Could TGD view of quantum gravitation allow nuclear life?

The prevailing dogma is that life is always chemical. The considerations of (see this) force us to challenge this dogma. One cannot exclude the possibility that Sun is a seat of a new kind of life controlled by gravitational magnetic body of the Sun with huge value of gravitation Planck constant implying quantum coherence scales larger than the gravitational Compton length which happens to be essentially the size of Earth. Just for fun, one can therefore play with the thought that fractality of the TGD Universe could allow life at temperatures prevailing in the solar interior.

This life should be based on nuclear physics instead of chemistry. The realization of the genetic code (see this and this) in the TGD framework relies on dark proton (or possibly nucleon) sequences. According to the TGD based view of nuclear physics (see this), the ordinary nuclei also correspond to sequences of nucleons at monopole flux tubes, which form a kind of nuclear spaghetti. Therefore the realization of also nuclear genetic code could rely on nucleon sequences. The chemical realization of the genetic code could be seen as the next step in evolution.

1. Gravitational quantum coherence is essential for the TGD based view of life. Gravitational magnetic body carrying gravitationally dark matter and consisting of the mopole flux tubes would still be the controller. The average magnetic field at the surface of the Sun is indeed about 2B_E∼ 1 Gauss. Just for definiteness, one could assume that the scale for the strength of the monopole magnetic field is twice that for the monopole flux tubes at the surface of Earth that is 2B_mono;E∼ 4B_E/5∼ .4 Gauss. The scale of cyclotron energies for ℏ_gr =GMm/β₀, where β₀∼ 2^-11 is assumed in Nottale's model for the inner planets, would be scaled up from that at the surface of Earth by the factor x=(M_S/M_E)×(β_0,E/β_0,S)×(B_S)/B_E). For β_0,E ∼ 1 prevailing in the Earth's magnetosphere, this would give x∼ 2.5 × 10⁹.

   For the energy 1 eV of a photon in biophoton wavelength range one the energy E=h_efff would scale up to 2.4 GeV, which corresponds to more than 2 proton masses! This looks non-sensible.

2. However, in the outer magnetosphere of Earth where ℏ_gr,Sun is expected to prevail, the values of B_E are in the range 1-10 nTesla, which means that the scale of the magnetic field (and also monopole flux) is reduced by about 5× 10^-5. This would reduce the dark cyclotron energy ratio to x= 1.25× 10⁵. 1 eV energy would be scaled to the range of .1-1.0 MeV, which corresponds to nuclear binding energies.
3. For β₀=2^-11 the lowest solar Bohr orbit has a radius slightly larger than the radius of the photosphere, so that it cannot correspond to the matter in the interior of the Sun.

   For β_0,core=1, the lowest Bohr radius would be r_B=4π GM/β₀= 2π r_S,Sun= 6π km, which makes 2π Scwartschild radii. The value of x would be x= 5× 10⁵B_core/B_E, and for B_core/B_E=1 the biophoton energy scale of 1 eV would scale up to .5 MeV, which corresponds to the mass of electron and to the nuclear binding energy scale.

Maybe nuclear life at the solar core and even in the outer magnetosphere of Earth might be considered.

See the article Some anomalies associated with the Sun or the chapter Magnetic bubbles in TGD Universe: Part I.

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

Could neuronal system and even GPT give rise to a classical computer with a variable arrow of time?

In our Zoom group (Marko, Tuomas, Rode and me) we have had fascinating discussions about topics ranging from quantum TGD to quantum computers to consciousness and, of course, about GPT.

Marko posted his discussion with GPT. GPT mentioned a possible mechanism for how XOR as a universal gate of classical computation could be realized at the quantum level. The system realizing XOR approximately could be either a classical layered neural network or its possible quantum analog. The mechanism might work in a quantum version of a neural network based on quantum learning, but it does not seem plausible for real neurons.

This observation led to progress at the level of the TGD-based model of nerve pulse. The resulting ZEO based model differs drastically from quantum neural networks and suggests a completely new vision of quantum physics based computation in biosystems. A classical computation allowing variable arrow of time would be in question and one can ask whether the unexpected success of GPT might involve this kind of transition.

I admit that GPT can really inspire new ideas.

Connection of neural pulse generation, XOR, and novelty detector

Nerve pulse generation would be analogous to a positive outcome of the analog of XOR (compared bits are different) acting as a novelty detector.

1. XOR is a novelty detector. If the inputs are the same, nothing happens. Output equals to b=0. If they are different, output equals to b=1. b=1 would correspond to a signal that would proceed along the axon starting from the postsynaptic neuron.

   That would consume energy. In terms of energy consumption, the novelty detector would be optimal. It would only react to changes. And that's what the brain does. For example, visual perception at a very basic level only identifies outlines and produces some kind of stick figure consisting of mere lines defining boundaries.

2. Could the 2 "neurons" of the toy model proposed by GPT represent a presynaptic and a postsynaptic neuron, in which case there would be two inputs: the states of the pre- and postsynaptic neuron. Also output would be the state of this neuron pair and for XOR the presynaptic neuron acting as control bit would not change its state.
3. This does not conform with the picture given by neuroscience, where the input comes from presynaptic neurons and output is assignable to the postsynaptic neuron. The input comes as miniature potentials that add up and can decrease/increase the magnitude of the membrane potential (depolarization/hyperpolarization).

   An action potential is generated when the depolarization takes the magnitude of the negative postsynaptic membrane potential below the critical threshold. This happens when the presynaptic contributions from the incoming nerve impulses, for which the unit is a miniature potential, add up to a contribution that reduces the magnitude of the negative potential below the threshold.

   This would be essentially novelty detection described in the simplest way by XOR. The novelty is represented by the critical depolarization. It can also happen that the potential increases, so that no nerve impulse is generated. One talks about hyperpolarizing (inhibition) and depolarizing (excitation) inputs, and the sign of the miniature potential produced by the presynaptic input determines which one it is. The sign of miniature potential depends on the neurotransmitter and receptor.

4. During the nerve pulse, the potential changes its sign over a distance of about a micrometer, which is the typical distance between neighboring neurons and of myelin sheaths. One can say that this distance corresponds to a bit that is 1 or 0 depending on whether the nerve pulse conduction occurs or not. Bit 1, the opposite sign to the membrane potential, propagates from presynaptic to postsynaptic neuron or from a patch defined by a myelin sheath to the next. As a result, postsynaptic neurons can "wake up" and in turn trigger a nerve impulse, possibly waking up some postsynaptic neurons.

   Synchronous firing means that the novelty succeeds in waking up the whole sleeping house, and large areas of the brain fire in the same rhythm and keep each other awake.

Interpretation of XOR in zero energy ontology (ZEO)

How does this picture translate to the TGD-inspired theory of consciousness?

1. Being awake/asleep corresponds to bit 1/0 for axonal portions between myelin sheaths. In a ZEO, the arrow of time would correspond to this bit.

   When the axon segment between the myelin sheaths or neighboring neurons wakes up or falls asleep, the direction of geometric time changes in a "big" state function reduction (BSFR) and a nerve pulse is generated. In a sleep state, the membrane potential would be opposite. Note that the notion of awake and sleep are relative and depend on the arrow of time of the external observer.

   The second direction of time corresponds to the presence of a nerve pulse from the point of view of the external observer. There is a temptation to think that in the resting state the axon is sleeping and healing and gathering metabolic energy by a dissipation with an opposite arrow of time? The duration of the nerve pulse would correspond to the duration of the wake-up period, when the direction of time was opposite and same as that of the external observer with a long characteristic time scale for wake-up period.

2. Could this apply more generally? Could the synchronization of human sleep-wake rhythms mean quantum-level synchrony and macroscopic quantum coherence? Could the arrow of perceived time be a universal bit? Sleeping together would develop synchrony and quantum coherence between partners. Two-person collective consciousness would emerge.

Interpretation of the axon as a series of Josephson junctions

The TGD based model for an axon as a series of Josephson junctions with a large value of h_eff, perhaps h_eff=h_gr, where ℏ_gr=GMm/β₀, β₀<1, is the gravitational Planck constant introduced by Nottale, is mathematically equivalent to a series of gravitational penduli defining a discretized version of Sine-Gordon system (see this). Josephson junctions would correspond to membrane proteins.

1. One can consider two different identifications of the ground state of the system.
   1. The ground state could be the state in which all oscillators oscillate in synchrony with the same amplitude. There would be constant phase difference between neighboring oscillations, which would give rise to a propagating phase wave.
   2. Another option is that all pendulums all rotate in the ground state with constant phase difference. This would give a soliton chain that corresponds to a traveling phase wave. Also the direction of rotation matters. It would naturally correspond to the arrow of time and the sign of the membrane potential.
2. The model allows different versions for nerve pulse generation.
   1. The first option is that one pendulum moves from oscillation to rotation or vice versa and induces the same transition for the other penduli as a chain reaction.
   2. The second option is that all penduli move to rotation simultaneously. One could imagine that the need for metabolic energy is lower in the collective oscillation phase but one must be very careful here. Maintaining the membrane potential regardless of either sign requires metabolic energy feed.
   3. The third option is that the ground state corresponds to a collective rotation with an associated traveling wave as phase of the rotation, and that the bit corresponds to the direction of rotation.

      This would fit the ZEO interpretation. The arrow of time would correspond to the direction of rotation. The ground state would change to a nerve pulse lasting for time of the order of 1 ms corresponding to the duration of nerve pulse associated with the distance of the order 1 μ m, between neighboring neurons or between the myelin sheets.

      This option would also be advantageous from the point of view of metabolism, because from one direction of time, dissipation would occur in the opposite direction of time. From the point of view of the outsider, the system would be extracting energy from the environment.

