Monday, February 26, 2024

Could a TGD analog of Weinstein's proposal help to define the QFT limit of TGD?

Eric Weinstein has proposed "Geometric Unity", which is a proposal for a unification of the standard model and gravitation based on the notion of 14-D manifold U(14), which according to my understanding is the bundle of metrics of X reducing locally to a product space-time and 10-D internal space which could consist of 4× 4 symmetric matrices. Weinstein wants to endow U(14) with some additional structure and explain gauge symmetries in terms of the fiber of U(14) consisting of symmetric 4× 4 matrices. Group SO(10) acts as the 10-bein group of this space in the Euclidean case and the proposal is that it acts as a gauge group.

The first problem is that if the 10-bein group defines the gauge group, the gauge group for a Minkowskian signature of X is non-compact variant of SO(10), which is the group of isometries for the space of M10 with Euclidean signature. In gauge theories non-compactness of the gauge group implies the loss of unitarity. Weinstein admits that his proposal works only in the Euclidean case.

Second problem is posed by the general coordinate invariance. General coordinate transformations do not induce a mere gauge transformation of the matrix of M10 as they should. This could mean severe difficulties in the realization of the general coordinate invariance.

In the TGD framework, one of the challenges is the more precise definition of the QFT limit of TGD. In this article I will consider a variant of Weinstein's theory obtained by replacing H=M4× CP2 with M4× Sn as a possible manner to approach the problem. For n=9 and n=10 one obtains SO(n+1) as maximal isometry group and holonomy group. It turns out that one can obtain standard model symmetries but the predicted number of fermion families turns out to be wrong. In TGD fermion families have a topological explanation. M can be replaced by a sphere Sn, and n=10 gives 4 generations and n=8 and n=9 2 generations. For larger values of n the number generations increases exponentially. Whether the QFT model could serve as a phenomenological description of the family replication phenomenon remains open.

In this article, I will consider a variant of Weinstein's theory obtained by replacing H=M4× CP2 with M4× Sn. For n=9 and n=10 one obtains SO(n+1) as maximal isometry group and holonomy group. It turns out that one can obtain standard model symmetries but the predicted number of fermion families turns out to be wrong. In TGD fermion families have a topological explanation. M can be replaced by a sphere Sn, and n=10 gives 4 generations and n=8 and n=9 2 generations. For larger values of n the number generations increases exponentially. Whether the QFT model could serve as a phenomenological description of the family replication phenomenon remains open.

See the article Could a TGD analog of Weinstein's proposal help to define the QFT limit of TGD? or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Friday, February 23, 2024

Are planets and stars gravitational harmonic oscillators?

I learned (thanks to Mark McWilliams and Grigol Asatiani) about a proposal that black-hole like stars, gravatars, could develop Russian doll-like nested structures, nestars (see this). Gravastar is a star proposed to replace blackhole. It has a thing layer of matter at horizon and de-Sitter metric in the interior. Nestar would consist of nested gravastars.

The proposal is interesting from the TGD point of view because TGD raises the question whether stars and astrophysical objects in general could have a layered structure.

  1. One of the early "predictions" of TGD for stars coming from the study of what spherically symmetric metrics could look like, was that it corresponds to a spherical shell, possibly a hierarchical layered structure in which matter is condensed on shells. p-Adic length scale hierarchy suggests shells with radii coming as powers of 21/2.
  2. Nottale's model for planetary systems suggests Bohr orbitals for planets with gravitational Plack constant GMm/β0. The value of the velocity parameter β0=v0/c≤1 is from the model of Nottale about 2-11 for the inner planets and 1/5 times smaller for the outer planets. This might reflect the fact that originally the planets or what preceded them consisted of gravitationally dark matter or that the Sun itself consisted of gravitationally dark matter and perhaps still does so.
1. Could harmonic oscillator model for stars and planets make sense?

The Nottale model is especially interesting and one can look at what happens inside the Sun or planets, where the mass density is in a good approximation constant and gravitational potential is harmonic oscillator potential. Could particles be concentrated around the orbitals predicted by the Bohr model of harmonic oscillator with radii proportional to n1/2, n=1,2,3,.. . The lowest state would correspond to S-wave concentrated around origin, which is not realized as Bohr orbit. The wave function has nodes and would give rise to spherical layers of matter.

One can perform the simple calculations to deduce the energy values and the radii of Bohr orbits in the gravitatational harmonic oscillator potential by using the Bohr orbit model.

  1. The gravitational potential energy for a particle with mass m associated with a spherical object with a constant density would be GmM(r)/r = GMmr2/R3, where M is the mass of the Sun and R is the radius of the object. This is harmonic oscillator potential.
  2. The oscillator frequency is

    ω= (rS/R)3/2/rS,

    where rs= 2GM is the Schwartschild radius of the object, about 3 km for the Sun and 1 cm for Earth.

  3. The orbital radii for Bohr orbits are proportional to n1/2 inside the star. By the Equivalence Principle, the radius does not depend on particle mass. One obtains

    rn = n1/2 (2β0)-1/2 (rS/R)1/4 × R.

Of course, one must remember that in the recent Sun and Earth ordinary matter is probably not gravitationally dark: only the particles associated with the U-shaped monopole flux tubes mediating gravitational interaction could be gravitationally dark and would play an important role in biology.

The situation could have been different when the planets formed. I have proposed a formation mechanism by an explosive generation of gravitationally dark magnetic bubbles ("mini big bangs"), which then condensed to planets (see this and this). This would explain why the value of β_0 for the Earth interior is the same as for the system formed by the interior planets and Sun. The simple calculations to be carried out that for the outer planets only the core region emerged in this way and the gravitational condensation gave rise to the layer above it. The core should have the properties of Mars in order that it could correspond to S-wave state.

The model turns out to be surprisingly successful. The condition that the interior of the planet corresponds to an S-wave ground state with a maximal radius is satisfied for 3 inner planets and Mars. Also Mercury satisfies the inequality. For the Sun the n=1 S-wave orbital is 1.5 times the solar radius . For outer planets the conditions are not satisfied, which suggests that they are formed by gravitational condensation of matter around the core which must have the size and mass of Mars to satisfy the ground state S-wave orbital condition. Also the rings of Jupiter (and probably also of Saturn) can be understood quantitatively, which gives strong support for the assumption that the core is Mars-like. This picture would suggests that at the fundamental level the planetary system is very simple.

2. Application of the oscillator model to solar system

In this section the above simple model is applied to the solar system.

2.1 Oscillator model for the Sun and Earth

Consider first the model for the Sun.

  1. For the Sun one has rS/R = 4.3×10-6. For β0=2-11 for the inner planets one obtains r1= 1.45R so that this value of β0 is too small. For β0=10-3 would give r1≈ R. Solar interior would correspond to ground the S-wave concetrated around origin for β0≤ 0-3.

    β0=1 gives r1=.032R, which is smaller than the radius of the solar core about .2R. β0=0.026 would give r1= .2R. r25 would be near to the solar radius. The set of the nodes of a harmonic oscillator wave function would be rather dense: at the surface of the Sun the distance between the nodes would be .1R. Note that the convective zone extends to .7R.

What about the Earth?

  1. One has rS= 1 cm and R= 6,378 km. At the surface of Earth β0=1 is the favoured value and would give r1= ≈ 151.6 km. The radius of the inner inner core is between 300 km and 400 km. n=4 would correspond to 300 km and n=7 to 400 km. β0 scales like (r1/RE)2. At the surface of Earth one would have n = (RE/r1)2≈1784 and the distance between two nodes would be RE/2n≈1.8 km.
  2. One can write β0(r1) as β0(r1)= (151.6/r1)2.
    1. For r1=3471 km, the core radius, this gives β0≈1.9× 10-3.
    2. The gravitational Compton length of the Sun is one half of Earth's radius, which conforms with the Expanding Earth hypothesis, and is not far from the radius of the core. This gives β0= 2.2× 10-3.
    3. For r1=RE, one has β0≤5.6× 10-3, which is quite near to the nominal value of β0=2-11 for the magnetic body of the Sun, the Earth interior would correspond to the ground state S-wave concentrated around origin.

      β0≈ 1 should hold true above the surface of the Earth, which suggests that it characterizes the gravitational magnetic body of Earth.

2.2 Do inner planets correspond to S wave ground states for gravitational harmonic oscillator?

The above observations suggest that the value of β0 for Sun and inner is such that both the entire Sun and planets correspond to ground state S-wave states. This would indeed mean that the n=1 state corresponds to a thin layer at the surface (note that the orbital in plane is replaced by a wave function in Schrödinger equation). The large size of giant planets does not favor this hypothesis them. In any case, the condition r1≤ RP would predict

rS,P/RP≤ 4β20(Sun,P).

Using ME and RE as units, this condition reads for inner planets as

rS,P/RP≤ 1

and for outer planets as

rS,P/RP≤ K2.

where the value of K= 1 or 1/5 depending on what option is assumed.

  1. The first option assumes that the principal quantum numbers n are of the form n= 5k, k=1,2,.. for the outer planets and n= 3,4,5 for inner planets. This gives K=1. This is possible although it looks somewhat un-natural.
  2. The second option, proposed originally by Nottale, is β0(outer)= Kβ0(inner)/5, K=1/5.
It is interesting to see whether the condition holds true (for the tables providing among other things masses and radii of planets see this).

