About long range electromagnetic quantum coherence in TGD Universe

The focus of TGD inspired quantum biology has been hitherto in long range quantum gravitational coherence characterized by quantum gravitational Planck constant introduced by Nottale. The notion of gravitational Planck constant however generalizes also to other classical fields, in particular electric fields and one can define electromagnetic Planck constant. DNA, cells, and the Earth's surface carry negative charge. In this article, the possible presence of the long range quantum coherence in these systems is considered. Also a model for the interaction between living matter and computers is discussed.

See the article About long range electromagnetic quantum coherence in TGD Universe or the chapter with the same title.

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

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

A possible mechanism of radiative energy transfer from the Earth's core to underground oceans near the surface of Earth

The recent observations (see this) strongly suggest that there is an ancient seabed on top of the Earth's core, and there are also mountains with a height of about 10 km. The proposed model, in which convection moves the sea floor to the region above the mantle, is probably correct.

This finding combined with the discovery of the so-called superionic ice (see this), which could exist above the Earth's core, allows to develop a proposal for a mechanism of metabolic energy transfer from the Earth's core to the underground oceans near the surface of Earth. This would make possible the development of photosynthesizing life forms in underground oceans. The generalization of the Pollack effect (see this and this) would play a key role in the mechanism.

Ultralow velocity zones

The following abstract of the article (see this) published by a group led by Dr. Samantha Hansen gives an overall view of what has been observed.

Ultralow velocity zones (ULVZs) are the most anomalous structures within the Earth s interior; however, given the wide range of associated characteristics (thickness and composition) reported by previous studies, the origins of ULVZs have been debated for decades. Using a recently developed seismic analysis approach, we find widespread, variable ULVZs along the core-mantle boundary (CMB) beneath a largely unsampled portion of the Southern Hemisphere. Our study region is not beneath current or recent subduction zones, but our mantle convection simulations demonstrate how heterogeneous accumulations of previously subducted materials could form on the CMB and explain our seismic observations. We further show that subducted materials can be globally distributed throughout the lowermost mantle with variable concentrations. These subducted materials, advected along the CMB, can provide an explanation for the distribution and range of reported ULVZ properties.

The so called S waves (see this) are transversal acoustic waves caused by the shear force parallel to the propagation. This force is proportional to viscosity and is negligible in liquids but much larger in solid phase waves reflected at mantle-core boundary. The core of Earth is in a liquid phase. Therefore sound waves from the surface of Earth are reflected back at the mantle-core boundary.

This makes it possible to deduce information from the structure of the mantle-core boundary and it has turned out that it has a highly complex structure. First of all, these waves propagate very slowly. This allows us to conclude that there is a relatively thin layer with a high density, which could consist of the same material as the seabed. This layer contains mountains with heights of order 10 km.

The TGD inspired view of the evolution life, inspired by the Cambrian Explosion and TGD based view of cosmology, is that photosynthesizing life evolved in underground oceans and that the expansion of the Earth radius by about factor 2 bursted these oceans to the surface of Earth in Cambrian Explosion (see this, this,this,this, and this).

The existence of an underground ocean immediately above the mantle is impossible due to the high pressure and temperature so that the convection remains the natural explanation for the presence of seabed.

The second objection is that life in the underground oceans is not possible because solar energy needed by photosynthesis is not available. How could photosynthesis have developed in the underground oceans? The key observation is that energies of the photons of thermal radiation coming from the core are of the same order as the metabolic energy currency with nominal value of .5 eV: could this radiation have served as a source of metabolic energy.

How would this energy be transferred? The Pollack effect (see this and this) and its reversal, whose TGD based understanding (see this, this, this,this, and this) has increased considerably during this year, could provide a fast energy transfer mechanism, but in its standard form the Pollack effect requires liquid water. Could the so-called superionic ice (see this and this), which has been speculated to be found even near the mantle of Earth, make possible the analogy of the Pollack effect?

Ordinary water cannot survive near mantle

Although it is obvious that ordinary liquid water cannot exist at temperatures and pressures prevailing near the mantle, it is useful to look at the situation more quantitatively.

In mechanical equilibrium, pressure gradient and the gravitational force, expressible in terms of the gradient of gravitational potential, cancel each other in good approximation. One can estimate the change of pressure as Δ p = ρ Δ Φ_gr= ρ GMΔ (1/R). The equation of state allows an estimate for Δ T.

Pressure is estimated to increase from 100 MPa at the surface of the Earth to 139 GPa above the mantle, that is by a factor 1000. Temperature, converted to thermal energy E=kT, is estimated to increase from .03 eV→ to 0.42 eV. The increase is by a factor of 10. Ordinary water cannot survive in this kind of environment so that underground water is possible only sufficiently near to the surface of Earth.

Could one imagine a phase of water allowing the analog of Pollack effect so that the transformation of protons to dark protons at the gravitational MB could make it possible to transfer metabolic energy to the higher heights, where underground liquid water can exist. This would have made possible the development of photosynthesizing life and would also solve the "faint Sun" paradox (see this) meaning that the solar energy feed was not enough for the metabolic needs of life at the surface of Earth.

Pollack effect for superionic water and metabolic energy feed from the core of Earth

Superionic ice (see this and this) existing at extreme pressures. The density of superionic ice is slightly less than 4 times the density of ordinary ice. In superionic ice O^2- ions form a lattice whereas H⁺ ions float freely. This phase is conductor with H⁺ ions serving as charge carriers. Superionic ice is proposed to appear in the mantles of giant planets such as Uranus and Neptune and I have proposed the possibility that it could occur in the Earth's mantle (see this and this).

Could water appear as superionic ice above the Earth's core and allow Pollack effect and its reversal so that gravitational flux tubes would carry dark protons? Could dark photons emitted in the reverse Polack effect transfer the energy along gravitational flux tubes to the underground oceans near the surface of the Earth?

Let's assume that there exists superionic ice above the mantle.

1. Could the radiation from the core kick part of the protons of the superionic water to the gravitational magnetic body? The gravitational binding energy of protons at the surface of Earth is about .5 eV and now roughly by a factor 4 larger, that is 2 eV, at the top of the mantle. At the gravitational magnetic flux tubes the reduction of gravitational binding energy is therefore below 2 eV. The temperature of the core corresponds to the metabolic energy currency of about .4 eV so that the radiation could have played the same role as the solar radiation in photosynthesis.
2. If the reverse Pollack effect occurs, dark photons are emitted and they propagate to the MBs of water volumes near the surface of Earth and could provide energy for photosynthesis. Also time reversal can occur for the water near the surface of Earth and the proton can gain the energy required by darkness by emitting a negative energy dark photon propagating to the MB near the mantle. I have called this mechanism remote metabolism or quantum credict card and asked whether it could play a key role also in the ordinary biology.
3. If the temperatures of the lower part of the mantle and the core are the same, the energy input from the core could feed protons to gravitational MB, maintain the superionic water phase and compensate for the energy loss due to the reverse Pollack effect. The transfer of energy near the earth's surface would take place at the speed of light and dissipation would be very small.
4. The number of ordinary-to-dark transitions of protons per unit time determines the energy flow to the MB and the energy flow to the uppermost layers of the mantle. In a steady state, this flow must be the same as the radiative heat flow from the core. This transfer rate is determined by the rate for the photon absorptions kicking protons to the MB. The energy flow of energy coming as radiation is proportional to T⁴.

See the article A possible mechanism of radiative energy transfer from the Earth’s core to underground oceans near the surface of Earth or the chapter Expanding Earth Hypothesis and Pre-Cambrian Earth.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this."https://tgdtheory.fi/tgdmaterials/curri.html">this.

Pollack Effect, Lightnings and Ball Lightnings

A TGD inspired model  for the ball lightning-like structures in silicon and for the real ball lightnings is developed. The model  relies on following assumptions. The TGD view  of space-time predicting fractality and inspiring the hypothesis that   biosphere could be regarded as a system analogous to neuronal membrane and that lightnings could be analogous to nerve pulses; the identification of  dark matter as phases with non-standard value of Planck constant allowing quantum coherence in arbitrarily long scales; the TGD view of quantum gravitation and its role in quantum biology; and the TGD inspired model of nerve pulse.

See the article Pollack Effect, Lightnings and Ball Lightnings or the chapter EEG and the structure of magnetosphere .

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.

Virtual touching of a virtual body part generates a real sensation of touching

This post was inspired by a highly interesting finding related to an experiment in which the subject person creates a virtual sensory input to a virtual hand that represents her own hand. The popular article is here and the original article "Phantom touch illusion, an unexpected phenomenological effect of tactile gating in the absence of tactile stimulation" of Pilacinski et al can be found here.

It was found that the virtual touching of the virtual hand creates a sensation in the corresponding body part of the subject person, say forearm. This occurs even if the person does not see the corresponding virtual body part. This suggests that more than visual cues are needed.

Consider first the TGD inspired view of sensory perception (see for instance this and a HREF= "https://tgdtheory.fi/pdfpool/emotions.pdf">this).

