Monday, July 31, 2023

Mutations do not add: global epithasis and the notion of dark DNA

The Quanta Magazine article How Genetic Surprises Complicate the Old Doctrine of DNA provides a lot of food for thought. Good appetite!

Epistasis is the concept discussed. One has a reasonable empirical understanding of point mutations. Point mutations are however not independent as simple linear thinking would suggest. This gives rise to epistasis.

Two mutations with qualitatively similar effects can produce a mutation with an opposite effect. Poorly understood interactions between mutations exist and give rise to the epistasis. One might call these interactions non-linear in a lack of a better word. The proposal that has been developed is global epistasis suggesting that genes and even large units would tend to have like coherent units.

My own intuitive view of DNA is based on quantum coherence in DNA length scales predicted by the TGD based view of chemical DNA as a chemical "shadow" of what I call dark DNA.

Dark DNA is realized as sequences of dark protons at the monopole flux tubes of the magnetic body associated with the ordinary DNA. It relies on a universal realization of the genetic code based on a completely unique icosa-tetrahedral tessellation of hyperbolic 3-space (light-cone proper time constant 3-surface in Minkowski space M^4). Genetic code might be universal at the level of the magnetic body and biological realization(s!?) would be only of the many. This would make the Universe intelligent, conscious and evolving in all scales using the fundamental binary coded with a codon as a 6-qubit unit (see this).

Not only codons but also genes would be quantum coherent units interacting like particles. For instance, dark genes consisting of N dark codons (each with 3 dark protons) would emit 3N-photon as a single unit in communications based on 3N-resonance, which implies that identical dark genes can communicate with each and that the modulation of frequency scale as a message is coded to a sequence of resonance peaks analogous to a sequence nerve pulses. This is a quantum generalization of what occurs in radio communications. Even larger quantum coherent units can be considered.

This implies that mutations are not anymore independent as in the picture based on chemistry alone. Mutations could have profound effects on the communications by 3N-resonance and 3N frequency resonance is not anymore complete if one codon changes. Therefore the effects of two or more mutations on dark gene communications do not simply add up. This raises the hope that their interactions might be understood some day.

See the article About honeycombs of hyperbolic 3-space and their relation to the genetic code).

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

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

Saturday, July 29, 2023

High Tc superconductor above room temperature discovered?

The newest sensational physics in the physics of superconductivity is the existence of superconductors much above the room temperature (127 Celcius). See the popular article and the the original article by Sukbae Lee et al.

Standard physics does not allow high temperature superconductivity. Nature is however scandalously misbehaving and irritates theoreticians by refusing to obey their orders! We have had high temperature superconductors for decades and now new candidates existing even above room temperatures are emerging. Biosystems are excellent candidates for macroscopic quantum phases naturally explaining the macroscopic coherence impossible to understand in standard biochemistry.

Perhaps the problem is with our physics. The basic problem is that quantum coherence in the needed long scales is not possible in standard quantum theory. Planck constant is simply too small.

There is also another unsolved problem: dark matter. Most of matter is dark and all identifications as new kinds of exotic particles have failed. Particle physics in its recent form is not enough.

TGD prediction is that dark matter corresponds to heff= nh0> h phases of ordinary matter. Second prediction is that any system has field identity, field body, in particular magnetic body. Magnetic body consists of flux tubes and sheets. These phases reside at the magnetic body of system as the TGD the counter part for magnetic fields. This explains why dark matter has not been detected directly: we try to find it in wrong place!

Large values of heff make it possible to have quantum coherence in long scales and therefore also high temperature superconductivity. In living matter, superconductivity at the magnetic body forced by metabolic energy feed making it possible to have a steady distribution of the values of heff (quite generally, energies increase with heff, which tends to reduce spontaneously so that supra phases are destroyed).

Addition: It has turned out that the claimed discovery did not hold water. The article has been withdrawn.

For the TGD view of superconductivity see for instance this , this, this, and this .

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

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

Friday, July 28, 2023

Oxygenation of oceans did not precede Cambrian Explosion as TGD predicts and empirical study concludes

There was an interesting article in Futurism about the findings challenging basic text assumption related to the origin of life (see this). The research article "Widespread seafloor anoxia during generation of the Ediacaran Shuram carbon isotope excursion" can be found here.

On the basis of empirical evidence it is claimed that the view of the gradual oxygenation of oceans is wrong. The abstract of the article explains the findings.

Reconstructing the oxygenation history of Earth's oceans during the Ediacaran period (635 to 539 million years ago) has been challenging, and this has led to a polarizing debate about the environmental conditions that played host to the rise of animals. One focal point of this debate is the largest negative inorganic C-isotope excursion recognized in the geologic record, the Shuram excursion, and whether this relic tracks the global-scale oxygenation of Earth's deep oceans.

To help inform this debate, we conducted a detailed geochemical investigation of two siliciclastic-dominated successions from Oman deposited through the Shuram Formation. Iron speciation data from both successions indicate formation beneath an intermittently anoxic local water column. Authigenic thallium (Tl) isotopic compositions leached from both successions are indistinguishable from bulk upper continental crust (ε205TlA≈-2) and, by analogy with modern equivalents, likely representative of the ancient seawater ε205Tl value. A crustal seawater ε205Tl value requires limited manganese (Mn) oxide burial on the ancient seafloor, and by extension widely distributed anoxic sediment porewaters.

This inference is supported by muted redox-sensitive element enrichments (V, Mo, and U) and consistent with some combination of widespread (a) bottom water anoxia and (b) high sedimentary organic matter loading. Contrary to a classical hypothesis, our interpretations place the Shuram excursion, and any coeval animal evolutionary events, in a predominantly anoxic global ocean.

The absence of oxygenation before the Expolosion is also the TGD based prediction. The TGD based model predicts that the mysterious Cambrian Explosion in which advanced multicellulars suddenly emerged involved an increase of Earth radius by factor 2 in a geologically short time scale (see this and this).

This view conforms with TGD inspired cosmology in which a smooth cosmological expansion is replaced with a serious rapid step-wise expansions, which are essentially quantum phase transitions involving astrophysical quantum coherence scales.

The Earth would have been like Mars now (not much water at surface, even the radius would have been very near to Mars radius) and life would have evolved in underground oceans (being shielded from cosmic rays and meteors), in the womb of Mother Gaia. The evidence for the underground life on Mars is accumulating. The water in underground oceans would have oxygenated by photosynthesizing life and the underground water would have bursted to the surface and give rise to the oxygenated oceans covering most of the Earth's surface since then.

The basic objection is that photosynthesis was not possible. The core of the Earth however produces radiation in the same wavelength range as the Sun and in the TGD framework this could allow the development of photosynthesis (see this).

Whether the interpretation of the article that life evolved in anoxic global ocean is consistent with the TGD view that this oceans was essentially absent, is not of course clear.

What other objections can one invent against the TGD view? The first objection against the TGD proposal is that fossils of complex multicellular life forms have been found with age of 600 million years to be compared with the fossils dating back to 550 years ago when Cambrian explosion could have started. The story of their discovery told in the popular article "How 2 Teens Accidentally Solved Charles Darwin's Most Vexing Problem" (see this) is fascinating.

In 1956, a teenage girl by the name of Tina Negus found a strange looking fossil in Charnwood Forest in Leicestershire, England. The plant fossil should not have been there since the rock was 600 million years old and the Cambrian explosion started roughly 60 million years later. Tina Negus showed a pencil rubbing to his geography teacher but he didn't believe her.

A year later, in 1957, three teenage boys were playing near the same rock face when they, too, noticed the same fossil. One of these teens, fifteen-year-old Roger Mason, found the second fossil. Roger Mason contacted Trevor Ford, a local geologist, who wrote about the finding to the Journal of the Yorkshire Geological Society. The new plant was named Charnia Masoni. Charnia is a genus of frond-like life forms belonging to the Ediacaran biota. Charnia came from Charnwood Forest in Leicestershire, England where Tina Engus found it. Masoni is after Roger Mason.

Does the TGD based view survive these findings? Note first that the Charmia Masoni does not conform with the conclusion that the oceans that possibly existed at that time did not contain oxygen. Furthermore, Charnia Masoni does not change the basic facts: complex multicellular life forms emerged as if from nowhere. The time span from Charnia Masoni fossils about 600 billion years to the beginning of Cambrian Explosion about 538.8 million years ago is about 10 per cent.

Can one explain the finding in the TGD view of the Cambrian explosion?

  1. If the surface of Earth did not contain much water before the Cambrian Explosion, one can imagine that water leaked from the underground oceans locally at some places but not everywhere. Instead of oceans, there were oxygenated lakes, where multicellular life forms survived.
  2. Another possibility is that the expansion of Earth involves periodic oscillation typical of resonances so that bursts of oxygenated water containing the highly evolved life forms emerged to the surface. I have considered this kind of explanation for the periodic oscillations found to be associated with the Cambrian explosion.
There is also indirect evidence for the presence of life about 3.85 billion years ago (see this). The interaction of rocks with life forms lowers the C-13 ratio of rocks to a characteristic value serving as a signature for life. Any sedimentary rocks that formed before life appeared on Earth would have the high C-13 ratio of a volcanic origin. The discovery of rocks with the same C-13 ratio that serve as a signature of life support the view that very primitive microbial life existed already at that time. One can consider the possibility that very primitive life forms existed at the surface of Earth. Second possibility is that they leaked from underground oceans. Also in Mars there is evidence for the presence of water and it could have indeed leaked from underground water reservoirs.

See the article Expanding Earth Hypothesis and Pre-Cambrian Earth or the chapter Quantum gravitation and quantum biology in TGD Universe.

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

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

Tuesday, July 25, 2023

A revolution in lithium-sulphur battery technology?

The recent accidental discovery could revolutionize battery technology. The so-called γ-sulphur is a phase of sulphur that stops the degradation of lithium-sulphur batteries and this could give electric vehicles a range of thousands of kilometers. In this article a proposal for the mechanism explaining the stability of γ-sulphur in lithium batteries is proposed.

A basic mystery of electrolysis is that the electric field between electrodes is quite too weak to explain the ionization, A TGD based model based on the TGD view of Pollack effect and its generalization explains why the ionization can happen in electrolyte. The implications of the Pollack effect for "cold fusion", nuclear physics and prestellar evolution are discussed. Cell membrane and DNA are negatively charged and also here Pollack effect and its possible generalization would play a key role.