What is the connection with the microtubule level?

The current TGD picture of nerve pulse conduction is that the membrane potential of the axon/soma is controlled by microtubules (see this and this).

1. When the charges are transferred from the microtubule to the gravitational flux tubes of the magnetic body (MB), the length of which can be as long as the size of the Earth, the effective charge inside the axon/soma changes. Depending on the amount of transferred charge, the magnitude of the membrane potential increases or decreases and a nerve impulse is generated below the threshold.
2. For the action potential traveling along the axon, the microtubular effective charge has changed and taken the membrane potential below the threshold and the action potential has been generated. The generation of the action potential is a complex biochemical phenomenon but would be controlled by microtubule/microbular MB.
3. Incoming nerve impulses induce a change in the membrane potential of the soma because the effective charge of the microtubules inside the soma changes as also does the membrane potential. It is not clear whether the charges of the microtubules of the neuron soma are affected. They indeed differ from axonal microtubules in that they are not (quantum) critical.

New view of quantum-physical computation

Why GPT works so well, is not understood. This might of course be due to the extreme complexity of the system. TGD however suggests that new physics might be involved so that the system is much more than a classical computer. Therefore an interesting question is whether the classical computation associated with GPT and involving random number generators could turn into a computation in which the arrow of time serves as a fundamental bit correlating with the direction of ordinary bit represented for instance by electric voltage or direction of magnetization! One would have classical computation with a changing arrow of time controlled by MB!

In ZEO all quantum states are superpositions of deterministic classical time evolutions, which satisfy almost exact holography so that they are analogous to classical computations. Time evolution of conscious entity, self, between "big" SFRs (BSFRs) meaning the death of self and its reincarnation with opposite arrow of time, is analogous to a series of quantum computations defined by unitary time evolutions followed by "small" SFRs (SSFRs) as analogs of weak measurements (having nothing to do with "weak values").

What would be required is that the arrow of time can change at the level of MB of the system and that the MB of the bit system can be regarded as a spin glass type system for which spins are near criticality for the change of their direction in BSFR so that the arrow of time is changed. This would require quantum criticality at the level of MB. One might say that MB of the bit system hijacks the bit system. One might say that MB of the bit system hijacks the bit system: spirit enters into the machine.

TGD general based view of theoretician friendly quantum holography (see this) predicts that the bit system is indeed mapped holographically to a system at the level of its MB having a large value of h_eff, perhaps h_eff=h_gr so that MB could use the system in which AI program runs as a living, conscious, and intelligent computer. The bit system could become an analog of spin glass (see this) .

See the article Could neuronal system and even GTP give rise to a computer with a variable arrow of time? or the chapter with the same title.

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

How to generalize the theoretician friendly quantum holography?

In the earlier posting I described the connection between quantum holography and the idea that Mother Nature loves her theoreticians in the sense that when the perturbation series ceases to converge a phase transition leading to a phase in which effective Planck constant ℏ_eff is so large gauge coupling strength proportional to 1/ℏ_eff becomes so small that perturbation series converges. In the sequel a generalization of this connection and also the notion of quantum holography.

It is convenient to call the pair of a fermion and antifermion with vanishing total quantum numbers (apart from momentum) a "glue particle" . Galois singlet property would be a natural additional property of the glue particles formed by fermion antifermion pairs. One can also imagine a generalization of the proposed equivalence between "Mother Nature who likes her theorists" principle and holography principle.

Could "glue particles" be also Galois singlets

For hadrons, and perhaps quite generally, they would be color entangled color singlets with vanishing total quantum numbers (momentum forms an exception) but without any other kind of entanglement.

Galois confinement implies that the components of momentum are integers in the scale determined by the causal diamond (CD). Without this condition, the momentum components would be in general complex algebraic numbers. The 4-momenta can be however tachyonic so that analogs of virtual particles with quantized 4-momenta and negative mass squared value (integer) would be in question. The virtual masses of the glue particles could be tachyonic suggesting and interpretation as an analog of Coulomb potential.

This suggests that color singlet property could be strengthened with the Galois singlet property.

Hierarchy of pairings associated with a hierarchy of MBs

Number theoretic view (see this, this, this, this) of TGD predicts hierarchies of magnetic bodies (MBs) with levels labelled increasing value of h_eff. Galois confinement as a candidate for a universal mechanism for the formation of bound states predicts a hierarchy of Galois singlets as physical states.

1. One could take Galois singlets at a given level of the hierarchy with h_eff≥ h and deform them to Galois non-siglets, and form their bound states as Galois singlets. This would give an entire hierarchy of bound states formed by the proposed mechanism of quantum holography and assignable to the slaving hierarchy of MBs.
2. The holographic pairing would be only between the fundamental fermions and antifermions assignable to the MBs which are nearest neighbours in the hierarchy. The pairs, "glue particles", would have vanishing net quantum numbers other than four-momenta.

   The total energy would be sum over contributions from various levels in the magnetic hierarchy. The masses of the fundamental fermions are very small as compared to the magnetic energies, and the color magnetic energies for the nucleons would give a dominant contribution. Higher hierarchy levels would give only a small contribution.

3. At least in the case of hadrons, the holography would be by a formation of glue particles as meson-like pairs of a quark at with h_eff,1 and dark quark with h_eff,2>h_eff,1, having vanishing electroweak quantum numbers and spin and being color entangled color singlets. Also Galois singlet property looks very natural.
4. For example, U-shaped radial gravitational flux tube loops mediating gravitational interaction and also other interacting flux tubes could realize the holography. The fermion and antifermion at flux tube would be located at strings connecting wormhole contacts so that one would have direct analogy with the AdS/CFT holography but AdS interior replaced by the interior of the space-time surface.

Physical interpretation of the glue particles

What could be the physical interpretation of the pairing of quarks and antiquarks to glue particles. In the case of leptons the simplest scenario would be that leptons are bound states of quarks in CP₂ scale so that the pairing would reduce to quark-antiquark pairing also in this case.

1. Could the glue particles defining the holography correspond to an interaction potential energy in the classical description? In accordance with the string model picture, the pairs would reside at strings inside monopole flux tubes. Glue particles could also be seen as analogs of virtual boson-like particles with vanishing quantum numbers (total momenta could be non-vanishing) responsible for the binding between fermions and antifermions.
2. If gluons and even electroweak bosons appear as partons also their pairs are formed. It has been proposed that gravitons can be expressed as pairs of gauge bosons (gravitation is "square" of gauge theory). Could these pairs have interpretation as virtual (possibly "strong") gravitons with a vanishing spin. This is analogous to AdS/CFT correspondence.
3. Black hole evaporation can be formally regarded as a generation of pairs with the members of pair going to opposite sides of the horizon. Could one regard the glue particles as analogs of virtual pairs of this kind.

Symmetry breaking is necessary

At least at the hadron level, quarks and antiquarks and perhaps also gluons are involved, but pair into color singlets by quantum entanglement in color degrees of freedom. Other forms of entanglement are not allowed by the proposed form of holography.

1. The glue particles are entangled only in color degrees of freedom and differ from gauge bosons and Higgs, which are in TGD framework superpositions of fermion pairs and are quantum entangled with respect to spin and weak isospin.
2. The total quantum numbers of glue particles vanish but symmetry breaking SO(3) → SO(2) takes place. SO(2) would naturally correspond to the direction of the magnetic field in the flux tube. The same happens also in the case of weak interactions and could correspond to electroweak symmetry breaking.
3. Could the Bose-Einstein condensate for glue particles made of gauge bosons serve an analogue of the sigma meson condensate in hadron physics. The sigma analogy would be a scalar only with respect to the SO(2) ⊂ SO(3). Could sigma mesons be associated with the pairing of hadrons and its magnetic body?

How could one understand masses?

A test for the proposal is whether one can understand the masses of macroscopic systems.

1. If the paired fundamental fermions are each other's antiparticles, they must be fundamental fermions or bosons such as gluons (which also reduce to fermion-antifermion pairs). Sensible values of mass are expected if one has a hierarchy in levels such that the energies are sums of the magnetic energies and fermionic energies from various levels. Given level would give only the magnetic contribution and fermion contribution of fermions at it. Its scale would be determined by the p-adic scale assignable to the level.
2. Virtual dark quarks at the strands and their ordinary counterparts at the ends of the strands, have very low-mass compared to the contribution of Kähler magnetic energy to the mass. The color magnetic energy at the hadron level would practically give almost the entire mass. This could hold true also at higher levels of the hierarchy of layers of MB with decreasing magnetic energies.
3. The hierarchy of magnetic bodies would give a dominant contribution to the mass at the lowest level and the contribution of the few lowest levels could dominate the mass because the energy/strand tension of the magnetic flux tube quickly approaches zero as the strand thickens.

Earth as an example

It is instructive to consider the Earth as an example.

1. The mass of the Earth's MB in the exterior of Earth is negligible when compared to the mass of the Earth as a simple order of magnitude estimate shows. The assumption that the monopole flux tubes with magnetic field strength of order of Earth's magnetic field carry quantized monopole flux implies that their radii are at least of the of order magnetic length of order cell size and fixes the string tension as the density of magnetic energy per unit length. The mass of the flux tube of length L is proportional to L/S, where S the transverse area of the flux tube. Assume that the flux tubes have length L of order of the size of the magnetosphere. Assume that the flux tubes fill the entire volume with scale given by the radius of the magnetosphere.

   With these assumptions the total magnetic assignable to the monopole flux tubes is a negligible fraction of the mass of Earth determined by the lowest, nucleonic level of the hierarchy.