1. Sensory data at sensory organs is very fuzzy and the building up of sensory experience by pattern completion and recognition is almost a miracle. The process building sensory perception consisting of standard mental images must involve virtual sensory input to sensory organs, in particular eyes.
2. The sensory input would be communivated from sensory organ to cortex as dark photons (decaying to biophotons) with light velocity along flux tubes parallel to axons. From the cortex a signal to the MB would be sent. After that MB would make a guess about the final sensory perception very different from the actual sensory input. This guess must generate at sensory organs a diffuse sensory signal and must be compared with the diffuse sensory input.
3. This is achieved if the first guess generates a virtual sensory signal with a reversed arrow of time propagating to the sensory organs and becoming a diffuse sensory input at the sensory organs. The usual sensory processing in the brain would take place but in the opposite time direction. When the difference between virtual and real signal is small enough, the process stops.

   Note that the original model assumed that the virtual signal corresponds to the final percept but this is not the case for this variant of the model and ZEO becomes an absolutely essential element of the model.

4. At the next step, the virtual sensory signal would be compared with the real sensory input from the external world and the difference would be signalled via the cortex to MB. MB would make an improved guess. The iteration of this process would lead to sensory percept consisting of standardized mental images as pieces.
5. Dreams would be generated by a mere virtual sensory input coming from MB. Also imagination would rely on this process. Now the signals from the MB would not propagate to sensory organs but would stop at some higher level of hierarchy so that no real sensory experience would be generated.

It is known that intentional stimulation of (say) the skin by person himself creates a considerably weaker sensory signal than the simulation by an external input.

1. The reason for this would be savings in metabolic energy. There is no need to build intense sensory mental images if the stimulus is already known to be there. This would be achieved by sensing a virtual sensory input from the MB to the sensory organ, which would tend to cancel the real sensory input.
2. This happens also when one swims in a windy sea. When one returns to the beach, one experiences the sensation of being in the windy sea and the sensation can continue for quite a long time. The explanation is that the virtual sensory input from MB continues but is not cancelled by the real sensory input. Magnetic body would generate a compensating virtual sensory input tending to cancel the sensory input caused by the motion of biological body.
3. Correlational opponent processing seems to be a more general concept inspired by this phenomenon. Ron Blue has proposed in his correlational opponent-processing theory (see this) that the right and left hemisphere form opponents for each other creating opposite reactions. Magnetic body would tend to generate compensating effect cancelling the effect caused by the motion of biological body with respect to the MB to minimize metabolism. This would in general lead to a habituation.

Consider in this framework the situation in which a person induces virtual sensory input to a virtual body part. The mere intention about producing this virtual sensory input progates to MB which however believes that the sensory input is real (why this is the case?) and sends the compensating sensory input to the real body part. The situation is very much like swimming in a windy sea.

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.

Chronic pain as a sensory memory of pain

There was an interesting popular article related to the phenomenon of chronic pain as phantom pain. The article has title "Understanding that chronic back pain originates from within the brain could lead to quicker recovery, a new study finds". The original article "Reattribution to Mind-Brain Processes and Recovery From Chronic Back Pain A Secondary Analysis of a Randomized Clinical Trial" of Ashar et al can be found here.

It is known that for patients a chronic pain in the back, without actual problems in the back anymore, continues although the physiological reason for the pain is not present anymore. The proposal is that this pain originates in the brain.

The TGD interpretation is the same as in the case of phantom limb. The pain would not be imagined but would be real pain as a sensory memory of the pain, just as in the case of phantom limb. We indeed have sensory memories: long ago it was learned that the stimulation of parietal regions of the brain created sensory memories as direct experiences. The memory feats of some idiot savants are very probably based on sensory memories. Instead of a verbal representation, they have a direct sensory experience about say landscape or a music piece.

The view about memories provided by zero energy ontology is that they are in space-time where the original painful event occurred and involve a communication with the brain and body of the geometric past. This is essentially seeing in the direction of geometric time: time reflection takes place from an appropriate region of the brain or MB. Therapy might allow us to get rid of these sensorily painful memories in the same way as it allows us to get rid of psychologically painful memories.

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.

Quantitative support for the model of blackhole-like object as flux tube spaghetti

The TGD based model for blackhole-like object is as monopole flux tube spaghetti (see this) containing one proton per proton Compton length and filling the entire volume. There is no need to emphasize that the model means giving up the standard view of blackhole-like objects and that the model does not differ very much from the model for neutron stars.

Consider now the estimation of the total mass of the flux tube spaghetti.

1. Assuming additivity and neglecting self-gravitation, the total mass in units of m_p is M/m_p (here m_p≈ m_n is proton mass, the star would consist of neutrons).
2. Self gravitation for a spherically symmetric mass constant distribution inside sphere of radius R and given as ρ= M/Vol(R) created by the flux tube spaghetti gives to the stationary metric the deviation of g_tt from flat Minkowski metric is given by Δ g_tt = - Φ_gr, where one has

   Φ_gr (r)= 2G(2M(r)/r= (8π/3)×(GM/Vol(R)) r²= 2GM(r²/R³) .

   The gravitational potential energy of the mass distribution is in the Newtonian appproximation given by

   E_gr= -∫ρ(r)Φ_gr (r)dV=-6GM²/5R .

   For R= r_S= 2GM this gives

   E_gr=- 6GM²/10GM = -(3/5)M .

   Therefore the observed mass M_obs using m_p as a unit is given by

   M_obs=E_tot/m=(2/5) (M/m_p) .

3. Suppose that the flux radius of thickness R contains a single proton per length zR so that one proton fills the volume π× zR³. Suppose R corresponds to the proton Compton length L_p = h/m_p.

   Assume that h_eff ≠ h is possible so that L_p is scaled by y= h_eff/h. One would have

   L_p(h_eff)= y L_p .

4. The total mass M using m_p as unit and neglecting gravitational potential energy is given by the ratio of the volume V of the blackhole regarded as region of Minkowski space to the volume V_p taken by a single proton:

   M/m_p= V/V_p= (4/3z) × (r_S/L_p)³) y^{-3 .}

   Taking into account gravitational potential energy, one obtains

   M_obs/m= (2/5)(V/V_p)=(8/15z) × (r_S/L_p)³ y^{-3 .}

One can test the model for the Sun. One has M_S=2× 10³⁰ kg and r_S= 3 km. Proton has mass m_p= 1.6× 10^-27 kg and Compton length L_p= 1.3× 10^-15 m. Substituting the values to the above formula, one obtains (y,z)= (1,.992)≈ (1,1).

In the above formula M_obs/m on r.h.s decreases slightly in m_p→ m_n and 1/L_p³ on l.h.s increases slightly in m_p→ m_n. The changes of l.h.s and r.h.s are proportional to -ε × l.h.s and 3ε × r.h.s, where one has ε= (m_n-mp)/m_p&asymp: 1.811× 10^-3. This requires Δ (1/z) ≈-4ε (1/z) so that z=.992 is replaced with z_new=z(1+ 4ε)≈ .9992, which deviates from unity by -8× 10^-4.

The conclusion is that the simple flux tube model for h_eff=h and neutron taking a volume of Compton length, which is definitely different from the general relatistic model, is surprisingly realistic.

See the article Cosmic string model for the formation of galaxies and stars 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.

Ajatuksia sanasta jota on vaikea lausua

Rakkaus on sana, jota nykyisessä materialistisen tieteen hallitsemassa maailmassa on vaikea sanoa. Se tuntuu vain,... nololta. Ei se kuulu reaalimaailmaan, jossa taseet ovat töissä ja bisnes on bisnestä.

Rakkaus ei sovi nykytieteen, tai tarkemmin sanoen, kahdeksannentoista vuosisadan tieteen, maailmankuvaan, jossa maailman on deterministinen kone eikä ole sijaa tietoisuudella, vapaalle tahdolle eikä rakkaudelle.

Tässä vanhentuneessa maailmankuvassa me kuitenkin elämme, ainakin yhteiskunnan jäseninä, ja uskottelemme olevamme tämän determinismin täysin avuttomia uhreja. Yhteiskuntamme on tässä maailmankuvassa rakkaudeton kone ja meidän on alistuminen sen pieneksi rattaaksi. Ei voisi olla parempaa ilmaisua tälle uskolle kuin pääministerimme pakkomielteen omainen toistelu "On pakko!". Verohelpotukset rikkaille ja köyhät kyykkyyn. Perusteluksi on keksitty velka: sen lyhentäminen edellyttää tämän kaiken ja tämä kaikki on tietysti määrätty tapahtumaan jo alkuräjähdyksessä joten köyhän turha pullikoida.

Maailmankuvassamme on kuitenkin edellisen kanssa täysin ristiriitainen elementti: vulgaari-darwinimismi. Elämä nähdään armottomana olemassaolon taisteluna, jossa vahvempi voittaa, nopeat syövät hitaat, ja kaverille ei jätetä. Mutta eikötässä olekin ristiriita: miten ihmeessä tämä on mahdollista, jos yhteiskunta on tiedoton kone ja me sen mukana? Onko meillä sittenkin vapaa tahto, jos ei muuta niin ainakin jättää kaveri ilman?

Nyt mieleen tulee luvaton ajatus. Olisiko niin, että jotkut, ne jotka hallitsevat, tajuavat tämän ristiriidan aivan mainiosti. Mikä onkaan parempi tapa hallita kuin uskotella hallittaville että heillä ei lainkaan vapaata tahtoa: että he ovat vain pieniä rattaita isossa koneistossa. Toisaalta voi vapautua omantunnon vaivoista kun voi todeta olevansa vain pieni ratas suuressa koneistossa.

