Pure quantum version of Pollack battery and Biefeld-Brown effect

Wikipedia informs that there are a number of battery voltages that are preferred and that chemistry forces them (see this). 1.5 eV deducted for the Donut battery is one of them. Why?

1. The answer to the question reduces to the notion of electronegativity characterized by chemical potential. For example, oxygen is willing to accept electrons from less electronegative atoms and hydrogen, alkali atoms and carbon are ready to give them up in oxidation. In the process oxygen is reduced and one speaks of redox reactions. These reactions are basic processes of biochemistry.

   In a typical situation, molecule A receives oxygen atoms from molecule B when it is oxidized. The process is more general: for instance, nitrogen, phosphorus or sulfur could replace oxygen. When an atom, say Carbon gives up oxygen atoms or C=O bonds transform C-OH bonds, reduction also occurs. When A is oxidized, B is reduced.

2. When an electron moves from one electrode to another, the stored energy is determined by the difference of chemical potentials. Charge transfer occurs when the difference is non-vanishing. The difference in chemical potential between atom A and some reference atom determines the electronegativity. Depending on its sign, either A or B tends to give up electrons. At equilibrium (without load), the voltage between the electrodes at equilibrium equals the difference of chemical potentials. This voltage is created during charging and does not have to be the opposite of the charging voltage, which is decoupled from the system after the charging is complete.

   Chemical potential is a thermodynamic parameter and can be considered as chemical energy that also includes electrostatic energy. It should be noted that we are talking about electrons now and electrons flow in the case of the Pollack battery when the battery is used because an ohmic electron current passes through the load.

Consider now the Pollack batteries.

1. In the charging of a Pollack battery there is very little dissipation because the dark protons flow through the magnetic body and the chemical potential is reduced to the electrostatic energy determined by the voltage. For semiclassical Pollack batteries the dark protons transform to ordinary ones at the target electrode E2. For purely quantal Pollack batteries, the dark charges at MB do not transform to ordinary ones during the charging. It seems that different descriptions are needed at the level of the magnetic body and for ordinary matter, where the description would be purely chemical and involve chemical potentials.
2. The difference of chemical potentials at the level of ordinary matter changing during charging should be equal to the changing voltage during charging. How does the initial charging voltage V₀ relate to the voltage V_use after charging?

One can start from a problem.

1. Assuming a 100 g electrode and accepting the claims of Donut Lab, the energy gained by a dark proton in the Pollack effect is 1.44 eV, which corresponds rather accurately to the standard battery voltage of 1.5 V. 104 g gives a value of 1.5 V. Is it time to shout Eureka? Not quite yet.
2. Marko informed that in some VTT based estimates the voltage was around 3.5 V. Is this voltage the charging voltage V₀ or the post-charging voltage V_use, whose magnitude need not be the same as that of the charging voltage. Which option is correct: V₀=3.5 V and V_use =1.5 V or vice versa?

Intriguingly, the pondering of this problem lead to a possible connection between pure quantum battery (see this) in which the capacitor behaves as if it had a net charge. The TGD explanation (see this) assumes that the capacitor indeed develops a net charge. The charge separation would be not only between the capacitor plates but also between the magnetic body (MB) and capacitor as a whole would be opposite. Biefeld-Brown effect would be also involved with the em drive (see this).

1. The pure quantum version of the Pollack capacitor indeed assumes two kinds of charge separations so that the Biefeld-Brown effect is possible. The charge separation between E1 and magnetic body (MB) would induce charge separation between E1 and E2. Could the Pollack effect take place also at E2 and induce a charge separation between E2 and MB and make the Pollack battery charged and imply that the charges of E1 are not of the same magnitude so that the Biefeld-Brown effect is implied?
2. But is the Pollack effect for E2 possible energetically? The TGD inspired quantum biology serves as a guideline here (see this and this). The proposal is that for DNA and cell membranes with a permanent negative state, the state formed by dark protons at the magnetic body forms what might be called dark nucleus having a binding energy much smaller than the ordinary nuclear binding energy.

   Could the presence of dark protons at the magnetic body forming dark nuclei serve as a seed of phase transition for the Pollack effect also at E2 occurring spontaneously? The generation of dark nuclear binding energy would make the transition energetically possible.

   This would increase the negative charge at electrode E2 but would not affect the negative charge at the electrode E1. Pure quantum batteries would allow more negative charge to E2 than the semiclassical Pollack battery for the dark protons drop to E2 during the charging. The Pollack effect at E2 would increase the effective charging voltage V_eff during charging whereas Pollack effect at E1 would tend to reduce it.

3. A reasonable expectation is that too much positive charge near E2 at MB makes the system unstable and some maximum dark proton charge can be loaded from E1 and E2 by the Pollack effect. There would also be an upper bound for the number of protons, which can be transferred from E2 to MB. The outcome would be a state in which MB and the battery would have opposite charges but this would not be the case for E1 and E2.

   V_eff= V₀+V_P, would be the sum of the charging voltage V₀ and the contribution V_P = -V_P,E1 +V_P,E2 due to the generation of negative charge by Pollack effect at both E1 and E2. This would give V_eff= V₀ -V_P,E1 +V_P,E2. The increase of V_eff during charging would transfer more positive charge to E2.

4. Intuitively it seems clear that saturation occurs and the decoupling of the original charging voltage V₀ is possible. The user voltage would be V_use= -V_P,E1 +V_P,E2 and should have a sign, which is opposite to that of V₀. For V_P,E2=0 the upper bound for | V_use| would be | V_P,E1| = | V₀| corresponding to complete compensation of the positive charge at E1 by the generation of negative charge in Pollack effect.
5. V_P,E2 and V_P,E1 have opposite effects on the magnitude of V_use. The dielectric between capacitor plates is replaced now by a catalyst of the Pollack effect. A reasonable guess is that the Pollack effect at E2 has the same effect as the presence of dielectric.

   For dielectrics, the voltage is given by V = CQ/ε_r and by ε_r>1 smaller than without dielectric. Same is expected now. This conforms with the estimate for the energy per dark proton if the final voltage is indeed about 1.5 V and smaller than the initial voltage. If so, V_use=| -V_P,E1 +V_P,E2| would be about 1.5 V and by a factor 1.5/3.5= 3/7 smaller than the estimate 3.5 V by VTT using standard chemical picture if this estimate indeed corresponds to the charging voltage. Pollack effect at E2 would make possible a larger charge/voltage ratio just as the use of a dielectric.

See the article Are Pollack batteries possible? and 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.

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.

A pure quantum model for the Pollack battery based on dark protons

The development of the notion of Pollack battery as a possible model explaining the claims of Donut Lab has been rather painful process. At least formally, the notion of a pure quantum Pollack battery makes sense for dark hydrogen atoms (see this). Does it also make sense for dark protons? In the charging of the Pollack battery, the ordinary protons at monopole flux tube states are transferred to flux tubes and localized near the opposite electrode. When the Pollack battery is used, the voltage generated during charging has an opposite sign. The addition of load suggests that a localization to the electrode E1 takes place so that a reverse Pollack effect occurs.

Concerning the construction of the model of Pollack battery for dark protons, the technical problem is that the potential is repulsive if it is taken to vanish at the first electrode E1 so that Schrödinger equation does not give bound state solutions.