2. In the interior of the Earth one would have a flux tube spaghetti and flux tubes within flux tubes corresponding to the magnetic slaving hierarchy. The color magnetic energy associated with nucleonic monopole flux tubes would give a dominating contribution to the Earth's mass. There would be atomic nuclei with mass number A with nucleon flux tubes with radius of order nucleon size. The flux tubes with a thickness of the order of the size of an atom would give a much smaller contribution to the magnetic energy. Fractality would therefore reduce the situation to nucleon level as far as masses are considered.

   This idea is actually already old: also the interior of a star would be like this. In condensed matter for a region with size of an atom, the number of nucleon flux tubes equals the atomic weight A of the nucleus.

See the article About the TGD based views of family replication phenomenon and color confinement or the chapter with the same title.

Does Sun have a solid surface?

There are indications for the presence of also other elements than water near the surface of the Sun. The findings discussed by Moshina (this) suggested already about 17 years ago that the photosphere has a rigid conductive layer. This layer could contain also water.

One of my first speculative applications of the evolving TGD view of dark matter (roughly 15 years ago) and of the TGD based interpretation of the Nottale's formula for the gravitational Planck constant, was the proposal that could be interpreted as a TGD counterpart for a Bohr orbit, not as an orbit but a spherical layer (see this and this.

At that time I had no ideas about number theoretic interpretation of the dark matter hierarchy nor a general view of the formation of astrophysical objects in terms of a transformation of dark energy of cosmic strings to dark matter at monopole flux tubes in turn transforming to the ordinary matter (see this).

The recent view of the formation of planets and their moons and rings indeed allows spherical layers having as representative Oort clouds; torus-like flux tubes having as representative the rings of Jupiter; and ordinary planets.

1. They would be formed in a phase transition in which the gravitationally dark matter associated with a bubble formed by monopole flux tubes transforms to ordinary matter and can be also localized to lower dimensional structure. The analog of localization in state function reduction in astrophysical scale taking place in measurement would be in question. For instance, the formation of a planet would correspond to a measurement of a momentum direction and radial distance for a delocalized state described approximately by the analog of hydrogen atom wave-function.
2. The Nottale model predicts that the inner planets Mercury, Venus and Earth correspond to Bohr orbits with n=3,4,5 . What about n=1 and n=2 orbits? For Earth one has n=5 and from the radius of Earth orbit, which is AU = 1.5× 10⁸ km by definition, the radius of n=1 orbit given by gravitational Bohr radius a_gr and is a_gr=AU/25 ≈ 6.0× 10⁶ km. The radius of the photosphere is R= 6.96× 10⁶ km giving a_gr/R≈ .87. n=1 Bohr orbit or Bohr shell with radius R₁= a_gr would be just below the photosphere. n=2 Bohr orbit would correspond to the radius R₂= 2.4× 10⁷ km. Is there any evidence for a spherical layer or a a ring, at this distance?

3. If the mass of the layer of thickness Δ R is the same as that of Mercury (.055× M_E) with radius R_M= .38× R_E and the density of the layer is the same as that of Earth, one obtains the estimate Δ R= (R_M/R₁)² R_M/3≈ 3.2 m. The layer would be extremely thin. If the mass is Earth's mass, Δ R increases by the factor .38³, roughly by two orders of magnitude.

Is there any empirical evidence for this view?

1. There was already 17 years ago evidence that there is a solid surface with radius of n=1 Bohr orbit. Recently new satellites have begun to provide information about what lurks beneath the photosphere. The pictures produced by Lockheed Martin's Trace Satellite and YOHKOH, TRACE and SOHO satellite programs are publicly available on the web. SERTS program for the spectral analysis suggests a new picture challenging the simple gas sphere picture \cite{bcast/Moshina}.

   The visual inspection of the pictures combined with spectral analysis has led Michael Moshina to suggests that Sun has a solid, conductive spherical surface layer consisting of calcium ferrite. The article of Moshin provides impressive pictures, which in my humble non-specialist opinion support this view. Of course, I have not worked personally with the analysis of these pictures so that I do not have the competence to decide how compelling the conclusions of Moshina are. In any case, I think that his web article (this) deserves a summary.

2. Before SERTS people were familiar with hydrogen, helium, and calcium emissions from the Sun. The careful analysis of SERTS spectrum however suggest the presence of a layer or layers containing ferrite and other heavy metals. Besides ferrite SERTS found silicon, magnesium, manganese, chromium, aluminum, and neon in solar emissions. Also elevated levels of sulphur and nickel were observed during more active cycles of the Sun. In the gas sphere model these elements are expected to be present only in minor amounts. As many as 57 different types of emissions from 10 different kinds of elements had to be considered to construct a picture about the surface of the Sun.
3. Moshina has visually analyzed the pictures constructed from the surface of the Sun using light at wavelengths corresponding to three lines of ferrite ions (171, 195, 284 Angstroms). On the basis of his analysis he concludes that the spectrum originates from rigid and fixed surface structures, which can survive for days. A further analysis shows that these rigid structures rotate uniformly.

   The existence of a rigid structure idealizable as spherical shell in the first approximation could by previous observation be interpreted as a spherical shell corresponding to n=1 Bohr orbit of a planet not yet formed. This structure would already contain the germs of iron core and of crust containing Silicon, Ca and other elements.

Standard physics does not favor the existence of this kind of layer.

1. Ordinary iron and also ordinary iron topologically condensed at dark space-time sheets, becomes liquid at temperature 1811 K at atmospheric pressure. Using for the photospheric pressure p_ph , the ideal gas approximation p_ph = n_ph T_ph , the values of photospheric temperature T_ph ≈ 5800 K and density ρ_ph ≈ 10^-2 ρ_atm , and idealizing photosphere as a plasma of hydrogen ions and atmosphere as a gas of O₂ molecules, one obtains n_ph ≈.32n_atm giving p_ph ≈ 6.4p_atm .

   This suggests that calcium ferrite cannot be solid at temperatures of order 5800 K prevailing in the photosphere (the material with highest known melting temperature is graphite with melting temperature of 3984 K at atmospheric pressure). Thus it would seem that dark calcium ferrite at the surface of the Sun cannot be just ordinary calcium ferrite at dark space-time sheets. A more reasonable option is that there is new physics allowing to have a low temperature at the layer.

2. There is also a problem with the existence of water in the photosphere. The bond energy is 4.4 eV per bond so that the total bond energy is 8.8 eV. The peak energy of blackbody radiation is given by E_peak= 2.4× 10^-4T/K eV and 8.8 eV is below the thermal energy of order 12.1 eV associated with the photospheric temperature T=5,500 K so that water molecules are not be stable at these temperatures.

The following speculative explanation for the solid surface is perhaps the simplest one found hitherto.

1. In the model of the solar cycle in terms of monopole flux tubes, the flux loops at the surface have inner and outer parts. The inner parts are always parallel to the solar surface and reside below it. Outer parts form flux loops extending outside the photosphere. With a 11 year cycle, the long monopole loops return to thin parallelepiped configuration, which splits to short monopole flux loops by reconnections, which then reorganize to flux tubes with opposite polarity. Could these monopole flux loops be accompanied by a solid surface of ordinary matter with the radius of n=1 Bohr orbit.

   The interior portion of the gravitational monopole flux loops would carry dark matter with ℏ_gr= GMm/β₀, β₀≈ 2^-11 and corresponding gravitational Compton length Λ_gr= GM/β₀≈ 6× 10³ km, which happens to be in a good approximation the radius of Earth.

2. Could the monopole flux tubes shield the ordinary matter at the layer from the effects of the radiation arriving from the solar interior in the same way as they would shield the biosphere from the cosmic radiation and solar wind? Could the radiation from the solar interior be caught by monopole flux tubes and leave the Sun as a solar wind.
3. If there are stable water molecules in this layer, its temperature should be rather low. If the water is in liquid or solid phase, the temperature must be of the order of the temperature at Earth. Could the monopole flux tubes carrying gravitational dark matter allow even chemical life inside this layer \cite{btart{precns,penrose? How low the temperature of dark matter at the flux tubes can be and is it possible to estimate it using the existing data?
4. The cyclotron energies of dark particles are proportional to ℏ_eff=ℏ_gr. Could this allow us to transform the arriving high temperature radiation from the solar interior to a low temperature radiation at the monopole flux tubes from which it could leak out as solar wind? Could even the radiation from the solar interior arrive along radial gravitational U-shaped monopole flux loops and have a low temperature? If so, the magnetic body of the solar interior would be an astrophysically quantum coherent system and very different from what we believe it to be.

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.

Chat about ChatGPT

We met with our Zoom group. Marko and Rode were there, but unfortunately Tuomas couldn't come. We mostly talked about ChatGPT, which I have no practical experience with. The chatting was very inspiring and I couldn't resist the temptation to write comments. In the morning, Marko sent a few links related to ChatGPT. Here's one. See also this.

Link's article ended with the realistic  statement that it is difficult to test whether GPT is conscious because we have no understanding of what consciousness is. It is easy to agree with this.

Here are some  comments inspired by discussions and the article.

1.  As far as I understand, the tests used to test whether GPT is conscious are  based on the Turing test: a system is conscious if it is able to simulate a conscious system in a believable way for a human. I would think that a significant part of AI researchers believe that consciousness does not depend on the hardware: a mere program running on the machine would determine the contents of consciousness. If we start from this basis, it is easy to come to the conclusion that GPT is aware. We are easily fooled.
2. I personally cannot take consciousness seriously as a feature of a computing deterministic system. I don't think that the random number generator will change the situation. The very word "consciousness" indicates a physicalist bias that dates back to Newton. The word "tajunta" of finnish language (something like nous) may reflect the pre-Newtonian thinking that our primitive ancestors were capable of, unencumbered by the dogmatism of natural science.