Ja tässä tullaankin persuihin. Hallituksessa on monia uusnatseja ja natsismin perusidea on että vahvoilla on oikeus ja jopa velvollisuus käyttää hyväkseen heikkoja. Tämän Nietche muotoili niin karskiksi filosofiaksi, ettei edes hänen oma mielenterveytensäkään ei sitä kestänyt. Empatiat pois politiikasta niinkuin Riikka Purra asian ilmaisee! Hallituksen irtisanoutuminen rasismista ja uusnatsismista oli puhdasta poliittista kosmetiikkaa. Koko hallitusohjelma on konkreettista yli-ihmis-ideologian toteuttamista. Enkä epäile, etteikö taustalla olisi tietoinen ajatus siitä että vahvemmmilla oikeus on nujertaa heikommat. Sitä ei tietysti voi ääneen sanoa, joten on kätevää vedota taloudelliseen determinismiin.

Mutta miten sitten rakkaus voisi auttaa tässä? Tiedämme, että rakkaus saa kirjaimellisesti ihmeitä aikaan. Se voi antaa uuden suunnan kokonaiselle ihmiselämälle. Ja voidaanko esimerkiksi yhteiskuntien käsittämättömän nopea toipuminen sotien tuottamasta täydellisestä hävityksestä ymmärtää materialistisessa kuvassa? Voisiko rakkaus olla todellinen vaikuttaja?

Nykyistä talouselämää luonnehtii rakkaudettomuus: kaikkialla vallitsee raaka kilpailu jossa vastustaja pyritään nujertamaan. Ei ole ystäviä, on vain liittolaisia. Luomme yhä uusia teknologiasia innovaatioita ja lopputuloksena on vain uusia ongelmia. Voisiko rakkaus auttaa?

Maailman uskontojen takana on oivallus rakkauden ainutlaatuisesta voimasta. Tieteessä esimerkiksi Einstein näki sen mysteerinä, jota emme ymmärrä. Mutta materialistinen nykytieteemme, joka on yhteiskuntafilosofiamme perusta ei halua rakkaudesta puhua, se vain sotkisi finanssi-teollisuuden yhtälöt. Ekonomistisessa maailmankuvassa on mahdotonta kuvitella, että rakkaus, joka rikkoisi tekisi mahdottoman mahdolliseksi rikkomalla determinismin pakkopaidan, voisi ratkaista yhteiskunnallisia ongelmia ja jopa pelastaa ihmiskunnan umpikujastaan johon materialistinen filosofia yhdistettynä vulgaaridarwinismiin on sen ajanut.

Kun esittää ekonomistille tai tieteentekijälle väitteen, että rakkaus voisi pelastaa sivilisaatiomme, on esitettävä myös tieteelliset perustelut. On kerrottava jotain oleellista siitä mitä rakkaus on tieteen näkökulmasta ja miten se kykenee vapauttamaan meidät determinismin. Tämä varmastikin vaatii tietoisuuden teorian ja sellainen on paraikaa kehittymässä: tosin YLEn uutiset eivät siitä ole kertoneet sanallakaan.

Ensimmäinen lohdullinen havainto on, että kvanttimekaniikka korvasi klassisen fysiikan determinismin tilastollisella determinismillä jo vuosisata sitten. Toinen lohdullinen havainto on että tilastollinen determinismi pätee vain tietyin edellytyksin. Skaaloissa, joissa kvanttikoherenssi vallitsee, ei tilastollinen determinismi pädekään ja maailma ei olekaan enää tiedoton kone vaan ennemminkin elävä ja tietoinen organismi.

Edelleen, kokeelliset havainnot jopa astrofysikaalisissa skaaloissa sekä kehittyvät tietoisuuden teoriat pakottavat kysymään onko kvanttikoherenssi vain atomaaristen systeemien ominaisuus vain onko se mahdollinen jopa elävän aineen tasolla?

Tekisikö kvanttikoherenssi mahdolliseksi elävälle aineelle uudelleen-luoda itseään ja ympärillä olevaa maailmaa? Jos vapaa tahto olisi jotain todellista niin myös etiikka ja moraali löytäisivät paikan maailmankuvassamme. Tietoiset olennot joutuisivat tällaisessa maailmankuvassa valitsemaan hyvän ja pahan välillä. Hyvät teot kasvattavat kvanttikoherenssia ja maailman ymmärrystä itsestään, pahat pienentävät sitä. Hyvät teot lisäävät rakkautta ja ne tehdään rakkauden motivoimina.

Voisiko siis rakkauden ohjaama vapaa tahto vaikuttaa jopa yhteiskuntamme tasolla? Kysymys saattaa kuulostaa maallikon korvissa hassulta: ilmeiseltähän tämä tuntuu. On kuitenkin muistettava, että tieteentekijä on dogmiensa vanki ja kykenee kyseenalaistamaan ne vain kun on ehdoton pakko (ja urakehitys ei vaarannu). Näyttää siltä, että tieteentekijät, joilla on papiston rooli nykymaailmassa, ovat avainasemassa. Jos haluamme pelastaa pallomme, on heidän pakko muuttaa dogmejaan. Pidetään siis peukkuja, aikaa ei ole paljon.

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.

Dirac and Bohr orbits

I received from Baba Ilya lyo Azza the following piece of text from Dirac. Since "Bohr orbit" appears in the text and I have used this word to  describe holography as  it is realized in TGD, I could not resist  the temptation to comment since Bohr orbit is such a word that colleagues cannot resist the temptation to label TGD as a childish  attempt to do theoretical physics by using some ancient notion.

“I want to emphasize the necessity for a sound mathematical basis for any fundamental physical theory. Any philosophical ideas that one may have play only a subordinate role. Unless such ideas have a mathematical basis they will be ineffective.

As an example of a philosophical idea without a precise mathematical basis I would like to mention Mach's principle. Einstein has stated that he was indebted to this principle in his line of thought which led him to general relativity. But I do not see how this could be. I do not see how the principle can be formulated in a sufficiently definite way to be of any value in the search for a precise physical theory.

One should keep the need for a sound mathematical basis dominating one's search for a new theory. Any physical or philosophical ideas that one has must be adjusted to fit the mathematics. Not the other way around.

The need for putting the mathematics first comes from its more rigid nature. One can tinker with one's physical or philosophical ideas to adapt them to fit the mathematics. But the mathematics cannot be tinkered with. It is subject to completely rigid rules and is harshly restricted by strict logic.

The reason I feel so strongly about the views expressed above is because of the success I have had with them in the past. My early research work, in the early 1920's, was based on Bohr orbits, and was completely unsuccessful. I was taking the Bohr orbits as physically real and trying to build up a mathematics for them. I worked hard on this problem…

One sees now how futile such work was. Heisenberg showed that one needed a completely new mathematics, involving non-commutative algebra. The Bohr orbits were an unsound physical concept and should not be used as the basis for a theory.

I learnt my lesson then. I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting an interesting mathematics.”

Paul Dirac  Mathematical Foundations of Quantum Theory (1978).

My comment:

Bohr orbit was a brilliant physical  idea but was not of course mathematically sound. The mistake  was to give up this notion instead of trying to develop it further.  The price paid was the basic paradox of quantum measurement theory which is still with us. Wave functions in the space of Bohr orbits generalize the  standard notion of wave function, give precise connection with the classical theory,  and  lead to zero energy ontology. The classical determinism is consistent with the quantum jumps since they occur between these wave functions.  The experiments of Minev et al provide direct experimental evidence for the zero energy ontology. Quantum jumps correspond to smooth classical developments leading to the final state of quantum jump.   Second big mistake was the neglect of the fact that the conservation laws are lost in general relativity.

The notion of Bohr orbit,  in the sense that I use  it in TGD,  realizes holography. In   TGD  holography is forced by 4-D general coordinate invariance. Otherwise one would  have path integral over all space-time surfaces,  plagued by horrible infinities. This is  certainly consistent with the idea of sound mathematics as a basis of theoretical physics.

TGD provides a concrete realization of holography as a   4-D generalization of holomorphy in  terms of combination of 2-D complex and hypercomplex structures   as analogs of complex structures.   I call these structures Hamilton-Jacobi structures.  An explicit general solution of field equations is in question so that TGD is an exactly solvable theory. See this and this .

Irrespective of the  action principle, Bohr orbits are minimal surfaces locally if    the action is a general coordinate invariant constructed in terms of induced geometry. Only the singularities such as light-like boundaries and   interfaces of Minkowskian and Euclidean regions, and string world sheets depend on action. This reflects the universality of quantum criticality. Kahler action plus volume term is the action implied by the twistor lift of TGD.

The  holomorphic ansatz works also in the case of string models based on area action. In TGD the conformal and Kac-Moody symmetries of string model are replaced by an  infinite algebra of a  4-D generalization of conformal symmetries in terms of Noether currents and act as isometries of ther "world of classical worlds". Remarkably,  the action is *not* invariant under these symmetries as the naive expectation would be. Also symplectic symmetries assignable to the orbits of partonic symmetries and satisfying field equations for Chern-Simons-Kahler action are symmetries of the theory and act as isometries of WCW.

