Could expolanet K2-18b serve as a seat of life in TGD Universe?

I have just developed a model for the evolution of geology and biology of Earth and this leads to a criterion for whether life can evolve on the planet (or moon) (see this). The criterion relies heavily on new physics predicted by TGD. The margin is very narrow. The criterion is rather tight and not satisfied for planets with too large Schwartschild radius to radius, for instance giant gas planets of the Earth.

1. The p-adic transition k=139→ k=137 from ordinary atomic physics to scaled down atomic physics (for which Mills has found evidence), having 4 times higher atomic binding energy scale than ordinary atomic physics, would reduce the atomic radius by factor 1/2 and increase the density by factor 8. This transition would induce scaling of the radius of Earth by factor 1/2 and subsequent Cambrian Explosion in which it increases by factor 2. This transition would bring life from underground oceans to the surface of the Earth.
2. The liberated atomic and gravitational binding energies make it possible in the case of Earth to throw out a surface layer condensing to form the Moon and metabolic energy burst generating dark atoms, analogous to Rydberg atoms with very large size, making possible large scale quantum coherence inside Earth. This generates p-Adic length scales, which correspond to biologically important scales. Large scale quantum coherence makes possible the evolution of life in the interior of the Earth. The condition that the CE in which expansion to the original radius occurs, can take place requires that gravitational binding energy per proton is larger than the atomic binding energy. This gives for the lower bound of atomic weight A as A>.3 which is satisfied.

The recently found exoplanet K2-18b is regarded as a candidate for a seat of life. In particular, there are indications that it has water at its surface. Its distance is 124 light years. Its radius and mass are R=2.61R_E and M= 8.6M_E. This gives r_s/R= 8.6/2.61∼ 3.3. The condition for A in the case of the Earth is scaled up from A>.3 to estimate A>.99 satisfied already for hydrogen atoms. K2-18b would be just at the border line but the condition making possible the expansion and burst of life to the surface of K2-18b, would be satisfied.

See the article Could the notions of quantum geology and quantum biology make sense? 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.

Has solar system lost two planets or is the standard model for the formation of the solar system totally wrong?

Sabine Hossenfelder (see this) told about a possible solution of a problem plaguing the standard model of the solar system. The model cannot explain the formation of planets as a gravitational condensation of a proto disk. The narrative discussed by Sabine is that actually 2 additional planets would have formed but would have been lost later due to collisions of the planets.

TGD suggests an alternative solution to the problem. Instead of two planets missing from the model, the entire view about the formation of planets by gravitational condensation from the primordial matter disk would be wrong. The TGD proposal is that the planets were formed in explosions throwing out a surface layer of the Sun. There is an obvious analogy with supernova explosions (see for instance this, this and this).

This kind of explosion could have also led to the formation of the moons of the Earth and Mars.

1. It is now known that the Moon consists of same stuff as the Earth, which strongly disfavors the earlier model, which assumes that Moon was formed as a planet, christened as Theia, having a mass about mass of Mars collided with the Earth and threw out mass that condensed to form the Moon (see this).
2. By taking the formation of Moon and the mysterious Cambrian explosion in which photosynthesizing multicellular life suddenly popped up out of nowhere, as starting points, one ends up to a rather detailed quantum view of the geological and biological evolution of the Earth (see this).
3. The formation of the Moon would be associated with the contraction of the radius of the Earth by factor 1/2 about 4.5 Gy ago. Much later an expansion of radius by factor 2 would have given rise to Cambrian Explosion (CE) .5 Gy ago. Life would have evolved in underground oceans and bursted to the surface in CE.

There are several questions to be answered.

1. The energetics of the expansion is not possible in the standard physics. How metabolism and evolution of photo-synthesizing multicellular life were possible in underground oceans? How were the underground oceans possible in the first place? TGD based new physics suggests answers to these questions.
2. p-Adic length scale hypothesis applied in condensed matter scales makes the model quantitative. A crucial step would have been the reduction of atomic radius by factor 1/2. There is evidence for this kind of transition in lab scale (experiments of Mills (see this) and Holmlid (see this). The liberated atomic binding energy makes possible the formation of the Moon and also provides the metabolic energy making possible the formation of quantum coherent large h_eff phases even in the scale of the Earth.
3. The large scale quantum entanglement reduces the number of translational degrees of freedom and makes possible low pressure and temperature essential for life. Pollack effect is also an essential aspect of the model. This could make possible the evolution of life in underground oceans or water reservoirs under paradize-like conditions in the womb of Mother Gaia.