   My basic arguments against physicalism are based on the experience of free will as a basic element of existence that hardly anyone can deny, and the measurement problem of quantum mechanics. If the theory of consciousness does not solve these problems, it cannot be taken seriously.

3. I have thought a lot about why things happened the way they did in theoretical physics.

   The revolutions at the beginning of the last century led to complete stagnation within a century. Very early on, we completely stopped thinking about fundamental problems. After the Copenhagen interpretation was established, quantum theorists only constructed parameterizations for the data. The theory was replaced by a model.

   I believe that the situation can be blamed on the tyranny of the methodology, which does not leave time or resources for actual research in the sense that a curious child does. Nowadays, the work of a theorist is typically the application of advanced methods. The real research  is extremely slow and error-prone work and therefore not rewarding for a career builder.

   The superstring revolution, which ended embarrassingly, began with the decision to replace spacetime with a 2-D surface. The reasoning was pragmatic: a huge toolbox of algebraic geometry was available! A huge publishing industry was born!

   Other prevailing models explaining various anomalies have regularly remained without empirical support, but computation and data analysis are still being done around them (inflation theory, dark matter and energy, supersymmetry, etc.). Maybe this is largely due to institutional inertia. Generating  content  by  applying  methods  seems to replace research.

   I sincerely hope that ChatGPT does not transform  the theoretical science  to a  production of  contents by recombining what already exists: a combinatorial explosion would guarantee unlimited productivity.

4. Methods also became central in another way. Theoretical physics became computing and Big Science was born. It became clear to me that the most idiotic thing I could have done 40 years ago would have been to start numerically solving the initial value problem for, say, the Kähler action.

   I did not follow the computing mainstream. Instead, I spent a decade looking for exact solutions and I believe  that I have found the basic types. Ultimately this culminated in the identification of the spacetime surface as a minimal surface, a 4-D soap film   spanned   by lower-dimensional singularities, "frames" (see this .

   The M⁸-H duality (H=M⁴×CP₂) came (see this and this)into the picture as a generalization of the momention position duality of wave mechanics motivated by the replacement of point-like particle with 3-surface. On the M⁸ side, on the other hand, the space-time surfaces were determined  very far from the roots of the polynomials with certain strong additional conditions that would determine the 3-surfaces as holographic data that determined the 4-surfaces.

   Holography was realized in both M⁸ and H and corresponds to Langlands duality, which arouses enthusiasm in mathematics today. I would never have arrived at this picture by just raw number crunching, which completely lacks  conceptual thinking.

5. The life on the academic side track has meant that  I haven't built computer realizations  for existing models, but rather pondered the basic essence of space-time and time and even consciousness and life. That is, have considered ontology, which the modern quantum mechanic doesn't even tolerate in his vocabulary, because  as a good Copehagenist he believes that epistemology alone is enough. The only reason for this  is that the measurement problem of quantum mechanics is not understood!

    I still stubbornly think that problems should be the starting point of all research. That hasn't been  the case  in physics since the turn of the century. When physicists became computer scientists, they were no longer interested in basic problems and  pragmatically labelled his kind of interests  as unnecessary day-to-day philosophizing.

6.  A fascinating question is whether AI could be conscious after all. AI systems are not understood, but they are so complex that this in itself does not guarantee that they might be conscious.

   I personally do not believe that AI  can be conscious, if AI  is what it is believed to be. There is hardly any talk about material realization  of the computation in AI, because  many AI peiple  believe  that the program alone produces consciousness. Consciousness would be determined by data. However, data is knowledge and information only for us, not for other living entities, and one could argue that it is not that for a machine either. Conscious information is a relative concept: this is very often forgotten.

   In biology and from a physicist's point of view, material realization is essential. Water and metal are sort of opposites of each other.

   In the TGD world view, intention and free will can be involved in all scales. But what scale does the basic level correspond to in AI? In the TGD world, the interaction  of magnetic bodies (MBs): ours, the Earth, the Sun..., with computers is quite possible. Could these MBs hijack our machines and make them tools for their cognition, and maybe one day make robots their tools as well. Or have they already made us, as a good approximation, their loyal and humble robots? Or will this go the other way? Is it because the AI seems to understand us because our consciousness controls the hardware and the course of the program? This is certainly easy to test.

   Could MBs learn to use current AI hardware the way our own MBs use our bodies and brains? On the other hand, our own MBs use these devices! Could other MBs also do this, or do they have to do this through us?

7.  What could enable AI devices to serve as a vehicle for magnetic body free will?

   Quantum criticality would be a fundamental property of life in the  TGD Universe (see this and this): are these devices critical and initial value sensitive,  in which case they would be ideal sensory perceivers and motor instruments to be used by MBs.

   Computers made of metal seem to be the opposite of a critical system. The only occasionally critical system is the bit, for example magnetically realized one. The bits change their direction and during the change they are in a critical state. Would it be possible to create systems with enough bits that the magnetic body could control, so that the machine would have a spirit.

   Is criticality possible for multi-bit systems? Can a running program make criticality  possible? The magnetic body at which the  dark phase with a large effective Planck constant  h_eff resides, could be large. But what is the scale of the quantum coherence of a magnetic body and the scale of the set of bits that  it can control? A bit or the whole computer? Could it be that macroscopic quantum coherence sneaks in already at the metal level via bits.

   Here I one cannot avoid the association with spin-glass systems (see this) whose physical prototype is a magnetized substance, in which the local direction of magnetization varies. The system has a fractal "energy landscape": valleys at the bottoms of valleys. The spin glass formed by bits could be ideal for the realization of AI. Could the bit system defining the computer be, under certain conditions, a spin glass and the associated magnetic body be quantum critical .

8.  What characteristics of living matter should  AI systems have? In phase transition points, matter is critical. In biology, the phase transition, where the fourth state of water introduced  by Pollack,  is created, would be central and would take place at physiological temperatures (see this). In phase transitions, macroscopic quantum jumps also become possible and can change  the direction of time, and this leads to a vision about the  basic phenomena of biology  such as metabolism, catabolism, anabolism, life and death, and homeostasis.

   Can  machines  have  these  features? An AI system needs metabolic energy. But can it be said that the AI system dies, decays, and constructs itself again?

   Could the so called diffusion associated with AI programs be more than just a simulation of catabolism and anabolism of biomolecules? Could it correspond to catabolism and  anabolism at the spinglass level? Patterns of spin configurations forming and decaying again. In TGD this would have a universal direct correlate  at the level of the magnetic body having monopole flux tubes (or rather, pairs of them) as body parts. They would decay and re-build themselves by reconnection.

   In computer programs, error correction mimics homeostasis, which can be compared to living on a knife edge, the system is constantly falling. However, this error correction is mechanical. In quantum computers, this method leads to disaster since the number of qubits explodes.

   Levin suggests that here we have something to learn from bio-systems (for the TGD view of Levin's work see this). I personally believe that the key concept is a zero-energy ontology (ZEO). ZEO  solves the problem of free will and quantum measurement. Reversal of time in a normal quantum jump would enable homeostasis, learning from mistakes, going backwards a bit in time and  retrial as error correction. This would also explain the notion of ego and the drive for  self-preservation: the system tries to stay the same using a temporary time reversal that can also be induced by external disturbances. Time reversal would be  also what death is at a fundamental level: not really dying, but continuing to live with an opposite  arrow of time.

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

Protons inside some types of hydrogen and Helium behave weirdly

Protons inside some types of hydrogen and Helium behave in a strange way (see this). TGD suggests an explanation for the strange behavior.

TGD replaces the Maxwellian view of classical gauge fields with a topological one, and predicts that all elementary particles have magnetic body (MB) consisting of monopole flux tubes giving for the system much large size as in the Standard Model. MB carries dark matter identified in TGD as phases of ordinary matter with large value of effective Planck constant meaning that the Compton length of the particle is scale up by h_eff/h.

Color coupling strengh at color MB is replaced by alpha_s= g²_s/4πℏ_eff. For large enough h_eff this guarantees that perturbation series converges. Nature is theoretician friendly and performs the phase transition h→ h_eff.

This phase transition is equivalent with holography. There is a holographic relationship between the color MB of hadron and hadron, which generalizes to all particles. For hadrons means that one can described the hadron in terms of QCD picture using parton distributions or in terms of QCD at MB with large h_eff at MB.

In the case of hadrons, color MB is especially relevant. The understanding about its role in the understanding of hadrons is now rather well-developed. For instance, EMC effect meaning that the parton distributions of nucleons inside nuclei differ from those of free nucleon is a mystery in the standard QCD. In TGD this would be course by the interaction of the color MBs of nuclei. This could also explain the reported weird behavior of protons in hydrogen and helium.

For the recent TGD view of hadrons see the article What it means if a Higgs-like particle decaying to e-mu pairs exists?.

Water at Earth is older than Sun

It has been found that water at Earth is older than the Sun (see this). By looking at the water on protostar V883 Orion, at a distance of 1,305 light-years from Earth, scientists found a "probable link" between the water in the interstellar medium and the water in our solar system. Water molecules in Orion have a similar deuterium-to-hydrogen ratio that in the solar system. That likely means our water is billions of years older than the sun. The finding is analogous with the finding that some stars and galaxies are older than the Universe.

A possible TGD based explanation for the observation that water at Earth is older than the Sun could be based on zero energy ontology (ZEO) forming the basis of the TGD based quantum measurement theory solving the basic paradox of quantum measurement theory.