1. By gauge invariance it is however possible to add to the potential function a constant so that it vanishes at the second electrode E1. Schrödinger equation for the states localized E2 however gives rise to bound states since voltage with respect to the opposite electrode is negative and increases. Gravitational bound states in the gravitational potential of Earth near the surface of Earth defines a completely analogous system.
2. The Schrödinger equation appears in WKB approximation and solutions are Airy functions satisfying a simple differential equation. The solutions for ordinary value of Planck constant are discussed here) and for general Planck constant here).
3. The situation can be approximated as effectively 1-dimensional. The Schrödinger equation is

   (ℏ²_eff/2m)∂_z² + eE(z-z₀) )Ψ = E_nΨ .

   Here z denotes the coordinate along the monopole flux tube and E denotes the strength of the electric field. E_n is the energy eigenvalue. In the recent case the identification of h_eff is as the gravitational Planck constant ℏ_gr(M_E,m) = r_s(e)m/2β₀= Λ_grm for the pair formed by Earth and charged particle with mass m, in the recent case proton mass. β₀=v₀/c ∼ 1 is true for the Earth.

4. One can introduce the dimensionless coordinate variable

   x= (z-z₀)/z₁ ,

   where the scales z₀ ad z₁ are defined as

   z₀= (E_n/eE)= (E_n/eV₀) r_s ,

   z₁= (ℏ_gr²/2meE)^1/3 = (m_p/8eV₀)^1/3 r_s ,

   eV₀= eEr_s .

   1. In semiclassical approximation, z₀ has interpretation as a classical turning point for Bohr orbits and is of the same order of magnitude as the distance d between the electrodes E1 and E2 of the Pollack battery. Also r_s∼ 1 cm is expected to be of the order of magnitude as d.

      For proton and eV₀= 1 eV one z₁(p)∼ 10³r_s/2∼ 5 m and z₀/z₁∼ 2× 10^-3(eV₀/E_n). For electrons one has z₁(p)(m_em_p)^1/3 ∼ z 10³r_s/2∼ .4 m.

   2. That z₁ is larger than z₀ has interpretation as quantum tunnelling beyond the classically allowed region. One could say that the charges can get along flux tubes outside the region bounded by the electrodes of the battery.
5. Using the variable x, the Schrödinger equation reduces to a differential equation for Airy functions (see this) given by

   (∂_x² +x)Ψ=0 .

Just for fun, one can compare the situation to that for the gravitational potential of the Earth assuming gravitational Planck constant. In this case the value of z₁= (m_p/(8GMm_p/R_E))^1/3 r_s = (R_E/r_s(E))^1/3r_s∼ 1.08× 10³r_S(E)∼ 8.6 m. This is the size scale of trees and many animals and one can wonder how relevant this scale is for biology. Note that z₀ corresponds now to the classical turning point in the gravitational field.

See the article Are Pollack batteries possible? and 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.

Comparing the TGD view of color perception to the geometric models of color perception

Gary Ehlenberger sent an interesting link related to the theories of color perception (see this). It has been known for a long time that colors are not properties of the light or of any stimulus producing color sensation. The notion of color space tries to geometrize hue, lightness and saturation as attributes of color perception. Already Riemann suggested that the Riemannian geometry alone could explain the perceived color differences in terms of a distance in this color space. Schrödinger proposed later a geometric theory of color perception but it has its own problems.

Bujac et al (see this and this) have proposed a non-Riemannian geometric model for color perception claiming to solve the problems of the Riemannian models. TGD suggests a quantum theory of color perception (see this) involving in an essential way the new physics predicted by TGD.

1. Problems of models based on Riemannian geometry of color space

The theories based on Riemann geometry of color space have however problems.

1. Bezold- Brücke effect (see this) is a phenomenon in which a changing light intensity can make a color appear to shift in hue. Neuroscientists would say the geometric model is simply unrealistic. This effect could be due to varying responses of light-receptors to the increasing light intensity. For instance, decreasing the intensity, the contribution of rods which is white or black increases and the hue changes.
2. The sum of small color differences along a geodesic line connecting two different colors is larger than the perceived color difference: this is known as the problem of diminishing returns and is not consistent with Riemnannian geometry. The principle of diminished returns (Weber-Fechner law) is actually a general principle of sensory perception.
3. There is also a problem with the identification of neutral direction along which the color dominated by white becomes dominated by black. A non-Riemannian variant of color space has been proposed. The link indeed describes a new theory (see this) claiming to solve a basic problem of Schrödinger's geometric theory of color perception. This theory would not rely on Riemannian geometry and claims to solve the also the problem of diminished returns (see this). The assignment of Weber-Fechner law to the geometry of color space looks to me an implausible idea. However, it would seem to me that the notion of color space is too naive.

In the sequel the TGD view is summarized and compared with the geometric theories of color. The surprising outcome is that the condition that there are 3 colors and their conjugate colors fixes the choice of the internal space S ⊂ H=M⁴× S to S=CP₂ so that TGD is completely fixed! It is also found that polarization sense can be understood in terms of perceptions related to electroweak quantum numbers identifiable in TGD as color quantum numbers in CP₂ spin degrees of freedom. Also the connection with the findings of Barbara Shipman suggesting a connection between quark symmetries and honeybee dance are discussed.

2. TGD view of color perception

In the TGD framework, the notion of color space is given up and instead a model of color perception as quantum measurement is developed. This model relies in an essential way to the new physics predicted by TGD but also involves geometrical considerations.

2.1 Color perception as measurement of color quantum numbers

Consider first the general observations motivating the proposal.

1. In TGD inspired theory of consciousness (see this and this), sensory perceptions can be identified either as the quantum numbers of outcomes of a quantum measurement or their differences for the states in the quantum jumps: for vision both options give 3+3 fundamental colors. It turned out that in zero energy ontology (ZEO) of TGD only the first option is correct: conscious self corresponds to a sequence of "small" state function reductions and sensory qualia correspond to the quantum numbers measured in SSFR and moment of consciousness has duration measured by the geometric time between two subsequent SSFRs.
2. The first option allows two variants. Fundamental colors could correspond to
   1. the color quantum numbers for quark triplet and their complementary colors to antiquark triplet.
   2. or to 3+3 pairs of gluons forming a color octet: the 2 states with vanishing color quantum numbers do not have color.
   At this moment I cannot distinguish between these options.
3. The number of fundamental colors is however 3+3 only for the symmetries of CP₂.
   1. The sum of the numbers n(F)) +n( F)(=3+3) of charged states in the fundamental representation F and its conjugate F and their number n(Ad)(=3+3) in the adjoint representation are equal for SU(3). For SO(5) equivalent to Sp₂ or B₂, the number n(Ad) of charge states in 10-dimensional adjoint representation is n(Ad)= 10-2=4+4 = 2n(F). This condition does not hold true for any other simple Lie group.
   2. For SO(5) the problem is that F is self-conjugate. Two interpretations are possible: either there are no conjugate colors or that F decomposes to two 2-D representations with 2 complementary colors to give 2+2 colors. Therefore CP₂ is completely unique and it seems that for CP₂ there is an additional symmetry analogous to supersymmetry. Intriguingly, the existence of 3 colors would fix TGD completely!
   3. For SO(5), F corresponds to spinor representation and color would correspond to spin quantum numbers for 4-sphere S⁴. For SU(3), F and F are realized as color triplet partial waves in CP₂.

