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.