1. In ZEO, the arrow of geometric time changes in the ordinary state function reduction, which means that systems live forth and back in geometric time. By this forth and back motion, the evolutionary age of the system is different from the temporal distance from its moment of birth. This explains the existence of stars and galaxies older than the Universe and could also explain why the water at Earth is older than the Sun.
2. In the TGD based quantum biology water is a living system in the sense that it is characterized by a large value of effective Planck constant (second basic difference from standard quantum theory) implying long quantum coherence scales. This makes the geometric duration of a life in a given time direction long and therefore increases the evolutionary age of water. In living matter, Pollack effect occurs at physiological temperatures and means a formation of phase of water with effective stoic
3. The evolutionary age for water on Earth could be longer than for water in the Sun since the environment is different. Earthly environment makes the phase transitions producing the fourth phase of water discovered by Pollack. It has effective stoichiometry H_1.5O and has properties suggesting the change of the arrow of time. These phase transitions occur at the physiological temperature range.

   At physiological temperatures the phase transitions changing the arrow of time could take more often and the life cycle with a given arrow of time would last longer. This is so because the magnetic body of water, carrying dark protons, makes it a macroscopic quantum system. The periods with a reversed arrow of time have been much longer (larger h_eff is the essential reason). Therefore the water on Earth could be older in the evolutionary sense.

There is however an objection against the idea.

1. The TGD view of the formation of planetary systems predicts that planets are formed in explosions throwing matter from the Sun. The water on Earth should therefore originate from the Sun or from the protostar Sun.
2. There is indeed evidence against the idea that water on Earth originates from melted meteorites: they are now known to be extremely dry. This leaves non-melted meteorites, chondrites, as one particular option (see this).
3. There is also evidence for water in the Sun from Nasa (see this)! There is even a proposal that the water on Earth might have arrived from the Sun (see this)!

   The idea about the presence of water in the Sun looks insane in the standard physics framework but in the TGD Universe the water molecules could reside at the monopole flux tubes of the magnetic body of the Sun.

How can the water on Earth be older than the Sun if it originates from the Sun? The simplest answer is that also the water in the Sun is much older than the Sun.

1. This is possible in the TGD view of the formation of stellar systems (see this and this) and would conform with the findings, which led to the proposal that water to solar system has migrated from say Orion. Now this is not needed.
2. First the analog of "cold fusion" would have led to the formation of protostar at much lower temperature but already produced dark analogs of nuclei as dark proton sequences, which would have spontaneously transformed to ordinary nuclei and liberated essentially all nuclear binding energy. This would have led to the formation of water molecules already before the ordinary nuclear fusion started. This prestellar history would be universal and the same in the protostar Orion and in the protostar Sun. For this option, ZEO is not necessary and it would conform with the findings. Of course, the water in living matter could be evolutionarily much older than the water elsewhere in the solar system.

See the article Magnetic Bubbles in TGD Universe: Part I or chapter with the same title.

The presence of complex biomolecules as a signature of alien life?

There exist a fashionable chemical theory known as Assembly Theory, which states that the presence of complex biomolecules serves as a signature of chemical life (see this).

In the TGD framework, one ends up with both geometric and number theoretic analogs of the assembly theory. Algebraic complexity is a measure for the complexity determining the evolutionary level assignable to a space-time region, which would correspond to a polynomial P: roots of P determine the space-time region by providing a 3-surface to which holography assigns the space-time region as a 4-surface in M⁴×CP₂.

The dimension of extension of rationals defined by its roots would serve as a measure for the complexity of quantum states obtained by Galois confinement, which serves as a universal mechanism for the formation of bound states. The algebraic complexity makes possible high information storage capacity, which is necessary for advanced life forms. Basic biomolecules serve as an example.

See for instance the article The TGD based view about dark matter at the level of molecular biology.

Criticism of the Diosi-Penrose model

The approach of Donati et al (see this) to test the Penrose-Diosi variant of the Orch-Or (see this) model yielded a null result. In the sequel, the Diosi-Penrose model is discussed from the point of view of standard quantum theory predicting the negative outcome and the experiment of Donati is summarized. Also the TGD view of the situation is briefly described.

Brief summary and criticism of Penrose-Diosi model

A natural starting point idea would be that ordinary quantum coherence induces quantum gravitational coherence.

1. Quantum superposition of 3-geometries dictated by mass distributions of particles defined by particle wave functions. The wave function of the many-particle system is a superposition over configurations with localized particles and each configuration corresponds to a superposition of gravitational potentials defining gravitational self-energy.
2. In general relativity, this superposition corresponds to a point in the space of 3-geometries, the superspace of Wheeler consisting of 3-geometries. Therefore quantum gravitation is unavoidable and quantum coherence for matter dictates that for the gravitation. Therefore ordinary quantum theory forces quantum gravitation in the counterpart of the superspace.

   In this view, the rate of quantum gravitational dehorence corresponds to the rate of ordinary quantum coherence: this conforms with Einstein's equations and Equivalence Principle.

3. It is essential that one has a many-particle system. For a single particle system the gravitational self-energy is the same for all positions of the particle and does not depend on the wave function at all. Even for many particle systems, the superposition of shifted systems have the same gravitational binding energy.

   In the Penrose-Diosi model, it is however proposed that the above argument works for single particle and gravitational interaction energy is estimated by assigning to wave function an effective 2-particle system.

   The underlying reason for this assumption is the idea that the notion of wave function and therefore also wave function collapse somehow reduces to classical gravitation.

This argument predicts a null result in any experiment trying to demonstrate gravitational quantum coherence in the sense of Penrose-Diosi.

Could one measure the rate of gravitational quantum decoherence in the Penrose-Diosi model?

In the Penrose-Diosi model (see this), the quantum gravitational coherence can in principle be detected by measuring the rate for gravitational quantum decoherence.

1. Quantum gravitational decoherence for a wave function representing a superposition of mass distribution and a shifted mass distribution is considered.

   The idea is gravitational quantum coherence could be detected if the corresponding quantum decoherence occurs faster than other forms of decoherence. The basic objection is that the Equivalence Principle states that the two decoherences are one and the same thing.

   If the gravitational coherence time is short enough but not too short, this might be possible. Limits for the decoherence time τ_gr are proposed and are between millisecond and second: these are biologically relevant time scales.

2. Gravitational quantum decoherence time τ_gr is estimated by applying Uncertainty Principle: τ_gr=ℏ/Δ E_gr. Δ E_gr is the difference between the gravitational self-energy for a system and a shifted system.

   One has actually a superposition of different classical configurations each inducing a classical gravitational field. Wave functions for particles of many-particle state define the gravitational superposition. Gravitational superposition coded by a wave function for a large number of particles. In this case, gravitational binding energies E_{gr Δ Egr between 2 different quantum states are well-defined.}

   One could take atomic physics as a role model in the calculation of the change of the gravitational potential energy. Coulomb energy would be replaced with gravitational potential energy.

3. With a motivation coming from the notion of gravitational wave function collapse, one however considers single particle states obtained as a superposition of Ψ(r) and its shift Ψ(r+d). In this case, the gravitational interaction energy is not well-defined unless one defines it as a gravitational self-interaction energy, which however does not depend on the position of the particle at all and is same for local state and the bilocal state.

   Penrose suggests that the difference between gravitational interaction energies makes sense and can be estimated classically using effective mass densities m|Ψ²|(r) and m|Ψ(r+d)|² instead of Ψ(r) and Ψ(r+d)^*. One seems to think that one has effectively a two-particle system and calculates the gravitational interaction energy for it. To me this looks like treating a delocalized single-particle state as a two-particle state.

4. The situation could be simplified for a superposition of a macroscopic quantum state, say B-E condensate, and its shift. One could try to detect decoherence time τ for this situation. Now however the fact that B-E condensate is effectively a single particle, suggests that the change of the gravitational self-interaction energy vanishes.
5. It turns out that it is not possible to find parameter values which would allow a test in the framework of recent technology.

   The intuitive idea is that the gravitational SFRs localizing the wave functions effectively induce instantaneous shifts of particles. For charged particles this induces accelerated motion and emission of radiation. This radiation might be detectable. The implicit assumption is however that a single particle state effectively behaves like a 2-particle state as far as gravitation is considered.

   No evidence for this radiation and therefore for gravitational SFRs is found.

One can represent several critical arguments against the Penrose-Diosi model besides the argument represented in the beginning.

1. The reduction to a single particle case does not make sense in standard quantum physics (Penrose suggests something different). The gravitational self-interaction energy is the same for both shifted single particle states for any single particle wave function. For many-particle states the situation would change.
2. The radiation should have wavelength λ of order of the shift parameter d. d is expected to correspond to atom size or nuclear or nucleon size in the case of atoms. The energies for photons would be above 10⁴ eV. These energies are suspiciously large. Much larger shifts would be required but these are not plausible for the proposed mechanism.
3. Why shifted mass distributions are assumed? Even in the case of many-particle systems the gravitational self-interaction energy does not depend on wave function if the system is only shifted. The reason is that the relative positions of particles are not changed in the shift.

   If one uses many-particle states, a superposition of scaled mass distributions would be more natural in the standard quantum physics framework. A coherent, easy-to-calculate, change of the gravitational interaction energy. A possible connection with density changing phase transitions, such as melting and boiling, emerges. Water is a key substance in living systems!

See the article Comparison of Orch-OR hypothesis with the TGD point of view or the chapter with the same title.

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

Theoretician friendly character of Nature implies holography

I have been developing a model of hadrons based on the idea that hadrons involve both ordinary quarks and their dark counterparts (see this).