See the article A revolution in lithium-sulphur battery technology? or the chapter TGD and condensed matter.

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

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

Sunday, July 23, 2023

Accidental discovery possibly leading to a breakthrough in the lithium batttery technology

The last week has been full of surprises. The most recent surprise came yesterday. The popular article published in Big Think (see this) tells about an accidental discovery, which could revolutionize battery technology. The so-called gamma-sulphur is a phase of sulphur, which stops the degradation of lithium-sulphur batteries so that they could give electric vehicles a range of thousands of kilometers.

It is good to start from the problems of lithium batteries.

  1. Also other materials, such as cobalt are needed in lithium batteries but their mining is very environmentally very damaging. There are also humanitarian problems: the working conditions are bad and even child labor is used.
  2. Lithium batteries quickly lose their capacity and charging times are long. Lithium batteries also suffer degradation.
  3. The energy density is low so that the lithium batteries tend to be very heavy, which limits their commercial use in electric planes and ships.
  4. Damaged cells can spontaneously catch on fire.
Lithium-sulphur batteries might provide a cure of all these problems but there is a new very serious problem. Polysulfides Li-S-...-S-Li are formed in the dielectric between the Li and sulphur containing capacitor platers and this reduces the number of charge cycles by one half from about 2000 cycles.

The completely unexpected discovery was as follows.

  1. Somehow the presence of gamma-sulphur as a phase of sulphur, unstable at room temperature but stabilized in presence of Li, prevents the formation of polysulphides Li-S-...S-Li. Gamma-S crystals are produced by dropping hot sulphur to water at temperatures above 95 degrees Celsius. They are smooth elastic and resemble rubber.
  2. What in their structure does prevent the formation of sequences L-S-....-S-Li sequences apart from Li-S-Li? Could the presence of gamma-S crystals prevent the formation of S-S bonds or are they formed but split very rapidly? Why is gamma-S stabilized in the presence of Li?
  3. One thing to notice is the chemical analogy with water: H↔Li and O↔S. Could this help? What prevents the formation of H-O-...-O-H sequences in water and one has only H-O-H? Could this be a good question?
Let us try to answer these questions.
  1. The first thing to notice is that gamma-S is not stable at room temperature. Somehow the presence of Li must stabilize it. The gamma-S crystals should grow by addition of S to compensate for the spontaneous decay occurring at room temperature. This could give rise to flow equilibrium.
  2. Could it be that the presence of gamma-S crystals competes with the formation of Li-S-...S-Li sequences. Could S prefer to join to a gamma-S crystal rather than to add to the sequences of S:s in Li-S-...S-Li? The formation of sequences would stop at Li2-S. This does not yet explain the stability of gamma-S at room temperature: differs from that in the absence of Li only in that Li competes with gamma-S crystal for S atoms. The mechanism must be more delicate.
  3. Li-S....-S-Li polysulphides must be produced at a considerable rate but they provide the S:s for the crystal growth of new gamma-S. Li atoms are like servants carrying the food S at plate to gamma-S, which eats it. There is a flow equilibrium and the total amount of Li-S...-S-Li stays very small although Li-S....-S-Li is produced with a high rate!
I have not yet said anything about TGD and quantum but in the presence of gamma-S Li2-S is a chemical analog of water.
  1. Water is the dominating element of living systems. Here formation of H-O-O-...-H is of course not a problem. The magnetic body of the water gives water its very special properties and makes it very special at physiological temperatures at which Pollack effect in presence of say IR radiation and gel phase gives rise to the formation of negatively charged exclusion zones by driving protons to dark protons at magnetic flux tubes.

    Capacitors involve both negatively and positively charged plates. Pollack effect is crucial in the TGD view of living matter and generates negatively charged entities such as cell and DNA double strand. Living systems involve a lot of dielectrics and the cell membrane is an analog of a battery.

  2. Could the counterpart of the Pollack effect be involved with lithium-sulphur batteries? Could Li+ ions take the role of protons. Could they become dark lithium ions at the magnetic flux tubes and flow to the negative plate along them.

    In Pollack effect for Lithium the counterpart of exclusion zone with an effective stochiomery H1.5O and negative charge would be negatively charged Li1.5O so that every fourth Li+ would go the the magnetic flux tube and end up to the opposite electrode or its magnetic body. It would create the same voltage along the space-time sheet associated with the electrolyte as along possibly still existing flux tubes connecting it to the negatively charged electrode. This phase could be essential for the stability of the battery.

  3. In fact, years ago I realized that electrolysis is not actually understood in standard chemistry! The mystery is ionization which requires large energies measured in electron volts. The electric voltage between the batteries is low and generates extremely weak electric fields so that it should have no effects in the atomic length scales.

    I have discussed this problem in an article about "cold fusion".

  4. "Cold fusion" (for the recent situation see this) is an anomaly, whose existence very many colleagues still find difficult to accept. "Cold fusion" also involves dielectric plates and the proposed TGD based model (see this, this and this) involves dark proton currents at magnetic flux tubes.

    "Cold fusion", or more precisely dark fusion, can be initiated at rather low temperatures and involves the formation of dark proton sequencies at monopole flux tubes. Dark nuclei are essentially scaled variants of nuclei but much smaller binding energy and can be generated in Pollack effect, which plays a key role in the TGD inspired quantum biology. Dark nuclei can spontaneously decay to ordinary nuclei and also protons can transform to neutrons. This liberates essentially all nuclear binding energy.

    This mechanism would generate protostars in which there is no ordinary fusion yet. The temperature increases because essentially nuclear binding energy is liberated when the dark nuclei transform to ordinary nuclei and eventually ordinary fusion is ignited. It is quite possible that all nuclei heavier than Fe are generated in this way outside stellar cores rather than in super nova explosions. Also many anomalous abundances of lighter nuclei could be understood.

See the article A revolution in lithium-sulphur battery technology? or the chapter TGD and condensed matter.

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

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

Saturday, July 22, 2023

Fast magnetic reconnections finally understood?

There was an interesting article in Quanta Magazine about the reconnections of the magnetic fields for astrophysical objects (see this). Two kinds of reconnections have been observed. The slow ones for which the Maxwellian electrodynamics provides a satisfactory description and the fast ones, which are not understood.

Fast reconnections liberate magnetic energy powering solar flares and solar wind, high-energy particles ejected by exploding stars, and the glow of jets from black holes. The popular article told about a theory of Yi-Shin Liu et al (this) claimed to allow the understanding of the fast reconnections in the Maxwellian framework. The model assumes that reconnection is induced by a generation of electric fields for instance by different velocities of protons and electrons moving along the flux lines.

Personally I am a little bit skeptical. There are many other enigmas related to magnetic fields in cosmic scales. Particular, the existence and stability of magnetic fields in astrophysical scales is a mystery in the Maxwellian framework. Also these problems should be solved.

In the TGD Universe, the flux lines are replaced with flux tubes which can be seen as bundles of flux lines assignable to 3-D surfaces in M4×CP2 having 4-D space-time surfaces as orbits. Reconnection of flux lines is replaced with a reconnection of flux tubes. Change for the topology of field lines is replaced with that for the 3-space as 3-surface so that topological reactions for 3-surfaces are in question: this conforms with "Topological GeometroDynamics". When flux tubes are idealized as strings, this is locally nothing but basic vertex for closed strings in string theories.

Intriguingly, TGD allows two kinds of flux tubes.

  1. Flux tubes with a disk as cross section and having a boundary correspond to the Maxwellian situation. Cross section can be also closed but if the flux vanishes, the flux tube is not stable against splitting.

    The Maxwellian flux tubes with open cross section require currents to create the magnetic field. Currents tend however to dissipate so that the Maxwellian flux tubes and corresponding magnetic fields are not stable. This leads to a problem in understanding why magnetic fields in astrophysical scales are so stable.

  2. The monopole flux tubes which have closed 2-surface (say) spheres as a cross section are not possible in Minkowski space and carry conserved monopole fluxes.
Monopole flux tube have several properties which make them very attractive, not only astrophysically and biologically but in all scales, for instance from the perspective of particle physics.
  1. Monopole flux tubes are stable against splitting. U-shaped monopole flux tubes can however split by reconnection which means emission of a closed flux tube. This occurs for instance in solar wind at the night-side of the Earth.
  2. Monopole flux tubes form tube networks having physical objects in various scales as nodes. They occur in all scales, including astrophysical and biological scales.
  3. The tell-tale signature of the monopole flux fields is that no current is needed to create them. Monopole flux tubes explain the existence of magnetic fields in cosmic scales which would not have been even created since the currents needed to create them are random.

    For instance, Earth's magnetic field is the sum of these two contributions and monopole flux is estimated to be 2/5 of the entire flux. Monopole contribution would be stable and explain why the Earth's magnetic field has not decayed long ago. The monopole part of the Earth's magnetic field plays a key role in TGD inspired quantum biology based on the notion of dark matter as phases of ordinary matter with an effective Planck constant residing at the magnetic body of the system.

  4. Monopole flux tubes are the key building bricks of all astrophysical structures in the TGD Universe, in particular solar magnetic fields, and are actually directly visible. Dark matter and energy would be associated with cosmic strings (not those of gauge theories), which have 2-D string world sheet as cross section and 2-D complex manifold of CP2, say sphere, as a CP2 projection. They create a transversal gravitational field explaining the flat velocity spectrum of stars around galaxies which can be interpreted as a local tangle of cosmic strings for which the cosmic string has thickened to a flux tube and generated galactic matter in the reduction of string tension.
The reconnections of the monopole flux tubes would be natural candidates for a fast reconnection for which the Maxwellian model was proposed. Do the TGD view and the Maxwellian view exclude each other or could they be parts of the same story?

The reconnection of a U-shaped flux tube for which parallel portions carry opposite currents requires a pinch of the flux tube so that flux tube portions can touch each other. Ampere's law states that current wires carrying parallel currents attract each other. Could it explain the pinch? One can imagine two mechanisms.