TGD also leads to a very detailed new  geometric and topological view of atoms, nuclei and hadrons and the relationship between strong and electroweak interactions relying strongly on the topology of the space-time surfaces representing the system and making strong and testable predictions. In particular, a  problem in the standard atomic theory is discovered: the atoms with many electrons are not classically stable and the TGD view provides stability.    See this and this .

So sum up, theoreticians must always start from the requirement that the theory is free of logical contradictions. Quantum measurement theory gave up this requirement and this stopped the progress.

TGD involves of course extremely beautiful mathematical structures: WCW as a mathematical construct  based on Bohr orbitology and making physics unique from its mere mathematical existence, physics as geometry and physics as number theory as  the basic approaches dual to each other,   M^8-H duality generalizing momentum position duality and strongly suggesting a connection with Langlands duality, number theoretic vision predicting standard model symmetries and giving rise to   possible correlates of cognition, hyperfinite factors and their inclusions,...

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.

The Notion of Generalized Integer

The inspiration for this contribution came from the article "Space Element Reduction Duplication (SERD) model produces photon-like information packets and light-like cosmological horizons" by Thomas L. Wood. published in Metodologia IV B:  Journal of International and Finnish Methodology, expressess the basic assumptions of the SERD approach very coherently and in a systematic way so that it easy easy to criticize them and compare with other views, in my case the TGD view.

My criticism is based on a different interpretation of the discreteness. It would be assignable to cognitive representations based on p-adic numbers fields involving extensions of rationals. Bringing in also the continuous number fields (reals, complex numbers, quaternions, octonions) brings in real space-time as sensory representation and one ends up to a generalization of the standard model proving a number theoretic interpretation for its symmetries.

The approach of Thomas looks to me essentially topological: for instance, the information propagating in the hypergraph is assumed to be topological. In TGD, discrete structures analogs define cognitive representations of the continuous sensory world and are basically number theoretic. The description of the sensory world involves both topology and geometry.

The articulation of this view led to the main result of this article, which is a generalization of the number concept as a fusion of all p-adic number fields and rationals to a single structure that I call generalized integers. Besides being useful in TGD, this framework could be very useful in the modelling of spin glass-like systems.

See the article The Notion of Generalized Integer or the chapter Trying to fuse the basic mathematical ideas of quantum TGD to a single coherent whole

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.

Doubly magic mystery for nuclei

Recently I learned of a nuclear physics finding, which is interesting from the point of view of TGD based model for nuclei in terms nuclear strings that I managed to develop to a rather detailed form quite recently \cite{btart}{nuclatomplato}. This model extends to a model of both atoms and hadrons based on the same general basic ideas and makes rather non-trivial and testable predictions.

1. The first basic notion is nuclear string identifiable as a monopole flux tube. The nucleus would consist of one or more nuclear strings and they would define Hamiltonian cycle going through all vertices of the Platonic solid assignable to j-shell with angular momentum j=l +/- 1/2 and number of states N_-=2l or N₊=2l+2.
2. The fact that flux tubes involve also Coulomb flux does not allow closed Hamiltonian cycles: these are possible only for electromagnetically neutral systems.

   One can however eliminate one edge from the cycle. This kind of quasicycle for which the flux tube arrives point A from another Platonic solid and flows through all the remaining points of the cycle and returns to a neighboring point B and continues to a neighboring Platonic solid. This kind of quasicycles can be generated when the flux tube portions defining edges of closed cycles form reconnections: in this case however both the incoming and outgoing flux tube would correspond to missing edges. This would also allow degenerate quasi cycles with 2 vertices required by the model.

   One can ask whether one should one allow Hamiltonian paths in which incoming and outgoing fluxes are not associated with neighboring vertices. Their number is obviously larger than the number of cycles.

3. Both the harmonic oscillator potential used in the simplest nuclear model and Coulombic potential used in the model of atoms are characterized by a principal quantum number n such that l=1,2,..,n orbital angular momenta are realized for it.

   This motivates the idea of nucleus-atom holography meaning that the protonic states of the nucleus correspond to the states of electrons of the atom. This also leads to a speculative question whether neutrinos could play the role of neutrons in atoms.

One can imagine two options for how the particles are assigned to Hamiltonian cycles.

1. For the first option the particles could be assigned to V vertices of the platonic solid or to the V edges of the Hamilton cycle: if the quasi-Hamilton cycles are allowed, then only the vertices are allowed. The numbers of vertices are given by V= 4,6,8,12,20 for T,O,C,I,D.

   It is interesting to look in detail at the assignments of states at different n-shells.

   1. n=0: l=0. There are 2 states. Degenerate Platonic solid as diametrically opposite points of the sphere.
   2. n=1: l=0,1. There are 2+2+4 states. 2 degenerate Platonic solids + T
   3. n=2: l=0,1,2: 4+6 additional states to n=1-shell. Additional T and O.
   4. n=3: 6+8 additional states to n=2-shell. Additional O and C.
   5. n=6: 8+10 additional states to n=3 shell. 6 corresponds to C. 10 has no counterpart as a single platonic solid. 10 → T +O.
   6. n=6: 10 +12 states: 12 corresponds to I. 10→ T+O.

2. For the second option one assigns particles at the centers of complementary edges which by definition do not belong to the Hamiltonian cycle. There are F-2 complementary edges.

   One has F-2\in {2,6,4,18,10} for T,O,C,D,O.

   1. n=0: The 2 states correspond to T.
   2. n=1: The 2+4=6 additional states correspond to T+C:
   3. n=2: l=0,1,2: The 4+6=10 additional states correspond to C+O.
   4. n=3: There are 6+8 additional states. 6 corresponds to O but 8 corresponding to j=3+1/2 is missing. T+O would give 2+6=8 and C+C would give 4+4=8. j=3+1/2 cannot therefore correspond to a single platonic solid.
   One could worry about the fact that the magic number N=20 does not find an explanation in this picture. Rather, N=18 would correspond to 3 full shells. As if l=0 doublet would stabilize N=18 state. Why should this be the case? Interestingly, N=18 is atomic magic number.

   Energy shell can be defined in terms of an energy gap to the next state with a higher energy and this suggests that the discrepancy relates to the fact that l=0 state of n=3 shell are near to the energy of the highest state of the n=2.

   Spin-orbit interaction comes first into mind since it distinguishes between the energies for a given value of n and comes first to mind. L•S term is vanishing and its spin-orbit interaction is therefore expected to be smallest for l=0 state. In the case of atom, the interaction energy is nonvanishing since it involves expectation value of 1/2dV/dr, where V is in the atomic case Coulomb potential, in l=0 state and gives a term proportional to 1/l which at the limit l→ 0 gives a non-vanishing net result. In the case of a nucleus, the harmonic oscillator potential would give vanishing interaction energy.

   The F-2 option does not require the somewhat questionable degenerate Platonic solid but the V option works also for n=3.

3. One can ask whether the notion of n-shell could allow a description in terms of Platonic solids? In atoms l=0 and l=1 shells for n=1 shells give 2+2+4 =8 states, which could be assigned to the 8 vertices of the cube. F-2=8 is not satisfied by any Platonic solid.

   l=0,1,2 shells for the n=2-shell correspond to 2+ 2+4+4+6= 8+10=18 states assignable to the n=2 shell. These 18 states cannot be assigned to the vertices of a single Platonic solid. These states can be however assigned with the complementary edges of the icosahedron with F-2 =18. It would look however strange to assign the n=2 shell to complementary edges of the icosahedron and n=1 shell to the vertices of the cube.

With this background one can try to answer the question whether the recent findings, suggested to involve new nuclear physics, could help to test and even fix the details of the TGD based model.

1. ²⁸O nucleus has 8 protons and 20 neutrons and is doubly magic and should be therefore stable. It has 12 surplus halo neutrons and decays to a state with 8 surplus neutrons plus 4 neutrons with a life-time about 10^-21 seconds. The 12 surplus neutrons in the halo cannot correspond to a full shell. This could explain the short life-time.
2. ²⁸O decays by emitting 4 neurons to ²⁴O with 8 surplus neutrons. This state should be rather stable.

What could TGD say about this?

1. The reason why one cannot apply the magic nucleus rule could be that halo neutrons are different from the core neurons and must be treated separately. A possible reason is that the halo neutrons correspond to a non-standard value of h_eff=nh₀>h. This can occur also for the valence electrons of rare earth metals.
2. The 12 surplus neutrons in the halo do not correspond to a full n-shell. Both V and F-2 options are doomed to fail if the stability corresponds to a full n-shell.

   The ordinary 8 neutrons of ¹⁶O could correspond to a full n=1 shell. 8+4=12 halo neutrons would naturally correspond to a partially filled n=2 shell having 8+4+6=18 neutrons. This does not depend on whether one has V or F-2 option.

3. The 8 halo neutrons have the same quantum numbers as the full n=1 shell, which suggests stability. This conforms with the experimental findings. 4 neutrons, which correspond to j=3/2-plet could be assigned with the complementary edges of the cube but cannot form a full shell since the 6 j= 5/2-plet is missing.

See the article About Platonization of Nuclear String Model and of Model of Atoms 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.