  1. Consider first the rocky planets, which include inner planets and Mars. For Mercury the ratio of this factor to that for Earth is .145 which conforms with the inequality hypothesis. For Venus and Earth with nearly equal masses and sizes the equality is true. For Mars, which is a rocky outer planet, the condition is also true for K=1/5 option. Therefore the equality holds true for 3 rocky planets.
  2. The outer planets are gas giants apart from Neptune, which is an ice giant. For Jupiter , Saturn, Uranus, and Neptune, the ratios using ME and RE as units are 28.4, 10.4, 3.6, 4.6.The values of the core radii would be by a factor x/K too large, where x is 28.4, 10.4, 3.6, 4.6, where K is 1 or 1/5 depending on the option.
2.3 Do giant planets have a shell structure for gravitational harmonic oscil- lator in some sense?

Do the above observations imply that the giant planets have a layered structure predicted by the gravitational harmonic oscillator potential and they have a rocky core as an analog of the S-wave state with a size predicted by the equality?

  1. A natural mechanism for the formation of the giant planet would be gravitational condensation of matter from the environment around the core region.
  2. The first guess for the core region is as a rocky planet, either Mars or Earth. This determines the mass and radius of the core and it would correspond to the S-wave state of a gravitational harmonic oscillator with gravitational Planck constant proportional to ME or MM. The n=1 harmonic oscillator orbital corresponds to the radius of the core. Mars with K=1/5 remains the only option.
  3. The region outside the core could correspond in the first approximation to harmonic oscillator orbitals determined by the average density with radii given as rn= n1/2Rcore(P).

One can develop a more detailed model as follows.

  1. Newton's law for circular Bohr orbits and quantization condition for angular momentum in the gravitational potential V(R)= GmM(R)/R, where M(R) is

    M(R) = M(core) + M(layer)×[(R/RP)3-(Rcore/RP)3) .

    Slightly below R(core) the force is harmonic force the interior R increases, the gravitational potential approaches to harmonic oscillator potential determined by MP. For outer planets the average density is considerably smaller than the density of the core.

  2. The first condition is

    v2/R= dV(R)/dR = -d(GM(R)/R)/dR = GM(R)/R2-G(dM/dR)/R,

    where one has

    dM/dR= 3R^2/RP3 .

    One obtains

    v(R)2= (1/2)× (rS(core)/R- 3rS(layer)× (R/RP)3).

  3. The second condition corresponds to the quantization of the angular momentum

    vR= GM(core)/β0

    gives for R the equation

    R/RE= (rS(core)/RE)/β0v(R) .

    Mars is the natural choice for the core. From these data the radii of the Bohr orbits can be calculated. Near the boundary of the core the radii would go like n1/2RM. For large enough radii one would obtain harmonic oscillator potential.

Jupiter serves as a representative example. One has MJ= 317.8ME and RJ= 11.2RE≈22.4RM. The density of Jupiter is fraction .22 of the density of Earth. Most of the mass of Jupiter would be generated by the gravitational condensation of gas from the atmosphere. At least the dark matter at the gravitational magnetic body would be at the harmonic oscillator orbitals.

2.4. Could one understand the rings of Jupiter and Saturn in terms of a gravitational analog of a hydrogen atom?

Could one understand the rings of Saturn and Jupiter in terms of Bohr orbits with a small principal quantum number n for the gravitational analog of a hydrogen atom assuming the same gravitational Planck constant as for the interior of the planet and determined by the mass of the core?

The basic formulas for hydrogen atom generalize and one obtains that the radius of hydrogen atom as a0= ℏ/2α me, α= e2/4πℏ is replaced with agr= ℏgr/2αgrm, ℏgr= GMMarsm/β0, αgr= GMMm/4πℏgr= GMm β0/4π. This gives

agr =(2π/β02)× (rS,Mars2/rS,J) .

Consider Jupiter as an example. By using MJ/MMars≈ 3178 and β0≈2-11/5, one obtains the estimate agr= (π/3.178)/× 104 ≈ 104 km. The radius of Jupiter is 7.4× 104 km. agr is proportional to the square of the mass of the core. That orders of magnitude are correct, is highly encouraging. The radii of Bohr orbits are given by rn=n^2agr. Could the radii for the rings correspond to n=3 Bohr orbit?

See the article Are planets and stars gravitational harmonic oscillators? or the chapter Magnetic Bubbles in TGD Universe: Part I

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Tuesday, February 20, 2024

A fresh look at M8-H duality and Poincare invariance

M8-H duality is a proposal to integrate geometric and number theoretic visions of TGD. M8-H duality has several questionable features. For various reasons it seems that M8 must be replaced with its complexification M8c interpreted as complexified octonions Oc. This however leads to several problems. The modified variant of M8-H duality identifying M8 as a quaternionic sub-space of octonions O with a number theoretic norm defined by Re(o2), rather than oo*, solves these problems.

The proposal has been that octonionic polynomials P(o) define the number theoretic holography. Their roots would define 3-D mass shells for which mass squared values are in general complex and the initial data for the holography would correspond to 3-surfaces at these mass shells. Also this assumption has problems. There is however no need for this assumption: the holography on the H side is induced by the M8-H duality!

The hierarchy of polynomials defines a hierarchy of algebraic extensions defining an evolutionary hierarchy central for all applications of TGD and one must have it. Luckily, the recent realization that a generalized holomorphy realizes the holography at the H side as roots for pairs of holomorphic functions of complex (in generalized sense) coordinates of H comes to rescue. It can be strengthened by assuming that the functions form a hierarchy of pairs of polynomials.

Twistor lift strongly suggests that M4 and space-time surfaces allow a Kähler structure and what I call Hamilton-Jacobi structure. These structures force a breaking of Poincare and even Lorentz invariance unless they are dynamically generated. It indeed turns out that M8-H duality generates them dynamically.

See the article A fresh look at M8-H duality and Poincare invariance or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Wednesday, February 14, 2024

Direct evidence for cosmic strings in TGD sense from weak lensing

The cosmic plot is finally starting to unravel! For almost twenty years I have been trying to communicate a TGD-based theory for the galactic dark matter but in vain. Now empiria has come to rescue.  

There is now evidence for   dark matter filaments from the detection of weak-lensing caused by them (see the popular article).  See also  the article "Weak-lensing detection of intracluster filaments in the Coma cluster" by   HyeongHan et al in Nature Astronomy, 2024. This kind of dark filaments are a basic prediction of TGD and their classical energy corresponds to dark energy.

Before radiation-dominated cosmology, the matter in the TGD Universe   matter consists of extremely massive objects, which I call cosmic strings. They are string-like 3-surfaces in M^4xCP_2 space, where spacetimes are 4-surfaces. The monopole flux   associated with these string-like objects  stabilizes them against splitting. They are typically more or less perpendicular to the galaxies they have generated in a local decay process and create a gravitational field in the plane of the galaxy behaving like 1 over transversal distance.

The string tension alone explains the constant velocity spectrum of distant stars and the model avoids the problems of the LambdaCDM  and MOND. However, cosmic strings are unstable against decaying into ordinary matter by thickening, which  reduces  the string tension, and in this process galaxies are formed. In particular, the collisions of the cosmic strings trigger decay to ordinary matter as  the TGD  counterpart of inflation.

The extremely fast star formation in the very early universe, recently observed by JWT, is a mystery  for which an explanation is proposed in terms   of giant black holes which,  contrary to standard wisdom, were born before the galaxies and  formed directly from plasma rather than as the end result of evolution.  See https://scitechdaily.com/unlocking-the-secrets-of-cosmic-dawn-the-primordial-race-between-black-holes-and-galaxies/

For the TGD vision of the formation of galaxies  see for instance this, this, this, and this .

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Which Came First: Supermassive Black Holes or Galaxies?

The revolution initiated by the the James Webb Telescope continues: see the popular article and the article “Which Came First: Supermassive Black Holes or Galaxies? Insights from JWST” by Joseph Silk et al published in The Astrophysical Journal Letters.

The objects identified as gigantic primordial blackholes are introduced to explain the extremely fast formation for a few million years after the Big Bang. After this period the formation of stars should have slowed down and the recent galaxies and galactic blackholes would evolve very slowly.

The very existence of this kind of blackholes is in conflict with the standard general relativistic wisdom, which assumes that blackholes were formed as the final state of the development. The primordial blackholes should be formed directly from the concentrations of the primordial plasma without formation of stars. Their presence would catalyze the rapid formation of stars and lead to formation of galaxies.

These visions can be seen as part of the desperate battle of general relativity based cosmology in order to survive the empirical facts. In the TGD framework, space-time is replaced with a 4-surface in H=M^4xCP_2: this predicts standard model symmetries and unifies gravitation and standard model. The choice of H is unique both mathematically and physically.

The TGD based space-time concept led to a new view of cosmology involving cosmic strings (not those of GUTS) as string-like objects carrying monopole magnetic fluxes. They are extremely thin 4-surfaces with a huge string tension carrying energy having interpretation as analog of dark energy. They provide explanation for the galactic dark matter involving only string tension as a paerameter and solving the problems of LambdaCDM and MOND.

  1. Cosmic strings dominated before the radiation dominated phase and their decay to ordinary matter was the TGD counterpart of inflation. Cosmic strings were unstable against the thickening of their 1-D M^4 projection to a 3-D flux tube. The string tension of the thickened portion of the flux tubes formed a tangle and the associated dark energy transformed to ordinary matter forming a galaxy around it. Also collisions of cosmic strings generated this kind of tangles.
  2. This decay process as an analogy of inflation generated ordinary matter, galaxies and stars and generated the counterparts of the postulated primordial blackholes. During this period the formation of stars was extremely rapid and later slowed down as the findings of the JWT demonstrate.
See for instance this, this, this, and this .