This kind of model could apply also to the formation of planets by explosions throwing out a surface layer of the Sun and even to supernova explosions. The physics in the interior of the Sun could be completely different from the standard view.

1. I have already earlier proposed a model for solar wind and solar energy production, which would not be based on fusion in the solar core but to a transformation of nuclei of M₈₉ hadron physics with mass scale by a factor 512 higher than ordinary hadron mass scale to ordinary hadrons. The unexpected strange features of quark gluon plasma provide evidence for M₈₉ hadron physics (see this).
2. The model suggests that the interior of the Sun, about which we have only speculations, is actually more analogous to a huge living cell rather than a superhot hell inside which hot fusion takes place. See (see this).

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.

About the TGD counterparts of blackhole entropy and temperature

Gyanprakash Raj asked about the TGD view of blackhole entropy. In particular, does TGD predict blackhole entropy excess predicted by various models of blackhole trying to understand blackhole information paradox?

TGD forces us to give up the standard view of blackholes as systems having mass concentrated at a single point. The QFT limit of TGD replaces the topologically extremely complex space-time surface with a single region of M⁴ made slightly curved.

1. Outside the horizon, the blackhole-like object (BH) would be like an ordinary blackhole. Inside BH the description as a volume filling flux tube spaghetti, giving rise to maximal density, would be more appropriate.
2. For the TGD counterparts of the ordinary blackholes the flux tube would have thickness of nucleus size scale but an entire hierarchy corresponding to predicted hierarchy of hadron physics labelled by ordinary and Gaussian Mersenne primes is highly suggestive (see this). The difference between stars and blackholes would not be so dramatic as in GRT.

In TGD, the formulas for BH entropy predict dramatic results if ordinary Planck constant is replaced by gravitational Planck constant.

1. The standard blackhole entropy is extremely small. It is proportional to 1/ℏ and if ℏ is replaced with its gravitational counterpart ℏ_gr it becomes even smaller.
2. The standard blackhole temperature is proportional to ℏ and increases equally dramatically. The explanation would be gravitational quantum coherence which increases the geometric pixel proportional to Planck length squared and increases the energy scale.

Just for fun one can look for the standard formulas for S_B and T_B in the TGD framework.

Consider first the blackhole entropy.

1. Blackhole entropy S_B is essentially the area A of black hole divided by the area unit l_P² propto ℏG:

   S_B propto A/l_P² .

2. Suppose one replaces ℏ with gravitational Planck constant

   ℏ_gr= GMm/β₀ = r_Sm/2β₀ .

   Here the mass m would be naturally the mass of the nucleon characterizing monopole flux tubes of spaghetti as gravitationally dark giant nuclei.

3. This scales up the l_P² l_P²→(r_sm/2β₀*ℏ)l_P² = (Λ_gr/λ)l_P², where Λ_gr=r_s/2β₀ is mass independent gravitational Compton length (Equivalence Principle). λ is the ordinary Compton length.
4. β₀ is a velocity parameter whose interpretation I have finally understood. TGD is distinguished from GRT in that it allows flat warped space-time surfaces for which light velocity c in M⁴ is reduced to β₀. See (see this) .
5. The black hole entropy is scaled dramatically downwards so that one cannot speak of excess entropy. One could say that the scaling of Compton length to gravitational one increases the size of the pixel defining the bit. The interpretation of small entropy could be in terms of gravitational quantum coherence. A BH-like object would be an extremely ordered quantum coherent system, totally unlike the standard BH. Also the centers of the stars could be these kinds of objects.

What about blackhole temperature?