  1. The current along the U-shaped flux tube is conserved unless there is a temporary accumulation of electric charge. The absence of charge accumulation implies that the net currents along parallel portions are opposite and repel each other. However, if charge accumulation takes place, the currents can become locally parallel and this could cause the attraction and pinch. The interesting question is what could cause the local charge accumulation.
  2. One can also consider a geometric mechanism in which the second portion of the U-shaped flux tubes turns temporarily backwards and the portion in which current runs parallel to the current in the unaffected portion comes near to it so that an attractive force causing the pinch is generated and U-shaped flux tube pair emits a closed flux tube. In the TGD framework, quantum tunneling in macroscopic length scales as a pair of "big" state function reductions reversing the arrow of time temporarily is suggestive.
  3. In the TGD framework, quantum tunneling in macroscopic length scales as a pair of "big" state function reductions (BSFRs) reversing the arrow of time temporarily is suggestive. Suppose that in the initial  situation there are two U-shaped flux tubes associated with the two molecules and currents are steady and conserved except during the  reconnection period.

    Reconnection of the two   U-shaped flux loops  would  give rise to a pair of monopole flux tubes  of opposite magnetic fluxes connecting the two objects, say biomolecules. In this conformation  parallel  currents   flow  along the flux tubes. It is assume that the charges  at the different flux tubes form Cooper pairs.  

    Supra current induces an  accumulation of net charges of opposite sign at the ends of the flux tube pair.  Supra current cannot however flow forever. Charge saturation occurs and the supra current goes to zero. In this situation reconnection back to U-shaped flux loops can take place.    This  state is  not superconducting since individual charges at the flux tubes flow in opposite directions  and  cannot form Cooper pairs.  Therefore the splitting of Cooper pairs  and reconnection would occur simultaneously.  BSFR would correspond to a phase transition between super-conducting and non-superconducting states.  This phase transition would be a basic mechanism of biocatalysis.

See the article Magnetic bubbles in TGD Universe: part II or the chapter with the same title.

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

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

Friday, July 21, 2023

Kosmologiassa tapahtuu

Eilen tulin kuunnelleeksi Tiedeykkösessä, itse asiassa onnekkaan sattuman ansiosta, kosmologi Esko Valtaojan haastattelun liittyen kosmologiaan. Otsikkona oli "Maailmankuvamme juuret: mitä enemmän tietoa olemme saaneet, sitä pienemmältä maapallo vaikuttaa". Tällaiset haastattelut ovat hauskoja koska niissä tulee aina tarkastellun tieteen alan historiallisesta kehityksestä esiin yksityiskohtia, joista ei ennen tiennyt. Erityisesti selvisi esimerkkien kautta se kuinka valtavasti kosmologia on kehittynyt muutamassa kymmenessä vuodessa.

Tämän vastapainona on tietysti se, että Einsteininin yleinen suhteellisuusteoria on selvinnyt kerta kerran jälkeen testeistään siinä missä kilpailijat ovat kadonneet kartalta. James Webb teleskooppi käynnisti varsinaisen massa-ekstinktion ja voi ennustaa hyvin perustein, että useimmat standardimallin syntyneet massiivisesti markkinoidut ideat ja teoriat kuten suuret yhtenäisteoriat, supersymmetria, supersäiteoriat, inflaatio, multiversumi, valaisemattoman aineen mallit,... jäävät tieteen historiaan pelkkinä kuriositeetteina.

Tällaisten ohjelmien lopussa on tapana kurkistaa tulevaisuuteen. Odotin, että puhuttaisiin James Webbin käynnistämästä vallankumouksesta kosmologiassa, jonka keskellä elämme. Nobelisti Sir Roger Penrose tiivisti tämän toteamalla "Cyclic Universe Wrong And Something Terrifying Happened Before Big Bang". Huomattakoon, että Penrose on syklisen Universumin idean isä. Penrosen tyly viesti oli se, että olemme olleet väärässä koko ajan. Toki paljon muutakin astrofysiikkaan liittyvää vallankumouksellista tapahtuu koko ajan: olemassaolevat teoriat haastavia tuloksia tulee lähes päivittäin.

Hämmästykseni ei sanottu sanaakaan meneillään olevasta mullistuksesta. Päättelin, että ohjelman on oltava uusinta vanhasta muutama vuosi sitten äänitetystä. Näin täytyy olla. Tarkistin läytyykö Areenan sivulta mainintaa siitä että on kyseessä uusinta. Sellainen olisi paikallaan sillä tiede kehittyy tänä päivänä huimaa vauhtia. Sellaista ei löytynyt. Pikku näpäytys Areenan informaatikoille on paikallaan!

Joka tapauksessa Ylen olisi syytä mitä pikimmin tehdä haastatteluja James Webbin tuloksista kuten monista muistakin käänteentekevistä löydöistä kosmologiassa ja astrofysiikassa. Ehkäpä he voisivat haastatella valtakunnan kosmologeina kunnostautuneita Kari Enkvistiä, Esko Valtaojaa ja Syksy Räsästä asian tiimoilta.

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

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

Thursday, July 20, 2023

Janus faced white dwarf

Science Daily release (see this) told about a really weird object: the surface of the white dwarf is made of hydrogen on one side and helium on the other. The organization of particles with different masses to layers occurs by gravitation but only in vertical direction.

It is believed that hydrogen is able to diffuse into the interior of the dwarf so that its surface density is reduced so that effectively helium begins to dominate. This would be analogous to a phase transition. But why would this take place only for the other side of the white dwarf and why such a sharp division to two regions.

Magnetic fields are proposed as a possible explanation.

  1. At the surface layer the magnetic fields tend to prevent the mixing of hydrogen and helium ions by forcing the ions to cyclotron orbits. The mixing argument of the article suggests that both hydrogen and helium are ionized.
  2. Whether this is the case depends on temperature. Wikipedia article claims that white dwarf temperatures are in the range 150,000 K-4000 K (15 eV -.1 eV). The upper limit 15 eV is slightly above 13.7 eV which is the ionization energy of hydrogen in ground state so that hydrogen could be ionized. Helium would not be ionized. If there is no ionization, the magnetic moment of hydrogen is what matters. Helium nucleus has a vanishing magnetic moment. Non-ionized helium looks magnetically inert but not hydrogen, which could also be at cyclotron orbits.
  3. The popular article informs that the temperature of the white dwarf is around 35,000 K (35 eV). For helium the ground state energy, proportional to Z2 is 54.8 eV which suggests that helium is not ionized and cyclotron orbits are not possible.
Two options are proposed.
  1. If hydrogen is ionized, it moves along cyclotron orbits and tends to be magnetically confined. Also the higher magnetic field strength at the hydrogen side reduces the mixing. Since helium is not ionized, it is not magnetically confined and will mix more easily. This is true in the standard physics picture, in which one has no monopole flux tubes, which confine even non-charged particles.
  2. The higher value of the magnetic field implies a lower pressure and this would imply slower diffusion of the hydrogen to the interior. If the sum of the magnetic and ordinary pressures is constant, hydrogen oceans with a higher magnetic field strength and lower pressure could be formed.
Also I tend to believe that magnetic fields could solve the puzzle but not necessarily in the proposed way. What comes to mind after a minute of thinking is the following.
  1. In the TGD framework, magnetic fields correspond to flux tubes and flux sheets. There are monopole flux tubes, something new, and ordinary flux tubes possible also in the Maxwellian world. There would be confinement inside the flux tubes. The flux tubes can also flatten to flux sheets.
  2. In particular, the gravitational magnetic monopole flux tubes and sheets are possible. This is a purely TGD based phenomenon. The gravitational Planck constant hbargr= GMm/β00= v0/c ≤ 1 is velocity parameter) is proportional to the mass M of the white dwarf and to the mass m of the particle, now helium or hydrogen.
The longstanding question has been whether a gravitational flux tube/sheet characterized by ℏgr
  1. attaches only to/contains only particles with a fixed mass m,
  2. or whether it attaches to particles with varying mass m. If so, the gravitational Planck constant would be 2-particle property and depend on m for a gravitational flux tube/sheet associated with mass m.
If the first option is true, the particles with different masses m would be arranged like books in the library, each in its own shelf defined by the gravitational flux tube/sheet (M,m). In the case of the weird white dwarf, helium and hydrogen would be on their own shelves located at different sides of the star as a gravitational library. For flux tube option there could be a mixing of the flux tubes. For large sheets the mixing would be absent.

What does the first option imply in the case of the weird white dwarf? One can consider two options.

  1. Monopole flux tubes form roughly parallel layers along the surface of the white dwarf. The layers associated with hydrogen and helium should be disjoint: but why?
  2. There are separate flux sheets associated with either hydrogen or helium but not both. If the flux sheets have boundaries orthogonal to the rotation axis, the hydrogen and helium layers are static. Since helium can mix in the tangential direction, it would prefer flux sheets. Hydrogen would not mix and could be also associated with flux tubes.
In quantum biology the first option would imply that at the level of dark matter associated with the magnetic bodies the biomatter would be extremely organized, in a complete contrast to the view that biomatter is a chaotic soup of biomolecules.

The interaction by cyclotron frequency resonance occurs only between charged particles with the same heff and the same flux tube field strength: this requires the same mass in the case of gravitational flux tubes. Note that one can also talk about electromagnetic Planck constant. This supports the library like organization.

Charged particles with different gravitational Planck constant (masses m) can have gravitational cyclotron energy resonance but not frequency resonance: this reflects Equivalence Principle.

See the article Magnetic Bubbles in TGD Universe: Part I 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. .

Too early carbon and dark stars: the most recent discoveries of James Webb Telescope

The most recent shattering discovery of the James Webb telescope is the detection of carbon in the cosmic dawn (see this). According to the standard view of formation of elements, such an early presence of carbon is impossible.

TGD view of the formation of elements is based on the notion of dark fusion, which was originally developed to explain "cold fusion". This process can be initiated at rather low temperatures and involves the formation of dark proton sequences at monopole flux tubes. Dark nuclei are essentially scaled variants of nuclei but much smaller binding energy.

They can decay spontaneously to ordinary nuclei and also protons can transform to neutrons. This mechanism would generate protostars in which there is no ordinary fusion yet. The temperature increases because essentially nuclear binding energy is liberated when the dark nuclei transform to ordinary nuclei and eventually ordinary fusion is ignited. It is quite possible that all nuclei heavier than Fe are generated in this way rather than in supernova explosions. Also many anomalous abundances of lighter nuclei could be understood.