The assignment of perceived colors to the quantum numbers characterizing quarks or gluons looks of course complete nonsense in the standard physics framework. The irony is that the properties of QCD color fit nicely with the properties of visual colors and it is this observation which must have motivated the terminology as a kind of joke.

1. Also black and white would be complementary colors and color black is a sensation produced by dark current, which gives rise to a genuine stimulus in the brain. In its absence there is no sensation of darkness. This would suggest that the notions of lightness and saturation could be reduced to the contribution of black and white colors in the total visual input. The contribution of cones (color sensitive in ordinary sense) and rods involved with night vision would be in the same role. Lightness would be determined by the relative contributions of white and black colors and saturation by the ratio of ordinary colors as compared to that of black and white.
2. The sums of two color quantum numbers vanish for both triplet and antitriplet: this explains why the third fundamental color can be produced by superposing the other 2 colors.
3. For the physical states total color quantum numbers vanish by color confinement (see this, this and this). A region of a given color is surrounded by a narrow frame with a complementary color. Could this be related to color confinement?
4. This model requires that one can speak of color at least in cellular scales. TGD indeed allows colored states in arbitrarily long length scales. The predicted hierarchy of Planck constants makes color symmetries, in particular scaled variants of color symmetries possible in arbitrarily long scales and in living matter the length scale range 10 nm-2.5 μm contains the p-adic length scales for 4 Gaussian Mersenne primes. This number theoretical miracle makes also scaled down possible copies of hadron physics possible in these scales (see this, this, this and this).

What could be the interpretation of the electroweak quantum numbers, identifiable as spin quantum numbers in the holonomy degrees of freedom for CP₂ and also as color quantum numbers? Could also they define sensory observables?

1. H=M⁴× CP₂ spinors are tensor products of M⁴ and CP₂ spinors (see this, this and this). Quarks and leptons are distinguished by the value ± 1 of the H-chirality as a product of the CP₂ and M⁴ chiralities so that these two chiralities are correlated. This implies separate conservation of quark and lepton numbers and that H-spinors are massless in the 8-D sense.

   In principle there are 3 observables: quark and lepton numbers, electromagnetic charge, and the M⁴ chirality (correlating with CP₂ chirality). Quark and lepton numbers and electromagnetic charge obey super selection rules, being fixed for a given particle so that they cannot define sensory observables.

2. Only the M⁴ chirality can vary. Could electromagnetic circular polarization be its counterpart? Humans can't perceive the polarization of light directly like some insects or marine animals. It is however possible for humans to perceive it using a phenomenon called Haidinger’s brush (see this). A subtle, bowtie-shaped visual illusion (yellow and blue) that appears in the center of the visual field when one is looking at a polarized light source, such as a bright blue sky or a white computer screen.

2.2 The findings of Barbara Shipman as support for the TGD view of color perception

In the standard physics framework, the presence of QCD color in the physics of color perception is impossible since the length scale for hadron physics is hadron scale. Topologist Barbara Shipman (see this) has found direct evidence for the appearance of the mathematics of color symmetries of strong interactions in a mathematical model for the dance of honeybee.

1. The mathematics used by Barbara Shipman involves so-called momentum maps associated with the symplectic action of a group G, now SU(3) in a space X with a symplectic structure. SU(3) itself, SU(3)/U(1)× U(1) and CP₂ are examples of the space X. Symplectic action means that the elements of the Lie algebra g of G correspond to Hamiltonians as functions in X. The Lie algebra commutator in g is represented as a Poisson bracket.

   The points of Lie algebra g of G can be mapped by exponential map to the points of X and the duality between g and g^* a map of the points of X to the adjoint g^* of g. What this means physically is that n commuting coordinates and the n values of their conjugate coordinates representing conserved charges as Hamiltonians determine the orbit of a point in X.

   The space F=SU(3)/U(1)× U(1) is a 6-D space, which can be identified as the twistor space of CP₂ that is a a bundle having CP₂ as a base and 2-sphere as a fiber. F has also an interpretation as the space for the choices of color quantization axes. F plays a key role in the construction of quantum TGD (see this) and the existence of the twistor space with Kähler structure makes M⁴ and CP₂ unique (see this) so that TGD is unique.

   A comparison with M⁴ helps here. For the rotation group SO(3) acting in CP₁=S², the space of quantization axis of angular momentum is SO(3)/SO(2)=SU(2)/U(1)=CP₁= S². For Minkowski space M⁴ the twistor space is a bundle having M⁴ as a base and the 2-D sphere of light-like rays from a given point of M⁴ as a fiber.

2. Also the double coset space F₁= CP₂/U(1)× U(1)= U(2)\ SU(3)/U(1)× U(1) is 2-dimensional. Eguchi-Hanson coordinates are standard coordinates for CP₂ (see this). Since the phase-like angle coordinates of CP₂ associated with U(1)× U(1) have as conjugates the coordinates r and θ of CP₂, this space does not allow a symplectic structure.

   The lower-dimensional case of CP₁ helps to get some idea of the topology of F₁. U(1)\ CP₁/U(1) can be identified as a half geodesic from the North Pole to the South pole and is not a symplectic space. The identification as a half-geodesic is not unique since it is determined only apart from local U(1) rotation of the half-geodesic. F₁ has a sphere with 3 circles S¹ as boundaries and also now the identification is unique only modulo local U(1)× U(1) rotations. The full space CP₁ of quantization axes is needed also at S² and also at CP₂ so that F₁ cannot be identified as a kind of reduced space for the quantization axes.

3. The honeybee dance represents geometric information about the direction and distance of the food source so that only 2-D data are involved. Could the 2-D F₁ code for this information? Perhaps a more plausible option is that since F is a sphere bundle, the points of the fiber sphere S² code for the 2-D data, essentially the direction of color quantization axes. The path of the honeybee to the food source would be mapped to a path in S² and would represent the history of color perceptions of the honeybee along the path.

   Also polarization matters and bees can perceive the polarization of the sunlight (see this) and use this information to determine the direction of the Sun, which is part of the information expressed in the dance of the honeybee.

   The path to the food source ends up with detection involving pattern recognition. The color pattern of the food source must play a key role in the recognition. Does the dance also represent this information?

2.3 The role of the twistor space of CP₂ in color perception

The space F is of obvious interest concerning the understanding of color perception.

1. From a given state characterized by color isospin and hypercharge, one can obtain all possible colored states by making SU(3) color rotations. The action of the elements of the Cartan group U(1)× U(1) multiplies the state with a mere phase factor so that the physical state is not changed.

   Therefore the 6-D space F=SU(3)/U(1)× U(1) describes the space of all color perceptions for a given irreducible representation of the color group when the choice of quantization axes is allowed to vary? Is the perceived color independent of the choice of the quantization axes but that the probability for a given color quantum numbers in the measurement of color quantum numbers is determined by the state as in quantum measurement theory? This kind of view is suggested by the analogy of the Relativity Principle for color symmetries. For a fixed choice of quantization axes, one has only a discrete set of colors: 3+3 for both quark and gluon states.