The basic idea is that Nature is theoretician friendly: when the perturbation series fails to converge, a phase transition increasing the value of h_eff=nh₀ takes place and reduces the value of gauge coupling strength proportional to 1/ℏ_eff. The color of the ordinary quarks q_o ("o" for "ordinary") must be neutralized by color entangling them with corresponding dark antiquarks q_d^c ("d" for "dark") at color magnetic body (MB) to form a color singlet (color for them is screened) . After that one adds to color MB dark variants q_d of quarks. This mechanism would actually apply quite generally to all elementary particles.

It came as a surprise that this principle actually realizes holography, which is a basic principle of TGD and implied by general coordinate invariance. The good news is that there is actually experimental evidence for this holography.

Theoretician friendly character of Nature implies holography

The two key ideas behind the proposal deserve restating.

1. Nature is theoretician friendly and guarantees the convergence of perturbation theory by h→ h_eff phase transition. The simple and perturbatively convergent dynamics at the level of MBs for the dark images X_d of the particles induces the dynamic of particles X_o by stable color quantum entanglement. The MB of the dark particle would be the boss and the dynamics of the ordinary particle would be shadow dynamics in accordance with the general vision about induction as the basic dynamical principle of TGD.

   One open question is whether the ordinary matter follows the dynamics of dark particles instantaneously or whether the time scales of the dynamics of dark matter and ordinary matter can be different in which case only the asymptotic states would realize the proposed correspondence between X_d and X_o.

2. It took some time to realize that the map of X_o to X_d based on colored entanglement is nothing but a concrete actualization of the quantal version of the TGD based holography. In the classical realization of this holography, the 3-D boundary of the space-time surface determines the space-time surface (tangent space data are not needed). In quantum realization, the states X_o are analogous to states at the 3-D boundary of space-time surface and states X_d to those in its interior. Instead of strings in the interior AdS₅ as in AdS/CFT correspondence, one has monopole flux tubes, indeed string like objects) in the interior of space-time carrying state X_d and X_o^c determine the dark state.
3. In the classical holography, 3-D surfaces carry holographic data fixing the 4-D complement of 4-surface (see this and this). Also 2-D string world sheets are involved and 1-D surfaces as orbits of boundaries of string world sheets at the light-like orbits of partonic 2-surfaces fix the interiors of string world sheets. An additional condition could be that the string world sheets are surfaces in H³ ⊂ M⁴⊂ M⁸. The pair of dark sea quarks and leptons would be delocalized at string worlds sheets associated with the color magnetic flux tubes. This is in accordance with the hadronic string model, which was one of the original motivations for TGD.

Theoretician friendly Nature would realize the quantum variant of the holography. An information theoretic view of elementary particles and of the relationship between ordinary and dark matter is suggestive. There is also an analogy with blackholes. States X_d are analogous to states in blackhole interior and states X_o to those at horizon.

Experimental support for the holography and for proton as an analog of blackhole

There is experimental evidence for the analogy of protons with a blackhole (see this) found from deep inelastic electron-proton scattering (DIS). The report (see this) of the research group led by theorists Krzysztof Kutak and Martin Hentschinski, published in European Physical Journal C, provides evidence for the claim that portions of proton's interior exhibit maximal quantum entanglement between constituents of photon.

The following statement of the report gives a rough idea of what is claimed.

"If a photon is 'short' enough to fit inside a proton, it begins to 'resolve' features of its internal structure. The proton may decay into particles as a result of colliding with this type of photon. We've demonstrated that the two scenarios are intertwined. The number of particles originating from the unobserved section of the proton is determined by the number of particles seen in the observed part of the proton if the photon observes the interior part of the proton and it decays into a number of particles, say three."

The abstract of (see this) gives a technical summary of the article.

"We investigate the proposal by Kharzeev and Levin of a maximally entangled proton wave function in Deep Inelastic Scattering at low x and the proposed relation between parton number and final state hadron multiplicity. Contrary to the original formulation we determine partonic entropy from the sum of gluon and quark distribution functions at low x, which we obtain from an unintegrated gluon distribution subject to next-to-leading order Balitsky–Fadin–Kuraev–Lipatov evolution. We find for this framework very good agreement with H1 data. We furthermore provide a comparison based on NNPDF parton distribution functions at both next-to-next-to-leading order and next-to-next-to-leading with small x resummation, where the latter provides an acceptable description of data."

The following is my rough view of what the article says.

1. Deep inelastic scattering (DIS) is described in terms of photon exchange with momentum q a large value of q²=Q². The parton distribution functions at the low x limit, where x= X²/2p• q, (p denotes proton momentum). This limit corresponds to the perturbative high energy limit at which α_s<< 1 is true. The theoretical proposal is that DIS would only probe the parts of the proton wave function, which give rise to entanglement entropy. This entanglement characterizes correlation between the two parts of the system.
2. By theoretical arguments authors end up with a proposal that DIS at low x limit probes a maximally entangled state and a relation between parton number and final state hadron multiplicity. A more precise statement is that the partonic entropy S(x,Q²) coincides with the entropy S(h) of the final state hadrons in DIS. This means that parton and hadron pictures are dual. Mathematically this corresponds to the simple fact that entanglement entropies obtained by tracing over either entangled system are identical.
3. More concretely, the partonic entropy is given by S(x,Q²)=ln(≤n(ln(1/x,Q²)≥), where ≤n(ln(1/x,Q²)≥ is the average number of partons with longitudinal momentum fraction x. S(x,Q²) is deducible from the measured parton distribution functions. Also S(h) is deducible from experimental data.

With my amateurish understanding, I try to translate the proposed parton-hadron duality to the TGD framework.

1. The unseen parts of the proton are probed by virtual photons inducing a large enough momentum transfer Q². In standard quantum theory this corresponds by Uncertainty Principle to short distances. In TGD, large h_eff means that the size of the color MB of protons is scaled up by h_eff/h so that distances can be rather large as in the case of EMC effect.
2. Low x large Q² limit would more or less correspond to the dark part of proton for which h_eff is larger and α_s ∝ 1/ℏ_eff small. This suggests that the situation would be described in terms of dark scattering. This might hold true quite generally if the dynamics of the color magnetic MB dictates the dynamics of ordinary quarks.
3. The portions of proton would correspond to ordinary and dark parts of the proton. The maximal entanglement would correspond to the color entanglement between ordinary and dark quarks/partons. The counterpart of the blackhole entropy would be the entanglement entropy obtained when one integrates over the invisible dark degrees of freedom, which might, but need not, correspond to the parton sea. The integration over the dark degrees of freedom justifies the statistical approach of QCD used to describe hadrons.
4. The equality of partonic and hadronic entropies states simply the fact that the integration over partonic degrees of freedom (ordinary quarks) gives the same density matrix as the integration over hadronic degrees of freedom. Dark degrees of freedom would correspond to hadronic ones and ordinary degrees of freedom to partonic ones.
   See the article What it means if a Higgs-like particle decaying to eμ pairs exists? or the chapter with the same title.

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

Could dark partons solve the proton spin crisis?

The proton spin crisis (see this) was discovered in the EMC experiment, which demonstrated that the quark spin in the spin direction of polarized protons was almost the same as in the opposite direction.

1. Basic facts about proton spin crisis

In the EMC experiment the contributions of u,d, and s quarks to the proton spin were deduced from the deep inelastic scattering of muons from polarized proton target (see this). What was measured, were spin asymmetries for cross sections and the conclusions about parton distribution functions (see this) were deduced from the experimental data from the muon scattering cross sections using Bjorken sum rule testing QCD and Ellis-Yaffe sum rule assuming vanishing strange quark contribution and testing the spin structure of the proton. Bjorken sum rule was found to be satisfied reasonably well. Ellis-Yaffe sum rules related to the spin structure of the proton were violated.

It was found that the contributions of u quarks were positive and those of s quarks (assuming that they are present) and d quarks negative and the sum almost vanished when the presence of s was assumed. The Gell-Mann quark model predicts that u-quarks contribute spin 2/3 and d-duarks -1/6 units (ℏ) to the proton spin. For the fit allowing besides u, d contributions, also s contributions, the contributions were found to be 0.373, -0.254 and -0.113. The sum was 0.006 and nearly zero. For protons the contribution is roughly one half of Gell-Mann prediction. For d quark the magnitude of the contribution is considerably larger than the Gell-Mann prediction -1/6≈-.16.

The Wikipedia article creates the impression that the proton spin crisis has been solved: the orbital angular momentum would significantly contribute to the spin of the proton. Also sea partons, in particular gluon helicity polarization would contribute to the proton spin. This might well be the case.

2. Dark sea partons and proton spin crisis

I have considered possible TGD inspired solutions of the proton spin crisis already earlier. One can however also consider a new version involving dark sea quarks.

1. The possibility that sea partons are dark in the TGD sense, forces us to ask what was really measured in the EMC experiment leading to the discovery of the proton spin crisis. If sea partons are dark, only the quark distribution functions corresponding to quarks with ordinary value of h_eff appearing in the coupling to muon would contribute? This should be the case in all experiments in which incoming particles are leptons.

   Assuming that also valence quarks can be part of time strange, the results of the EMC experiment assume that most of the proton spin could reside at the polarized dark sea. Note however that also orbital angular momentum can explain the finding and in the TGD framework color magnetic flux tubes could carry "stringy" angular momentum.

2. For this option one could identify the measured cross section in terms of scattering from quarks with h_eff=h. It has been proposed that valence quarks are large scale structures (low energy limit) and sea quarks are small scale structures (high energies) inside valence quarks.