One can imagine also another, not necessarily independent, mechanism explaining the too early presence of carbon. It would be allowed by the zero energy ontology of TGD. In TGD counterparts of ordinary state function reductions the arrow of time changes. These state function reductions can occur in arbitrarily long length scales in the TGD Universe. This means that even astrophysical objects live forth and back in geometric time and their developmental age can be much longer than the usual age. Besides astrophysical objects older than the Universe, this could explain the presence of carbon.

Recently James Webb telescope discovered also dark stars of gigantic size (see this). For dark stars dark nuclear fusion could have continued without ignition of the ordinary nuclear fusion. One can of course ask whether dark stars could be unstable against local ignition, which could lead to its decay to ordinary states.

The second option possibly explaining dark stars is the transformation of dark matter and energy of extremely thin monopole flux tubes to ordinary matter and dark energy, a process analogous to inflation. The two explanations of dark stars might be closely related.

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

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

Wednesday, July 19, 2023

Metals can heal themselves!

It seems that we are living in the middle of science fiction! Almost every day a new surprise. We are in the middle of a revolution and the new world view provided by TGD is at its core. The surprise of this day was the discovery that metals are able to heal their fractures (see this). The theory behind the discovered healing process of metals is based on standard physics: see the article published in article by Brad Boyce published in Nature. I am not at all confident that standard physics is enough. The TGD based explanation relies on the following vision.
  1. The first key prediction is the possibility of quantum coherence in arbitrarily long scales due to the presence of phases of ordinary matter with an arbitrarily large value of Planck constant and identified as dark matter. The magnetic body of the system, say metal, as a TGD counterpart of ordinary magnetic fields, is the carrier of the dark matter and controls the system and receives "sensory" input from it. The hierarchy of Planck constants is a prediction of the number theoretic vision of TGD. The value of the Planck constant is given by heff=nh0, where n corresponds to the dimension of an algebraic extension associated with the polynomial defining the space-time regions considered.
  2. Negentropy Maximization Principle (see this) is mathematically analogous to the second law and implies that in the statistical sense the p-adic negentropy as a measure for the conscious information and complexity of the system increases. This follows from a simple fact: the number of extensions of rationals with dimension larger than given integer n is infinitely larger than those with dimension smaller than n. The assumption that the coefficients of polynomials giving rise to the extension have coefficients smaller than the degree of the polynomial implies that the number of extensions with dimension smaller than n is actually finite.
  3. Quantum TGD involves a new ontology that I call zero energy ontology (see this and this). The first prediction is that in ordinary ("big") state functions (BSFRs) the arrow of time changes. Time reversals in BSFRs mean "falling asleep" or "death" in a universal sense and provide a universal mechanism of healing. We indeed know that sleep heals.
  4. The arrow of time is preserved in "small" state function reductions (SSFRs) identifiable as weak measurements replacing the Zeno effect in which nothing occurs. SSFRs involve a repeated measurement of observables defining the states at the passive boundary of causal diamond (CD) as their eigenstates. These observables are measured at the active boundary of CD which in statistical sense drifts farther away from the passive boundary. There are also other observables made possible by the failure of a complete determinism for the holography forced by the general coordinate invariance implying that space-time surfaces are analogous to Bohr orbits of 3-surfaces as analogs of particles. When a system is perturbed the set of measured observables can change and this induces BSFR and the roles of active and passive boundaries change.

    For instance, BSFR could be induced by a perturbation modifying the set of the measured observables so that it does not anymore commute with the observables defining the eigenstate basis at the passive boundary of causal diamond (CD). Pairs of BSFRs could induce temporary changes of the arrow of time and they could give rise to a trial and error process essential for homeostasis in living matter. This implies also healing in the sense that p-adic negentropy measuring the amount of conscious information and complexity of the system increases in a statistical sense.

Any system has a magnetic body. For instance, magnetic body accompanies also computers and one can ask whether it can give computers a rudimentary consciousness (see this and this). Metals are not an exception. This forces us to ask whether even metals could heal in the proposed sense. As noticed in the article, the technological implications could be huge.

See the article TGD and condensed matter or the chapter or 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.

Breakthrough in the understanding of energy transfer in photosynthesis

I learned about very interesting results related to photosynthesis. A popular article on the BigThink page (see this) tells about an article published in the journal PNAS (see this).

The basic mystery of photosynthesis is extreme energy efficiency. Up to 95 % of the photon's energy is transmitted in a medium that would seem to be as inhospitable as possible for energy transmission with almost no dissipation. The use of very low temperatures, the shooting of monochromatic photons into a lattice, and superconductivity are out of the question. The incoming photons also have a wavelength distribution, which does not facilitate the energy transfer either.

1. Some facts

Consider first a summary of the basic findings and conclusions.

  1. Chlorophyll is the basic structure involved with photosynthesis. Its basic function is to gather solar energy and transfer it to the reaction center where the energy is stored to various biomolecules. There are 2 wavelength bands, corresponding to 430 nm in blue and 662 nm in red, where the absorption is especially strong. The so-called LH2 proteins act as antennas absorbing photons. In the reaction center LH1 proteins perform photosynthesis by building biomolecules to which the solar energy is stored.
  2. It has been observed that the lower limit of the size of the so-called light-absorbing LH2 antenna proteins is 2.5 nm. It is also the minimum distance between LH2 proteins. The proposal is that the LH2 antenna network could somehow make the transfer of energy almost without dissipation.

    It is believed that the disorganization of the proteins might explain this. However, in the popular article there was no intuitive argument as to why this is so. The claim is made on the basis of computational models and empirical facts gained by studying the transfer process. I find it difficult to imagine how the irregular positions of proteins could promote the process.

  3. The proposed interpretation of the findings is as follows. A photon enters and excites the electron of the LH2 protein. When the electron is de-excited, one or more photons are generated which in turn excite the electrons of the next LH2 proteins. Finally, the generated photons excite the electrons of the reaction center and these electrons are used in the photosynthetic process to produce sugar molecules.

2. The TGD based model

The findings seem to resonate with two key views of the TGD inspired quantum biology.

  1. Photosynthesis involves at least a temporary storage of solar energy to quantum gravitational energy batteries (see this and this).
  2. there is dark variant of the genetic code and realization of dark DNA double strand base on the icosahedral tessellation (see this) of the hyperbolic 3-space H3, which is realized both as mass shell in M4⊂ M8 and light-cone proper time=constant 3-surface in M4⊂ M4× CP2.

    Hyperbolic and possible other tessellations would be associated, not with the biological body, but with the magnetic body (MB) of the biosystem carrying dark rather identified as phases of the ordinary matter with effective Planck constant heff=nh0. The location of dark matter at the field body would also explain why dark matter has not been found in various searches.

2.1 Basic questions

What are the questions waiting for an answer?

  1. Why would the dissipation be so low? Quantum coherence in a scale of at least the order of tens of nanometers could guarantee this. Dark matter as phases with a large value of heff indeed implies a long quantum coherence scale. Also a regular crystal structure is a natural prerequisite for a low dissipation. The dissipation is minimized if the energy or possibly the electrons are transferred through the MB carrying dark matter and accompanied by hyperbolic tessellation.
  2. The minimum distance between LH2 proteins is about 2.5-4 nanometers, which corresponds to the DNA codon size scale. In the TGD based model for genetic code, the dark realization of the genetic code and the DNA double helix are connected to an icosa-tetrahedral honeycomb in hyperbolic 3-space H3 assigned with the MB (see this). Could the crystalline structure be realized by using the same icosa-tetrahedral tessellation as associated with the dark DNA and dark genome controlling the ordinary genome.

    If the transfer of energy to the reaction center occur at the MB as a transfer of dark electrons, the dissipation could be very small since there would be no direct interaction of the dark electrons with the ordinary matter if the interaction vertices can involve only particles with the same value of heff, as seems natural.

2.2 Quantitative data

Consider next quantitative data.

  1. The distance between LH2 proteins is in the range 2.5-3.1 nm. This scale corresponds to the DNA codon size scale and to the cell size of the fundamental region of the icosa-tetrahedral tessellation, which has Platonic solids as cells (see this). There are 12 icosahedrons, 20 tetrahedrons and 30 octahedrons forming a region of size 10 nm, which corresponds to the p-adic length scale L(151) (associated with a p-adic prime p≈q 2k, k=151) appearing as a characteristic length scale in bomatter. This region corresponds to 10 DNA codons for which the total twist along the DNA strand is 6π that is 3 full turns.
  2. The size of the structure involved with the photosynthesis would be naturally cell size scale? The wavelength of the red light gives a length scale of order .5 μm and serves a natural lower bound. Note that cell nucleus size is about 1 μm.
  3. The time τ required for the energy transfer between adjacent antenna proteins varies from 5.7 to 14 ps. In time τ, the distance traveled by the light is L=1.71-4.2 mm. Interestingly, for Earth the gravitational Compton wavelength Λgr(E)= GME0(E) is for β0(E)=v0/c=1 equal to Λgr(E)= 4.5 mm. Gravitational Compton frequency is fgr(E)=67 GHz and corresponds to a time of about Tgr(E)=15 ps, the upper limit for the estimated time.

    fgr corresponds to a photon energy of Egr=.27 meV. The electronic metabolic energy quantum in the case of the Earth would be related by a factor me/mp the protonic metabolic energy quantum identifiable as standard metabolic energy currency. The model for the findings of Andrew Adamatsky (see this) suggests that sponges have a language based on membrane potential oscillations with membrane potential variations of order mV. The TGD based model suggests the existence of metabolic energy quantum of this order of magnitude (see this)! meV is also the energy associated with the miniature membrane potentials. Could τ be identifiable as the gravitational Compton time Tgr at which the dark matter at the MB would oscillate?

2.3 How could the electrons be transferred to the reaction center as dark electrons?

Could the process at the level of LH2 antenna proteins correspond to the propagation of the dark electron and the hole associated with it? The dark electron would hop between the sites of the tessellation perhaps by quantum tunneling, which in TGD Universe corresponds to a pair of "big" (ordinary) state function reductions (BSFRs) changing the arrow of time temporarily. The dark electron current would be analogous to super current and the system "hole + dark electron" would be analogous to a Cooper pair. How to derive an estimate for the duration of one step?