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Monday, February 12, 2024

Missing baryon problem from the TGD point of view

The following piece of text was meant to be a comment to an FB post telling about the missing baryon problem (see this). My FB is however plagued by a virus, which makes the addition of comments very difficult: the page disappears just when I try to add the comment. This happened also now.

What is the problem of missing baryonic matter.

  1. 1/7 of the matter of the Universe is dark matter in the sense of galactic dark matter. The identification of the dark matter is still a mystery. LambdaCDM people have decided dark matter to be some exotic particles forming halos around galaxies. MOND people have decided that Newtonian gravity is modified for weak fields.
  2. Besides 30 per cent of the ordinary matter, baryons, seems to be missing. This is known as the missing baryon problem (see this>).

    The prosaic explanation for the puzzle is that with the available technology we are not able to detect the missing part of ordinary matter and it has been argued that the missing baryonic matter can be assigned with long filamentary structures. This explanation might be correct.

What can one say about dark matter in the TGD framework?
  1. In the TGD Universe, the radiation dominated phase was preceded by cosmic string dominance. They would have decayed to ordinary matter like inflaton fields and led to the radiation dominated Universe.
  2. The galactic dark matter could be actually dark energy assignable with long cosmic strings with a gigantic string tension. Monopole flux would make them stable. This dark energy would decay to ordinary matter since the cosmic strings are unstable against thickening and generation of flux tube tangles giving rise to ordinary galaxies.

    This process would be the TGD counterpart of inflation: inflaton fields would be replaced by cosmic strings. This view predicts the flat velocity spectra of galaxies using only string tension as a parameter and makes a long list of predictions allowing us to understand the anomalies of LambdaCDM and MOND.

  3. TGD predicts also matter behaving like dark matter. This analog of dark matter is identifiable as heff>h phases of THE ordinary matter and could contribute to the missing baryonic matter. I have used to talk about dark matter but this matter need not be galactic dark matter, which could be mostly dark energy for cosmic strings. The dark phases can have arbitrarily long quantum coherence scales and they play a fundamental role in living matter as controllers of the ordinary matter. In TGD inspired biology dark protons identified as this kind of phase at monopole flux tubes play an essential role.

    What could one say about the missing baryonic matter in this framework? I have considered this question in more detail earlier (see this), and the following general comment explains why ordinary baryons should transform to dark ones during the cosmic evolution.

    1. Could the missing ordinary matter correspond to heff>h phases of the ordinary matter? The intuitive view is that the density of dark protons is much smaller than the number of ordinary protons. Could this be true only in the regions containing high density of ordinary matter. Could the fraction of ordinary protons be much larger than that of dark protons only in the regions where the visible matter is concentrated.
    2. Why would ordinary nucleons transform to dark nucleons? Evolution means the increase of complexity. In the TGD Universe this means the increase of heff, which corresponds to a dimension of algebraic extension of rationals characterizing polynomials which at the fundamental level characterize space-time regions. Number theoretic evolution would transform the ordinary matter to dark matter as heff>h phases residing at the monopole flux tubes. Could 30 per cent of ordinary matter have transformed to dark matter in this sense?
    See the article Cold fusion, low energy nuclear reactions, or dark nuclear synthesis? or the chapter Cold Fusion Again.

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

    For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Sunday, February 11, 2024

Could classical electromagnetic and gravitational fields give rise to collective consciousness in even historical time scales?

Paul Kirsch made an interesting question about whether the proposed gravitational and electric collective levels of consciousness assignable to Sun and planet could carry information about the history of biosphere and human kind. It is interesting to consider this question quantitatively by using the basic length and time scales predicted by TGD inspired quantum biology.
  1. For the gravitational magnetic body of Earth the gravitational Compton length is Lgr= GME/2/β0 ≈.5 cm (β0=1). For Sun one has Lgr,S≈ RE/2 (β0= 2-11 for the inner planets), where RE the radius of Earth. The corresponding time scales are rather short: .16 ns for the Earth and 10 μs for the Sun.
  2. For the electric fields of Earth and Sun the values of "IQ" defined by the electric Planck constant heff= ℏem are considerably higher than for the corresponding gravitational fields.
    1. The electric Compton length Lp,em for protons in the case of Earth corresponds to the thickness of the thermosphere where the plasmoids would live, which puts bells ringing.
    2. For the Sun the electric Compton length Lp,em is about 1 AU, the distance of Earth from the Sun, bells are ringing again. The time scales Tp,em = Lp,em/c would be rather short. For the Earth one would give Tp,em ≈ 4.8 ms, the time scale of the nerve pulse. For the Sun one would have Tp,em ≈8 minutes. This time scale might be perhaps assigned with short term memories or an attention span of some kind. For the electron the time scale is 26.7 hours which is slightly longer then one day (24 hours).
    3. For a pair formed by say charge Z and mass M and Sun, the electric Compton length and time are scaled up by a factor Zmp/M from those of protons. This factor is in general smaller than one so that historical times scales cannot be obtained by increasing the charge.
The natural guess is that electric and gravitational fields correspond to collective consciousness of some kind. Could it be the collective consciousness of the human kind or of the biosphere? Could our understanding of our physical environment rely on direct sensory experience of these collective levels of consciousness about their electromagnetic and gravitational bodies? Could our science based conscious information be represented on astrophysical scales so that the target of science could determine the scale of the corresponding cognitive representations?
  1. Consider first gravitational magnetic bodies.
    1. For the Milky Way the mass is about 1.55× 1012MS, the gravitational Compton length Lgr would be for β0=1 equal to about Lgr≈ 1.55×1012 × β0(Sun) km ≈.8×109 km, which would give Tgr ≈ .8× 107 seconds, which rather near to year which is 3.2× 107 seconds! For β0=1/4 one would obtain a year. Also now the bells are ringing.
    2. To get historical time scales in the gravitational case, one should have a larger astrophysical object, perhaps a local galaxy cluster. Galaxy clusters have masses 102-103 times the mass of the Milky Way. This would give a time scale of 100-1000 years which is historical.
  2. What about electric Compton time for the Milky Way in the case of dark protons? Galaxy is estimated to have a Coulomb charge of about 1031 Coulombs. For β0=1, this would give for proton Compton time of about Tem,p=1015 years, considerably longer than the age about 1010 years of the cosmos!
As already noticed, the increase of the charge Z of the particle paired with a large mass does not allow us to get historical time scales.
  1. The gravitational Compton length does not depend on the mass of the particle (Equivalence Principle).
  2. Quite generally, the increase of the charge of the paired particle is accompanied by corresponding increase of the mass which tends to reduce the value of electric Compton length from that for protons (or electrons).
  3. The example of DNA illustrates the situation in the electric case.
    1. DNA is exceptional since there is constant change density of 2 elementary charges per nucleotide making the charge of DNA very large. Therefore DNA maximizes the electric Compton length and time. The length of DNA does not however increase these parameters.
    2. Human DNA has about 3.2× 108 base pairs. Base has an average mass of 320 proton masses. Base pair has a charge of 2e. The mass and charge are scaled by a factor of order 1011 from those of protons. Hence the charge per mass ratio using proton mass as a unit is about 1/320. The electric Compton lengths and times are scaled down by factor about 1/320.
    3. For DNA, Tem,p=1015 years for proton-Milky-Way pair would scale down to Tem,DNA= 3× 1012 years, still 300 times longer than the estimated age of the Universe. For an ion with charge Z and mass of Mega Dalton (million proton masses) electrically paired with the Milky Way, one would have Tem= Z × 109 years and thus same order of magnitude as the age of the Universe.
    4. The charge/mass ratio is for biomolecules in general smaller than for DNA so that as macroscopic quantum systems they would correspond to shorter Compton lengths and times. For instance, for ions with mass number A, one would have Tem,A=Tem,p/A.
See the article About long range electromagnetic quantum coherence in TGD Universe or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Wednesday, February 07, 2024

Did plasmoid life serve as a midwife for biological life?

Somehow the plasmoid life should have evolved to biological life. The natural guess is that biomolecules evolved in the dust particles interacting with the plasmoids. For instance, they are known to become electrically charged. Carbonaceous chondrites (see this) are especially interesting dust particles since they contain water, silicates, and basic organic molecules such as amino acids serving as natural candidates for the storage of metabolic energy. Chondrites also contain glass balls, which must have emerged from liquid silicon, which suggests the occurrence of dielectric breakdowns. The TGD based model of ball lightning this) involves the transformation of silicate to silicon in liquid phase. The presence of the molecules pairing with their dark analogs (in information theoretic sense) could have led to the evolution of the chemical metabolic energy storage.

Could carbonaceous chondrites associated with double plasma membranes with layers having opposite charges have evolved in the thermospheres of the planets and stars from systems involving mostly silicates and water to systems containing basic information molecules like DNA, RNA, amino acids and tRNA? Could plasmoids have served as midwives in the process?

Here the theory of Oparin (see this) and the support for it provided by Miller-Urey experiment (see this) provide guidelines. Oparin suggested that life evolved in a strongly reducing (able to donate electrons and thus becoming easily oxidized) atmosphere lacking oxygen and containing methane, ammonia, hydrogen and water vapor.

In the Miller-Urey experiment a system assumed to simulate an ancient ocean containing very simple organic molecules was studied. Also heat gradient was involved. Lightnings were simulated as dielectric breakdowns in a strong voltage. Almost all amino-acids necessary for life emerged in the process. I have commented on the more recent findings related to this experiment from the TGD point of view in this and this). This leads to a long series of questions.