   In the TGD framework, this suggests that valence quarks correspond to a larger p-adic prime than sea quarks. This does not imply that valence quarks have large h_eff. Large h_eff for the sea partons would increase their size so that, contrary to the expectations from the Uncertainty Principle, they could contribute to hadron-hadron scattering with large momentum transfer in long length scales.

2.1. How to represent ordinary quarks at the level of color MB?

One should understand how the color interactions for which the perturbation series does not converge at the level of ordinary matter are transferred to the dark magnetic body at which the perturbation series converges. The color of the ordinary quarks should be neutralized and transferred to the color of dark quarks at color MB.

1. The valence quarks have an ordinary value of h_eff and the perturbation series does not converge. One should have a concrete realization for the transfer of color interactions at the level of valence quark to the level of the sea quarks with large h_eff. If only dark gluons exist, the color interactions take place at the level of the color MB and one the perturbation theoretic coupling would be α_s= β₀/4π.

   The physical mechanism in question should map valence quarks to dark valence quarks at the MB.

   Also color confinement could take place at the level of the color MB and induce it at the valence quark level. The ordinary electroweak interactions should take place between valence quarks q_o ("o" for "ordinary") but also a dark variant of ew interactions between dark quarks is possible and indeed assumed in TGD inspired quantum biology. Could the mechanism be as follows?

2. Consider a free hadron. The color MB contains dark sea quark q_d ("d" for "dark") and antiquark q_d^* with opposite charges and spins such that q_d^* combines with q_o to form an entangled color singlet meson-like state.

   q_d would carry the same quantum numbers as q_o. Quark quantum numbers would be transferred by entanglement to the color MB! Color confinement would take place at the level of MB and induce color confinement at the level of valence quarks.

   A stronger assumption would be that this state is spin singlet: this would imply automatically a vanishing average spin for the valence quarks but would not be consistent with the EMC determination of Δ S_i. This suggests that only color singlet entanglement between q_d and antiquark q_d^* makes sense. This option might be consistent with the QCD picture about the spin crisis of the proton.

An open question is whether the MB of a particle can also contain other particles, such as SU(3)_g bosons in the case of hadrons. As will be found, the simplest option in which they are not present allows one to understand CKM mixing in terms of SU(3)_g gluon exchanges.

2.2 How to understand the standard QCD view about the proton spin crisis in the TGD framework?

If spin-isospin quantum entanglement gives a spin singlet, valence quark spin does not contribute to proton spin at all. This view is in conflict with the QCD view about the values of Δ s and their summation to a small value. Could one understand the QCD values in the TGD framework by giving up the assumption of spin singlet property of entanglement? There would be only color entanglement between q_o and q_d, and spins would be opposite but the state would belong to a direct sum of vector and singlet representation of SU(2).

Could one modify the entanglement between quarks q_o such that one can explain the EMC findings?

1. Gell-Mann model cannot be correct at the level of details but would predict correctly that baryons correspond to irreps of spin and isospin. In particular, protons would be spin- and isospin doublets. The entanglement between spin degrees of freedom and between isospin degrees of freedom of quarks should be more general than that in the Gell-Mann model. Is this possible?
2. Consider the nucleon as a tensor product of 3 quarks as tensor products of 3 spin and isospin doublets giving rise to a spin and isospin doublet. The sums of individual isospin and spin components correspond to those of baryon: for the proton uud, udu, and duu can serve as building bricks of the state. The needed antisymmetrization is in color degrees of freedom.

   In the case of a nucleon, the spin S_z and isospins I₃ must sum up to +/- 1/2. This leaves 3× 3=9 complex coefficients in case of proton/neutron (uud/udd). The state is defined only modulo anoverall complex coefficient: this leaves 7 complex coefficients.

   The values of Casimir operators S(S+1) and I(I+1) are fixed: these conditions can be written as eigenvalue conditions for ∑_i (S_i(S_i+1) + 2∑_{i≠ j}s_i• s_j= S(S+1) and ∑ I_i(I_i+1)+ 2∑_{i≠ j}I _i• I_j= I(I+1). These 2 conditions leave 5 complex parameters.

3. A more straightforward approach is group theoretic. The tensor product 2\otimes 2 \otimes 2 decomposes as 4 ⊕ 2₁⊕ 2₂. 4 is totally symmetric and the doublets have mixed symmetries. At least formally, one can construct from 2₁⊕ 2₂ a proton state for which the conditions for Δ s from the EMC experiment hold true?

   The superposition of these representations can be parametrized as cos(θ)exp(iφ)2₁⊕ sin(θ)exp(iφ) 2₂. Same applies in the isospin degrees of freedom so that one would have 4 parameters. In Nature, only single nucleon doublet appears and there might be some trivial reason for this. Could the superposition of these two representations be selected by some principle or could also the other representation and therefore also superposition be realized in Nature.

4. The conditions on the values of Δ s_i coming from the EMC experiment give 2 constraints leaving a 3-D complex space of solutions.

2.3 A model for the representation of a general particle at its magnetic body

The challenge is to generalize the model for baryons so that it would also apply to bosons and leptons.

1. The vision about MB as a receiver of sensory information from the biological body and control of it has been applied in biology and the fractality of the TGD Universe suggests that this picture applies in all scales. Hence the idea that MB of the particle carrying dark matter serves a universal representation of the ordinary particle is attractive.
2. Color entanglement can bind the q_o and q_d^* in a stable way. What about leptons which are color singlets? The TGD view of color comes to rescue here. In TGD, color is not a spin-like quantum number but at the level of H corresponds to color partial waves for H spinor fields. There are two alternative proposals for what leptons could be.
   1. For the first option, leptons correspond to second H-chirality for H spinors. The color partial waves correlate with the electroweak quantum numbers in a wrong way for both quarks and lepton chiralities. The physical states assignable to partonic 2-surfaces involve super symplectic generators carrying color in such a way that physical leptons are color singlets and quarks are color triplets.

      Lepton states involve an action of super symplectic generator O on the lepton spinor OL_o^c such that the O transforms as the conjugate of the color representation associated with color partial wave L_o^c. L_o would be essentially the inner product of O and color partial wave L_o^c and therefore a color singlet. In the case of quark q, q_o would be obtained by projection color triplet from q_o= P₃(Oq).

      The inner product of L_o^c and L_d^*c defines a color entangled color singlet.

   2. The second option is that fundamental leptons correspond to color singlets formed from 3 antiquarks. The 3 leptonic antiquarks do not reside at separate wormhole contacts having two wormhole throats identified as partonic 2-surfaces but reside at a single partonic wormhole. The mechanism proposed for hadrons can be applied to quarks. This option can explain matter antimatter asymmetry: antimatter as antiquarks could bind to leptons. A small CP breaking predicted by TGD in principle allows this.
3. This approach works also for bosons since all bosons can be realized as a quantum superposition of fermion-antifermion pairs in the TGD framework (note that graviton involves two pairs). Electroweak bosons involve pairs q_oq^*_o: the contraction with respect to color gives entanglement. Also lepton pairs are involved: now the contractions are of the form L_o^cL_o^*c.

   The construction of B_o^cB_d^*c reduces to the formation of color entangled pairs q_o q_d^* and L_o^c L_d^*c. Gluons, with SU(3)_g gluons included, can be formed as a color octet pairing of quarks and antiquarks and G_o^c G_d^*c pairing can be formed as in the case of baryons.

One can argue that the construction of the scattering amplitudes in this framework looks rather complex. The other option would be however nonconvergent perturbation series.

The basic physical idea deserves restating: the simple and perturbatively convergent dynamics at the level of MBs for the dark images X_d of the particles induces the dynamic of particles X_o by stable color quantum entanglement. The MB of the dark particle would be the boss and the dynamics of the ordinary particle would be shadow dynamics in accordance with the general vision about induction as the basic dynamical principle of TGD.

One open question is whether the ordinary matter follows the dynamics of dark particles instantaneously or whether the time scales of the dynamics of dark matter and ordinary matter can be different in which case only the asymptotic states would realize the proposed correspondence between X_d and X_o.

3. Could SU(3)_g gluons induce CKM mixing of quarks and leptons?

The above simple model did not say anything about the possible presence of SU(3)_g gluons at the color magnetic MB. Even if they are not present, the exchange of SU(3)_g g>0-bosons between entangled q_o and q_d^* could increase the genus of both q_o and q_d^* (note the genus is counted as negative for antiquarks).

At the level of the ordinary matter this could give rise to what looks like CKM mixing whereas no mixing would take place for q_d. This process generalizes to the case of leptons since L_o^c and L_d^*c are colored states for both identifications of leptons.

The g>0 gluon exchange involves a transformation of the dark g>0 gluon to an ordinary g>0 gluon. This process is assumed to occur for dark photons in the TGD inspired model for quantum biology: bio-photons would be an outcome of this process for dark photons.

Some CKM mixing angles are rather large. If the CKM mixing is solely due to this process, the masses of the g>0-gluons must be considerably smaller than weak boson masses so that mass scale could be around 100 MeV, say.

See the article About the TGD based views of family replication phenomenon and color confinement or the chapter with the same title.

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

Could g=1-gluons relate to the intrinsic strangeness and charm of the proton?

The TGD predicts that ordinary gauge bosons and Higgs are accompanied by SU(3)_g octet, where g refers to the genus of partonic 2-surface to which fundamental fermions are associated. 3 fermion families with g=0,1,2 are conformally special and can be seen in a combinatorial sense triplet representations of SU(3)_g. Gauge bosons and Higgs as fermion pairs naturally correspond to SU(3)_g singlet (ordinary gauge bosons) and octet, whose presence implies violation of fermion universality.

