SO(4) of E⁴ and by high energy hadron physics relying on color group SU(3) are dual to each other.

Number theoretic origin of p-adic primes and dark matter

There are several questions to be answered. How to fuse real number based physics with various p-adic physics? How p-adic length scale hypothesis and dark matter hypothesis emerge from TGD?

The properties of p-adic number fields and the strange failure of complete non-determinism for p-adic differential equations led to the proposal that p-adic physics might serve as a correlate for cognition, imagination, and intention. This led to a development of number theoretic vision which I call adelic physics. A given adele corresponds to a fusion of reals and extensions of various p-adic number fields induced by a given extension of rationals.

The notion of space-time generalizes to a book like structure having real space-time surfaces and their p-adic counterparts as pages. The common points of pages defining is back correspond to points with coordinates in the extension of rationals considered. This discretization of space-time surface is in general finite and unique and is identified as what I call cognitive representation. The Galois group of extension becomes symmetry group in cognitive degrees of freedom. The ramified primes of extension are exceptionally interesting and are identified as preferred p-adic primes for the extension considered.

The basic challenge is to identify dark scale. There are some reasons to expect correlation between p-adic and dark scales which would mean that the dark scale would depend on ramified primes, which characterize roots of the polynomial defining the extensions and are thus not defined completely by extension alone. Same extension can be defined by many polynomials. The naive guess is that the scale is proportional to the dimension n of extension serving as a measure for algebraic complexity (there are also other measures). Dark p-adic length scales L_p would be proportional nL_p, p ramified prime of extension? The motivation would be that quantum scales are typically proportional to Planck constant. It turns out that the identification of CD scale as dark scale is rather natural. In the article p-adic length scale hypothesis and dark matter hierarchy are discussed from number theoretic perspective. The new result is that M⁸ duality allows to relate p-adic length scales L_p to differences for the roots of the polynomial defining the extension defining "special moments in the life of self" assignable causal diamond (CD) central in zero energy ontology (ZEO). Hence p-adic length scale hypothesis emerges both from p-adic mass calculations and M⁸-H duality. It is proposed that the size scale of CD correspond to the largest dark scale nL_p for the extension and that the sub-extensions of extensions could define hierarchy of sub-CDs.

See the article About p-adic length scale hypothesis and dark matter hierarchy.

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

Articles and other material related to TGD.

Rejuvenation and zero energy ontology

Biologist Harold Katcher (see this) claims that the epigenetic age (there are several measures for it such as methylation level of DNA) of rats has been reduced up to 50 percent. The theory goes that epigenetic age of molecules would be controllable by hormonal signalling globally.

I have been just working with the view about state function reduction in zero energy ontology of TGD providing a theory of quantum measurement free of its basic paradox and having profound implications in the understanding of mysteries of life and death.

For ordinary "big" state function reductions (BSFRs) the arrow of time changes. BSFR would mean death of conscious entity and its reincarnation with opposite arrow of time. The system would rejuvenate in the transition starting a new life in opposite time direction from childhood so to say- rejuvenation would be in question. Doing this twice would lead to life with original arrow of time but starting in rejuvenated state.

Returning cells to the stem cell state inducing de-differentiation as reversal of differentiation would be one example of rejuvenation. The claims of the group suggests that living matter is doing this systematically using hormonal control.

See the article When does "big" state function reduction as universal death and re-incarnation with reversed arrow of time take place?.

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

Articles and other material related to TGD.

When does "big" state function reduction as universal death and re-incarnation with reversed arrow of time take place?

In ZEO based view about quantum measurement theory as theory of consciousness one has two kinds of state function reductions (SFRs) ( see this and this). The ordinary "big" SFRs (BSFRs) and "small" SFRs (SSFRs) (see this). BSFR changes the arrow of geometric time and is identified as death of self identified as a sequence of SSFRs, which do not change arrow of time but increase the size of self by keeping passive boundary in place and states at it unaffected but increasing the size of CD by shifting the upper boundary towards future. Both boundaries increase in size. The 3-surfaces at the active boundary form a kind of log file about events in the life of self and - contrary to expectations - the memories are stored to geometric future.

Under what conditions does "big state function reduction (BSFR) changing the arrow of time take place? I have proposed several ad hoc guesses about this. One example is following. If the h_eff=n× h₀ assignable to the CD or its active boundary does not change in SSFRs, the entanglement can become such that the diagonalized density matrices does not have eigenvalues in the extension of rationals considered and one can argue that BSFR is forced to occur. The proposal for how the sequence of SSFR could in special case correspond to a sequence of iterations for a polynomial of degree n (see this) is however in conflict with the constancy of n.

The hypothesis is that BSFR corresponds to the death of self followed by re-incarnation with opposite arrow of geometric time in universal sense. This suggests that one should look what one can learn from what happens in the death and birth of biological organism, which should now take in opposite arrow of time.