  1. In the thermosphere the scale is that of a protocell. Could the protocell be realized as a double plasma membrane containing carbonaceous chondrites?
  2. Could carbonaceous chondrite act like a strongly reducing atmosphere? Could the chondritic water take the role of the ocean in the Urey-Miller experiment and could the thermal gradient of the thermosphere replace the thermal gradient? Could dielectric breakdowns in the voltage of the double plasmoid membrane replace the lightnings?

    Pollack effect requires energy feed. Could generalized Pollack effect induce the formation of the basic biomolecules such as amino-acids as bound states this). Could the binding of oxygen to silicon to form silicates by the generalized Pollack effect make the chondrites strongly reducing by removing the free oxygen?

  3. Did proto cellular life evolve in this way and migrate to the surface of Earth? At the surface of Earth the possibly existing oceans had a very low oxygen content and the energy flux from the Sun was too low (faint Sun paradox). It seems that the oxygen based photosynthesizing multicellular life could not evolve at the surface of the Earth. This conforms with the presence of multicellular fossils before the Cambrian explosion that occurred about 500 million years ago.
  4. TGD suggests that the photosynthesizing, oxygen based multicellular life actually developed in the underground oceans below the surface of Earth, in the womb of Mother Gaia, where the conditions for the development of photosynthesis and multicellulars were more favorable (see this and this). It bursted to the surface of Earth in the Cambrian Explosion in which photosynthesizing multi-cellulars suddenly appeared. In the TGD Universe, the dark photons from the core of Earth might have provided the metabolic energy: the thermal radiation from the core is in the same energy range as solar radiation.
See the article About long range electromagnetic quantum coherence in TGD Universe or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Tuesday, February 06, 2024

What about the electric body of the Sun?

In the Zoom session, Ville Saari made a question related to the Sun as an astrophysical quantum system, and I realized that although I had estimated the electric Planck constant hem for the Sun.
  1. Recall, that the electric Planck constant hem for the pair determined by a relatively small charge Z and the charged system with large charge Q, is as a generalization of the gravitational Planck constant determined by the formula hem= Qe20, where β0=v0/c <1 is a velocity parameter.

    For the Earth, there are reasons to believe that β0≈ 1 holds true in the gravitational case. This implies that hem has minimal value. For the inner planets of the Sun, Mercury, Venus, and Earth, one has in a good approximation β0,S= 2-11 as was deduced by Nottale. For the outer planets, one would have β0=2-11/5.

  2. The charge is identified as the electric flux over a surface containing the charge. In the case of a spherically symmetric charge density within a sphere of radius R one has

    Q = ε0 ES= ε0 × E(R)× 4π R2,

    where ε0= 8.85× 10-12 C/Vm is the dielectric constant of vacuum. Note that one has E(R) ∝ 1/R2. One can restrict the consideration to the surface of the system so that E(R) is the electric field at the surface, S is the surface area of the sphere, and R is the radius of the sphere.

  3. One can use the scaling law QS/QE= (ES/EE)× (RS/RE)2 .

    to deduce QS for the Sun from QE. From the values RS≈ 6.9 × 108 m and RE≈ 6.3× 106 m, one has RS/RE ≈ 101.

    For the Earth one has EE=.1-.3 keV/m. For the charge of Earth one obtains the estimate Q≈ 4.4x× 106 C =27.5× 1024e. To get some perspective, note that aluminium capacitors can have a maximum charge of about 103 C whereas the maximal charge of a van de Graaff generator is about .14 C. From C= 6.24 × 1018e one obtains ℏem,E ≈ 2.75x × 10250,E, x in the range [1,3].

    The value of the electric field at the surface of the Sun is ES= 1.5 V/m: this gives ES/EE= x× 10-2, x in the range [1,3] and

    QS/QE ≈eq x× 100, x in the range [1.3,.43] .

  4. Using these data, one can estimate the ratio heff,S/heff,E. For the inner planets (Mercury, Venus, Earth), in the case of gravity, β0,E=1 and β0,S= 2-11. If one assumes the same values in the electric case, one obtains the estimate

    heff,S>/heff,E= (QS/QE) × (β0,E0,S) .

    heff,E= EE 4π R20,E has been already estimated and is much larger than the gravitational Planck constant.

Consider now the electrical Compton wavelengths for the Earth and the Sun and restrict the consideration to the proton.
  1. In the case of the Earth, the electric Compton wavelength Λem= hem/m for proton is Λem,p≈ x× 650 km, x in the range [.33.,1] for a proton (m=mp). There are numerical factors of order 1 involved. The radius of the thermosphere is about 340-350 km, one half of the upper bound. This puts bells ringing since the thermosphere is the area where the terrestrial plasmoids live!

    The gravitational Compton length of the Earth is same for all particles and given by Λgr=.5 cm. One has

    Λem,pgr≈ 1.3x × 108 .

    In the number theoretic sense, the electric body would be considerably smarter than the gravitational body.

    For a capacitor with capacitance of 1 μF and at voltage 1 V, the charge would be 1 μ C. For β0=1 would have Λem,pgr≈ 2.9× 10-3 so that one would have Λem,p ≈ 1.5 × 10-5 m. Could electronic systems be intelligent and conscious at least on this scale?

  2. The electric Compton wavelength of the proton for the Sun would be obtained from the scaling law

    Λem,Sem,E = hem,S/hem,E = (QS/QE) (β0,E0,S)

    from that for the Earth. This gives

    Λem,Sem,E ≈ 2× 105/x, x in the range [.33,1].

    For the proton this would give Λem,S≈ 1.3x× 108 km for β0,S=2-11. The astronomical unit AU, that is the distance of the Earth from the Sun is AU= 1.5 × 108 km! The Earth would live on the outskirts of the thermosphere, assignable to the inner planets of the Sun? Could this be a mere coincidence?

    The interpretation would be in terms of a hierarchy of electric and magnetic bodies and the electric body for the Sun + inner planets would be near the top of the hierarchy.

  3. What about the outer planets? Nottale noticed that for the outer planets β0 scales by a factor of 1/5 to β0= 2-11/5 so that the electric Compton wavelength at the level of the entire planetary system would be about 5AU. The corresponding thermosphere can accommodate Mars, whose radius is roughly 4 times the radius of Earth, but no other outer planets. Mars and Sun living at the outer boundaries of two thermospheres of Sun would be very special in that the thermal gradients of plasma would be very strong: this is the prerequisite for self-organization as development of complexity. Mars and Sun would have a very special position in the planetary system.
See the article About long range electromagnetic quantum coherence in TGD Universe or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Extraterrestrial life in space plasmas in the thermosphere, UAP, pre-life, fourth state of matter

Extraterrestrial life in space plasmas in the thermosphere, UAP, pre-life, fourth state of matter

Paul Kirsch sent a link to an article "Extraterrestrial Life in Space Plasmas in the Thermosphere, UAP, Pre-Life Fourth State of Matter" by Rhawn et al (see this) describing sensational findings giving support for the existence of plasma life forms 320 km above the Earth in thermosphere. I have been talking for decades about plasmoids as primordial life forms so that these findings are extremely interesting from the TGD point of view. Here is the abstract of the article.

"Plasmas up to a kilometer in size, behaving similarly to multicellular organisms have been filmed on 10 separate NASA space shuttle missions, over 200 miles above Earth within the thermosphere. These self-illuminated "plasmas" are attracted to and may "feed on" electromagnetic radiation. They have different morphologies: 1) cone, 2) cloud, 3) donut, 4) spherical-cylindrical; and have been filmed flying towards and descending into thunderstorms; congregating by the hundreds and interacting with satellites generating electromagnetic activity; approaching the Space Shuttles. Computerized analysis of flight path trajectories, documents these plasmas travel at different velocities from different directions and change their angle of trajectory making 45 , 90 , and 180 shifts and follow each other. They've been filmed accelerating, slowing down; stopping; congregating; engaging in "hunter-predatory" behavior, and intersecting plasmas leaving a plasma dust trail in their wake. Similar lifelike behaviors have been demonstrated by plasmas created experimentally. "Plasmas" may have been photographed in the 1940s by WWII pilots (identified as "Foo fighters"); repeatedly observed and filmed by astronauts and military pilots and classified as Unidentified Aerial-Anomalous Phenomenon. Plasmas are not biological but may represent a form of pre-life that via the incorporation of elements common in space, could result in the synthesis of RNA. Plasmas constitute a fourth state of matter, are attracted to electromagnetic activity, and when observed in the lower atmosphere likely account for many of the UFO-UAP sightings over the centuries."

To my best knowledge, this article, published in the Journal of Modern Physics, is the first article mentioning UFOs and UAPs. As becomes clear from the article, many of the findings have been known. Article says that there is still secrecy and fears related to the observations of plasma structures (plasmoids in the sequel) on Earth which are often interpreted as UFOs-UAP sightings. People do not want to get the label of a mad scientist. After 46 years as a mad scientist without funding and research positions, I understand their fears!

As becomes clear from the article, many of the findings have been known. Article says that there is still secrecy and fears related to the observations of plasma structures (plasmoids in the sequel) on Earth which are often interpreted as UFOs-UAP sightings. People do not want to get the label of a mad scientist. After 46 years as a mad scientist without funding and research positions, I understand their fears!

For more than 10 years ago (2007) I participated a conference held in Hessdalen, Norway, where "UFOs" appear regularly and learned that they behave like living intelligent beings and considered these objects in TGD framework (see this). The findings related to plasmoids in the thermosphere support this kind of behavior both at the level of individuals and collectively. The structures involved can be very large: size scales range up to kilometer scale.

The article of Rhawn et al contains a detailed summary of both the history of the development of the theoretical ideas related to plasmoid as a self-organizing structure bringing in mind prebiotic life forms and discusses various findings supporting these speculations made in both lab and in thermosphere. The experiments carried out in the thermosphere satisfy stringent scientific requirements so that it is very difficult to dismiss the findings.