1. The blackhole temperature is given by T_B= ℏ/(8πr_s) and is extremely low.
2. In the replacement ℏ→ℏ_gr , T_B would be replaced by

   T_B= m/8πβ₀, where m is the nucleon mass.

3. For β₀=1, one one would have T_B ∼ 37.4 MeV. However, the Nottale's Bohr orbit model for planets predicts for the Sun the value β₀ ∼ 2^-11. This would give

   T_B= 79m_p ,

   which is not far from the mass of Z boson 85.7 m_p, which would correspond to M₈₉ hadron physics TGD indeed predicts that solar wind and solar energy production is due to the decay of M₈₉ hadrons (basically nucleons) at the surface of the Sun. The mass of the M₈₉ pion is 512 times that of the ordinary pion and equals 71.7 GeV.

4. Could one think of detecting gamma radiation from the Sun with this energy? Note that the decay of M₈₉ would produce gamma rays with energy 39.5 GeV. There is indeed a mysterious gamma ray emission from the Sun around 40 GeV energy (see this).

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.

About the energetics of the proposed compression and expansion of Earth

One should also understand the energetics of compression and expansion. Under what conditions these transitions are possible? Gravitational and atomic binding energies are involved. Gravitational binding energies per atom are proportional to the ratio r_s/R_P for the planet. The binding energy liberated in the transition k=139→ 137 is independent of planetary parameters. In the case of Earth, this transition should provide the energy making possible formation of the Moon and the proposed formation of Rydberg atoms making possible large scale quantum coherence.

One can ask whether the transition is possible for all planets and whether the Earth and Venus, with almost the same value of r_s/r_P, are in a special position. For large values of r_s/r_P the electric binding energy needed for the formation of a moon might be too large. r_s/r_P is indeed large for Jupiter and Saturn which suggests that the transition k=139→ 137 essential for the emergence of life and for the formation of the Moon cannot reduce the radius by factor 1/2. The mechanism for the formation of moons must be different. For small values of r_s/r_P electromagnetic binding energy would be more than needed. A rough estimate for r_s/R is as r_s/R∼ (R/R_E)² (r_s(E)/r_E) and decreases with the size of the object.

Consider next estimates for the changes of the gravitational and electric binding energies per atom. For simplicity, restrict the consideration to the case of the Earth first.

1. The gravitational binding energy per atom with mass number A increases in the transition R_E→ R_E/2.

   Δ E_gr=(r_s/2R_E) A m_p ∼ A × 3.14 ~eV .

2. The change Δ E_B of the binding energy in the transition k=139→ 137 can be estimated by using the expression for the ground state binding energy of atom with nuclear charge Z for k=139 assigned for ordinary atoms

   E_B(139)= Z² ×α_em²/8m_e ∼ Z² ×13.6 eV .

   One has E_B(137)= 4E_B(139) so that the increase of the binding energy is

   Δ E_B= 3E_B(139)∼ 3Z² ×13.6 ~eV .

   From Z≤ A/2 one has

   Δ E_B≤ A²× (3/4)× 13.6 ∼ ~eV

3. The condition Δ E_gr= Δ E_B gives a lower bound A≥ .3 .

   This condition is true for all atoms in the case of Earth and there is also surplus energy to throw out a layer forming the Moon.

For a general planet, the lower bound for A scales as the ratio x_P=(r_s/r_P)/(r_s/R_E). The values of x_P for Venus Mercury and Mars (.85,0.14 .20). It has been proposed that Venus has had a moon but has lost it. Also the nearness of the Sun is unfavourable for having a moon. The formation of the moon could have led to a compression of the Venus and if the life evolved in the interior it would not have survived at the surface after the expansion since the atmosphere (95 percent CO₂ and 3.5 percent nitrogen) has temperature of 467 ^_ºC and pressure, which is 93 times that on the Earth.

For the gas giants Jupiter resp. Saturnus with ratio x_J∼ 29.0 resp. x_s∼ 10 the lower bound for A is 7.7 resp. 3.3. Moon resp. Titan has x_J∼ .07 resp. x_T∼ .056.

See the article Could the notions of quantum geology and quantum biology make sense? 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.