1. Death certainly occurs if there is no metabolic energy feed to the system. Metabolic energy feed is guaranteed by nutrition using basic molecules as metabolites. Since the increase of h_eff quite generally requires energy if other parameters are kept constant and since the reduction of h_eff can take spontaneously, the metabolic energy is needed to keep the distribution of values of h_eff stationary or even increase it - at least during the growth of organism and perhaps also during the mature age when it would go to increase of h_eff at MB.
   

   If the size of CD for at least MB correlates with the maximum value of h_eff or its average, the size of CD cannot grow and can be even reduced if the metabolic energy feed is too low. The starving organism withers and its mental abilities are reduced. This could correspond to the reduction of maximum/average value of h_eff and also size of CD.
   

   One can argue that if the organism loses metabolic energy feed or is not able to utilize the metabolic energy death and therefore also BSFR must take place.
   
   

2. In ZEO self-organization reduces to the second law in reversed direction of geometric time at the level of MB inducing effective change of arrow of time at the level of biological body (see this)). The necessary energy feed correspond to dissipation of energy in opposite time direction. In biological matter energy feed means its extraction from the metabolites fed to the system. One could say that system sends negative energy to the systems able to receive it. A more precise statement is that time reversed subs-system dissipates and metabolites receive the energy but in reversed time direction.
   

   In living matter sub-systems with non-standard arrow of time are necessary since their dissipation is needed to extract metabolic energy. The highest level dissipates in standard time direction and there must be a transfer of energy between different levels. This hierarchy of levels with opposite arrows of geometric time would be realized at the level of MB.
   
   

These observations suggest that one should consider the reincarnation with opposite arrow of time with wisdom coming from the death of biological systems.

1. We know what happens in death and birth in biological systems. What happens in biological death should have analogy at general level. In particular, in death the decay of the system to components should occur. Also the opposite of this process with reversed arrow of time should take place and lead at molecular level to the replication of DNA and RNA and build-up of basic biomolecules and at the cell level to cell replications and development of organs. How these processes could correspond to each other?
   
   
2. The perceived time corresponds to the hyperplane t=T/2 of CD, where T is the distance between the tips of CD and therefore to maximal size of temporal slice of CD. The part of CD above it shifts towards future in SSFRs. In BSFR part of the boundary of space-time surfaces at the active boundary of CD becomes unchanging permanent part of re-incarnate - kind of log file about the previous life. One can say that the law of Karma is realized.
   

   If CD decreases in size in BSFR the former active boundary keeps its position but its size as distance between its tips is scaled down: T → T₁≤ T. The re-incarnate would start from childhood at T-T₁/2 and would get partially rid of the permanent part of self-hood so that new permanent part would be between T/2 and T-T₁/2 . Reincarnate would start almost from scratch, so to say. The part between T-T₁/2 and T would be preserved as analog of what was called BIOS in personal computers.
   
   

3. At the moment of birth CD possibly would thus decrease in size and the former passive boundary between t=T/2 hyperplane and lower tip of new CD at T-T₁ would becomes active and the seat of sensory experience. Where the analog of biological decay is located? The region of CD above T/2 and T-T₁/2 is the only possible candidate. This region is also the place, where the events related to birth in opposite time direction should take place.
   

   The decay of previous organism should correspond to the development and birth of re-incarnated organism. The decay of organism dissipates energy in standard time direction: this energy could used by the re-incarnate as metabolic energy.
   

   This vision might be tested. The replication of DNA and RNA and build-up of various bio-molecules should be time-reversals for their decays. The same applies to the replication of cells and generation of organs. Replication of DNA is self-organization process in which second DNA strand serves as a template for a new one. The decay of DNA should therefore involve two DNA strands such that the second DNA strand serves as a template for the time reversed replications. The double strand structure indeed makes possible for the other strand to decay first. One could even ask whether the opposite inherent chiralities of DNA strands correspond to opposite arrows of time. Maybe this could be seen as a kind of explanation for the double strand structure of DNA.
   

   In biology pairs of various structures often occur and maybe they could correspond in some sense to time reversals of each other. Also cell replication should use another cell as replicate and same would happen in the cell decay.
   
   

4. Eastern philosophies talk about the possibility of liberation from Karma's cycle. Can one imagine something like this? The above picture would suggest that in this kind of process the reduction of the size of CD does not occur at all and therefore there would be no decay process equivalent to the growth of time reversed organism. This would serve as an empirical signature for the liberation if possible at all. CD would continue to increase in size or perhaps keep its size. It would seem that a new kind of non-biological source of metabolic energy is needed.
   
   
5. Mental images should correspond to sub-selves and therefore sub-CDs of CD. The idea that the re-incarnations of mental images correspond to re-incarnations with a reversed arrow of time is very attractive. After images is the basic example. Only the after images with standard arrow of time would be experienced by us. Are the after images sensory memories of subjective past involving communication with re-incarnated visual mental image?
   