The difference between plasmoids and biological life forms might not be as large as one might think. Biology involves cold plasmas.

  1. Negatively and positively charged ions play a key role in the physics of cell membrane. One of the mysteries is what ionizes them! We have thought that electrolysis is understood. At least I find that I cannot understand it in terms of standard chemistry. The energies of ions gained in the electric fields involves are quite too small to induce ionization of atoms.

    Intriguingly, also "cold fusion" (see this), so bitterly hated by colleagues, appears in electrolytic systems and would involve formation of dark nuclei as dark proton sequences at monopole flux tubes decaying to ordinary nuclei and liberating almost all nuclear binding energy (see this and this). Magnetic flux tubes with large heff would allow dissipationless acceleration of say dark charged particles to very high energies making it possible to ionize that atoms.

  2. In the TGD Universe, the charged ions communicate with the magnetic body of the system using "dark" (in the TGD sense) Josephson radiation and cyclotron radiation (see this). Resonance, generalizing to multi-resonance, would be the basic mechanism. Same communications and control mechanisms would be realized in plasma life in which chemical realization of genetic code is not yet present. The genetic code could be realized in terms of dark protons and dark photons with genes realized as sequences of dark proton or dark photon triplets realizing genetic codons (see this, this, and this).

    The proposal is that genetic code is universal and based on so called completely unique icosa tetrahedral tessellation of hyperbolic 3-space H3 involving tetrahedra, octahedra, and icosahedra and appearing naturally in the TGD framework (see this). This tessellation could be realized in the plasma phase where crystal lattices are reported to appear. Information theoretically, biological life and plasma life could be very similar. Besides the basic morphologies of plasmoid mentioned in the abstract of the article, helical structures are formed and could serve as analogos of DNA and RNA and amino-acids: the information would be stored by the dark DNA realized as sequences of dark proton triplets.

  3. One fascinating discovery is that the plasmoids seem to behave as if they were moving in water. Water is a key element of biological life. The temperatures in the thermosphere are in the range 200-500 Celsius and beyond the boiling point of water. What could serve as the plasma counterpart of water?

    Long range coherence (mystery in the biology-as-nothing-but-chemistry approach) is required, in fact several scales of coherence are needed. In the TGD framework, the quantum coherence of the monopole flux tube network, making it behave more like a liquid rather than gas, would induce the coherence of water. Could the monopole flux tube network also transform the plasma phase to a liquid-like system?

    What could make possible quantum coherence at such high temperatures? TGD suggests that cell membranes realize high Tc superconductivity (see this, this and this). High Tc superconductivity would be based on the hierarchy of heff>h phases at monopole flux tubes for which cyclotron energies are scaled up by factor heff/h.

    The most recent version of the model of superconductivity (see this) suggests that the transition to high superconductivity could quite generally involve the generation of what I call half-monopole flux tubes (possible as Maxwellian flux tubes requiring a current at the boundary to generate the magnetic field) with a disk-like cross section at a critical temperature Tc1 higher than Tc. At Tc, half-monopole flux tubes would fuse along their boundaries to monopole flux tubes with a spherical cross section (possible only for homologically non-trivial space-time surfaces) and requiring no current. The difference between the total cyclotron energies associated with these configurations would be proportional to heff/h and the critical temperature would increase with heff/h.

  4. The plasmoids are reported to have a double layered structure with both layers consisting of plasma with the inner layer carrying a negative charge and outer layer a positive charge. This structure is very similar to the double lipid layer associated with the cell membrane. Also these structures could be generalized Josephson junctions such that the voltage between the layers would define the counterpart of membrane potential.

    The layers could be super conductors forming a generalized Josephson junction (see this and see this). There would be monopole flux tubes transversal to the layers and the difference of energies for charged particles at the two sides of the structure would be sum of Josephson energy ZeV and the difference of cyclotron energies heffZeB/m. The structure would communicate to its magnetic body by dark Josephson radiation. The communicated information would be about the electromagnetic environment coded by the modulations of the membrane potential in turn coded to frequency modulations of the Josephson radiation.

    The message would be received by cyclotron resonance generating as a response a sequence cyclotron resonance pulses analogous nerve pulse patterns sent to the biological body where they would act as control commands. Neural system would rely on this mechanism. The response would generate an analog of stochastic resonance whereas the Josephson radiation would generate the analog of the reversal of stochastic resonance (see this).

  5. Also a gel-like behavior has been observed. Gel phases (see this) are essential in biology and involve a network plus medium (see the Wikipedia article). The medium can be gas, liquid, or solid and also the network can be one of these phases. Also the plasma phase could serve in the role of medium in the recent situation. The network formed by the monopole flux tubes and carrying dark particles as heff>h phases of ordinary particles could play the role of the network and together with the plasma phase forming the medium give rise to a gel-like phase.

    In the TGD framework, the Pollack effect (see this), generating a gel phase by transferring ordinary protons to dark protons at monopole flux tubes and in this way creating negatively charged exclusion zones (EZs, such as cell interior and DNA double strand), would be a building brick of key mechanisms of quantum biology. Pollack effect requires energy and solar radiation provides it and Pollack effect would be a key mechanism of also photosynthesis.

    As I developed a model for ball lightning (see this), I realized that the Pollack effect generalizes. The particles could transform to dark particles at the magnetic body, not only by absorbing a photon, but by a formation of a molecular bound state. Pollack effect and its reversal could control transformation of silicates (quartz) to silicon in a liquid phase: the energy of lightning would provide this energy and in this way generate ball lightning as a primitive life form. Is the generalized Pollack effect one of the key mechanisms of plasma life?

  6. Quite generally, the energies of dark particles increase with heff and heff tends to decrease spontaneously. The basic purpose of metabolic energy feed is to compensate for the decrease in the value of heff. Plasmoids should use electromagnetic radiation as a metabolic energy source just as biological life forms use. Can one imagine a plasma counterpart of photosynthesis? Pollack effect is essential in the TGD based model of photosynthesis and defines a prebiotic form of photosynthesis, which would temporarily store energy to the magnetic body of the system, where dissipation is extremely small. The same temporary storage could take place when the metabolic energy, extracted from metabolites, is temporarily stored to MB in ADP→ ATP transformation.

    It is known that plasmoids radiate even at the dark side of the Earth. This supports the view that they are able to store metabolic energy. The long term storage of metabolic energy could emerge when the charged dust particles interact with plasma and form colloidal gel phases (see this) with it. The molecules of the dust particles would store the energy for longer periods of time. Carbonaceous chondrites (see this) are especially interesting dust particles since they contain water, organic molecules, and silicates. The model of ball lightning involves the transformation of silicate to silicon in liquid phase. The presence of the molecules pairing with their dark analogs (in information theoretic sense) could have led to the evolution of the chemical metabolic energy storage.

  7. Plasmoids are found to gather above thunderstorms and descend to them. Thunderstorms involve large charges and strong electric fields and therefore give rise to MBs with very large values of heff=hem, which has an interpretation as a measure for number theoretical complexity and also serves a universal IQ. Thunderstorms could also serve as metabolic energy storages. The acceleration of dark particles in the strong electric fields at monopole flux tubes would increase the value of heff of the particles.
One especially interesting experiment involves a charged conductor wire (a tether connecting a module to the satellite) carrying an Ohmic current making the wire charged. The charge generates a radial electric field.
  1. The nearly orthogonal motion of tether in the Earth's magnetic field BE gives rise to Faray effect generating to a voltage along the tether, which in turn induces an ohmic current and charge density creating a radial electric field. The current flows out at the other end of the tether. It is also possible to generate a current to the tether. The charge moving along the tether experiences Lorenz force orthogonal to BE and tether and forces motion. The article provides a quantitative view about the currents flowing along the tether, electric field strengths and total charges possible for the tether.
  2. What is observed is that plasmoids gradually appear around this structure and make contacts with the wire. It is not clear whether they arrive from outer space or whether artificial prebiotic life forms are created as a response to the electromagnetic fields and electric current created by the electrons running in the tether!
In the TGD framework, the wire carrying a charge could give rise to a very large electric Planck constant heff= hem= QZe20, where the velocity parameter β0 satisfies β0=v0/c<1, is defined as generating large scale quantum coherence (see this). Qe is the charge of the large object and Ze is the charge of the small object.

This proposal generalizes the notion of gravitational Planck constant introduced by Nottale (see this). I wrote just a few weeks ago two articles relating to this. The first one proposed a model of ball lightning (see this) and lightning. The second article (see this) discussed large scale quantum coherence in presence of electrically charged objects carrying large electric charge (Earth is the basic example and the charged wire second one).

Plasmoids would gather around the tether since this would increase the value of "personal" heff since the acceleration in the strong electric field would provide metabolic energy making it possible heff increasing phase transition. The presence of a tether's magnetic body would also help to reach a higher level of collective consciousness.

One can estimate the value of hem for the tether system using the data provided in the Wikipedia articles (see this).