2. For the tensor products of the simplest color states, color representations with a much larger repertoire of color quantum numbers are possible and the number of different hues becomes large. The number of the tensor factors contributing to the observed color, determining the possible dimensions of the irreducible color representations, should correspond to the intensity of light. This should correspond to the physiological situation and large quantum number limit behaving classically.
3. An interesting challenge is to understand the change of the hue with the increase of the intensity (Bezold- Brücke effect, see this) and therefore with the number of the contributing tensor factors. The increase of the intensity could increase the number of the active tensor factors involved and therefore extend the color palette. The probabilities of the receptors to respond to the incoming light depend on its intensity.
4. It is also possible to construct color multiplets in F consisting of color eigenstates. Two degrees of freedom correspond to 2 angle variables related to color quantum numbers and the remaining 4 to additional degrees of freedom which should geometrically relate to CP₂. Are these multiplets realized physically as the twistor lift of TGD suggests (see this)?

A note about the role of CP₂ coordinates is in order. Induced classical electroweak gauge fields depend on gradients of CP₂ coordinates. The CP₂ part of the trace of the second fundamental form, involving second derivatives of CP₂ coordinates, is vanishing except at the 3-D edges of the space-time surface at which minimal surface property fails: it has quantum numbers of the Higgs field. The 2 complex CP₂ coordinates appear as such in the spinor harmonics associated with CP₂.

2.4 What could happen in color perception?

What could happen in color perception identified as quantum measurement.

1. Does the perceived color correspond to the sum of the colors quantum numbers assignable to the color sensitive receptors reducing to the quark or gluon level? How are the common color quantization axes determined?
2. Is the choice of the quantization axes for a given individual determined somehow? In TGD, electroweak interactions are color interactions in the spin degrees of freedom for CP₂ and color isospin and hypercharge correspond to electroweak isospin and hypercharge. The directions of the latter quantization axes are fixed. This would mean that the directions of color quantization axes are always the same. If so, the perceived color would be determined by the sums of the discrete color quantum numbers for receptors.
3. If the individual states in the tensor product have different color quantization axes, their states are not color eigenstates for the choice of quantization axes made in the tensor product. The state would decompose to a direct sum of irreducible color representations. State function reduction would occur and give rise to a state with definite color quantum numbers. One might hope that the outcome is highly unique at large color quantum number limit. One should however understand what determines the choice of the quantization axis for the entire tensor product.
4. Is it possible to test which option is correct? After images change color could this be due to different choices of the quantization axes or is it a genuine change of the analog of sensory input determining the after image?

See the article Comparing the TGD view of color perception to the geometric models of color perception or the chapter General Theory of Qualia.

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.

Questions related to language from the TGD point of view

I received from Taylor Reed Ramsey a set of 3 highly inspiring questions of how the TGD view of cognition might relate to the basic structures of language. Ramsey is an independent researcher working on a long-form project about how external symbolic systems writing, in particular restructure human cognition. The questions relate to adelic physics, the hierarchy of Planck constants, and the genetic code. In the sequel Q1:, Q2:,... and A1:, A2:,... to the corresponding answer.

1. A question related to language and adelic physics

Q1: In your adelic vision, cognition is p-adic and a system's cognitive complexity corresponds to the dimension of the extension of rationals it realizes, with evolution as the growth of that extension. Humans also install external encoding systems alphabets, numerals, calendars in childhood, and these measurably reorganize cognition within a single generation.

Could a writing system be modeled as a macroscopic, learning-heritable selection over p-adic cognitive representations a culturally fixed extension of rationals (or preferred Galois structure) governing which representations a brain's magnetic body can run? Would an alphabetic versus a logographic script differ at the level of the extension or the Galois group?

A1: Before answering the questions, I will discuss one of the key questions that I have been pondering is how the extensions of rationals defining cognitive hierarchies on one hand, and p-adic hierarchies relate to each other?

1. The extensions E of rationals appear as coefficients field for the functions (f₁,f₂): H=M⁴× CP₂→ C² and g=(g₁,g₂): C²→ C² appearing in the general solution of classical field equations. The solutions in turn can give rise to extensions of E so that the situation is very complex.
2. When the extension E of rationals is realized in terms of roots of polynomials, one can assign to it Galois group. This is not true for an abstract extension defining the coefficients of f and g. For polynomials of a single variable ordinary notion of Galois group can be applied and the situation can in some cases reduce to this. For the general case, the roots are not points but 4-D surfaces (f₁,f₂)=(0,0) of H for which roots correspond to different regions.
3. The maps f, which are prime in the sense that they do not have composition f= g_º f₁ could be interpreted as representing the substrate whereas the maps g would represent cognition giving information about f via the roots of g_º f which correspond to space-time surfaces f= (c₁,c₂) where (c₁,c₂) is a root of g. In computer science one speaks of substrate independence.
4. The Galois group as a group of flows transforming roots as different space-time regions to each other makes sense (see this). Note that also the space-time surfaces satisfying (f₁,f₂)=(c₁,c₂) are possible and correspond to the roots of (f₁-c₁,f₂-c₂). These surfaces emerges as roots of g_º f, where g: C²→ C² is a holomorphic map. One can say tha the hierarchy of maps g provides information of the map f=(f₁,f₂) as roots of g_º f.

   This generalized Galois group characterizes space-time surfaces. There is a temptation to assume that this kind of group characterizes space-time surfaces representing DNA and RNA. The description of pair creation in TGD is in terms of a particle turning backwards in time in a 3-D vertex acting as 3-D edge of space-time at which the arrow of geometric time changes.

   This inspires the proposal that the replication of space-time surfaces is also behind biological replication. If so, these cognitive structures would be inheritable and inherited via DNA replication. In particular, the abstract representation of the writing system would be realized already at the level of dark DNA at the level of the magnetic body, and it would be possible to learn the writing system. One could even see writing and speaking as expressions of the genetic code analogous to expression in terms of proteins.

Some comments concerning the question whether a writing system could be modelled as a macroscopic, learning-heritable selection over p-adic cognitive representations a culturally fixed extension of rationals (or preferred Galois structure) governing which representations a brain's magnetic body can run.

1. Genetic code would provide one realization for cognition and could be behind the written and spoken languages. The number of letters of language is typically somewhat larger than the number of amino-acids (20). On the other hand, the lower bound for the number of tRNAs is 32: could the phonemes correspond to tRNA coded by 64 genetic codons. Note that the analogy between the letters of language and 4 letters of the genetic code fails as a strict analogy.
2. If the genetic code is a cognitive representation based on functional composition of polynomials of degree 4 representing the code letters, the genetic inheritance would be behind the ability to learn language although the correspondence between the language and genetic code would be very flexible. The generalization of p-adic number fields to function fields would be involved and polynomials with degree 4 (not prime) would be prime polynomials in the Galois sense. One could say that the cognitive representations could be inherited. This could reduce quite concretely to gene replication as a replication of the corresponding space-time surfaces.

You also asked whether the alphabetic and logographic writing system correspond to different Galois groups. The basic question is what differentiates these writing systems.

1. The first view is that they could correspond to reductionistic ("western)"" and holistic ("eastern") views of genetic codons. In logographic writing codons and entangled triplets of letters represented as states of dark protons would not reduce to product states defined by letters. In the alphabetic writing system this would be the case. I will later return this.
2. In a model for the genetic code (see this) based on functional composites of maps g_i: C²→ C², i=1,...4 characterizing the 4 letters of the genetic code, codons as holistic entities would correspond to deformations of functional composites of 3 maps g_i, which do not reduce to functional composites of polynomials of lower degree with the same Galois group. They are primes in the Galois sense, which is weaker than the purely number theoretic characterization in terms of the polynomial degree. They would correspond to the logographic writing system. In absence of the small deformation they would however decompose. This would be the reductionistic representation and could correspond to the alphabetic writing system. The Galois groups would be indeed different.