Challenging the standard view of neutrinos

Marko Manninen sent me a highly interesting link to the work of Prof. Anca Tureanu (see this), who challenges the prevailing standard physics view of neutrinos (see this).

Why the neutrino physics goes wrong?

Also in my opinion, the theoretical physics picture of neutrinos is wrong.

1. Both neutrinos and quarks mix: we talk about CKM mixing. Neutrinos are no different from d-quarks in this respect. The mixing model for neutrinos coming from the Sun is in serious trouble. It assumes resonant mixing inside Sun and this is a completely ad hoc feature. This, along with many other anomalies, calls into question the entire view of the Sun's nuclear physics, on which the repeated failed attempts to build hot fusion reactors are based (see this). Strictly speaking, both U and D quarks as well as charged leptons and neutrinos mix: the difference in mixing corresponds to CKM mixing. What mixing is, is a complete mystery in the Standard Model.

   In TGD, mixing is reduced to topological mixing between different topologies of 2-dimensional parton surfaces (see for instance this). A sphere, a torus, and a sphere with 2 handles define the relevant parton topologies. For example, a torus collapses into a sphere in a mixing and a quantum state is a superposition of different topologies. TGD explains why there are 3 generations (why there couldn't be 3 handles, for example) and p-adic thermodynamics correctly predicts masses for different generations. Higher generations would be many particle systems of handles with continuum mass spectrum.

2. One problem is whether neutrinos are massless or not. There is strong evidence for their massivation and in TGD the masses can be predicted by p-adic thermodynamics (see this, this, this, this and this).

   However, a right-handed neutrino has one exactly massless mode (see this) and this), which is color singlet but also an infinite number of colored modes like other fermions which are associated with color singlet physical states. Color confinement therefore applies also to leptons. The new view of color leads to the prediction of a hierarchy of copies of Standard Model physics (see this). There is already support for this prediction.

   The problem with masses is more general: also quarks are effectively massless in quark-gluon plasma but massive in initial and final states. The concept of quark-gluon plasma seems to be a much more general notion than believed. The proper understanding of this notion could allow us to get out from the confines of QCD and the standard model. TGD indeed leads to a new view of what happens in particle reactions and generalizes the quark-gluon-plasma state to all particles (see this).

3. There is also the problem of the inert neutrino. It begins to be clear that there is no such thing as an inert neutrino. But the observations require something new to explain the observations. The observations are explained if neutrinos can be in a "dark" h_eff> h states (see this). Similar darkstate for protons, playhing a key role in TGD based quantum biology, explains the anomalous finding that the life-tme of a neutron depends on the way it is measured (see this).

The claims of Anca Tureanu

I looked at Anca Tureanu's article (see this). In the article, Tureanu claims that there is a logical contradiction in neutrino physics.

1. The reaction rates are calculated by considering incoming and outgoing neutrinos as mass eigenstates. In contrast, in neutrino mixing observed in laboratory experiments, quantum coherent superpositions of neutrino generations of different masses are assumed in the model of mixing. The model can be tested in laboratory experiments.

   The mixing model is applied to the solar neutrinos inside the Sun. One has to make a very ad hoc assumption about a resonance arising in the interaction with the environment (low energy neutrinos interact extremely weakly). Quarks are also mixed in incoming and outgoing states, but they are assumed to be eigenstates of mass. Note that we cannot study the possible dynamic mixing of quarks in the laboratory.

2. Can neutrino states with different masses be in quantum superposition? Or do they have to be massless for this to be possible? In what sense would they be massive? Tureanu proposes that neutrinos are massless but that in some sense also massive.

   The proposal is that the phenomenon is analogous to birefringence, which occurs in an insulator, where the dielectric constant for photons coming in perpendicular directions is different. The velocity of propagation is light speed c_#< c as in the case of a massive particle. The different polarizations of the incoming light are refracted differently because the speeds of light are different. The light beam splits into two beams travelling in different directions. In birefringence, the polarizations move at speeds v₁<c and v₂<c. In this sense there is a superposition of photons with different masses.