  1. The current density can be written as j=ρ v, where ρ is the average charge density of the tether and v is the velocity parameter assignable to the electrons. This gives for the current I the expression I= ρ v S, where S is the cross sectional area of the tether. One can solve ρ as ρ= I/vS and from this the total charge of the tether as Q= ρ SL= IL/v.
  2. One can use the length L=20 km of the tether and the reported typical values of the Ohmic current I and estimate v from a typical electron energy E as v=(2mE)1/2>. From the Wikipedia article, the typical values I= 100 mA and E=102 eV. The latter gives v=2× 10-2c. This would give Q=.33 mC, that is Q≈ 2× 1015e. The value of hem/h=Qe20 would be for Z=1 and β0=1 equal to 8π α × 1015≈ 1.4× 1014. 10 Hz alpha frequency would correspond to the energy of order .06 eV which happens to correspond to the Coulomb energy assignable to the cell membrane potential. This value of heff is near to the minimal value for which the cyclotron energy is above the thermal energy at room temperature.
See the article About long range electromagnetic quantum coherence in TGD Universe or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Saturday, February 03, 2024

Did the proposed Expansion of Earth during Cambrian Explosion lead to the formation of Moon?

The discussions related to the Expanding Earth hypothesis stimulated interesting questions. How planets and Moons would have been born in TGD-based astrophysics and could the formation of Moon relate to the Expanding Earth hypothesis (see for instance this) and whether the gradual growth of Moon's orbit could relate to it.

During the last year, I wrote two articles about the birth of stars and planets and also moons in TGD Universe last year (see this and this).

The first basic idea is the fractality of TGD-based cosmology, which follows from the TGD view of space-time as a 4-D surface in H=M4× CP2. Another key idea is the replacement of a smooth continuous cosmic expansion with a sequence of fast explosions.

  1. The scaled down versions of Big Bang would occur on different scales. For example, a star would produce shells of mass ejected in an explosion that would condense into planets.
  2. The planets could also do the same and this would lead to the birth of shells, from these the rings would be born and from these the Moons would be born.
The Cambrian explosion is also an explosion. The composition of the Moon is the same as that of the Earth. The crazy question that comes to mind (I can already hear my colleague's snoring laughter in my ears) is whether the Moon was born this way but .5 Gy ago (instead of 4.5 Gy), in the Cambrian explosion. This of course does not exclude the possibility that Moon was formed in a similar explosion for 4.5 billion years ago.

Can the Cambrian option be ruled out by comparing the ages of the Earth's Moon? Radiometric age determinations give the matter making up the Earth and the Moon (so not the Earth or the Moon itself!!) age estimates of 4.543 Gy and 4.46 Gy, i.e. an age difference of 80 million years.

  1. The age of the material composing Moon has been deduced from the radioactive decay of Zirconium and in the latest determination it increased by 40 million years. This inaccuracy is of the same order as the difference in the ages of the substances! So can the Moon be matter of the same age as the Earth? You can also critically ask why the Moon's and Earth's matter would be of different ages when the composition is the same? The most natural explanation is that the substance is the same and therefore of the same age.
  2. Radioactive age determinations would therefore not rule out the hypothesis of the formation of the Moon in the Cambrian explosion. In such an explosion, a layer with a thickness of about 6 km would have been thrown out and taken with it both the life on the surface and the fossils if there were any! .5 billion years old fossils would be products of underground life!
Is there any empirical evidence that the age of the Moon cannot be on the order of .5 billion years. Is there any evidence for the explosive origin of the Moon? Could one compare Theia hypothesis and the two variants of TGD proposal? Could the dynamics of the Moon-Earth system help here?
  1. It is known that the distance of the Moon from the Earth increases slowly: v=3.78 cm per year (see this). Could the recent rate for the increase of the orbital radius be interpreted in terms of cosmic expansion? The Hubble constant is about H= 70 km/sMpc, where parsec (pc) is 3.26 ly. This gives for the cosmic recession velocity of Moon v(now)= HR≈ 2.8 cm/y. This is 74 per cent of the observed velocity of increase for the orbital radius. This suggests that the velocity due to the explosion has gradually decreased and is approaching the cosmic recession velocity (, which increases linearly with the distance: this effect has been observed but surprisingly, has not been interpreted in terms of the cosmic recession velocity!).

    Could the deviation v-v(now) be a remnant of the rapid increase in the orbital radius associated with the Cambrian explosion?

  2. If Moon was born in about .5 billion years ago and the velocity would have been constant v= 3.78 cm/y, the Moon would have reached a distance of about 1.9× 107 m, which is about 2.97RE (three Earth radii) from the Earth and much smaller than R=60RE so that the speed should have been significantly faster at the beginning.
  3. If the Moon was born in such an explosion 4.5 Gy ago, the same rough estimate assuming constant velocity v= 3.78 cm/y would give for the distance of the Moon R=26.7 RE, RE=6,357 km. This is roughly by a factor 1/2 smaller than the recent distance R=60RE of the Moon. This option looks more reasonable than the Cambrian option.

    Cosmic expansion cannot explain the increase of the Moon's orbital radius. One would have dR/dt= HR giving the estimate R(t)= REexp(v(now)t/R) and R(now)=eRE , which is consierably smaller than R= 60RE.

  4. Could Theia hypothesis explain the growth of the distance of the Moon's to its recent in terms of the recoil momentum gained by the evaporated fragment giving rise to the Moon? This should have made the orbit elliptic. The orbit of the Moon is slightly elliptic: the eccentricity is .055 (see this). One should also understand the mechanism, which distributed the remaining matter evenly along the surface of the Earth.

    What is intriguing from the TGD point of view is that the radius of Earth could have increased by a factor 2 in the collision with Theia. This would explain the findings motivating the Expanding Earth hypothesis if the continents were formed already in the collision with the Theia.

See the article Expanding Earth Hypothesis and Pre-Cambrian Earth or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Friday, February 02, 2024

Does Expanding Mars hypothesis make sense?

There is a considerable evidence that ancient Mars has had lakes or even oceans.

This relates in an interesting way to the TGD based model explaining the Cambrian Explosion (roughly 500 million years ago) plus other strange geological observations.

A well-known problem in cosmology based on general relativity is that astrophysical objects do not seem to participate in cosmic expansion although they do co-move with it. In the TGD Universe cosmic expansion of astrophysical objects would occur as rapid jerks for. In accordance with this, the model assumes that Earth radius grew by a factor two in a rather short time scale. TGD indeed predicts a hierarchy of fundamental length scales coming as powers of two. This rapid expansion would have bursted the underground oceans, where photosynthesizing life had evolved, to the surface and gave rise to the recent oceans. This view has a lot of empirical support and the TGD based new physics allows to overcome the obvious objections.

Consider first in more detail various motivations for the Expanding Earth model.

The geological motivation is that the continents seem to fit nicely to cover the entire surface of Earth if the radius of Earth is one half of its recent value. This observation (, which was not made by me) generalizes the tectonic plate theory of Wegener.

Biology provides further motivations.

  1. There are extremely few fossils from the time before the Cambrian explosion and almost all of them are single-celled. Life should have evolved extremely rapidly during the time of Cambrian Explosion.
  2. The energy flow from the sun (faint Sun paradox) was too low for life to develop before the Cambrian Explosion.
  3. The hypothesized oceans would have been far too low in oxygen for the development of oxygen based metabolism necessary for multicellular life.
  4. Cosmic rays and meteor bombardment would have made it very difficult for the complex life forms to evolve at the surface of Earth.
As if life had suddenly bursted to the surface of Earth.
  1. Did it emerge from subterranean oceans providing shield against meteorite bombardment and a warm enough environment? Could this have happened in a rather rapid increase of the Earth radius by factor 2 splitting the crust into continents and led to a formation of oceans having the required oxygen concentration.
  2. But where did the necessary radiation that made photosynthesis leading to complex multicellulars come from? The temperature of the Earth's core happens to be such that the thermal radiation is concentrated at the same wavelengths as radiation from the Sun? It was also recently discovered that there is life so deep beneath the earth's surface that solar radiation cannot provide the metabolic energy.

    Could one think that the radiation from the Earth's core served as a metabolic energy source. Could this energy source be still at work? The standard model based physics does not allow this. The new physics predicted by TGD allows this.

For expanding Earth hypothesis, see for instance https://tgdtheory.fi/pdfpool/expearth.pdf and https://tgdtheory.fi/public_html/articles/expearth2021.pdf . What about underground life in Mars?
  1. The average density of Mars is near to that of recent Earth (mass is .1 Earth masses and radius roughly 1/2 of R_E). This leads to the question of whether Mars has already experienced a similar transition increasing its radius by 1/2 and density by factor 8? This would have brought the possible underground water to the surface. Later the water would have been lost. Mars would not have been as lucky as Earth.
  2. The objection is that Mars has no plate tectonics. The alternative option that I have discussed earlier is that Mars is still waiting for the expansion to take place. Intriguingly, it has the same radius as Earth before the Cambrian explosion. The ancient presence of oceans/large lakes does not support this view. One might however think that the water from underground oceans leaks to the surface and forms lakes and even shallow oceans.
See for instance the article Expanding Earth Hypothesis and Pre-Cambrian Earth. For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Thursday, January 25, 2024

Modified Dirac equation and the holography=holomorphy hypothesis

The understanding of the modified equation as a generalization of the massless Dirac equation for the induced spinors of the space-time surface X4 is far from complete. It is however clear that the modified Dirac equation is necessary.

Two problems should be solved.

  1. It is necessary to find out whether the modified Dirac equation follows from the generalized holomorphy alone. The dynamics of the space-time surface is trivialized into the dynamics of the minimal surface thanks to the generalized holomorphy and is universal in the sense that the details of the action are only visible at singularities which define the topological particle vertices. Could holomorphy solve also the modified Dirac equation? The modified gamma matrices depend on the action: could the modified Dirac equation fix the modified gamma matrices and thus also the action or does not universality hold true also for the modified Dirac action?
  2. The induction of the second quantized spinor field of H on the space-time surface means only the restriction of the induced spinor field to X4. This determines the fermionic propagators as H-propagators restricted to X4. The induced spinor field can be expressed as a superposition of the modes associated with X4. The modes should satisfy the modified Dirac equation, which should reduce to purely algebraic conditions as in the 2-D case. Is this possible without additional conditions that might fix the action principle? Or is this possible only at lower-dimensional surfaces such as string world sheets?
In the article Modified Dirac equation and the holography=holomorphy hypothesis a proposal for how to meet these challenges is proposed and a holomorphic solution ansatz for the modified Dirac equation is discussed in detail.