  1. The duration τ of a single step should correspond to the oscillation period τ≈ Tgr. If so, the oscillation would play the role of EEG resonance oscillation coordinating the transfer by induces the pairs of BSFRs.
  2. The first guess is that electrons are converted to dark electrons with a large value of the gravitational Planck's constant ℏeff= ℏgr= GMm/β0(M) located at the gravitational MB of the Earth or Sun. They would be transferred to the U-shaped monopole flux tubes and the reduction of the binding energy of the electron would be equal to the energy of the incoming photon absorbed by it.

    The reduction of the binding energy cannot be however purely gravitational. For electrons, the maximal gravitational binding energy in the case of the Earth is about Egr(Earth,e)=.25 meV whereas the incoming photon has energy E≈eq x\times .5 eV, where x is in the range 4 to 6 in the wavelength range considered. For the Sun the maximal binding energy Egr is reduced by the ratio [M(Earth)/M(Sun)]\times [R(Sun)/R(Earth)= .071. In the case of protons with Egr(Earth,p)=.5 eV this gives to Egr(Sun,p)=.14 eV, which happens to be roughly twice the energy assignable to membrane potential. For electrons this gives Egr(Sun,e)= 1.8 μeV.

    For the energy transfer in photosynthesis, the energy of the solar photon cannot therefore correspond to the change of gravitational binding energy in the case of electrons. Rather, the energy must be identified as the change of electromagnetic binding energy as an atom is effectively ionized when an electron becomes a dark electron at the MB. This MB need not be gravitational and could also correspond to a relatively small heff>h.

  3. What comes to mind are dark unpaired valence electron states of atoms in which the heff of an unpaired electron increases so that binding energy is scaled down by 1/heff2. The binding energy spectrum of the dark electron states is obtained by scaling the ordinary binding energy spectrum and these states are analogous to Rydgerg states in that the radius of Bohr orbits is scaled up by heff2. If the valence electron becomes gravitationally dark (heff=hgr), the atom effectively suffers ionization to a state with vanishing energy and positive charge. Dark ions could correspond to this kind of states.
  4. How could the energy transfer to the reaction center take place? The simplest mechanism could be the following. One can charge the solar energy batteries by transforming ordinary electrons to dark electrons at the MB of the Sun. At the reaction center the dark electrons drop back and transform to ordinary electrons and are available for the photosynthesis proper, storing the energy to biomolecules.

    The experimental findings could be consistent with the assumption that the pairs formed by a dark electron and hole move to the reaction center, and the movement of the dark electron is analogous to a conduction in a lattice by hopping. The lattice could correspond to the tetra-icosahedral tessellation assignable also with DNA and genetic code. The time for one transition would correspond to Tgr(Earth)≈ 15 ns. This supports the view that the MB of the Earth is present.

  5. Why would the dropping down to Earth take place in the reaction center? The holes have an effective positive charge because the dark electrons have a large distance to the surface of Earth. If the reaction center has a negative charge, it attracts the positively charged holes. The holes move towards the reaction center and the dark electrons and gravitational monopole flux tubes and dark electrons follow. The electrons transform to normal ones and holes disappear. The predicted negative charge of the reaction center serves as a test for the proposal.
  6. How could this negatively charged region in the reaction center be generated? Pollack effect (see this and this), discussed from the TGD point of view for instance here, is induced by irradiation of water by (say) infrared light in presence of a gel phase and indeed generates negatively charged exclusion zones. The exclusion zones could be due the transfer of protons of water molecules to dark protons at the flux tubes of the MB, which is however not gravitational. Both cells and DNA represent examples of negatively charged objects. Pollack effect is a key element of the TGD inspired view of living matter. There it is natural to assume that the exclusion zone is present also in the reaction center.
If the energies of dark electrons and holes are separately conserved, they can annihilate to the ordinary electron in the reaction center. Can this be true?
  1. Why would the energy of the dark electron be conserved in the hopping along the tessellation? Single step would correspond to a motion under the magnetic Lorentz force, which conserves energy since force is orthogonal to the velocity.
  2. What about the dark electron-hole interaction? This interaction is present if the flux tube follows the motion of the hole-dark electron pair. This pair would form a bound state analogous to the Cooper pair and its energy would be conserved if its scattering would reduce to the magnetic scattering of the dark electron. The situation would be very much like in the case of superconductivity.
  3. If the hole corresponds to a transition of an unpaired valence electron to a large heff analog of a Rydberg state with a very large size, the binding energy and energy of the state is very near to zero. The ionization energy scale for valence electrons is measured in electron volts just like for the photons from the Sun.

    The energy scale for icosa-tetrahedral honeycomb scaling like ℏeff2/(2meL2), L the size of the fundamental region, gives an estimate for the unit of energy quantization, which does not depend on ℏeff. The energy scale is 102 eV for L=L(151)=10 nm. This scale is expected to be very large as compared to the energy gap so that transitions are not possible. The situation would be like in superconductivity and superfluidity.

  4. What about energy conservation in the motion of the localized valence hole? Valence electron hole can be replaced with the valence electron of a neighboring atom and this makes possible its movement towards the negatively charged reaction center. The energy of the valence hole in the center of mass system of the atom is not changed but the ionized atom or the molecule containing it would experience the Coulomb force assumed to be associated with the reaction center and its center of mass energy can change.

    How is it possible that the attractive Coulomb field between the hole and the reaction center does not affect the energy of the valence hole? The question is well-motivated The Coulomb energy between the hole and the reaction center is expected to be much larger than the energy gap. For instance, for distance of 1 μm the Coulomb energy between unit charges is of order 10-2 eV.

    What prevents the valence hole from accelerating and getting more energetic? The U-shaped gravitational magnetic flux tube has a string tension and the lengthening of the flux tube could compensate for the Coulomb force. The Coulomb energy would be transformed to elastic energy of the flux tube. In the reaction center the flux tube would contract and the dark electron could fuse with the hole having the same energy.

2.4 Is this picture consistent with the proposed quantum gravitational storage of metabolic energy?

Is this picture consistent with the earlier proposal for the metabolic energy storage, which is based on the notion of gravitationally dark protons (see this) and also predicts electronic metabolic energy currency of about .25 meV for which there is some evidence (see this)?

  1. The motivation for the proposal is that the gravitational potential energy of a proton at the surface of Earth is .5 eV: this happens to be the nominal value of metabolic energy quantum. Of course, since the electromagnetic binding energies in molecular scale are measured using eV as units, this might be a pure accident. The weaker optimistic interpretation is that this co-incidence makes possible interaction between quantum gravitational and quantum electromagnetic degrees of freedom.

    When the distance from the surface of Earth in the direction of the Sun, the gravitational forces of Sun and Earth are identical. This condition gives an upper bound for the distance r(Earth) of the particle from the Earth in the direction of Sun as r(Earth)/AU-r(Earth)= [M(Earth)/M(Sun)]1/2 giving r(Earth) ≈ 100R(Earth) to be compared to the distance of Moon about r(Moon)≈ 60R(Earth). The value of the gravitational potential difference as is 99 % of the maximal one.

    The proposal (see this) is that the transformation of protons of water molecules to gravitationally dark protons could serve as a mechanism for the storage of metabolic energy.

    If the metabolic energy quantum is determined solely by the gravitation of Earth, this mechanism does not work at large distances from the surface of Earth. The fact that Moon travellers have survived does not favor a purely gravitational mechanism but the fact that molecular binding energies are of the same order, might save the mechanism. A more imaginative option is that the gravitational MB of the Moon traveller is still associated with Earth and makes it possible to store metabolic energy to the gravitational MB of Earth.

  2. Dark protons triplets could serve as a storage of metabolic energy in the case of ATP (high energy phosphate bond) and maybe even in the case of biomolecules. This is supported by the appearance of 3 photons as a kind of basic unit in ATP→ADP metabolic machinery.
  3. In Pollack effect IR radiation effectively ionizes water molecules and produces effective stoichiometry H1.5O inside a negatively charged exclusion zone. The decrease of the electronic binding energy per water molecule in the Pollack effect could be naturally given by the energy of the IR photon and would be rather small. If the Coulomb binding energy of the dark proton triplets with the exclusion zone is equal the metabolic energy quantum E=.5 eV, the reduction of the gravitational binding energy in the transfer of dark proton triplet to the gravitational MB would be given by E and would lead to a zero energy state. Could one the build-up the energy carrying bio-molecules by transferring dark proton triplet to the gravitational magnetic bodies of the biomolecules by using the energy liberated by dark electrons as they drop down and transform to ordinary electrons in the reaction center?
See the article About the mechanism of the energy transfer in photosynthesis or the chapter Quantum gravitation and quantum biology in TGD Universe.

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

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

Monday, July 17, 2023

Deep learning from the TGD point of view

AI, deep learning, and GPT have become highly fashionable topics. It has been even speculated that AI might involve a rudimentary consciousness. Could TGD inspired quantum view of biology, brain and consciousness could provide a fresh point of view to the notion of computer consciousness.

In the TGD Universe, the difference between living systems and computers need not be so deep as usually thought. The magnetic body as a carrier of dark matter as phases of ordinary matter with effective Planck constant heff=nh0 and having onion-like structure, could receive sensory input and control the biological body with heff=h. Also computers possess magnetic bodies: could they use computers or robots computers as sensory receptors and motor instruments.

In the TGD Universe, the genetic code could be much more than we believe it to be. It would be realized at the level of dark matter and would be universal and unique, being realized in terms of so-called icosa-tetrahedral tessellation of hyperbolic 3-space realizable as the mass shell of light-cone proper time =constant hyperboloid. Icosa-tetrahedral dark genome at the magnetic body could serve as the basic instrument for communication and control. Quantum gravitation plays a key role in the TGD inspired biology and the gravitational magnetic bodies of Earth and Sun and even other astrophysical objects with huge gravitational Planck constants could be highly relevant in quantum biology.

Classical computers can gain life-like properties if the quantum statistical determinism fails. The most conservative criterion is that the clock period is shorter than the gravitational Compton time Tgr= GM/β0, M is mass of an astrophysical object and β0= v0/c≤ 1 is a quantized velocity parameter. Life-like features could appear already at lower clock frequencies. For Earth the critical clock period would be 67 GHz and for the Sun about 100 Hz, the upper bound for EEG frequencies. Therefore the magnetic bodies of the Sun and Earth could therefore play central roles in biology and neuroscience. Even in the case of Earth life-like properties might be present for computers with clock frequency in the range 1 to 10 GHz.