Pollack Effect and Some Anomalies of Water

In the  Pollack effect (PE) negatively charged exclusion zones (EZs) are induced at the boundary between the  gel phase and water  by an energy feed such as IR radiation.  Pollack has  introduced the notion of fourth phase of water, which obeys effective stoichiometry H_1.5O and consists of hexagonal layers  having therefore an  ice-like structure. EZs e are able to clean up inpurities from their interior, which seems to be in conflict with the second law of thermodynamics. I have collected in the article Pollack Effect and Some Anomalies of Water examples of hydrodynamic anomalies, which might have an explanation in terms of the Pollack effect.  

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.

Some facts about birational geometry

Birational geometry has as its morphisms birational maps: both the map and its inverse are expressible in terms of rational functions. The coefficients of polynomials appearing in rational functions are in the TGD framework rational. They map rationals to rationals and also numbers of given extension E of rationals to themselves (one can assign to each space-time region an extension defined by a polynomial).

Therefore birational maps map cognitive representations, defined as discretizations of the space-time surface such that the points have physically/number theoretically preferred coordinates in E, to cognitive representations. They therefore respect cognitive representations and are morphisms of cognition. They are also number-theoretically universal, making sense for all p-adic number fields and their extensions induced by E. This makes birational maps extremely interesting from the TGD point of view.

The following lists basic facts about birational geometry as I have understood them on the basis of Wikipedia articles about birational geometry and Enriques-Kodaira classification. I have added physics inspired associations with TGD.

Birational geometries are one central approach to algebraic geometry.

1. They provide classification of complex varieties to equivalence classes related by birational maps. The classification complex curves (real dimension 2) is best understood and reduces to the classification of projective curves of projective space CP_n determined as zeros of a homogeneous polynomial. I had good luck since complex surfaces (real dimension 4) are of obvious interest in TGD: now however the notion of complex structure is generalized and one has Hamilton-Jacobi structure and Minkowski signature is allowed.
2. In TGD, a generalization of complex surfaces of complex dimension 2 in the embedding space H=M⁴× CP₂ of complex dimension 4 is considered. What is new is the presence of the Minkowski signature requiring a combination of hypercomplex and complex structures to the Hamilton-Jacobi structure. Note however the space-time surfaces also have counterparts in the Euclidean signature E⁴× CP₂: whether this has a physical interpretation, remains an open question. Second representation is provided as 4-surfaces in the space M⁸_c of complexified octonions and an attractive idea is that M⁸-H duality corresponds to a birational mapping of cognitive representations to cognitive representations.
3. Every algebraic variety is birationally equivalent with a sub-variety of CP_n so that their classification reduces to the classification of projective varieties of CP_n defined in terms of homogeneous polynomials. n=2 (4 real dimensions) is of special relevance from the TGD point of view. A variety is said to be rational if it is birationally equivalent to some projective variety: for instance CP₂ is rational.
4. A concrete example of birational equivalence is provided by stereographic projections of quadric hypersurfaces in n+1-D linear space. Circle in plane is the simplest example. Let p be a point of quadric. The stereographic projection sends a point q of the quadric to the line going through p and q, that is a point of CP_n in the complex case. One can select one point on the line as its representative. Another exammple is provided by Möbius transformations representing Lorentz group as transformations of complex plane.

The notion of a minimal model is important.

1. The basic observation is that it is possible to eliminate or add singularities by using birational maps of the space in which the surface is defined to some other spaces, which can have a higher dimension. Peaks and self-intersections are examples of singularities. The zeros of a birational map can be used to eliminate singularities of the algebraic surface of dimension n by blowups replacing the singularity with CP_n. Poles in turn create singularities.

   The idea is to apply birational maps to find a birationally equivalent surface representation, which has no singularities. There is a very counter-intuitive formal description for this. For instance, complex curves of CP₂ have intersections since their sum of their real dimensions is 4. The same applies to 4-surfaces in H. My understanding is as follows: the blowup for CP₂ makes it possible to get rid of an intersection with intersection number 1. One can formally say that the blow up by gluing a CP₁ defines a curve which has negative intersection number -1.

2. In the TGD framework, wormhole contacts are Euclidian regions of space-time surface, which have the same metric and Kähler structure as CP₂ and light-like M⁴ projection (or even H projection). They appear as blowups of singularities of 4-surfaces along a light-like curve of M⁸. The union of the quaternionic/associative normal spaces along the curve is not a line of CP₂ but CP₂ itself with two holes corresponding to the ends of the light-like curve. The 3-D normal spaces at the points of the light-like curve are not unique and form a local slicing of CP₂ by 3-D surfaces. This is a Minkowskian analog of a blow-up for a point and also an analog of cut of analytic function.
3. The Italian school of algebraic geometry has developed a rather detailed classification of these surfaces. The main result is that every complex surface X is birational either to a product CP¹× C for some curve C or to a minimal surface Y. Preferred extremals are indeed minimal surfaces so that space-time surfaces might define minimal models. The absence of singularities (typically peaks or self-intersections) characterizing minimal models is indeed very natural since physically the peaks do not look acceptable.

Mathematicians use invariants to characterize mathematical structures. In TGD birational invariants would be cognitive invariants. They would be extremely interesting physically if the 4-D generalization of holomorphy really to a fusion of complex and hypercomplex structrures make sense (see this and this).

There are several birationals invariants listed in the Wikipedia article. Many of them are rather technical in nature. The canonical bundle K_X for a variety of complex dimension n corresponds to n:th exterior power of complex cotangent bundle that is holomorphic n-forms. For space-time surfaces one would have n=2 and holomorphic 2-forms.

1. Plurigenera corresponds to the dimensions for the vector space of global sections H₀(X,K_X^d) for smooth projective varieties and are birational invariants. The global sections define global coordinates, which define birational maps to a projective space of this dimension.
2. Kodaira dimension measures the complexity of the variety and characterizes how fast the plurigenera increase. It has values -∞,0,1,..n and has 4 values for space-time surfaces. The value -∞ corresponds to the simplest situation and for n=2 characterizes CP₂, which is rational and has vanishing plurigenera.
3. The dimensions for the spaces of global sections of the tensor powers of complex cotangent bundle (holomorphic 1-forms) define birational invariants. In particular, holomorphic forms of type (p,0) are birational invariants unlike the more general forms having type (p,q). Betti numbers are not in general birational invariants.
4. Fundamental group is birational invariant as is obvious from the blowup construction. Other homotopy groups are not birational invariants.
5. Gromow-Witten invariants are birational invariants. They are defined for pseudo-holomorphic curves (real dimension 2) in a symplectic manifold X. These invariants give the number of curves with a fixed genus and 2-homology class going through n marked points. Gromow-Witten invariants have also an interpretation as symplectic invariants characterizing the symplectic manifold X.

   In TGD, the application would be to partonic 2-surfaces of given genus g and homology charge (Kähler magnetic charge) representatable as holomorphic surfaces in X=CP₂ containing n marked points of CP₂ identifiable as the loci of fermions at the partonic 2-surface. This number would be of genuine interest in the calculation of scattering amplitudes.

What birational classification could mean in the TGD framework?

1. Holomorphic ansatz gives the space-time surfaces as Bohr orbits. Birational maps give new solutions from a given solution. It would be natural to organize the Bohr orbits to birational equivalence classes, which might be called cognitive equivalence classes. This should induce similar organization at the level of M⁸_c.
2. An interesting possibility is that for certain space-time surfaces CP₂ coordinates can be expressed in terms of preferred M⁴ coordinates using birational functions and vice versa. Cognitive representation in M⁴ coordinates would be mapped to a cognitive representation in CP₂ coordinates.
3. The interpretation of M⁸-H duality as a generalization of momentum position duality suggests information theoretic interpretation and the possibility that it could be seen as a cognitive/birational correspondence. This is indeed the case M⁴ when one considers linear M⁴ coordinates at both sides.
4. An intriguing question is whether the pair of hypercomplex and complex coordinates associated with the Hamilton-Jacobi structure could be regarded as cognitively acceptable coordinates. If Hamilton-Jacobi coordinates are cognitively acceptable, they should relate to linear M⁴ coordinates by a birational correspondence so that M⁸-H duality in its basic form could be replaced with its composition with a coordinate transformation from the linear M⁴ coordinates to particular Hamilton-Jacobi coordinates. The color rotations in CP₂ in turn define birational correspondences between different choices of Eguchi-Hanson coordinates.

   If this picture makes sense, one could say that the entire holomorphic space-time surfaces, rather than only their intersections with mass shells H³ and partonic orbits, correspond to cognitive explosions. This interpretation might make sense since holomorphy has a huge potential for generating information: it would make TGD exactly solvable.

See the article Birational maps as morphisms of cognitive structures or the chapter New findings related to the number theoretical view of TGD.

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.

Cymatics, ringing bells, water memory, homeopathy, Pollack effect, turbulence

Warning: This post contains many words, which induce deep aggression in academic colleagues receiving a monthly salary: cymatics, the ringing bells of Buddhist monks, water memory, and homeopathy(!!). Pollack effect is perhaps not so aggression inducing and turbulence is quite neutral. All these words are linked: this is message that I try to communicate in the following.

Cymatics (see this) is a very interesting phenomenon. Thanks to Jukka Sarno for a post inspiring this comment. I lost the original link: Facebook has started to suddenly change the page content completely and this makes it very difficult to respond to the posts. Maybe some kind of virus is in question.