See the article Modified Dirac equation and the holography=holomorphy hypothesis or the chapter Symmetries and Geometry of the ”World of Classical Worlds”.

Tuesday, January 23, 2024

Questions related to the notion of color symmetry in the TGD framework

One of the longstanding open problems of TGD has been which of the following options is the correct one.
  1. Quarks and leptons are fundamental fermions having opposite H-chiralities. This predicts separate conservation of baryon and lepton numbers in accordance with observations.
  2. Leptons correspond to bound states of 3 quarks in CP2 scale. This option is simple but an obvious objection is that they should have mass of order CP2 mass. Baryons could decay to 3 leptons, which is also a problem of GUTs.
I haven't been able to answer this question yet and several arguments supporting the quarks + leptons option have emerged.

Consider first what is known.

  1. Color is real and baryons are color singlets like leptons.
  2. In QCD, it is assumed that quarks are color triplets and that color does not correlate with electroweak quantum numbers, but this is only an assumption of QCD. Because of quark confinement, we cannot be sure of this.
The TGD picture has two deviations from the QCD picture, which could also cause problems.
  1. The fundamental difference is that color and electroweak quantum numbers are correlated for the spinor harmonics of H in both the leptonic and quark sector. In QCD, they are not assumed to be correlated. Both u and d quarks are assumed to be color triplets in QCD, and charged lepton L and νL are color singlets.
    1. Could the QCD picture be wrong? If so, the quark confinement model should be generalized. Color confinement would still apply, but now the color singlet baryons would not be made up of color triplet quark states, but would have more general irreducible representations of the color group. This is possible in principle, but I haven't checked the details.
    2. Or can one assume, as I have indeed done, that the accompanying color-Kac Moody algebra allows the construction of "observed" quarks as color triplet states. In the case of leptons, one would get color singlets. I have regarded this as obvious. One should carefully check out which option works or whether both might work.
  2. The second problem concerns the identification of leptons. Are they fundamental fermions with opposite H-chirality as compared to quarks or are they composites of three antiquarks in the CP2 scale (wormhole contact). In this case, the proton would not be completely stable since it could decay into three antileptons.
    1. If leptons are fundamental, color singlet states must be obtained using color-Kac-Moody. It must be admitted that I am not absolutely sure that this is the case.
    2. If leptons are states of three antiquarks, then first of all, other electroweak multiplets than spin and isospin doublets are predicted. There are 2 spin-isospin doublets (spin and isospin 1/2) and 1 spin-isospin quartets (spin and isospin 3/2). This is a potential problem. Only one duplicate has been detected.
    3. Limitations are brought by the antisymmetrization due to Fermi statistics, which drops a large number of states from consideration. In addition, masses are very sensitive to quantum numbers, so it will probably happen that the mass scale is the CP2 mass scale for the majority of states, perhaps precisely for the unwanted states.
It is good to start by taking a closer look at the tensor product of the irreducible representations (irreps) of the color group (for details see this).
  1. The irreps are labeled by two integers (n1,n2) by the maximal values of color isospin and hypercharge. The integer pairs (n1,n2) are not additive in the tensor product, which splits into a direct sum of irreducible representations. There is however a representation for which the weights are obtained as the sum of the integer pairs (n1,n2) for the representations appearing in the tensor product.

    Rotation group presentations simplified example. We get the impulse moment j1+j2,... |j1-j2|. Further, three quarks make a singlet.

  2. On basis of the triality symmetry, one expects that, by adding Kac-Moody octet gluons, the states corresponding to (p,p+3)-type and (p,p)-type representations can be converted to each other and even the conversion to color singlet (0,0) is possible. This is the previous assumption that I took for granted and there is no need to give it up.
Let's look at quarks and baryons first.
  1. U type spinor harmonics correspond to (p+1,p) type color multiplets, while D type spinor harmonics correspond to (p,p+2) type representations.

    From these, quark triplets can be obtained by adding Kac-Moody gluons and the QCD picture would emerge. But is this necessary? Could one think of using only quark spinor harmonics?

  2. The three-quark state UUD corresponds to irreducible representations in the decomposed tensor product. The maximum weight pair is (3p+2,3p+2) if p is the same for all quarks, while UDD with this assumption corresponds to the maximum weights (3p+1,3p+1+3). The value of p may depend on the quark, but even then we get (P,P) and (P,P+3) as maximal weight pairs. UUU and DDD states can also be viewed.

    Besides these, there are other pairs with the same triallity and an interesting question is whether color singlets can be obtained without adding gluons. This would change the QCD picture because the fundamental quarks would no longer be color triplets and the color would depend on the weak isospin.

  3. The tensor product of a (p,p+3)-type representation and (possibly more) gluon octets yields also (p,p)-type representations. In particular, it should be possible to get (0,0) type representation.

    Consider next the identification of leptons.

    1. For leptons, neutrino nuL corresponds to a (p,p)-type representation and charged lepton L to a (p+3,p)-type representation.
    2. Could charged antilepton correspond to a representation of the type UDD and antineutrino to a representation of the type UUD?

      Here comes the cold shower! This assumption is inconsistent with charge additivity! UDD is neutral and corresponds to (p,p+3) rather than (p,p). You would expect the charge to be 1 if the correspondence for color and electroweak quantum numbers is the same as for the lepton + quark option!

      UUD corresponds to (p,p) rather than (p,p+3) and the charge is 1. You would expect it to be zero. Lepton charges cannot be obtained correctly by adding charge +1 or -1 to the system.

      In other words, the 3-quark state does not behave for its quantum numbers like a lepton, i.e. an opposite spinor with H-chirality as a spinor harmonic.

      Therefore bound states of quarks cannot be approximated in terms of spinor modes of H for purely group-theoretic reasons. The reason might be that leptonic and quark spinors correspond to opposite H-chiralities. Of course, it could be argued that since the physical leptons are color singlets, this kind of option could be imagined. Aesthetically it is an unsatisfactory option.

    To sum up, the answers to the questions posed above would therefore be the following:
    1. Quark spinor harmonics can be converted into color triplets by adding gluons to the state (Kac-Moody). Even if this is not done, states built from three non-singlet quarks can be converted into singlets by adding gluons.
    2. The states of the fundamental leptons can be converted into color singlets by adding Kac-Moody gluons. Therefore the original scenario, where the baryon and lepton numbers are preserved separately, is group-theoretically consistent.
    3. Building of analogs of leptonic spinor harmonics from antiquarks is not possible since the correlation between color and electroweak quantum numbers is not correct. I should have noticed this a long time ago, but I didn't. In any case, there are also other arguments that support the lepton + quark option. For example, symplectic resp. conformal symmetry representations could involve only quarks resp. leptons
    For a summary of earlier postings see Latest progress in TGD.

    For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Monday, January 22, 2024

Stochastic resonance and sensory perception

In the TGD framework, subjective existence corresponds universally to the sleep-wakeup cycle defined by the periods of wake-up with opposite arrows of time defined by a sequence of "big" state function reductions (BSFRs) changing the arrow of time. In BSFR, a self with a given arrow of time dies (or falls asleep) and reincarnates as a self with an opposite arrow of time.

The TGD view, the stochastic resonance would synchronize the signals realized as amplitude modulated carrier waves with the sleep-wakeup cycle. The wakeup period would correspond to T(spont)= 1/f(spont). Stochastic resonance would correlate the rhythms of subjective and physical existence.

The basic prediction is that this synchrony is optimal when the noise level is optimum. Taking the ordinary sleep-wake-up cycle as an example, one can understand what this means. If the stimulus level is too high, concentration to a given task is difficult and problems with sleep appear. If the stimulus level is too low, drowsiness becomes the problem and the resonance with the circadian rhythm tends to be lost.

Concerning the identification of the counterpart of the white noise, there are several guidelines.

  1. White noise could correspond to any signal for which the frequency distribution is constant in the time scale of modulations. The rate of BSFRs should be f(spont)= 2f. In stochastic resonance, the white noise would keep the system in optimal wakeup state.
  2. Many neuroscientists believe that the rate of nerve pulses codes for the sensory input. This need not be quite true but inspires the question whether the nerve pulses define the white noise and whether a single nerve pulse wakes up the neuron. If so, then the rate of nerve pulses could correspond to f=f(spont)/2 since only the nerve pulses with a standard arrow of time are observed.

    Nerve pulse duration is about 1 ms and defines the maximum rate of nerve pulses. On the other hand, f= 1 kHz frequency is a resonance frequency of the brain synchrony and also the average mechanical resonance frequency of the skull.

  3. This observation brings to mind an interesting old observation. For electrons with mass .5 eV the secondary p-adic time scale T2(e) corresponds to frequency 10 Hz, alpha frequency. The mass estimates for the light quarks u and d vary in the range 2-20 MeV. T2 scales like mass scale squared so that the mass scale estimate for quarks is T2≈ 1 kHz.

    The TGD inspired quantum biology indeed predicts that QCD allows dark variants with same masses but Compton length scaled up by \hbareff/\hbar. Does this mean that the kHz frequency scale of nerve pulses corresponds to T2 for quarks and 10 Hz EEG frequency scale corresponds to T2 for electrons? If this is the case, secondary p-adic length scales for electrons and quarks are fundamental for the brain.