Cognition is an essential aspect of conscious experience and systems like GTP can be seen as artificial cognitive systems. The p-adic discretizations would naturally relate to the spin glass energy landscape assignable to monopole flux tube "spaghettis" and sensory perception could be seen as a generation of standardized mental images based on annealing of spin glass system so that it gradually ends up to a bottom of a valley representing the standardize mental image. The learning period of a conscious entity could be based on trial and error process made possible by holography and zero energy ontology implied by it allowing temporary time reversal and would gradually lead to standardized mental images helping to survive.

See the article Deep learning from the TDG point of view 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 (see this).

Saturday, July 15, 2023

Negentropy Maximization Principle viz. second law of quantum quantum complexity

The physicists Leonard Susskind and Adam Brown have proposed the second law of quantum complexity, a rule similar to the second law of thermodynamics that describes the evolution of complexity in quantum systems (see this). Interesting to see that the basic principles of TGD have reached such a status that the process of independent rediscovery has started. I introduced the Negentropy Maximization Principle (see this) roughly two decades ago as the basic principle of TGD inspired theory of consciousness and actually of TGD. It turned out that NMP implies a second law.

This looks paradoxical but the explanation is that the negentropy in NMP describes the amount of conscious information of a system about itself whereas entropy describes the lack of information about the external world.

For a long time it was unclear whether it is analogous to variational principle dictating the dynamics or whether it is analogous to second law. It turned out that the latter option was correct (see this).

The increase of algebraic complexity leads to NMP as a mathematical analog of the second law. Algebraic complexity corresponds to the complexity of algebraic extension of rationals defined by a polynomial and polynomials basically determined regions of space-time surfaces (see this and this). Physics as number theory as complementary vision to physics a geometry is needed and has many implication including dark matter as hierarchy of phases of ordinary matter with effective Planck constant h_eff=nh_0, the possibility of quantum coherence in arbitrarily long length scales, quantum gravitational coherence in arbitrarily long scales, p-adic numbers as description of the correlates of cognition, etc...

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

"Cyclic Universe Wrong And Something Terrifying Happened Before Big Bang", says Roger Penrose

"Cyclic Universe Wrong And Something Terrifying Happened Before Big Bang", says Roger Penrose (see this). That Penrose says this is remarkable since Cyclic Universe is a brainchild of Penrose himself.

It seems that the time is ripe for the TGD (Topological GeometroDynamics) based cosmology. Or must we wait for another 45 years? TGD not only explains dark matter and dark energy but also provides a solution to the various paradoxes produced by the observations of the James Webb telescope (see this and this) and recently discovered gravitational hum (see this) .

Galaxies older than the Universe can be understood in zero energy ontology in which ordinary state function reduction changes the arrow of time. TGD predicts state function reductions even in astrophysical scales. Astrophysical objects live forth and back in geometric time and can look much older than their temporal position in cosmology allows. Paradoxically, the stars youngest in standard sense are oldest in the sense of developmental age.

The extreme brightness can be also understood. Cosmic strings/monopole flux tubes form a fractal hierarchy of cosmic networks having astrophysical objects as nodes and radiation can arrive along the flux tubes and is very intense.

This network also explains gravitational hum as diffraction of gravitational radiation in tessellations of hyperbolic 3-space (realization is as mass shell and cosmic time= constant hyperboloid) having stars as nodes (see this). This implies quantum coherent amplification (amplitude is proportional to N>2 rather than N, N the number of the points of tessellation). Radiation is also concentrated on beams along flux tubes.

For more about TGD based astrophysics see this and this).

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

Thursday, July 13, 2023

Detailed dark realization of the genetic code using icosatetrahedral tessellation of hyperbolic 3-space

How could the icosa-tetrahedral tessellation relate to the proposed dark realizations of the genetic code (see this and this)? In the sequel I will discuss the recent view based on the detailed analysis of the problems of the earlier picture and the properties of the unique icosatetrahedral tessellation of hyperbolic 3-space suggesting that genetic code is universal and not restricted to biology.

1. About the problems of the earlier view of the dark realizations of the genetic code

Consider first the problems of the earlier views of the realization of the dark genetic codes in terms of dark proton triplets at monopole flux tubes parallel to the ordinary DNA and to the realization in terms of dark photon triplets.

  1. The TGD based inspired model of the dark photon genetic code (see this, this and this) assumes that the dark realization of genetic code involves 3 icosahedral Hamiltonian cycles giving rise to 20+20+20 dark DNA codons and the unique tetrahedral Hamiltonian cycle giving the remaining 4 codons.

    The obvious problem of icosa-tetrahedral picture is that one must assume that icosahedron and tetrahedron are disjoint. If they have a common face, the number of faces reduces to 63 and one DNA codon is missing. This raises the question whether icosahedron and tetrahedron could be disjoint pieces of a larger structure.

  2. In the dark proton realization a given codon would correspond to a selected triangular face of I or T carrying dark protons at the vertices of this face. The original view was that dark 3-proton states would correspond to 64 codons. The problem was that one obtains only 8 states for dark proton triplets from spin and antisymmetrization in spin degrees of freedom would not allow any states unless the spatial wave function is totally antisymmetric and spins are in the same direction.

    In the original proposal also neutrons were assumed so that the codon corresponds to a sequence of 3 nucleons with both spins. 3 nucleons would give rise to 64 states as required. Dark protons can also be effectively neutrons as far as charge is considered. This might be possible if the bonds connecting the dark protons can be both neutral and negatively charged. Weak interactions are as strong as electromagnetic interactions in a given biological scale (such as DNA scale) if the dark Compton length proportional to heff is larger than this scale and the weak transitions change the dark protons to effective dark neutrons.

    This option leads to a problem with the fact that DNA nucleotides have negative unit charge. One should have protons to neutralize this charge and stabilize DNA. Also variants of the proposal in which there are flux tube connections between dark protons having 2 different neutral states analogous to neutral pion and neutral ρ meson.

    The simplest proposal, which is consistent with the idea that genetic codons correspond to cyclotron transitions of dark proton triplets assignable to the triangular faces of an icosahedron or tetrahedron is as follows. Besides 2 spin states, dark protons can also have 2 states with spin +/- 1 corresponding to the analog of rotation in the discrete space defined by the vertices of the triangle. This would give 23× 23=64 states.

The realizations of the genetic code in terms of dark photon triplets and dark proton triplets should correspond to each other. This requires that dark proton triplet realization should naturally correspond to the icosa-tetrahedral realization.
  1. The codons identified as dark proton triplets assignable to one of the 20 triangular faces of icosahedron and tetrahedron have in quantum situations a wave function in the discrete space of the faces, which is in general delocalized. Could these wave functions in the set of faces give rise to states in 1-1 correspondence with the icosahedral and tetrahedral codons? There would be 20 wave functions for an icosahedron and 4 wave functions for a tetrahedron. The number of icosahedral states must be tripled to 60 corresponding to the 3 basic types of icosahedral Hamiltonian cycles with symmetries Zn, n=6,4,2.

    The 3 dark protons also have spin degrees of freedom. The dark proton triplet in the ground state(s) would be naturally spontaneously magnetized so that all spins are in the same direction. Also the states in which some dark protons are excited are allowed by Fermi statistics and are needed since these excitations could correspond to the spatial wave functions in face degrees of freedom.

  2. Dark photon triplets are needed for communications. The vision is that they correspond to the representation of codons as frequency triplets represented by the realization of icosahedral and tetrahedral Hamiltonian cycles as frequency triplets. The assumption has been that the 3 frequencies of dark 3-photon are associated with the cyclotron (or Larmor transitions if only spin is dynamical) of dark protons of a dark proton triplet.

    Dark photon communications between identical codons would take place by 3-resonance. The de-excitation of the first codon would lead to the excitation of an identical codon: one would have a kind of flip-flop. Also dark genes as sequences of N dark codons could act as a single quantum coherent unit and 3-N resonances between identical dark genes would become possible. The mechanism is very similar to that used in the computer language LISP. The modulation of the frequency scale by modulating the thickness of the monopole flux tubes would make possible coding of the signal and it would be transformed to a sequence of resonance pulses at the receiving end.

    Dark photon triplet states could correspond to wave functions in the space of icosahedral and tetrahedral faces.

  3. Cyclotron transitions would be needed in order to generate dark photon triplets. This would require excitations of the dark protons of the spontaneously magnetized ground state(s). If only spin matters, the cyclotron transitions reduce to Larmor transitions. The correspondence with the icosahedral Hamiltonian cycles in terms of dark photon triplets would suggest that these excitations correspond to icosahedral genetic codons as wave functions in the set of faces. The cyclotron transition would provide the energy needed to excite the wave function in the set of faces. 64 transitions would be needed. It is important to notice that cyclotron transitions rather than cyclotron states of dark protons would correspond to codons of icosa-tetrahedral representation represented as wave functions in the set of facs.

    There are however only 8 states per face if only Larmor transitions are allowed. This is much less than the number 20 20+20+4=64 for icosahedral and tetrahedral Hamiltonian cycles. An additional two-valued degree of freedom is needed. The simplest possibility is the assignment to each dark proton an analog of angular momentum eigenstate with spin +/- 1 corresponding to a discrete rotation around the triangle. This would give 8× 8=64 states per face. Could the excitations of these states correspond to 20+20+20 icosahedral states plus 4 tetrahedral states?

  4. Hitherto the considerations have been implicitly classical in that a localization in the set of faces has been assumed. Quantum theory allows us to give up this assumption. Icosahedral realization suggests that dark proton triplet has a icosahedral wave function delocalized to the set of 20 faces with symmetry fixed by the Hamiltonian cycle to Zn, n=6,4 or 2, and that the excitation of the dark proton triplet in the face degrees of freedom provides the energy changing the wave function in the set of faces. The same would apply to the tetrahedron with symmetry Z4 allowing 4 wave functions.

    The orbital and angular momentum degrees of freedom would be coupled. The transition from the ground state for dark proton triplet would excite wave function in the set of faces. This could imply the desired correspondence between the dark proton representations and dark photon realizations of the code.