I came across a related phenomenon recently. The ringing of Buddhist monks' bells by running the bell along its edge has strange effects. The water started to boil so that a strong transfer of energy had to happen to the water by sound. Energy was supplied to the system by the ringer of the bells. This energy could play a role of metabolic energy and help in the problems resulting from its local deficiency in the patient's body.

Something analogous to turbulence also arises in cymatics. Turbulence and its generation are very interesting phenomena and poorly understood. Standard hydrodynamics, which was developed centuries ago, can't really cope with the challenges of the modern world: if only someone could tell this to the theoreticians working on it!

I myself have built a model for turbulence and related phenomena (see this and this). A core element of the model is the anomalous phenomenon observed by Pollack related to water. When water is irradiated in the presence of a gel phase with, for example, infrared light, negatively charged gel-like volumes are created in the water: Pollack talks about the fourth phase of water. Living matter is full of them: for instance cell interior is negatively charged as also DNA.

Some of the water's protons disappear somewhere: in the TGD world they would go to the magnetic body of the water and form dark matter there precisely because we cannot detect them with standard methods. This dark matter would be a phase of ordinary matter with a nonstandard, and often very large value of effective Planck constant. This would make it quantum coherent in much longer scales than ordinary matter.

Pollack's fourth phase resembles ice and very recently it has been discovered that there is a thin ice-like layer at the interface between water and air (see this and this). Could it be Pollack's fourth phase? The energy input is essential. In cymatics and in the case of bells the energy feeder would be sound rather than light. In homeopathy (one of the most hated phenomena of physics besides water memory; I have never understood why it generates so deep a hatred), the shaking of the homeopathic preparation would supply the energy. A fourth phase of water would be created and the water would become "living" as its magnetic body would "wake up" and start to control ordinary matter.

Homeopathy is one of the most hated phenomena of physics besides water memory; I have never understood why it generates so deep hatred), the shaking of the homeopathic preparation would supply the energy. A fourth phase of water would be created and the water would become "living" as its magnetic body would "wake up" and start to control ordinary matter.

In homeopathy, shaking would provide the energy making it possible to create magnetic organisms consisting of flux tubes associated with water molecule clusters connected by hydrogen bonds. Their cyclotron frequency spectrum would mimic the corresponding spectrum of the molecules dissolved in water. Water would magnetically mimic the intruder molecule and from the perspective of biology this would be enough for water memory explaining homeopathic effects. This should be trivial for scientists living in the computer age but some kind of primitive regression makes it impossible for colleagues to stay calm and rational when they hear the word "homeopathy".

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.

Birational maps as morphisms of cognitive structures

Birational maps and their inverses are defined in terms of rational functions. They are very special in the sense that they map algebraic numbers in a given extension E of rationals to E itself. In the TGD framework, E defines a unique discretization of the space-time surface if the preferred coordinates of the allowed points belong to E. I refer to this discretization as cognitive representation. Birational maps map points in E to points in E so that they define what might be called cognitive morphism.

M⁸-H duality duality (H=M⁴× CP₂) relates the number vision of TGD to the geometric vision. M⁸-H duality maps the 4-surfaces in M⁸_c to space-time surfaces in H: a natural condition is that in some sense it maps E to E and cognitive representations to cognitive representations. There are special surfaces in M⁸_c that allow cognitive explosion in the number-theotically preferred coordinates. M⁴ and hyperbolic spaces H³ (mass shells), which contain 3-surfaces defining holographic data, are examples of these surfaces. Also the 3-D light-like partonic orbits defining holographic data. Possibly also string world sheets define holographic data. Does cognitive explosion happen also in these cases?

In M⁸_c octonionic structure allows to identify natural preferred coordinates. In H, in particular M⁴, the preferred coordinates are not so unique but should be related by birational mappings. So called Hamilton-Jacobi structures define candidates for preferred coordinates: could different Hamilton-Jacobi structures relate to the each other by birational maps? In this article these questions are discussed.

See the article Birational maps as morphisms of cognitive structures or the chapter New findings related to the number theoretical view of TGD.

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.

Boundary conditions at partonic orbits and holography

TGD reduces coupling constant evolution to a number theoretical evolution of the coupling parameters of the action identified as Kähler function for WCW. An interesting question is how the 3-D holographic data at the partonic orbits relates to the corresponding 3-D data at the ends of space-time surfaces at the boundary of CD, and how it relates to coupling constant evolution.

1. The twistor lift of TGD strongly favours 6-D Kähler action, which dimensionally reduces to Kähler action plus volume term plus topological ∫ J∧ J term reducing to Chern Simons-Kähler  action. The coefficients of these terms are proposed to be expressible in terms of number theoretical invariants characterizing the algebraic extensions of rationals and polynomials determining the space-time surfaces by M⁸-H duality.

   Number theoretical coupling constant evolution would be discrete. Each extension of rationals would give rise to its own coupling parameters involving also the ramified primes characterizing the polynomials involved and identified as p-adic length scales.

2. The time evolution of the partonic orbit would be non-deterministic but subject to the light-likeness constraint and boundary conditions guaranteeing conservation laws. The natural expectation is that the boundary/interface conditions for a given action cannot be satisfied for all partonic orbits (and other singularities). The deformation of the partonic orbit requiring that boundary conditions are satisfied,  does not affect X³  but   the time derivatives ∂_t h^k at X³  are affected since the form of the holomorphic functions defining the space-time surface would change.   The interpretation would be in terms of duality of the holographic data associated with the partonic orbits resp. X³.  

    There can of course exist deformations, which require the change of the coupling parameters of the action to satisfy the boundary conditions. One can consider an analog of  renormalization group equations in which the deformation corresponds to a modification of the  coupling parameters of the action, most plausibly determined by the  twistor lift. Coupling parameters would label different regions of WCW and  the space-time surfaces possible for two different sets of coupling parameters would define interfaces between these regions.

 In order to build a more detailed view one must fix the details related to the action whose value defines the WCW  Kähler function.  

1. If Kähler action is identified as Kähler action, the identification is unique. There is however the possibility that the imaginary exponent of the instanton term or the contribution from the Euclidean region is not included in the definition of Kähler function. For instance instanton term could be  interpreted as a phase of quantum state and would not contribute.
2. Both Minkowskian and Euclidean regions are involved and the Euclidean signature poses problems. The definition of the  determinant as (-g₄)^1/2 is natural in Minkowskian regions but gives an imaginary contribution in Euclidean regions. (|g₄|)^1/2 is real in both regions. i(g₄)^1/2 is real in Minkowskian regions but imaginary in the Euclidean regions.

   There is also a problem related to the instanton term, which does not depend on the  metric determinant at all.  In QFT context the instanton term is imaginary and this is important for instance in QCD in  the definition of CP breaking vacuum functional. Should one include only the 4-D  or possibly only Minkowskian contribution to the Kähler function  imaginary coefficient for the instanton/Euclidian term would be possible?

3.   Boundary conditions guaranteeing the conservation laws at the partonic orbits must be satisfied. Consider the  |g₄| case.  Charge transfer between Euclidean and Minkowskian  regions. If the C-S-K term is real, also the  charge transfer between partonic orbit and 4-D  regions is possible.  The boundary conditions at the partonic orbit fix it to a high degree and also affect the time derivatives ∂_th^k at X³. This option looks physically rather attractive because classical conserved charges would be real.

   If the C-S-K term is imaginary it behaves like a free particle since charge exchange  with Minkowskian and Euclidean regions is not possible. A possible interpretation of the  possible M⁴ contribution to momentum could be in terms of decay width.  The symplectic charges do not however involve momentum. The imaginary contribution to momentum could therefore come only from the Euclidean region.

4. If the Euclidean contribution is imaginary, it seems that it cannot be included in the Kähler function. Since in M⁸ picture the momenta of virtual fermions are in general complex, one could consider the possibility that  Euclidean contribution  to the momentum is imaginary and allows an  interpretation as a decay width.

See the article Symmetries and Geometry of the "World of Classical Worlds" or the chapter Recent View about K\"ahler Geometry and Spin Structure of "World of Classical Worlds".

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.

Why the water flowing out of bathtub rotates always in the same direction?

In FB Wes Johnson wondered whether Coriolis force could explain why the water flowing out of bathtub forms a vortex with direction which is opposite at Northern and Southern hemispheres.

Coriolis effect is a coordinate force proportional to ω× v, where ω is the angular velocity of Earth directed to Noth and v is the velocity of the object. For bathtub v would be downwards, that is in the direction of Earth radius. At the  equator Coriolis force  is  along the equator  and non-vanishing. On the other hand, the force causing rotation of water in the bathtub is of opposite sign below and above equator and therefore vanishes at equator. Therefore Coriolis force is excluded as an explanation.

My own view is that this is a hydrodynamical effect and new physics might be involved.   Turbulence is involved and   vortex is generated.  The direction  of the  rotation of the vortex should be understood. The selection of a specific direction violates parity symmetry and this gives in the TGD framework strong guidelines.  