2. Bioharmony model of the genetic code, Galois groups, in relation to alphabetic/logographic writing systems

Q2: Your bio-harmony model derives the genetic code from icosahedral (A5) and tetrahedral (A4) symmetries read as Galois groups, with codons as 3-chords. Is there a linguistic analog one tier up does a script's phoneme grapheme inventory carry a comparable harmonic/Galois structure, so that an alphabet stands to dark-photon/EEG communication roughly as the genetic code stands to dark-nucleon chemistry? Could different scripts then correspond to different harmonies, and so to different baseline cognitive or emotional 'moods' at the population scale?

A2: I am not quite sure what you mean with the notion of script so that the following might involve misunderstandings.

1. Genetic code at the bit level is the same for all variants of the realizations of the genetic code in terms of frequency triplets providing the codons as 3-chords with emotional tone and allowing representation of moods. This representation would be analogous to computer code: there are no emotions. Music would also express emotions.

   The frequency triplets are differences of frequencies for a dark proton triplet. The transition between two states of dark proton triplet induces the frequency triplet as 3-chord. A full 3N-resonance means that the sender and receiver make opposite transitions. Resonance could be also partial.

   In the icosa tetrahedral realization of the genetic code, dark proton triplets are located to the triangular faces of 3 icosahedra and a tetrahedron. The transition transforming codons to each other would correspond to the transfer of dark proton triplet between two triangles determined by the Hamiltonian cycle. I have not previously considered the meaning of the predicted correlation between the state of the dark proton triplet and its location to a particular triangle.

2. The dark codons are (quantum) dynamical unlike the chemical codons. A possible interpretation is that the dynamics of dark codons is free so that they form a kind of R&D unit and perform processes analogous to quantum computations whereas chemical codons are frozen and represent the analog of classical computer program code.

   Dark codons are proposed to control chemical codons by energy resonance. The chemical codon would receive the control signal a 3-resonance when the frequency differences for the transition of dark codon correspond to resonance energies for the letters of the chemical codon. For a gene one would have 3N-resonance. The ordinary codons could also react only to the sum of the cyclotron frequency differences. In both cases, it is possible to have 1-1 correspondence if the frequencies for the letters depend on the position of the letter in the dark codon. These two ways of the chemical codon to react to the control signal could correspond to the reductionistic and holistic views of codons at the level of ordinary codons.

3. The representation of codons as 3-chords would add to the representation of emotions and emotional intelligence. Human moods are a phenomenon involving short time scales and the bioharmony characterizing can change in short time scales. An interesting question is whether moods appear at the whole body level so that every cell would involve the same Hamiltonian cycles or whether the cycle depends on the body part.

   Moods are expressed by gestures and by art. Writing expresses emotions but only via the generated associations. Therefore I would not be the first one to assign a "cultural" mood to the writing system.

Cultures might express themselves in writing systems differently.

1. At fundamental level genetic code would relate to the completely exceptional tessellation of hyperbolic 3-space (surface of M⁴ ⊂ H=M⁴× CP₂ with constant value of light-cone proper time analogous to cosmic time). The proposal is that it is completely universal and that the human language is only a special case appearing at a very high level.
2. The numbers for the letters of written language are consistent with the idea that they are basically coded by genetic codons: the most plausible interpretation as tRNA codons was already mentioned. It is important that the letters in western language do not have meaning, at least they do not have meaning at our level of self hierarchy.

   The time scale for the transcription is measured in a fraction of second and this is true also for speech. This supports the idea. Perhaps sequences of dark genetic codons realized as temporal patterns at the magnetic body are transformed to speech.

3. The following observation related to alphabetic and logographic writing systems might be highly relevant. There are languages such as China in which this composition of words to letters does not occur (correct me if I am wrong). To my understanding the letters are originally pictures representing words.

   Could this correspond to the use of 64 genetic codons as basic units without a decomposition to 3 letters? Codons correspond to entangled dark proton triplets rather than unentangled product states for protons. No (no state function-) reduction of codons to a product state would occur in Eastern languages!

   That I Ching has 64 symbols would support this intuition. Eastern philosophies are holistic, western philosophies are reductionistic. Could this difference make itself manifest already at the level of the basic symbol system of language.

3. Does the notion of cognitive qualia make sense?

Q3: Number-theoretical universality and the adele give an object holding the real (sensory) norm and all p-adic (cognitive) norms at once. If a self could realize an adelic rather than single-p-adic representation sensory and all cognitive views simultaneously available and self-consistent what would its qualia structure be? Would it coincide with the high-h_{eff, maximally negentropic states you associate with expanded consciousness? (Leibniz's characteristica universalis seems to gesture at the same object.)}

A3: Interesting questions. I cannot give a clearcut answer to them. I have spoken about sensory qualia. One can of course speak of cognitive qualia and ask how the two kinds of qualia correspond to each other. I would tend to see cognitive qualia as names for sensory qualia, as symbols representing them.

One thing is certain: p-adic number fields and its functional analogs define a hugely simplified picture of sensory reality. Cognition simplifies and abstracts the essential features.

Instead, I try to explain (and to understand at the same time!) what cognition, and in particular, linguistic cognition, in TGD might be. The general structure of TGD suggests 3 approaches to cognition. One approach is at the level of the space of space-time surfaces, "world of classical worlds" (WCW), the second approach is at the level of the 8-D imbedding space H=M⁴× CP₂ and the third approach is at the level of 4-D space-time surfaces. 3.1. WCW level

WCW is the space of space-time surfaces obeying holography = holomorphy principle and analogous to 4-D Bohr orbits for particles identified as 3-surfaces.

I have assigned p-adics and adeles with cognition. In the recent form of TGD a generalization of p-adic number fields and adeles to their functional counterparts emerges at the level of WCW.

1. Holography = holomorphy principle (H-H) (see this, this and this) dictates the classical dynamics of the TGD space-time surfaces as a universal dynamics independent of variational principle. Space-time surfaces with Minkowskian signature corresponds to roots for a pair of holomorphic (in generalized sense) complex valued functions f=(f₁,f₂): H=M⁴× CP₂→ C² are roots. To each solution one can assign an infinite hierarchy of new solutions g_º f where g is holomorphic map C²→ C². Here maps g allow functional composition and their iterates define analogs of Mandelbrot fractals and Julia sets as space-time surfaces.

   This brings in mind Turing's and Gödel's view of computation in which arithmetic operations involve a finite basis of primitive functions (see this). One can identify maps f which do not allow compotion to f=g_º f₁ as prime substrates. One can also decompose maps g: C²→ C² to "prime" g:s having no such composition.

   The space-time surfaces assignable to genes and genetic codons would provide examples of this kind of g:s.

   1. One could identify f as a "substrate" and the function g allowing functional composition would define a cognitive hierarchy. The "thoughts"/cognitions are assignable to the substrate. Substrate and cognition would be rather independent. Any system can cognize, which looks rather radical an idea. This brings in mind the substrate independence of computer science.
   2. For the functions g, one can generalize the notion of p-adicity and obtain function field counterparts of ordinary p-adics. The functional counterparts of p-adic number fields could relate to cognition. These p-adic function fields are mapped by category theoretical morphism to ordinary p-adics. Also the notion of functional adele makes sense. This generalization allows us to understand the p-adic length scale hypothesis.
   3. There is a proposal (see this) for how genetic codons and genes could correspond to slightly deformed compositions of maps g assignable to letters. Although the degree of the polynomials associated with the letters is d=4 and therefore not prime degree, they do not have functional compositions to lower degree polynomials (of degree 2). Codons would correspond to small deformations of 3-fold compositions of the letter polynomials having no functional compositions to lower degree polynomials with the same Galois group. The same would apply to genes.