   What about neutrinos? Instead of two polarizations for neutrinos, there would be 3 different generations moving at different speeds v₁, v₂, v₃ <c in a substance that would be analogous to a birefringent substance. This would give them an effective mass. The polarization direction would be replaced by mass. Now there would be no refraction.

The basic claim of Anca Tureanu and the notion of warping

How does this relate to TGD?

1. One of the fundamental differences between TGD and GRT are warped 4-surfaces, which are gravitationally and electroweak vacuums but for which the speed of light c_# is less than c (see this). The surfaces are analogous to a thin metal plate that is unstable and vibrates, but does not stretch. This means that the light signals along the surface propagate more slowly because the distance between two points is longer.
2. The simplest example of a warped (and therefore flat) space-time surface is obtained by considering a geodesic circle of CP₂ with radius R and angle coordinate Φ. Denote the Minkowski coordinates of M⁴ with m^k and the coordinates of space-time surface X⁴ by x^α. The 4-surface is defined as a map X⁴ → H=M⁴× CP₂ given by (m^k= δ^k_αx^α, Φ= ω x⁰), where k=(ω,0,0,0) is time-like vector. The time-like geodesic of M⁴ is mapped to a light-like geodesic of H. The induced metric is g_αβ ↔ (1-R²ω²,-1,-1,-1) =((c_#/c)²,-1,-1,-1). The light velocity is reduced to c_#/c=(g_tt)^1/2= (1-R²ω²)^1/2. Note that Lorentz transformations produce additional solutions.

   The square of M⁴ projection of the 4-velocity dm^k/dx⁰ equals constant R²ω² just as for a massive particle. Therefore warping has two interpretations. Particles are massless in the induced metric of X⁴. They are also massless in the metric of H but massive in the metric of M⁴.

   This generalizes from the level of flat space-time surfaces to the level of Hamilton-Jacobi structures (see this) and does not need to be limited to flat 4-surfaces.

3. There is actually empirical evidence for the warping from neutrino physics. In the case of SN1987A, the neutrinos arrived in two pulses (see this). I explained this using different warpings of the space-time sheets along which the neutrinos of pulses arrived. Quite recently, it turned out that warping also provides an elegant model for the Allais effect.
4. Ordinary refraction for electromagnetic waves would occur at the interface of two regions with different c_#. The phenomenon would be completely general and also occur for fermions (in TGD all particles are composed of fundamental fermions). In particular, massless neutrinos.

   In birefringence, different spin directions would be associated with different c_# values. Could there be substances, where this would happen for fermions as well. Polarizations would correspond to different helicities (M⁴ chiralities) correlating with CP₂ chirality by fermion number conservation.

5. It however seems that in some sense neutrinos are massless and in some sense massive. This is a paradox. In TGD this is true for all particles. Initial and final many particle states are 8-D and particle states in interaction volume are 4-D.

   In the interaction volume the system is a 4-D surface and fermions fulfill the analogy of the 4-D massless Dirac equation. From the initial and final states of scattering fermions fulfill the 8-D Dirac equation and are massless in the 8-D sense but massive in the 4-D sense. This would generalize the notions of hadron phase and quark-gluon plasma phase so that it applies to all particles. Hadrons appear in the 8-D initial and final states and quarks appear in the 4-D interacting states. Color confinement occurs for both quarks and leptons and there is an infinite hierarchy of standard model physics since there is infinite hierarchy of color partial waves in CP₂ for both quarks and leptons.

6. The 4-surfaces associated with fermions would be massless but characterized by the reduced speed of light c_#. Like photons, they would have an effective mass in the interaction volume. Warping gives a precise formulation of the intuition that fermions, in particular neutrinos, are massless in both H and X⁴ but massive in M⁴. Different neutrinos in 4-D states would be associated with different values of c_#: this would be the counterpart for M⁴ massivation. p-Adic thermodynamics allows us to calculate the M⁴ masses as thermodynamic expectation values (see this, this, this, this and this).