   The original, rather natural, proposal was that the after image is in the geometric past but according to the new view it would be shifting with the active boundary of CD towards geometric future at the active boundary of CD as a kind of log file. To remember it as sensory mental image requires communication with it along active boundary involving both future and past directed signals.
   

   One can imagine also more mundane explanation for after images in terms of propagation of dark photon signals along closed magnetic loops giving rise to periodically occurring mental images.
   
   

See either the article Some comments related to Zero Energy Ontology (ZEO), the article When does "big" state function reduction as universal death and re-incarnation with reversed arrow of time take place?, or the chapter Life and Death and Consciousness.

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

Articles and other material related to TGD.

Could Universe could have North-South direction: How?

Wes Johnson gave ) told about very interesting observations suggesting that cosmology has North-South (N-S) axis in the sense that fine structure constant has N-S variation with respect to this axis. See the popular article. Here is the abstract of the article of Webb et al.

Observations of the redshift z = 7.085 quasar J1120+0641 are used to search for variations of the fine structure constant, a, over the redshift range 5.5 to 7.1. Observations at z = 7.1 probe the physics of the universe at only 0.8 billion years old. These are the most distant direct measurements of a to date and the first measurements using a near-IR spectrograph. A new AI analysis method is employed. Four measurements from the X-SHOOTER spectrograph on the Very Large Telescope (VLT) constrain changes in a relative to the terrestrial value (α₀). The weighted mean electromagnetic force in this location in the universe deviates from the terrestrial value by Δ α/α = (α_z- α₀)/α₀= (-2.18 ± 7.27) × 10^-5, consistent with no temporal change. Combining these measurements with existing data, we find a spatial variation is preferred over a no-variation model at the 3.9 σ level.

To repeat: the difference from earthly value of α is small and consistent with no temporal change. If the measurements are combined with existing data, one finds that the model assuming spatial variation in north-south direction is preferred over no-variation model at 3.9 sigma level.

This kind of variation was reported years ago (see this). Thanks for Richard Ruquist for the link. I also wrote about the claim (see this).

The findings are very strange and counterintuitive and the effect probably disappears: there are many uncertainties involved since data from several experiments are combined. If the effect is real, there is challenge to understand it so that one cannot avoid the temptation for intellectual exercise.

In TGD framework many-sheeted space-time serves as a starting point.

1. The notion of space-time sheet requires that the M^4 projection of space-time surfaces is 4-D: I call these space-time sheets Einstenian. This was not true in primordial cosmology during which cosmic strings with 2-D M⁴ projection dominated (2-D in good approximation) - space-time was not Einsteinian yet. During the analog of inflationary period cosmic strings thickened to flux tubes and liberated energy giving rise to ordinary particles. Transition to radiation dominated cosmology took place during this period.
   
   
2. The fluctuations in the density of matter tell that this transition did not take at exactly the same value of cosmic time T but there are fluctuations of order ΔT/T ≈ 10^-5. This happens to be same order of magnitude as the reported value of Δα/α along North-South direction, which puts bells ringing. Could same cosmic parameter determine fluctuation amplitude ΔT/T and the relative change Δα/α along N-S direction?
   

   Could it be that the transition to radiation dominated cosmology took place in a wave propagating in North-South (N-S) direction so that there would be a gradient of T along N-S direction: ΔT/T - not fluctuation. This does not require gradient in fluctuations Δ T/T and Δ ρ/ρ. Could this gradient also explain the gradient in α along N-S direction?
   
   

How the N-S gradient in α could be understood?

1. At QFT limit particle experiences the sum of induced gauge fields assignable to the space-time sheets which it necessarily touches because it has same size of order CP₂size as the sheets on top of each other in CP₂directions. Standard model gauge fields can be indeed defined as sums of these induced gauge fields. Same applies to gravitational field identified in terms of metric of Einsteinian space-time having 4-D M⁴ projection.
   
   
2. The many-sheeted space-time was not quite the same thing in today and in ancient universe. The number of space-time sheets could have been different. Space-time sheets carried also induced classical fields with different strength.
   

   Monopole flux tubes created during the analog of inflationary period from cosmic strings indeed evolve during cosmic evolution. Their thickness increases in rapid jerks and in average sense this corresponds to a smooth cosmic expansion. This conforms with the fact that astrophysical objects do not seem to expand themselves in cosmic expansion although they co-move as particles in this expansion.
   

   The increase of the thickness of monopole magnetic flux tube reduces its magnetic field strength since monopole flux is conserved. This in turn reduces the contribution of this space-time sheet to the classical em field experienced by a charged particle. In particular, this would affect the binding energies of atoms slightly.
   
   

3. Could this together with the wave like progression of the transition to radiation dominated cosmology be responsible for the dependence α on N-S direction with the increase Δα/α ≈ 10^-5?
   
   

See the chapter More TGD inspired cosmology.

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

Articles and other material related to TGD.