   3.2. Embedding space level

   Icosa tetrahedral tessellation (see this and this) is a completely unique tessellation of the hyperbolic space H³ in the sense that 3 Platonic solids appear as its effective building bricks: octahedrons however define holes of this tessellation. This would make the genetic code universal. This realization would correspond to the level of embedding space H=M⁴× CP₂. There is evidence for its realization at the level of clustering of water molecules (see this).

   The sequences of codons and letters would define sequences of symbols giving rise to linguistic expressions. The proposal is that DNA/RNA gives rise to a representation of ordinary genetic code and a parallel quantal representation in terms of dark proton triplets associated with the magnetic body of DNA/RNA. Also temporal sequences as singularities at the level of space-time can be considered.

   3.3 Space-time level

   There is also an approach to the origin of language at space-time level. At space-time level it would basically relate to the small failure of classical determinism (no violation of field equations) for H-H principle (see this, this and this) exhibited already by 2-D minimal surfaces realized as soap films spanned by the frames: now space-time surfaces are holomorphic minimal surfaces: this irrespective of classical actions (see this).

   The loci of non-determinism correspond to the failure of classical non-determinism as 3-D edges of space-time. These edges define 3-D features characterizing the entire space-time surface information theoretically. They form temporal sequences analogous to expressions of language. An attractive idea is that a finite number of these edges determines a collection of symbols forming the basis of language for a given space-time surface. The space-time surfaces allowed by classical non-determinism would define a set of sentences as these symbol sequences. There would be a connection with the WCW level since the singularities as edges of space-time are the seats for failure of generalized holomorphy.

   What could be the counterparts of vowels and consonants in this framework?

   1. The consonants emerged to the written language first and the vowels came later. Consonants could correspond to features as 3-D edges at between two space-time regions serving as analogs of vowels.
   2. There would be an analogy with visual perception. At the lowest level boundaries define the basic features and the representation is analogous to a child's drawing. After that come colors and other visual attributes for the regions bounded by features. Vowels could be seen as analogs of colors.
   3. A further analogy relates to the sequence of "small" state function reductions (SSFRs) defining self as a sequence. Each SSFR would be analogous to a consonant and the period of subjective time between SSFR and the next SSFR, with qualia represented as quantum numbers, would be analogous to a particular vowel. In singing the notes could correspond to colors and vowels and the moments, when the note is replaced with a new one could be analogs of consonants as boundaries. The rhythm in music would define a regularly spaced sequence of 3-D space-time edges dividing it to constant periods. It would also provide a clock.

      One could see the written and spoken language as a representation for the time evolution of self as a sequence of SSFRs.

   See the article Questions related to language from the TGD point of view or the chapter Quantum Model for Hearing.

   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.

Giant rings as the most recent evidence for the notion of cosmic string

Sabine Hossenfelder's Youtube video (see this) about the observation of a giant ring (GR) having a diameter of 3 billion ly with a statistical significance is 4.1 σ (1/20,000) in constellation Bo tes at a distance of 7 billion light years. The article "Giant Ring in the Sky" by Lopez and Clowes (see this) reports the discovery.

GR has clusters of galaxies behind it. The light arriving from the galaxies is absorbed as it travels through the gas. There is an enhanced absorption at the ring. GR has as its part Giant Arc (GA) (see this) having northern and southern parts and encloses Big Ring (BR) (see this) having 4.5± .6 σ evidence. BR has diameter ∼ 400 Mpc.

Here is the abstract of the article:

We present the discovery of "A Giant Ring on the Sky" (GR); a ring-like, ultra-large-scale structure at z ∼ 0.8, located in the same field that contains the previously-documented Giant Arc (GA) and Big Ring (BR). The GR was predicted from the presence of a Northern Arc (NA) filament (noted in previous work), which looked like it could, with more or enhanced data, connect with the GA to form a giant ring that encompasses the BR.

There is now much evidence to support the reality of a GR. There appear to be two overlapping versions of the GR which differ by only the left-hand-side trajectory; this branching in the LHS of the GR was identified with the FilFinder algorithm and appears to correspond to both the GR prediction (the extended, elliptical, GR from the GA+NA ellipse), and the visually-identified ellipse (the visually-impressive, almost contiguous, roughly circular, GR which is enhanced by a tilted viewing angle). The branching in the GR seems to be hinting at multiple, overlapping ring features. The GR consists of a thin, filamentary northern region, a clustered, ambiguous southern region (including the members of the GA), and filamentary branching towards the LHS.

Statistical assessment with elliptical shells, and optimum elliptical-shell-matching, identified two ≥ 4σ ellipse features corresponding to the GR prediction and to the visually-identified GR. Additionally, the 2D Power Spectrum Analysis identified significant (3.5σ ) clustering on scales ∼ 320 Mpc. We also applied our statistical assessments to random data and to FLAMINGO-10K simulated data. The results demonstrate that, while superficially "significant" elliptical shells can be reproduced in random data with the optimum ellipse-matching method (many trials giving the "look-elsewhere" effect), with 2D PSA all of the random fields, and FLAMINGO-10K fields, were found to be entirely consistent with random.

The structures cannot have gravitational origin since the formation of bound states of this size by gravitational condensation is impossible in ΛCDM scenario. Some new interaction is needed. In TGD, space-times are 4-D surfaces in H=M⁴× CP₂ satisfying holography = holomorphy principle predicting that, apart from 3-D singularities representing edges of the space-time, space-time surfaces minimal surfaces obeying generalized holography satisfy the field equations for any general coordinate invariant variational principle constructible in terms of the induced geometry. Cosmic strings, which can thicken to monopole flux tubes, are fundamental structures predicted by TGD. They appear in all scales from cosmology to hadron physics and even down to CP₂ scale (see this and this). The natural identification of Giant Ring and Big Ring is as closed cosmic strings, whose immense gravitational field attracts gas around them.

See the article About the recent TGD based view concerning cosmology and astrophysics 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.

How did metabolism emerge?: breathing soil as a guideline

This finding relates in an interesting way to the TGD inspired view that life and even genetic code are universal. Even quartz crystals (see this) could be living in a primitive sense and the basic quantum mechanism would be the same as for ordinary life. Pollack effect (see this, this this, this, this, this) in which protons are kicked to the magnetic body and generate in this way negatively charged exclusion zone (EZ) would be fundamental for metabolism. The dropping of dark protons from the magnetic body in the reverse Pollack effect would liberate the metabolic energy.

The findings of Fontaine's Lab suggest that in soil a hugely simplified variant of Krebs cycle and electron transport chain (ETC) make possible breathing producing CO₂ originates basically from the COOH groups of proteins. Consider first how the process occurs in biology.