Particle massivation and warping

The light-like geodesics of H assigned with the fermion line at the partonic orbit provides a model for the M⁴ mass squared of particles given as m²= k²R²ω². This does not require that the space-time surface is a warped flat 4-surface everywhere and thus conforms with the idea that warped Hamilton-Jacobi structures for which M⁴ and CP₂ degrees of freedom are coupled. However, the information about the warping would be coded for the Bohr orbits of the particles by the light-like geodesics at partonic orbits.

1. If ω is identified as a Compton frequency for particle with mass m so that one has k= ℏ_eff/R and m= ℏ_effω giving c_#²= 1-R²ω²= 1-R²m²/ℏ_eff²= 1-R²/λ_c², where λ_c is the Compton length for h_eff. This predicts the value of c_#== β₀ once particle mass and h_eff are known.
2. The signature of the metric remains Minkowskian for ℏ_eff/m>R. For h_eff=h this requires that the particle mass is below CP₂ mass. The stringy mass squared spectrum predicted by generalized super conformal symmetry allows larger mass and for these masses the value of h_eff>h is required to avoid tachyonicity.
3. One can consider the situation for the electric Planck constant ℏ_em= Qq/β₀ and gravitational Planck constant ℏ_gr= r_sm/2β₀. In these cases the value of c_# is completely fixed. In the electric case, one has c_#²= 1-R²m²c_#²/Q²q² giving c_#/c= (1/(1+R²m²/Q²q²))^1/2 and c_# depends on the particle mass. The gravitational case gives c_#/c= (1/(1+4R²/r_s²))^1/2. There is no dependence on the mass m: this reflects the Equivalence Principle.

See the article Comparing the S-matrix descriptions of fundamental interactions provided by standard model and 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.

Could the notions of quantum geology and quantum biology make sense?

I have carried out a considerable work to fuse the existing TGD inspired ideas about the geological and biological   evolution of life  on Earth to a single coherent whole.  The strategy is to identify weak points of the existing vision and here the language models provide an extremely powerful tool.

 The evolution of life on Earth encountered several bottlenecks. In the  beginning, the generation of nitrogen atoms from N₂ molecules, having a very large binding energy, was made possible by the presence of volcanoes but soon it became ineffective.  Bacteria invented the nitrogenase enzyme for which oxygen was a poison.  Later  bacteria invented oxygen breathing and photosynthesis releasing oxygen as a waste. This led to the Great Oxygenation Event meaning a catastrophe destroying most bacteria. Ways to avoid   the destruction of nitrogenase were invented.

The sudden emergence of highly evolved multicellular life forms in Cambrian Explosion (CE)  with almost no fossils intermediate between them and monocellulars is an unsolved mystery.  It served as  the starting point of the development of  the TGD based view of biological and geological evolution of Earth. There is evidence that the continents of the Earth fit nicely together along the boundaries if the radius of the Earth is taken 1/2 of the recent radius. This inspires the proposal that CE involved a rapid expansion of the radius of Earth in a geologically short time interval and the multicellular life forms evolved in underground oceans before the CE.

This leads to what might be called quantum geology or rather, a combination of quantum geology and quantum biology.

1. The contraction of the Earth radius by factor 1/2 implies the increase of the density by factor 8. In the framework of standard model physics  implies a huge increase of pressure and temperature and life could not have evolved in underground water reservoirs  if they could be even  present.  Large scale quantum coherence could however change the situation.
2.  The liberated gravitational and  atomic binding energies would  have served as a metabolic energy  increasing the value of h_eff (a measure for complexity) and  given rise to phases of matter  labelled by biologically important p-adic length scales.  Assuming  that repulsive Coulomb energies decreased and that the  allowed p-adic integers k  are primes, a simple scaling argument implies that biologically relevant p-adic length scales characterize the quantum coherence regions space-time sheets.

   The compression would have induced a Pollack effect, which transferred protons and possibly also  other alkali ions from the silicate (SiO₄^-4) lattice  of the mantle to the gravitational magnetic body of the Earth characterized by a huge value of gravitational Planck constant ℏ_gr so that the system became quantum coherent in astrophysical length scales. The dramatic reduction of the number of  translational degrees of freedom  implied that the pressure and temperature could remain in the physiological range and multicellular life could evolve in underground water reservoirs and emerge to the surface in Cambrian Explosion involving an expansion of the Earh radius by factor 2.