1.   The   vortex is in the direction of the  Earth's gravitational force. In the TGD framework,  gravitational interaction is mediated by monopole flux tubes in the direction of the gravitational field. Quantum gravitation is involved and it is quite possible that the gravitational magnetic body (MB) induces the effect since quite generally MB plays a control role, in particular in living matter.
2.    The induced Kähler field contributes to both electromagnetic and classical (weak) Z⁰ field:  since the matter is em neutral but not Z⁰ neutral, it  seems that   Z⁰ field  must be in question. Could the gravitational MB  of Earth consist  of Z⁰ monopole flux tubes?

   If this is the case, a macroscopic quantum effect involving a very large value ℏ_gr=GMm/β₀ of gravitational Planck constant of the pair formed by Earth mass and particle must be in question since ordinary Z⁰ has extremely short range. The gravitational Compton length Λ_gr = ℏ_gr/m= GM/β₀= r_S/2β₀ does not depend on particle mass and Z⁰ is about .5 cm, one half of the Schwartschild radius of the Earth, for the favored β₀=v₀/c=1.

3.   In the classical Z⁰ field,  particles with Z⁰ charges rotate around the axis of the field and since magnetic flux is approximately dipole field, the flux lines  are radial but  are upwards/downwards above/below the equator. This would explain why the rotation directions of the vortex are  opposite and Northern and Southern hemispheres. The presence of the classical Z⁰ field, which violates parity symmetry, would also conform with the parity breaking and would be essential for the understanding of the mystery of chiral selection in biomatter.

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.

Mysterious lift of drill in downwards water flow

I learned of a very interesting and paradoxical looking phenomenon. Thanks for Shamoon Ahmed for the link. A drill with a helical geometry raises in a downwards fluid flow (see this) This is in conflict with the naive expectations.

1. Suppose first that momentum is conserved. By momentum conservation water must get downwards directed momentum if the drill obtains upwards directed momentum. If there is no slipping, just the opposite should happen. Therefore the situation could be like in a turbulent flow: the water and the drill do not directly touch each other. There is indeed turbulence as one can see.

   But what makes possible the slipping? It has been quite recently learned that the surface of water in air has thin ice-like layer for which TGD suggests and explanation (see this). The surface between drill and water would be covered by a very thin ice layer so that slipping would take place naturally. Drill is like a skater. Also the boundary layer in the water (liquid) flow past a body could be a thin ice-sheet. Second analogy is as a screw penetrating upstream.

2. But is the momentum really conserved? Water is accelerated in the gravitational field: this gives it momentum. Water is rotating already before the addition of the drill. The downwards kinematic pressure, which increases downwards, pushes the drill having a helical geometry. If there is no friction fixing the drill to water flow, the drill has no other option than raise. The constraint due to helicality forces the drill to rotate.

   Water in the vortex and drill would rotate in opposite directions and helicality constraint would transform the rotational motion of the drill to a translational motion and force the rotation of drill to gain upwards directed momentum.

3. This raises some questions.
   1. Could there be a connection with the fact that in the Northern/Southern hemisphere water flowing in a water tub rotates in a unique direction (kind of parity breaking)?
   2. What is the role of the handedness of the drill? One would expect that the drill with an opposite handedness rotate in an opposite direction? What if the handedness of the drill does not favor the natural rotation direction for the vortex? Do these effects tend to cancel.

There might be a connection with the "ordinary" hydrodynamics. The drill raising in the fluid flow is analogous to a propeller. Could also ordinary propeller involve the same basic mechanism and act like a skater and in this way minimize dissipative energy losses? It is known that propellers induce cavitation as evaporation of water and there is anecdotal evidence from power plants that more energy is liberated in the process than one would expect. Recently it was found that the mere irradiation of water by light leads to its evaporation as a generation of droplets, which would have ice-like surface layer consisting of the fourth phase of water (this requires energy): Pollack effect again! Could dark photons with a non-standard value of Planck constant provide the energy needed for the cavitation creating a vapour phase with a larger total area of fourth phase of water?

Runcel D. Arcaya informed me of the work of a brilliant experimentalist and inventor Victor Schauberger related to the strange properties of flowing water. This work relates in an interesting manner to the effect discussed. I have written about Schauberger's findings about to the ability of fishes too swim "too" easily upstream. Gravitation is involved also now. Could the bodily posture of the fish generate the counterpart of the helical geometry? Could the fish as a living organism help to generate the fourth phase of water in the water bounding their skin by Pollack effect, which requires the presence of a gel phase besides energy source (IR radiation for instance) to transform part of protons of water molecules to dark photons with a higher energy.

Schauberger also invented a method of water purification using vortex flow: the reason for why the method works remained unclear. In Pollack effect, the negatively charged exclusion zones (EZs) spontaneously purify themselves. This conflicts with the thermodynamical intuitions. The TGD explanation is in terms of reversed arrow of time which explains the purification process as normal diffusion leading to the decay of gradients but taking place with an opposite arrow of time. Could the purification of in vortex flow be caused by the Pollack effect creating the surface layers consisting of the fourth phase of water (EZs)?

Schauberger developed the notion of living water and believed that spring water is somehow very special in this respect. In TGD water is regarded as a multiphase system involving magnetic body with layers labelled by the values of effective Planck constant h_eff. The larger the value of the h_eff, the higher the (basically algebraic complexity) and "IQ" of the system. Gravitational magnetic body has the largest value of effective Planck constant. Spring water is pure and could be this kind of highly complex system. Also systems involving turbulence and vortices are very complex.

See the article TGD Inspired Model for Freezing in Nano Scales and the chapter TGD and Quantum Hydrodynamics.

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 universality of the holomorphic solution ansatz

The explicit solution of field equations in terms of the generalized holomorphy is now known. Also the emergence of supersymplectic symmetry is understood: it emerges as symmetries of Chern-Simons-Kähler action at the 3-D partonic orbits defining part of 3-D holographic data.

The solution ansatz is independent of action as long it is general coordinate invariance depending only on the induced geometric structures. Space-time surfaces would be minimal surfaces apart from lower-dimensional singular surfaces at which the field equations involve the entire action. Only the singularities, classical charges and positions of topological interaction vertices depend on the choice of the action (see this). Kähler action plus volume term is the choice of action forced by twistor lift making the choice of H unique.

The universality has a very intriguing implication. One can assign to any action of this kind conserved Noether currents and their fermionic counterparts (also super counterparts). One would have a huge algebra of conserved currents characterizing the space-time geometry. The corresponding charges need not be conserved since the conservation conditions at the partonic orbits and other singularities depend on the action. The discussion of the symplectic symmetries leads to the conclusion that they give rise to conserved charges at the partonic 3-surfaces obeying Chern-Simons-Kähler dynamics, which is non-deterministic.

Partonic 3-surfaces could be in the same role as space-like 3-surfaces as initial data: the time coordinate for this time evolution would be dual to the light-like coordinate of the partonic orbit. Could one say that the measurement localizing the partonic orbit leads to a phase characterized by a particular action? The classical conserved quantities are determined by the action. The WCW K\"ahler function should correspond to this action and different actions would correspond to different regions of WCW. Could phase transition between these regions take place when the 4-surface determined by the partonic orbit belongs to regions corresponding to two different effective actions. The twistor lift suggests that action must be the sum of the Kähler action and volume term so that only Kähler couplings strength, the coefficient of instanton term and the dynamically determined cosmological constant would vary.

See the article Symmetries and Geometry of the "World of Classical Worlds" or the chapter Recent View about K\"ahler Geometry and Spin Structure of "World of Classical Worlds".

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.

Some comments about the identification of leptons and matter-antimatter asymmetry

The mathematical formulation of TGD has now reached a stage in which one can seriously consider fixing the details of the physical interpretation of the theory. The discussion of the detailed physical interpretation in articles (see this), inspired by what I called Platonization, led to a proposal for a unification of hadron, nuclear, atomic, and molecular physics in terms of the notion of Hamiltonian cycles defined by monopole flux tubes at Platonic solids. This generated quite unexpected insights and killer predictions.

In (see this) a construction of strong, electroweak and gravitational interaction vertices, reducing them to partly topological 2-vertex describing a creation of fermion-antifermion pair in a classical induced electroweak gauge potentials, led to very concrete predictions relating also the topological explanation of family replication phenomenon and its correlation with homology charge of the partonic 2-surface.

In the articles (see this and this) the identification of the isometries of WCW were considered and explicit realizations of symplectic and holomorphic isometry generators demonstrated that the original intuitive view is almost correct. The new aspects were related to the holography suggesting also a duality between symplectic and holomorphic isometry charges and supercharges. Also the relationship of holography, apparently in conflict with path integral approach, was understood. The dynamics of light-like partonic orbits is almost topological and not completely deterministic, which implies that the finite sum over partonic orbits can be approximated with path integral at QFT limit.

The emergence of all these constraints raises the hope that one could fix the interpretation of the theory at the level of details. In this article, the identification of leptons and matter-antimatter asymmetry are reconsidered in light of the new understanding.

About two competing identifications for leptons

In the TGD Universe, one can imagine two competing identifications of leptons.

1. Leptons and quarks correspond to different chiralities of spinors of H=M⁴× CP₂.
2. Only quarks are fundamental fermions and leptons are anti-baryon like objects.

Option A: Are both leptons and quarks fundamental fermions?