1. The function of the Krebs cycle is to strip high energy electrons of the fuel and feed them to the electron transport chain (ETC) liberating the energy of electrons. According to the standard view, this creates electrochemical gradient pumping hydrogen ions across the mitochondrial membrane.
2. Krebs cycle strips electrons from the 2-carbon compounds obtained from the pyruvates combining with vitamin A to form Co-A involving citrate with 6 C atoms. Krebs cycle has as wastes CO₂ and water as the end product of ETC. The electrons striped from the counterpart provide the needed energy to kick the H⁺ ions to the magnetic body.
3. Krebs cycle is preceded by the splitting of glucose C₆H₁₂ O₆ with 6 carbon atoms to two pyruvate molecules C₃H₃O₃^- with 3 C atoms plus 2 net ATP molecules and NADH moleculefeeding high energy electrons into electron transport chain (ETC). Before entering the Krebs cycle, the 3-carbon molecule pyruvate is transferred into the mitochondrial matrix. Here, the enzyme complex pyruvate dehydrogenase removes a carbon atom from pyruvate to release the first molecule of CO₂. The outcome is H₂C=(CH)-O^- with two C atoms, which is attached to Coenzyme A to form Acetyl-CoA.  
4. First glucose molecule with 6 C atoms and serving as a fuel is decomposed to two pyruvate molecules. Before entering the Krebs cycle, the 3-carbon molecule pyruvate is transported into the mitochondrial matrix. Here, the enzyme complex pyruvate dehydrogenase removes a carbon atom from pyruvate to release the first molecule of CO₂.
5. The remaining 2-carbon fragment -(C=O)-CH₃, acetyl group, is fused to Coenzyme-A to form Acetyl-Co-A (Co-A is a complex molecule derived from vitamin B₅). Acetyl-Co-A is transported to the mitochondrial matrix and meets oxaloacetate with 4 C atoms to form citric acid with 6 C atoms. Citric acid flows through the cycle and comes back as C0-A ready to take to the process a new -(C=O)-CH₃ molecule.

Could TGD explain what happens in breathing without enzymes? The findings of Fontaine's Lab suggest that in soil a hugely simplified analogs of the process leading from glucose to two pyruvates, Krebs cycle and ETC make possible breathing producing CO₂ originates basically from the COOH groups of proteins.

In the case of the soil there are no enzymes, so that the splitting of glucose to pyruvates, the Krebs cycle and ETC should be replaced with something dramatically simpler.

1. Already in the splitting of glucose to pyruvate generates ATP and therefore also dark protons. What comes to mind is that the Pollack effect for some 6 -OH groups of glucose C₆H₁₂O₆ could transform them to O^- plus dark protons at the magnetic body. 2 pyruvate molecules would be obtained if only a single H⁺ per pyruvate ion is transformed to a dark proton.
2. In the TGD framework, the transfer of H⁺ ions from the interior of the mitochondria to their exteriors during ETC is replaced by their transfer to the magnetic body of the system. The transfer makes the system negatively charged and this provides the interior of EZ with additional negative charge. In fact, cells are always negatively charged: this can be explained by the charges of DNA and RNA strands carrying constant charge density which is 3 unit charges per codon. In this case, the units of 3 dark protons representing dark codons are stable against the reverse Pollack effect.
3. The energy liberated by the stripped electrons in ETC would be used to transfer ordinary H⁺ ions to dark protons at the magnetic body of mitochondria rather than to the exterior of the mitochondria. The dark protons would be attached to ADP to form ATP acting as a shuttle carrying dark protons to the user molecule. The metabolic energy would be used as the dark proton becomes an ordinary proton in the reverse Pollack effect.

One can also imagine a more effective option for metabolism.

1. All 6 -OH groups of the glucose transformed to O^- plus a dark proton. This would lead to 2 C₃H₃(O^-)₃ molecules with 3 dark protons at their magnetic bodies, which could liberate metabolic energy in the reverse Pollack effect.

   Remarkably, each molecule has 3 dark protons and in the TGD view of genetic code they would define dark codons. Large values of h_eff mean algebraic complexity and intelligence. Could these dark codons give for the system the IQ needed to drive the process further on?

2. The splitting of C₃ H₃(O^-)₃ to CO₂ and acetyl molecule (C-O^-)-CH₃, involving the dropping of 2 further dark protons back to oxygen ions to form -OH groups, would generate CO₂ and the acetyl group. This process could be an ultra simplified version of the steps preceding ETC. The further dropping of the third dark proton to acetyl ion would be the counterpart of ETC and would also liberate metabolic energy.

See the article A possible TGD based narrative for how life might have evolved 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.

A model for the variation of Newton's constant based on dark gravitation radiation pressure

The proposal (see this is that the radiation pressure of the dark gravitational radiation from the Sun and perhaps also from the Earth can produce effects comparable to the gravitational force of the Sun. This radiation is extremely weak. Could quantum coherence in the length scale defined by gravitational-Compton wavelength enhance the intensity of the gravitational radiation?

1. General description of the model

The first guess was that the gravitational radiation at energy range 1-10⁵ eV assumed to be produced by Sun could somehow transform to dark gravitons with Compton length equal to gravitational wavelength Λ= Λ_gr= r_S(Sun)/2β₀(Sun ∼ 3000) km ∼ R_E/2, which does not depend at all on the energy of the graviton. This would guarantee the quantum coherence in the Earth scale making possible large effects. In microscopic scales the gravitational radiation is generated by thermal collisions in solar plasma and in macroscopic scales by hydrodynamic fluctuations. The macroscopic mechanism is more plausible as a candidate for producing the gravitational dark gravitation.

The generation of quantum coherence as transformation of ordinary gravitons to dark gravitions is however difficult to understand. One can also consider a purely TGD based mechanism in which dark gravitons are generated at the gravitational magnetic body of the Sun, i.e. monopole flux tube loops associated with the Sun and mediating the gravitational interaction. The scale of Sunspots is indeed given by Λ_gr (see this. The gravitational radiation would be generated by the acceleration of charged particles in the magnetic field of the gravitational flux tubes.

The observed relative variation of Newton's constant is between .01-.1 percent. The value of c_#/c= 2^-11= .5× 10^-3 is one 1/2 of the lower bound. This observation might help in the attempts to understand about what is involved.

It is good to start with the possible gravitonic pressure caused by the Sun. The gravitational force of the Sun on the Earth must be compared to the total momentum flux produced by dark gravitons directed at the Earth to see whether the hypothesis can make sense. One must also test the corresponding hypothesis for other planets also in the case of the Earth's gravitational field.

1. The Sun is estimated to produce energy with a power of P=1.3× 10⁸ W through graviton radiation by thermal collisions and hydrodynamic fluctuations. The energy of the gravitons would in the range 1 eV-10⁵ eV. Thermal collisions, hydrodynamic fluctuations, and photoproduction by the decay of photons to gravitons.

   The generated total power is estimated to be P= 1.3× 10⁸ W and correspond to a single nuclear power plant. It would give to give rise to a total momentum flux of F= P/c = 1.3/ N which is extremely small

2. The gravitational force of the Sun on the Earth is

   F_gr ∼ 1.5× 3.54 × 10²² N .

   The order of magnitude difference between F_gr and the force caused by the ordinary gravitational radiation pressure is enormous.

3. In absence of quantum coherence, the radiated power is proportional to the number N of emitters. Quantum coherence should effectively replace N with N². At least for the thermal radiation with high energies, it is difficult to see how this could amplifty the momentum flux so that it would be comparable to the gravitational force between the Earth and the Sun.

   It seems more likely that the mechanism is related to the acceleration of gravitionally dark charged particles in the magnetic field of dark gravitational flux tubes characterized by ℏ_gr.