3.  p-Adic length scale hypothesis allows to make the picture quantitative. For   years ago, I considered  the possibility of a   phase transition reducing the p-adic size scale of atoms by factor 2. The p-adic length scale L(k=139) defining atomic size scale would have been reduced to L(137)=L(139)/2). This would have liberated a huge gravitational energy and thrown the surface layer out  giving rise to the formation of the Moon. The liberated gravitational and  atomic binding energies would  have served as a metabolic energy  increasing the value of h_eff (a measure for complexity) and  generated phases of matter  with long p-adic length scales.  Assuming  that repulsive Coulomb energies decreased and that the  allowed p-adic integers k  are primes, a simple scaling argument implies that biologically relevant p-adic length scales characterize the space-time sheets as quantum coherence regions.
4.   The presence of gravitational quantum coherence motivates quantum model for the Earth as an elastic ball based on quantum harmonic oscillator characterized by ℏ_gr coding Equivalence Principle and implying that the radii of harmonic oscillator states do not depend on the particle mass.

   The model suggests that the compression and expansion phases could have taken place in two steps. During the first step of the compression phase the particles of the upper mantle would have been transferred to   lower harmonic oscillator states. During the  second step this would have happened to the particles of the lower mantle.  One of the key questions is whether the oceans were at the surface of Earth before CE or not: also this question I try to answer in the sequel.

   This picture provides a qualitative understanding of the geological evolution, including formation of old mountains before the first step of contraction and emergence of plate tectonics after it. Also oceans could have emerged already in the first step. The model explains why the tectonic plates for the oceanic crust differ from those for the continental crust.

See the article Could the notions of quantum geology and quantum biology make sense? 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.

AI and TGD

Lian Sidorov, Ben Goertzel, Michael Levin, Matti Pitk&aul;nen, and Vasileios Basios, published a collective article entitled "At Play in the Fields of the Lord: On Goal Evolutionary Dynamics in Complex Adaptive Systems" in in Journal of Nonlocality (see this). I am grateful for the honour to be one of the authors.

The article was in a form of a panel discussion about various aspects of AI, in particular whether AI could be or become conscious. Lian Sidorov did a marvellous job in organizing the efforts of the authors. My own rather technical contribution was a separate article "AI and TGD". Using Claude, Lian prepared a layman version of "AI and TGD" with the title "TGD AI synthesis".

Here is the abstract of "AI and TGD".

Lian Sidoroff represented along series of questions related to AI, in particular conscious AI. In this article I discuss the general questions and the questions specific to TGD. TGD based view relies on TGD inspired theory of consciousness and quantum biology and the TGD based mechanism of quantum biology allow to imagine what conscious computers and networks witgh collective levels of consciousness might be.

The first building block of the vision is the view of space-time as a 4-surface in H=M⁴× CP₂ determined by holography = holomorphy (H-H) principle, which allows to solve classical theory exactly. The slight classical non-determinism forces to take Bohr orbit-like space-time surfaces as basic objects and the 4-D degrees of freedom related to non-determinism provide correlates of cognition.

Also the notion of gauge field generalizes. The notion of field body carrying phases of ordinary matter with a large value of effective Planck constant serving as a measure of algebraic complexity defining a kind of IQ. These phases behave like dark matter and are characterized by long range quantum coherence.

Number theoretical vision is a further notion and leads to a 4-D generalization of Langlands duality in which numbers in very general sense and even mathematical proofs have space-time surfaces as geometric representations. p-Adic number fields generalize to their function field counterparts. Also Boolean logic has fermionic representation.

Zero energy ontology (ZEO), which allows to solve the quantum measurement problem extends quantum measurement theory to a theory of consciousness and allows to understand the relationship between geometric time and subjective time. Macroscopic quantum coherence, Pollack effect and a universal realization of genetic code based on icosa tetrahedral tessellation of hyperbolic 3-space H³ are central notions of the TGD inspired quantum biology and the conjecture is that also conscious computers could be based on them.

See the article AI and 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.

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.