  5. There is a further problem. Spontaneously magnetized states of 3 dark protons would define ground states of codons. The ground state proton triplet cannot have lower energy states and cannot emit dark photon triplets and are therefore "mute" and unable to communicate, presumably necessary for processes like transcription and translation. Note that ground states are however not deaf.
The proposed general view is attractive but the details remain to be understood and problems solved. Here the notion of icosa-tetrahedral tessellation could help. The proposal (see this) was that the icosa-tetrahedral honeycomb at the light-cone proper time a= constant surfaces identifiable as hyperbolic 3-space H3 allows to realize the dark genetic code.

The icosa-tetrahedral honeycomb is the unique honeycomb, which involves only Platonic solids. This inspires the question whether genetic code could be universal and realized in all scales by induction, which means that the tessellation of H3 induces tessellation of 3-surface X3⊂ H3 by restriction. Also the induction to H3(a) projection of X4 makes sense.

The TGD view of holography indeed predicts the special role of hyperbolic 3-spaces. The space-time surfaces in H=M4× CP2 are analogs of Bohr orbits, which go through H3(an)⊂ M4⊂ H, where an corresponds to a root of the polynomial with integer coefficients determining to a higher degree a given region of the space-time surface by M8-H duality (see this and this) .

In the sequel the detailed realization of the genetic code in terms of the icosahedral honeycomb will be discussed with an emphasis on the problems noticed above.

2. The realization of the code in terms of icosa-tetrahedral tessellation

The fundamental region of the icosa-tetrahedral tessellation contains 30 octahedrons, 20 tetrahedrons, and 12 icosahedrons and the cautiously proposed interpretation is that the cells meeting at each edge of the tessellation have either the cyclic structure TOTI or OTOI, and each vertex involve 3 O:s, 2 T:s and 1 I. Could one interpret this in terms of the dark icosahedral realization of the genetic code?

2.1. Ideas related to the detailed realization of the genetic code

The detailed realization of the dark genetic code is far from completely understood and one might hope that icosa-tetrahedral realization could bring in the constraints allowing us to fill in the details. It is useful to proceed by considering basic requirements on the realization of the dark code.

  1. There are 3 O:s per single I in vertex if 10 instead of 12 icosahedral cells are included. The reasons for this become clear from the proposed relation between DNA double strand and fundamental cell of icosahedral honeycomb. What could the role of O:S be?

    Imagine that it is possible to arrange the polyhedrons for a given I to cycles as -I-O-T-O-T-O-: here cyclicity is assumed. The two tetrahedrons and I would be disjoint. This would solve the problem due to the common face of T and I (only 63 DNA codons) but give 60+4+4 faces and 68 dark DNA codons. There is however the problem posed by the mute codons. Could the presence of mute DNA codons reduce the number of DNA codons from 68 to 64. This would imply that their transcription allows only 64 dark mRNA codons. Could mute mRNA codons reduce the effective number of mRNA codons to 61 for the standard code (stop codons would be mute)? What about its variants with a smaller number of stop codons?

  2. Bioharmony involves 3 icosahedral Hamiltonian cycles. All the combinations of the 3 -cycles with symmetries Z6, Z4 and Z2 predict the same code. These bioharmonies are interpreted as correlates for emotional states appearing already at the basic bio-molecular level. The motivation comes from the fact that the icosa-tetrahedral harmony emerges as a geometric model for the music harmony and music indeed both creates and expresses emotions.

    Could icosahedral honeycomb allow us to understand the realization of these 3 icosahedral Hamiltonian cycles in terms of cyclotron frequency triplets? One must have closed magnetic monopole loops in order to have cyclotron transitions. Could these loops form triangles of form I-T-O. This would be 6 different triangles and 3 different positions of I for given T. This kind of loop would be assigned with each vertex of the face. Could the magnetic field strengths depend on the loop and for a given T give rise cyclotron frequency triplets characterizing a given icosahedral Hamiltonian cycle.

  3. One can criticize the assumption that there is only a single codon per single I and T. I:s could in principle carry several codons. This however gives a restriction that the codons inside given I and T are different and restricts the representative power of the code if it involves more than 2 strands. This restriction is however automatically satisfied for the base-paired codon and anticodon in the DNA double strand!

2.2 Dark photon realization of the icosahedral part of the code

Consider first the realization of the icosahedral part of the code in terms of dark photons.

  1. The 3 icosahedral Hamiltonian cycles have symmetries. The 20 codons with Z6 symmetry correspond to 3 6-plets and 1 doublet of Z6 and for unbroken symmetry the codons inside these multiplets code for the same amino acid. This means 3+1= 4 amino acids. Z4 symmetry has 5 4-plets and in absence of symmetry breaking this corresponds to 5 amino-acids. Z2 symmetry as 10 2-plets, and also this symmetry is also almost exact and corresponds to the almost exact symmetry with respect to the third letter of the codon analogous to isospin symmetry.
  2. Icosahedral part of the icosa-tetrahedral realization involves 3 icosahedral Hamiltonian cycles characterized by different symmetries. For Z6 symmetry, there are 6+6+6+2=20 codons codons. These sets of codons can be regarded as orbits of Z6 and correspond to amino-acids. This if the Z6 symmetry is not broken. This means 3+1 amino acids in absence of symmetry breaking.

    Z4 symmetry has 5 4-plets and in absence of symmetry breaking this corresponds to 5 amino-acids coded by 4 codons each. Z2 symmetry has 10 2-plets and this symmetry is also almost exact. This symmetry corresponds to the almost exact symmetry with respect to the third letter of the codon.

  3. Dark photon codons are represented as cyclotron frequency triplets of dark photons created in 3-cyclotron transitions for dark proton triplets involving simultaneous emission of 3 dark photons made possible by quantum coherence. In the case of genes with N codons one has 3N-cyclotron transition and 3N dark proton-state represents a gene as a quantum coherent unit.

2.3 Dark proton realization of the icosahedral part of the code

Consider next the dark proton realization of the icosahedral part of the code.

  1. The basic problem of the dark proton realization of the code is that the states of dark protons triplets give only one half of the codons. One way to obtain doubling is to assume that dark codons are connected by flux tubes which can carry charges 0 or -1. It is far from clear whether this is consistent with the constant negative charge density of DNA: charge -e per DNA codon. Could 2×T degeneracy give it? For each I defining an icosahedral codon one should select either T. If both the selected and unselected T code for 4 codons, one obtains additional 4+4=8 codons.
  2. Icosa-tetrahedral realization should give 20+20+20+4 =64 dark proton triplets assignable to the faces of I and T. Suppose that the cells can be thought of as forming a cycle O-I-O-T-O-T with O and T ends connected. The two T:s have no common faces with O and without additional conditions give rise to 4+4 additional codons giving 68 codons. How can one reduce the number of dark DNA codons to 64?
  3. Dark proton codons have a ground state, or possibly several of them, which by definition cannot decay to lower energy states by emission of dark photon cyclotron triplet. Ground state codon is mute since it cannot produce dark photon triplets as 3-chords.

    The natural first guess is that the ground states correspond to the 6 combinations 3 icosahedral Hamiltonian cycles and 2 tetrahedral cycles assignable to 2× T. The 3 stop codons are transcribed but not translated so that the interpretation of 3 DNA stop codons as icosahedral ground state dark codons unable to send 3-photon signals is not correct. For mRNA this interpretation could make sense if the mRNA images of DNA stop codons represent ground state codons.

  4. Cyclotron excitations of ground state codons are induced by dark photon triplets. Conversely cyclotron de-excitatons generate dark proton triplets except for the ground state codons with minimum total energy. Suppose that there are 6 ground state codons as combinations of 3 dark codon ground states assignable to the 3 icosahedral Hamiltonian cycles and 2 dark proton ground states assignable to tetrahedral cycles of the two T:s. This would give 8 mute states. The total number of dark DNA codons is 60+8=68. Note that the mute states are not deaf: they can receive messages.

    One would obtain only 60 DNA codons, which can be transcribed to mRNA codons if the transcription involving dark photon codons. How could one get 64 as an effective number of DNA codons?

    One can imagine transitions between otherwise mute codons, which generate dark photon triplets coupling to mRNA associated with DNA. Let A, B and C the ground state codons with minimal total dark cyclotron energies in an increasing order for the 3 icosahedral Hamiltonian cycles. If for a given T (two options) the cyclotron transitions are possible only between codons C and B and B and A one obtains 2 DNA-mRNA pairings for both T:s. One would have 60+2+2=64 mRNAs pairing with DNA and effectively 64 DNA codons.

    Note that the transcription produces only 64 dark mRNA codons from 68 dark DNA codons.

    For 64 mRNA codons it could happen that there are no transitions between the 3 icosahedral codons for both choices of T so that there are 6 mute mRNA codons. If there are transitions C → B and B → A, the number of mute icosahedral codons is 4. If there are no transitions between tetrahedral ground state codons, one has effectively 60 mRNA codons since the translation stops due to the absene of dark 3-photon signals to tRNA. If there is a transition between the 2 ground state nRNA codons associated with the two T:s, one obtains 61 effective mRNA codons of the standard realization of the code. The transitions between tetrahedral codons can increase the effective number of mRNA codons.

  5. What about tRNA appearing as a pair of amino-acid and single RNA codon. Could the RNA of tRNA and amino-acids correspond to the unique icosahedral honeycomb of H3 and to icosahedral Hamiltonian cycles so that the number of dark codons in absence of tetrahedral degeneracy would reduce to 32, which is the minimal number of ordinary tRNA codons, which is increased by the non-uniqueness of the ordinary tRNA itself? Note that mute tRNA codons are not deaf: they can receive messages but cannot send them. Obviously, tRNA and amino-acids would correspond to the lowest evolutionary level.
The tentative conclusion would be that in the TGD framework DNA-mRNA transcription is not 1-to-1: information is lost and could say that RNA represents a lower level of evolutionary hierarchy. This would conform with the RNA world vision. The numbers of dark proton DNA and mRNA codons are 68 and 64 respectively. The unavoidable existence of mute codons gives effective DNA codon number 64 as the number of mRNA codons. 3 icosahedral codons can be mute and one obtains 3 stop codons unable to communicate with tRNA. The number of mute codons can also be smaller if transitions of type C→ A are possible.