   Λ_gr is the same regardless of the energy of the graviton E. The origin of quantum coherence and large effect would be here. Λ_gr = 3000 km that would be a wavelength and about half the radius of the Earth and could lead to effect in the scale of the entire Earth. Also the emission rate of the radiation in constant magnetic field of the Sunspot is proportional go Gm²f_c², f_c= eB/m and is independent of the mass of the m charged particle so that the radiation power is proportional to the total number of charged particles.

2. A model for the emission of dark gravitons

Consider now a model for the emission mechanism of gravitationally dark gravitons from the monopole flux tubes mediating the gravitational interaction.

1. Dark charges at the gravitational flux tubes of radius Λ_gr and extending to the Earth would produce the force as radiation pressure F= P/c, where P is the emitted power.
2. For dark gravitons, quantum coherence is assumed to produce a momentum proportional to the square N² of the number of emitters in the emitting region rather than to N as in absence of coherence.
3. Emission power P and corresponding momentum transfer rate F=P/c due to the radiation pressure for gravitational waves in a magnetic field B. The force produced by radiation pressure should be about 10^-2-10^-3 times smaller than the gravitational force. The lower bound is one 1/2 of β₀ ∼ 2^-11.

2.1 Parameters of the model

Consider first the parameters of the model.

1. The flux tubes should extend to the Earth and therefore have the length L= 1 AU. Their thickness is

   Λ_gr = r_S(Sun)/2β₀(Sun) ∼ 3× 10⁶ m ∼ R_E/2 for β₀(Sun)= c_#/c= 2^-11.

   The volume of the flux tube is given by

   V= (π/2)LΛ_gr² .

2. A geometrically natural simplifying assumption is that there is about 1 unit charge per volume determined by the magnetic length L_B giving rise to a number density d/dV= 1/L_B³, L_B= (ℏ/eB)^1/2 .
3. The total number N of unit charges at the flux tube would be

   N= (dn/dV)× V = (1/L_B³)× (π/2) AU× Λ_gr²

2.2 Radiation power and force for the Earth-Sun system

There exists a formula for the power of the gravitational radiation in a constant magnetic field B prevailing inside the monopole flux tube. Since cyclotron frequency f_c is inversely proportional to the mass of the particle, the power does not depend on the mass m of the charge.

1. The power of the gravitational radiation emitted by the unit charge e in a constant magnetic field is given by

   P= (4/3) (Ge²/c³) β² γ⁴× y²~ J/s .

   Here one gas y=r× B/T, r= .2566∼ .26.

2. The total radiation force is

   F_rad= N²F=b× y⁵ β² γ⁴ × 5× 10²² ~N & y= r(B/T), r=.25 .

The outcome of the calculation is that the magnetic field at the monopole flux tubes cannot be much smaller than .25 Tesla unless one allows relativistic velocities for the charges. The based model for the generation of solar wind and radiation in the decay of M₈₉ protons to ordinary hadrons at the surface of the Sun (see this) indeed predicts relativistic energies.

2.4 The situation for the other planets

One can consider the situation for other planets using scaling arguments applied to F_gr and F_rad. The F_gr/F_rad scales like

(R_P/AU)⁴ (M^P/ME) B_P²

and the scaling

B_P B_E= (AU/R_P)²(M^E/MP)^1/2

leaves F_gr/F_rad invariant. Apart from mass ratio the scaling is that of a monopole magnetic field.

2.4 What about the Earth itself?

One can also ask whether F_rad due to the Earth itself could be important. In this case F_gr for a mass of 1 kg is scaled down to about 10 N and Λ_gr is scaled down to 5 mm. For a density of 10³ kg/m³, the volume Λ_gr³ corresponds to mass of 1.25 × 10^-4 kg so that the F_gr would be at the surface of the Earth about 1.25 × 10^-3 N. For the length L= R_{E/sub> of a monopole flux tube the (emanating from the interior of the Earth?) there would be a scaling down of Frad by (RE/sub>/AU) × (Λgr(E)/&Lambdagr(S))²∼ 10^-5× 10^-16 ∼ 10^-21.}

For F_rad= 3.5× 10¹⁹ N corresponding to the reduction factor 10^-3, one would have F_gr∼ 3.5 × 10^-2 N. F_gr would be by an order of magnitude larger than the naive estimate and corresponds to a reduction factor 10^-2, which corresponds to the upper bound for Δ G/G. Maybe the combined effects of the Sun and Earth could explain the fluctuations of G.

2.5. The upper bound for the strength of the magnetic field of monopole flux tube equals to the strength of the "endogenous" magnetic field

By using scaling arguments, one can deduce an upper bound for y_max for the Earth and therefore for the maximum value B_max of the Earth's magnetic field by starting from the Sun-Earth system with y_max(S,E)∼ .25 and from the proportionally y_max ∝ (F_gr/L²)^1/5, where L is the length of the monopole flux tube.

1. In the estimate the F_gr(Sun,Earth) is replaced with the force between Earth and a mass blob with the density of water ρ_w=10³ kg/m³ with a volume Λ_gr³(E) and having mass m(Λ_gr)=ρ_wΛ_gr(E)³ .

   This gives m(Λ_gr)∼ .75× 10²³m_p. F_gr is scaled down by the factor M_S/m(Λ_gr). From M_S/m_p= 1.189× 10⁵⁷ one has M_S/m(Λ_gr)= 1.59× 10²⁴.

2. In the estimate F_rad(Sun) is replaced by that for the Earth. The radiation force satisfies F_rad ∝ L². Assume that L= R_E holds true at the surface of the Earth. The scaling factor for F_rad is (R_E/AU)², where one has AU/R_E∼ .235× 10⁵.
3. The overall scaling factor in y_max(S,E)→ y_max(E) is (M_S/m(Λ_gr))^-1/5× (AU/R_E)^2/5. The outcome is y_max= .72× 10^-3. This gives B_max= 1.87× 10^-4 Tesla which corresponds to .187 Gauss. The strength for the Earth's magnetic field varies in the range .25-.65 Gauss. Amazingly, the empirical estimate for the strength of the "endogenous" magnetic field at monopole flux tubes is .2 Gauss!
4. The upper y_max(P)/y_max(E) scales like (R_E/R_P)^4/5: there is no dependence on Λ_gr. The planetary Bohr model inspired by the model of Nottale predicts y_max(P)/y_max(E)∼ 2.3 for Mercury. For outer planets the prediction is y_max(P)/y_max(E)∼ (1/n)^8/5, n=1,2,.. so that the strength of the "endogenous" magnetic field would weaken.
5. Jupiter is the largest planet with equatorial radius R_P= 11.2 R_E. Its surface density is ρ∼ xρ_w, x=2× 10^-4. This gives y_max(P)/y_max(E)∼ (R_E/R_J)^4/5× x^1/5 ∼ .026 for the endogenous magnetic field of Jupiter. The strength of Jupiter's total magnetic field, expected to be stronger than the endogenous magnetic field, is 2× 10⁴ times that of the Earth: there is a difference of 6 orders of magnitude.

One can argue that the model involves numerical constants of order unity. Since y_max is expressible as a fifth root, they do not have any significance. It seems that by applying these arguments Sun-planet pairs and planets could give very powerful constraints on the endogneous magnetic field strengths involved.

See the article Allais effect again 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.