This raises some questions.
  1. It would seem that cyclotron pulses inducing BSFRs correspond to the white noise behind stochastic resonance. The rate of the detected nerve pulses would correspond to f=f(spont)/2 and to a frequency of modulated carrier wave. Can one imagine a general mechanism for producing the noise realized as nerve pulses?
  2. One can also ask whether a system could keep itself awake and in stochastic resonance in presence of the necessary metabolic energy feed. Could the system itself produce the white noise as pulse patterns and stay in a stochastic resonance with it. If so, the amount of metabolic energy could control the level of noise in turn controlling the presence of the stochastic resonance.
  3. A nontrivial question is what one means with a system. In TGD, the system involves both the biological body and the magnetic body (MB) carrying dark matter associated with it. MB has a hierarchical structure with levels labelled by the values of heff.
The model for the communication of sensory input from the cell membrane to the magnetic body and for the control of the biological body suggests itself as a mechanism transforming sensory input at the cell membrane to pulse patterns.
  1. At the level of the cell membrane, sensory input corresponds to the oscillations of the membrane potential and to nerve pulses.
  2. This sensory input is communicated to the MB as a generalized Josephson radiation modulated by the variation membrane potential representing sensory input. The generalized Josephson frequency is the sum of two parts. The first part corresponds to the ordinary Josephson frequency fJ= ZeV/heff. The second, usually dominating, part corresponds to the difference of the cyclotron frequencies of monopole flux tubes at the two sides of the cell membrane and transverse to it. The energies involved are of the order of ZeV and just above the thermal energy as required by the minimal consumption of metabolic energy. Josephson frequencies are in the EEG range.
  3. At the MB, the dark Josephson radiation generates cyclotron resonance, which transforms the frequency modulated Josephson radiation to a sequence of pulses, which define a feedback to the brain. A natural proposal is that the cyclotron pulse sequences generate nerve pulse patterns serving as the white noise.

    The rate of nerve pulses would dictate the resonant frequency f which can vary from its maximum value of kHz down to 1 Hz and even below it. The cyclotron frequencies for the body parts of the MB would thus select, which frequencies from the frequency spectrum of the Josephson radiation are amplified. Essentially, a Fourier analysis of the sensory input is performed and the spectrum would be represented at the MB.

  4. The nerve pulse patterns would in turn generate a response as modulations of geneneralized Josephson frequency sent to the MB. There the response of the system to the white noise generates the white noise. This feedback loop would define a nearly autonomous system staying in a stochastic resonance in presence of a suitable metabolic feed.
  5. Only the frequency modulation by the sensory input appears in this mechanism. Frequency modulation however reduces to the amplitude modulation for the membrane potentials.
  6. The generalized Josephson frequency must be equal to the cyclotron frequency at a given body part of the MB. It can control by a variation of the flux tube thickness whether it receives information from the cell membrane at a given generalized Josephson frequency.
  7. The failure of the communication line between the brain and the MB could cause various disorders since the MB cannot anymore take care of BB. Since the cyclotron frequencies of the biologically important ions in Bend=.2 Gauss are in a key role, the concentration of these ions in biomatter is an important factor. Lithium ions serve as a basic example. Its cyclotron frequency is 50 Hz, which corresponds to fgr,Sun. The depletion of lithium ions in the soild is known to induce depression and even suicides.
How does sensory perception relate to the stochastic resonance in the proposed sense? The stochastic resonance would be associated with the communications with the MB and the information representable as a modulation of the carrier wave.
  1. Sensory qualia would be labelled by quantum numbers measured repeatedly during the sequences of "small" state function reductions (SSFRs) between BSFRs. Primary sensory qualia would be associated with the sensory organs and the feedback from the MB of the brain to the sensory organs could generate virtual sensory input explaining hallucinations and dreams. This picture fits nicely to vision, olfaction and tactile senses, which are spatial.
  2. The generation of sensory qualia at the level of sensory organs could involve stochastic resonance amplifying the primary sensory input. The sensory input would be transformed to dark Josephson radiation to the MB of the sensory organ and returned back as a pattern of cyclotron resonance pulses in turn generating BSFRs and a modified Josephson radiation but without modification due to nerve pulses.

    When the membrane potential is reduced below the critical value, a nerve pulse would be generated and lead to a processing of the signal at the higher levels of the hierarchy. The rate of the nerve pulses would determine the intensity of the signal at the higher levels of the hierarchy. Similar feedback loops with the local magnetic bodies would take place at the higher levels of the hierarchy and generate higher level representations of the sensory input. The virtual sensory input from MB would lead to the generation of standardized mental images as a pattern completion and recognition.

  3. Stochastic resonance for the sensory receptors would allow code for various characteristics of the sensory input (such as colors, intensity and frequency of light or sound,...) to cyclotron frequencies characterizing parts of the MB. Essentially a generalized Fourier analysis of the sensory input locating Fourier components to different parts of MB would be in question.
Hearing is an exceptional sense in that the temporal aspect is essential.
  1. It would be natural to identify the intensity and frequency of auditory qualia with the cyclotron frequencies labelling the magnetic body parts. In the case of speech and "almost heard" internal speech, the meaning of the speech represents a higher level element related to the temporal aspects, and could be associated with the communications to the MB rather than being purely spatial quale.
  2. If the heard sound frequencies correspond to Josephson frequencies, why are the other qualia not accompanied by an auditory experience? A partial answer is that hearing involves the sensation of the pitch and intensity of the sound as non-temporal qualia at the neuronal level.

    The temporal aspects of hearing responsible for the meaning of the speech would naturally correspond to the modulations of the membrane potential and of Josephson frequencies. But also other senses involve this aspect. Could these aspects correspond to internal speech providing a cognitive interpretation of the experience, its naming? Could this aspect be universal and accompany all experiences? This would also conform with the fact that the oscillations of magnetic flux tubes are analogous to acoustic waves.

The 12-note scale defines a set of very special frequencies in that these frequencies have a deep emotional meaning. Also octave equivalence is a fascinating phenomenon. Could this be due the fact that these audible frequencies appear as resonance frequencies in the spectra of the cell membrane Josephson frequencies and cyclotron frequencies for the magnetic flux tubes? If this is the case, magnetic flux tubes would define an analog of an organ played by the sensory input to MB. How do these special frequencies relate to the gravitational Compton frequencies?
  1. The model for bioharmony, leading to a model for the genetic code (see this, this, and this) leads to a proposal that Pythagorean scale defines a spectrum of preferred cyclotron frequencies and thus a spectrum of strengths of the endogenous magnetic field Bend. Quint cycle (3/2)n of fundamental frequency and octave equivalence would yield the 12-note scale.
  2. β0≈ 1 has been assumed for the Earth and β0≈ 2-11 for the inner planets of the Sun. Could β0≤ 1 have a spectrum? Could this spectrum explain in the case of the Sun the EEG spectrum below 50 Hz frequency spanning 7 octaves (DNA corresponds to 1 Hz), and in the case of the Earth the microwave spectrum in the range .5-67 GHz?
  3. I have considered the possibility that β0 is for number-theoretical reasons quantized as an inverse integer: β0=1/n (see this). Number theoretical constraints allow a more general quantization as rational numbers: β0=m/n. The spectrum of the gravitational Compton frequencies would resonate with the spectrum of the cyclotron frequencies if β0 in fgr = β0/GM obeys a quantization producing the 12-note scale. It would be interesting to check whether EEG exhibits 12-note scale as a finite structure realized as preferred frequencies.
Consider next the microwave hearing as a possible explanation of taos hum.
  1. In microwave hearing the carrier wave amplitude, modulated in the frequency scale of audible frequencies with typical frequency in the range of EEG frequencies and therefore below 100 Hz, creates a sensation of sound. The electromagnetic signal would be amplified by stochastic resonance to a variation of neuronal membrane potentials in turn generating an acoustic signal by piezoelectric effect.

    This acoustic signal could serve as a virtual auditory input to the ear and generate a sensation with auditory qualia. The mechanism would be the same as in the case of hallucinations and dreams.

  2. Assume that the frequency spectrum associated with the gravitational body of Earth (fgr=67 GHz) spans as many octaves as that for the Sun. Assume that the frequency spectrum for Sun (fgr=50 Hz) corresponds to that for EEG assumed to span 7 octaves (1-128 Hz). The scaling gives in the case of the Earth for the microwave scaled variant of EEG realized at biomolecular level the range .5-149.5 GHz: the upper bound corresponds to energy 1.5 meV and is somewhat below the maximum frequency 160 GHz for the frequency distribution of CMB. Note that miniature membrane potentials correspond to meV energy scale.

    If one replaces EEG range with the range of frequencies 20 Hz-20 kHz audible for humans spanning 10 octaves the upper bound for scale frequency spectrum would be 12 THz which corresponds to energy of .1 eV which is the energy of Cooper pair for cell membrane Josephson function with voltage .05 V. For bats the audible frequencies extend to 110 kHz and the upper bound would be now .510 THz and correspond to energy of .5 eV which is the nominal value of the metabolic energy quantum.

  3. There are indications that also the gravitational body of Moon (with mass 1/83 times that of Earth) (see this and this) could play a role in quantum biology. The proposed analog of the EEG range for the Earth would be scaled up by factor 83 with an upper bound corresponding to .12 eV, which corresponds to the energy of the Cooper pair for the cell membrane. For the range of audible frequencies the upper bound would scale up to 8.3 eV covering visible and UV frequencies.
See the article Taos hum, stochastic resonance, and sensory perception or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.