The first option means that both lepton and quark chiralities appear in the modified Dirac action fixed by hermicity once the action fixing space-time surfaces or their lower-dimensional submanifolds such as string world sheets and partonic orbits is known. In accordance with the experimental facts, lepton and quark numbers are conserved separately for this option. This is the original proposal and seems to be the most realistic option although the geometry of "world of classical worlds" (WCW) in terms of anticommutators of WCW gamma matrices, expressible as super generators of symmetries of H inducing isometries of WCW, seems to require only a single fermionic chirality.

The challenge is to explain why both chiralities are needed. It seems now clear that all elementary particles should be assignable to 2-sheeted monopole flux tubes with the fermion lines at wormhole throats (partonic 2-surfaces) of wormhole contacts identifiable as boundaries of string world sheets. The fermion numbers could be also delocalized inside string world sheets inside the flux tubes or inside flux tubes. Also in condensed matter physics states localized to geometric objects of various dimensions are accepted as a basic notion (for TGD view of condensed matter see (see this).

One can identify several dichotomies, which are analogous to the lepton-quark dichotomy. There is holomorphic-symplectic dichotomy, the dichotomy between light-like partonic orbits and 3-surfaces at the boundaries of Δ M⁴₊× CP₂, the dichotomy between Euclidean and Minkowskian space-time regions and the dichotomy between the 3-D holographic boundary data and interiors of the space-time surface. Could one unify all these dichotomies?

1. Consider first the Minkowskian-Euclidean dichotomy. Leptons could reside inside (string world sheets of) the Minkowskian regions of space-time surface and quarks inside (the string world sheets of) the Euclidean wormhole contacts. Euclidean regions with a fixed Minkowskian region or vice versa could be regarded as two sub-WCWs.

   The nice feature of this option is that it allows us to understand both quark/color confinement without any quark propagation and propagation of quarks in QCD. We would not see free quarks because they live inside the Euclidean regions of the space-time surface and do not propagate inside the Minkowskian regions of the space-time surface. Embedding space spinor spinor fields would however propagate in accordance in H which gives rise to quark propagators in the scattering amplitudes and conforms with the QCD picture. Notice that both quarks and leptons can appear at the partonic orbits forming the interfaces between Euclidean and Minkowskian space-time regions.

2. The holomorphic-symplectic dichotomy for the isometries of WCW is now well-established and one has explicit expression for the corresponding conserved charges and their fermionic counters defining gamma matrices as fermionic super charges which in anticommute to WCW metric.

   The symplectic representations of the fermionic isometry generators associated with the light-like partonic orbits at boundaries of CD defining 3-D holomorphic data could correspond to quarks. In accordance with color confinement, quarks would not appear at Euclidean 3-surfaces at light-cone boundaries Δ M⁴₊× CP₂. Classical gluon fields would define the simplest Hamiltonian fluxes and conserved quantities in the 3-D dynamics would be determined by the Chern-Simons-Kähler action with time defined by the light-like time coordinate. The Hamiltonians of S²× CP₂,organized to representations of color group and of rotation group restricted to partonic 2-surface, would define the Hamiltonian fluxes.

   The 4-D holomorphic representations in the interior of space-time surfaces and also assignable to the 3-surfaces at the boundaries of space-time surface at Δ M⁴₊× CP₂ would correspond to leptons. Also the anticommutators of the lepton-like gamma matrices would give contributions to the metric of WCW.

3. Holography as a dichotomy would suggest at quantum level that in an information theoretic sense the 4-D holomorphic dynamics of leptons represents the 3-D symplectic dynamics of quarks. The possibility of a kind of holography-like relation was already discussed in (see this), where it was found that the states of nuclei could be in rather precise correspondence with the states of atomic electrons. A generalization of this holography would correspond to a kind of quark-lepton holography.

One can argue that this general view could lead to a conflict with the possible holography-like relation between ordinary and dark quarks considered in (see this) as a way to guarantee that perturbation theory converges.

1. According to an intuitive argument, strong coupling strength is proportional to 1/h_eff so that the increase of effective Planck constant h_eff could guarantee the convergence of QFT type description expected at QFT limit of TGD. Ordinary quarks could transform in the h→ h_eff transition to states, which consist of pair of quark and dark antiquark with a vanishing total color, electroweak quantum numbers and spin whereas the second dark quark with a larger value of h_eff would have quantum numbers of the ordinary quark.

   The proposal was that dark quark and antiquark reside at the Minkowskian string world sheet. This does not conform with the above proposal, which requires that all quarks are at the partonic orbits.

2. This problem can be solved. Many-sheeted space-time however makes it possible to imagine that the dark quark and antiquark reside at the wormhole contacts of a larger space-time sheet and form a dark meson-like object. For instance, the ordinary quark would be associated with a wormhole contact connecting the other large space-time sheet to a third smaller space-time sheet, itself part of the monopole flux tube defining the ordinary quark. This would conform with the hierarchy formed by flux tubes topologically condensed to larger flux tubes.

Option B: Are only quarks fundamental fermions?

The second option stating that only quarks are fundamental particles, was motivated by the fact that only single fermion chirality seemed to be needed to construct WCW geometry. Leptons would be antibaryon-like states such that the 3 antiquarks are associated with single wormhole contact (see this). Lepton itself would be a closed monopole flux tube with geometric size defined by the Compton scale.

1. The first critical question is whether it makes sense to put 3 quarks to the same wormhole contact defining 2-D surface in CP₂ when the color degrees of freedom correspond to the "rotational" degrees of freedom in CP₂ but realized as spinor modes. One would have at least 2 antiquarks at the same wormhole contact. If the partonic 2-surface is homologically non-trivial geodesic sphere, the reduction of symmetry from SU(3) to U(2) subgroup with the same Cartan algebra occurs and the rotational degrees of freedom reduce to those at the partonic 2-surface. Wave functions for quarks would be wave functions for the end of the string at a partonic 2-surface having well-defined U(2) quantum numbers.
2. If multi-quark states at partonic 2-surfaces make sense, one can ask how to avoid the counterparts of Δ baryons with spin 3/2. Statistics constraint does not help to achieve this. Oscillator operators for color partial waves of quarks are anticommuting and there seems to be no reason excluding these states. In this sense color quantum numbers are like spin-like quantum numbers. One could of course hope that Δ-like states have a very high mass scale.
3. The third critical question concerns the origin of the CP breaking which would allow baryons as stable 3-quark states and only leptons as stable bound states of 3 antiquarks. Matter antimatter asymmetry would correspond to the stable condensation of antiquarks to leptons and quarks to baryons. This mechanism looks really elegant.

How matter antimatter asymmetry could be generated?

Both options A and B for the identification of leptons must be able to explain the generation of matter-antimatter asymmetry.

1. CP breaking involving M⁴ and/or CP₂ Kähler forms could explain the matter antimatter asymmetry along the same lines as in the standard picture. For Option A a small asymmetry between the densities of fermions and antifermions should be generated in the early cosmology and annihilation would lead to the antisymmetry. There would be space-time regions with opposite sign of asymmetries. For Option B the densities of leptons and antileptons and baryons and antibaryons would be slightly different before the annihilation and there would be no actual asymmetry.
2. For both A and B option, many-sheeted space-time and the hierarchy of magnetic bodies makes it possible to imagine many different realizations for the separation of fermion and antifermion numbers. For instance, cosmic strings could contain antimatter. The ordinary matter would be generated in the decay of the energy of cosmic strings to ordinary matter. This process is the TGD counterpart of inflation and highly analogous to black hole evaporation.

   In the simplest model, this energy would be associated with classical M⁴ type Kähler electric fields and CP₂ type Kähler magnetic fields inside the cosmic string. The decay of the volume energy and the energy of the classical electroweak fields would take place by a generation of fermion-antifermion pairs via fermion 2-vertex and classical electroweak gauge potentials would appear in the vertex.

3. If the CP breaking induced by the classical Kähler fields makes it more probable for antifermions to remain inside the monopole flux tubes, antimatter-matter asymmetry is generated. Also the CP breaking observed in meson decays could relate to the asymmetry caused by the induced Kähler field of the meson-like monopole flux tube.
4. In QCD, the topological instanton term gives rise to strong CP breaking as a CP violation of the vacuum state which is not invariant under CP (so called theta parameter describes the situation, (see this).

   In the TGD framework, the "instanton density" ∫ J∧ J for the induced Kähler field is non-vanishing and analogous to the theta therm. As a matter fact, instanton density is equal to the gluonic istanto action for the classical gluon field g_A= H_AJ. Instanton density can be transformed to the Chern-Simons-Kähler action as a boundary term and their contribution to the action is analogous to instanton number in QCD although it need not be integer valued. The Chern-Simons-Kähler action gives a contribution to the modified Dirac action at partonic orbits giving rise to fermionic vertices.

   The strong Kähler magnetic fields at the monopole flux tubes give rise to the analog of strong CP violation and provide a possible quantitative description for the generation of the matter-antimatter asymmetry in the decay of the energy of cosmic strings to fermion-antifermion pairs and bosons. For cosmic strings the Kähler magnetic field is extremely strong.

See the article Some comments about the identification of leptons and matter-antimatter asymmetry or the chapter About the TGD based views of family replication phenomenon, color confinement, identification of leptons, and matter-antimatter asymmetry 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.