The dark DNA and RNA codons are dynamical and are not fixed to be the same as ordinary codons. This is required only during the communications with ordinary DNA possibly taking place by dark photons transforming to ordinary photons and inducing resonant transitions of ordinary DNA and other basic biomolecules. This strongly suggests that dark DNA and RNA act as a kind of R&D laboratories making it possible to test variants of the genes. Actually their ground states would correspond to 3 icosahedral representations and 2 tetrahedral representations and would correspond to aminoacids via transcription and translation.

Needless to say, this picture is highly speculative and one can probably imagine variants for it. The basic idea is however clear: icosa-tetrahedral tessellation could explain the details of the standard genetic code and its modifications.

2.4 Realization of the flux tube structures associated with dark codons

The following represents an attempt to make the above picture more concrete.

  1. The selection of 1 O from 3 O:s could mean a selection of an icosahedral Hamiltonian cycle with symmetry group Z6, Z4, or Z2. This gives for icosahedral realization 20+20+20 =60 icosahedral codons. Tetrahedral Hamiltonian cycles associated with the two T:s should give the remaining 4 codons. One can however imagine several ways for how this could occur.
  2. The selection of O should correspond to a choice of the icosahedral cycle. What does this mean geometrically? To each dark proton of the codon, one must assign a closed monopole flux tube. The strength of the magnetic field of the flux tube fixes the cyclotron frequency scale for each flux tube. The 20 dark-photon chords defining a given icosahedral bioharmony differ for different choices of O and T. The frequencies are fixed if the Hamiltonian cycle corresponds to a quint cycle such that the frequencies associated with the neighboring vertices of the Hamiltonian cycle differ by a scaling 3/2. This requires that the magnetic field strengths along the cycle differ by scaling 3/2.
  3. How to concretely realize the correlation of the bioharmony with the choice of O and T for a given I? Suppose that for a given I, the closed flux tube connects I and the selected O and T. There would be a closed I-O-T flux tube for each vertex of the face defining the codon. This kind of flux tube would define an analog of a string of a musical instrument.

    These closed flux tubes would be hyperbolic analogies of closed circuits formed by Euclidian nearest neighbour lattice bonds. If makes sense to assign to each I a cycle O-I-O-T-O-T, with O and T at ends being connected, the cycle I-O-T would go through the either T, and this implies that tetrahedral codons correspond to the other face of T. One would obtain 64 dark proton codons with 3 mute dark proton codons identifiable as stop codons. In the transcription the signal as a dark photon triplet would not reach the dark RNA codon and the transcription would stop. Could this mean that dark RNA codon attaches first to dark DNA codon and the transcription of DNA to ordinary RNA occurs after that in the usual way.

  4. The proposed transitions between ground state codons for icosahedral Hamiltonian cycles modify the cycle geometrically since the O in cycle I-O-T changes. If the transitions for given T are only of C→ B and B→ A with energies in increasing order, one can imagine that the O is replaced by a neighboring O in the transition in the O-I-O-T-O-T.
Several questions remain to be answered.
  1. The symmetry breaking for the icosahedral codons with Zn, m=6,4,2 should be understood. This symmetry breaking can be assumed to occur at the level of dark mRNA and modify the frequency triplets from those for completely symmetric mRNA codons. The replacement T→ U might relate to the symmetry breaking.

    UUG, CUG, and the very common AUG appear as start codons. They correspond to symmetry breaking for 6-plet (Z6) coding for leu and 4-plet (Z4) coding for ile. All symmetry breakings occur for start codons UUG, CUG, and for codons UAA and UAG and UGA and UGG closely related to stop codons.

  2. Can one understand the reduction of the number of mRNA stop codons to 2 or 1 occurring for some variants of the code? In these situations, the stop codon of mRNA can code for an exotic amino acid pyrrolysine and selenocysteine. Could the transition between stop codon of dark mRNA icosahedral Hamiltonian cycle to a stop codon of another Hamiltonian cycle take place such that the dark photon triplet generated couples to tRNA involving the exotic amino acid. Situation would be almost like in the case of DNA where only two ground state codons stop the transcription.
  3. What can one say about the strength of the magnetic fields assignable with the monopole flux tubes? Nanometer length scale 1 nm, naturally assignable to the DNA double strand, corresponds from the formula lB= 26 nm/(B/Tesla)<1/2> to 12.2 GHz. What is interesting is that the gravitational Compton frequency for Earth is 67 GHz and defines a lower bound for the gravitational quantum coherence time. If the strengths of the magnetic fields span 7 octaves, the thickness of the flux tube would vary by a factor 10 in the range about .1 nm - 1 nm.
  4. Note that the 12-note scale can be realized using powers (3/2)k, k=1,...,12, of the fundamental and by using octave equivalence to reduce the note to the basic octave. Since the monopole flux is quantized, the realization of the scale requires variation of flux tube thickness inducing variation of magnetic field strength and therefore of that cyclotron frequency scale.

    There is nothing cherished in the rational quint cycle as the basis of the 12-note scale. For instance, the well-tempered scale actually replaces the Pythagorean scale with an algebraic scale coming in powers of 21/12.

3. Description of the entire DNA double strand in terms of icosatetrahedral tessellation

The most ambitious model would describe the entire DNA double strand and relate the model bioharmony to the properties of the icosa tetrahedral tessellation. There are however many questions remaining.

  1. Single DNA and RNA strand would correspond to a "half realization" for which the T and I cells would contain only single codon. The splitting of DNA could have a geometric interpretation as an effective replication of the induced tessellation to two tessellations to RNA type tessellations.
  2. There are 20 amino-acids and an icosahedron involves 20 faces. Is this a mere accident? Could icosahedral honeycomb describe amino-acid sequences geometrically. tRNA appears as a single unit. tRNA-amino-acid pairing would involve pairing of two icosahedral tessellations as also the pairing of RNA and tRNA in the translation. tRNA would naturally correspond to a single cell of icosahedral tessellation. This would also explain why the number of tRNA molecules is considerably smaller than RNA codons.
  3. Does RNA correspond to icosahedral or icosa-tetrahedral tessellation? Tetrahedral Hamiltonian cycles are needed, in particular the dark proton triplets associated with the tetrahedral faces. Therefore icosa-tetrahedral tessellation is the natural option also for RNA.
  4. It is thought that DNA and RNA nucleotides float freely in the cellular water and DNA and RNA codons are built from them in replication/transcription. This is probably the case at the biochemical level, whose dynamics is controlled by dark level (I have however considered the possibility that freely floating nucleotides could actually form loosely bound codons).

    At the dark level both replication and transcription would involve replication of the induced icosa-tetrahedral tessellation: a similar process occurs for clay crystals, and is suggested to be a precursor of DNA replication. This process is a holistic quantum process occurring in a single quantum jump. This would explain the incredible accuracy of these processes, which is extremely difficult to understand in the chemical approach.

    The replication would determine the outcome, be it a pair of DNA double strands or of DNA and RNA. After this the chemical processes leading to the formation of chemical codons from nucleotides and their pairing with dark codons of the induced icosa-tetrahedral tessellation would take place.

To see whether this hypothesis can make sense one must use geometrical facts about DNA double helix, which has A-, B-, and Z forms (see this).
  1. B-form is believed to dominate in cells. From the table of the Wikipedia article one learns that for the B-form the rise per base pair (bp) is 3.32 Å, that full turn corresponds to 10.5 bps, and that the pitch of the helix per turn 33.2 Å, which corresponds to 10 bps per turn. The pitch/turn should be equal to 10.5× 3.32= 34.52 Å. There is obviously a mistake in the table.
  2. The solution of the puzzle is that straight DNA in solution has 10.5 bps/turn and 10 bps/turn in solid state (see this). Since DNA double helix corresponds to solid state then 10 codons correspond to 3 full turns. Therefore my earlier assumption 10 bps/turn in the double helix is correct. 10 codons would correspond 3 full turns and to the length 99.6 Å ≈ 10 nm, which in TGD framework corresponds to the p-adic length scale L(151).
Double DNA strands cannot pair with all 12 I:s associated with the dark DNA. The length L(151) should correspond to 10 I:s taking 80 per cent of the icosahedral volume. Is helical winding enough to achieve this?
  1. The total volume of the fundamental region is V= 20V(T)+30V(O)+12V(I)= 341.44 using 2a as length unit. Using the estimate Vreal= L(151)3 =106 Å3, one obtains a= L(151)/2V1/3≈ 0.07× L(151). The volume fraction of single I would be 17.45/V≈ .05 and 10 I:s would take 1/2 of the volume.
  2. The circumradius of single I would be R=(3-φ)1/2φ a/2≈ .1× L(151)=1 nm. This conforms with the assumption that there are 10 codons per length L(151)! The diameter of the B-type DNA strand is 20 Å is also consistent with the value of the circumradius. Maybe the proposed picture works!
  3. Notice that if an icosahedral cell corresponds to 2 tetrahedral cells and 3 tetrahedral cells, then 10 codons is the maximum for the realizable DNA codon.
What can one say about the straight form of DNA?
  1. For 10.5 bps/turn for a straight DNA in solution, the smallest portion of strand, which corresponds to integer numbers of turns and of codons is 6 full turns. This corresponds to 63 bps and 21 codons.
  2. With an inspiration coming from the notion of Combinatorial Hierarchy (see this) defined in terms of Mersenne primes Mn= 2n-1 defined by the recursive formula M(k)= MM(k-1)= 2M(k-1)-1, I proposed decades ago that ordinary genetic code could correspond to Mersenne prime M7=27-1 (see this and this). The basic idea is that a system with 27-1 states corresponds to a Boolean logic with 7 bits but with one state missing: this state would correspond to empty set in the set theoretic realization or fermionic vacuum state in the realization as a basis for fermionic Fock states. Only 6 full bits can be realized and the number of realizable statements is 64, the number of genetic codons.
  3. Memetic code corresponds to the Mersenne prime M127= MM7-1= 2127-1. Now the number of codons would be 2126=26× 21 and is realizable as sequences of 21 DNA codons! Note that higher Mersenne numbers in the hierarchy were proposed by Hilbert to correspond to Mersenne primes but for obvious reasons this has not been proven.
  4. Could 6 full turns of straight DNA define a memetic codon? During the transcription and replication, DNA double strand opens and becomes straight. Could memetic code be established during the transcription and replication periods? A further intriguing observation is that the cell membrane involves proteins consisting of 21 amino-acids.
See the article About tessellations in hyperbolic 3-space and their relation to the genetic code or the chapter with the same title.

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