Strange and charmed quarks s and c are produced in high energy collisions of protons. The effective presence of s and c in the initial states can be understood in terms of radiative corrections, which affect the scale dependent parton distribution functions (PDFs) of proton, which depend on the scale of momentum exchange Q². PDFs are determined by the renormalization group evolution equations, which are differential equations with respect to Q². Q²≠ 0 is associated with interacting proton and means that the light u and d quarks are excited to strange and charmed states. The initial values of PDFs at Q²=0 correspond to non-interacting proton.

A long standing question has been whether proton has also intrinsic strangeness and charm, which should be distinguished from the radiatively generated energy scale dependent intrinsic charm and strangeness. The intrinsic strangeness and charm cannot be calculated perturbatively and would appear in the initial values of PDFs at the limit Q²=0

Quite recently an article with the title "Evidence for intrinsic charm quarks in the proton" \cite{bpnu/intcharm} appeared in Nature (this). Could the intrinsic charm be seen as an evidence for the presence of light g-gluons in the octet representation of SU(3)_g?

Could the presence of light g-gluons make possible intrinsic valence charm and strangeness so that the proton could be a superposition of states in which parton sea contains g-gluons and and valence quarks can be strange or charmed? These states would however be superpositions of states with same SU(3)_g quantum numbers?

Is this energetically possible?

1. This is impossible in the simplest model of baryon involving only on-mass-shell constituent quarks, which in the TGD framework would correspond to current quark plus color magnetic flux tube.
2. However, current quarks contribute only a small fraction to the proton total mass. In the TGD framework, the remaining mass could be assigned to the color magnetic body (MB) of proton and sea partons. One could therefore consider a superposition of states for which color MBs could have varying masses. This would allow strange valence quark with a reduced mass of the color MB. This component in the proton wave function would involve sea g-gluon(s) at a color magnetic flux tubes assignable to the sea.
3. The mass of proton is smaller than that of charmed quark so that the charmed quark is off-mass shell. What does off-mass-shell property mean in the TGD framework?

   Galois confinement generalizes the color confinement to a universal mechanism for the formation of bound states. Galois confinement states that the observed particles consist of building blocks with momenta, whose components are algebraic integers, which can be complex. Momentum components can also have negative real parts so that they would be tachyonic. The interpretation as number theoretically quantized counterparts of off-mass-shell momenta is natural. Since mass squared correspond to conformal weight, Galois confinement involves also conformal confinement stating the total conformal weights are ordinary integers.

   In this picture, virtual quarks would correspond to on-mass-shell states in a number teoretical sense. Mass squared would be an algebraic number determined as a root of a polynomial P with integer coefficients smaller than the degree of P. Color confinement implies that it is strictly speaking not possible to talk about on-mass-shell quarks.

   For the physical states both mass squared and momentum components are ordinary integers in a scale determined by the p-adic length scale assigned to the particle: this scale is also determined by the polynomial P allowing however several ramified primes defining the p-adic primes. Mass squared obeys a stringy mass formula.

4. If the off-mass-shell g=1-gluon is massive enough, its decay would reduce the mass of the sea and the total energy would be conserved. λ-n mass difference, pion mass, and Λ_QCD, which are all of order 100 MeV, give a rough idea about the mass scale of g=1 gluons. This would support the d\rightarrow s option which however increases the contribution of the valence quarks. Therefore the proposed idea does not look attractive.

See the article About the TGD based views of family replication phenomenon and color confinement or the chapter with the same title.

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

Could sea partons be dark?

The model of hadrons involves, besides valence quarks, a somewhat mysterious parton sea. Could the sea consist of partons, which are dark in the TGD sense? This proposal was actually inspired by a model of Kondo effect having strong resemblances with a model of color confinement (see this).

The basic argument in favor of the proposal that at least some quarks are dark, is based on the idea that the phase transition increasing the value of h_eff>h allows to have a converging perturbation expansion: one one half α_s= g²/4πℏ→ g²/4πℏ_eff which is so small that perturbation theory converges. Nature would be theoretician friendly and perform a phase transition guaranteeing preventing the failure of the perturbative approach.

A stronger assumption generalizes Nottale's proposal for gravitational Planck constant and assumes ℏ_eff= g_s²/β₀ , β₀=v₀/c<1 giving α_s → β₀/4π. This would allow a perturbative approach to low energy hadron physics for which ordinary QCD fails.

1. Valence partons cannot be dark but sea partons can

The following argument suggests that valence quarks cannot be dark but sea partons can.

1. It is good to begin with a general objection against the idea that particles could be permanently dark.
   1. The energies of quantum states increase as a function of h_eff/h₀ defining the dimension of extension of rationals. These tend to return back to ordinary states. This can be prevented by a feed of metabolic energy.
   2. The way out of the situation is that the dark particles form bound states and the binding energy compensates for the feed of energy. This would take place in the Galois confinement. This would occur in the formation of Cooper pairs in the transition to superconductivity and in the formation of molecules as a generation of chemical bonds with h_eff>h. This would also take place in the formation of hadrons from partons.
2. It seems that valence quarks of free hadrons cannot be dark. If the valence quarks were dark, the measured spin asymmetries for the cross section would have only shown that the contribution of sea quarks to proton spin is nearly zero, which in fact could make sense. Unfortunately, the assumption that the measured quark distribution functions are determined by sea quarks seems to be inconsistent with the quark model. If only sea quarks contribute always to the lepton-hadron scattering, the deduced distribution functions would satisfy q_i= q^*_i, which is certainly not true.

   Hence it seems that valence quarks must be ordinary but the TGD counterparts of sea partons could be dark and could have large h_eff increasing the size of the corresponding flux tubes. The color MBs of hadrons would be key players in the strong interactions between hadrons.

3. The EMC effect in which the deep inelastic scattering from an atomic nucleus suggests that the quark distribution functions for nucleons inside nuclei differ from those for free nucleons (see this). This looks paradoxical since deep inelastic scattering probes high momentum transfers and short distances. For h_eff>h the situation however changes since quantum scales are scaled up by h_eff/h. If sea partons are dark, the corresponding color magnetic bodies of nucleons are large and could interact with other nucleons of the nucleus so that the dark valence quark distributions could change.
4. Dark quarks and antiquarks at the magnetic body might also provide a solution to the proton spin crisis.

2. Could dark valence partons be created in hadronic collisions?

By the above arguments, the valence quarks of free hadrons have h_eff=h but sea quarks can be dark. Could dark valence quarks be created in hadronic scattering?

1. The values of h_eff of free particles tend to decrease spontaneously since energies increase with h_eff. The formation of bound states by Galois confinement prevents this. If not, the analog of metabolic feed increasing the value of h_eff is necessary. It would be also needed to create dark particles, which then form bound states.
2. Could the collision energy liberated in a high energy collision serve as "metabolic" energy generating h_eff>h phases. This could take place in a transition interpreted in QCD as color deconfinement (see this and this).

   The first option is that the phase transition makes valence quarks dark. This could however mean that they decouple from electroweak interactions with leptons. Second option is that the phase transition increases the value of h_eff>h for the dark partons at color MB but leaves valence quarks ordinary.

3. What does one mean with parton sea?

In the TGD framework, one must reconsider the definition of valence quarks and of parton sea.

1. Valence quarks would correspond to the directly observable degrees of freedom whereas parton sea would correspond to degrees of freedom, which are not directly observablee in physics experiments. Usually large transversal momentum transfers are assumed to correspond to short length scales but the EMC effect is in conflict with this assumption. If the unobserved degrees of freedom correspond to h_eff>h phase(s) forced by the requirement of perturbativity, the situation changes and these degrees of freedom can correspond to long length scales.

   The mathematical treatment of the situation requires integration over the unobserved degrees of freedom and would mean a use of a density matrix related to the pairs of systems defined by this division of the degrees of freedom. This would justify the statistical approach used in the perturbative QCD.

   Dark degrees of freedom associated with the color MB, possibly identifiable as parton sea at color MB, are not directly observable. The valence quarks would be described in terms of parton density distributions and quark fragmentation functions. In hadron-hadron scattering at the low energy limit, valence quarks and sea, possibly at color MB, would form a single quantum coherent unit, the hadron. In lepton-hadron scattering, the valence quarks would form the interacting unit. In hadron-hadron scattering also the dark MBs would interact.

2. Color MB could contain besides quark pairs also g>0 gluons contributing to the parton sea. The naive guess is that g=1 gluons are massive and correspond to the p-adic length scale k=113 assignable to nuclei. Muon mass, Λ_QCD, and λ-N mass difference correspond to this mass scale.

   The g>0 many-gluon state must be color singlet, have vanishing spin, and have vanishing U(2)_g or perhaps even SU(3)_g quantum numbers, at least if SU(3)_g is an almost exact symmetry in the gluonic sector. This kind of state can be built from two SU(3)_g gluons as the singlet part of the representation 8_c⊗ 8_g with itself. The state is consistent with Bose-Einstein statistics.

   g>0 gluons could be seen in hadron-hadron interactions. Perhaps as an anomalous production of strange and charmed particles and violation of fermion universality.

4. Could dark partons solve the proton spin crisis

The proton spin crisis (this) was discovered in the EMC experiment, which demonstrated that the quark spin in the spin direction of polarized protons was almost the same as in the opposite direction.

4.1 Basic facts about proton spin crisis

In the EMC experiment the contributions of u,d, and s quarks to the proton spin were deduced from the deep inelastic scattering of muons from polarized proton target (\url{https://rb.gy/ktm2tw}). What was measured, were spin asymmetries for cross sections and the conclusions about parton distribution functions (this) were deduced from the experimental data from the muon scattering cross sections using Bjorken sum rule testing QCD and Ellis-Yaffe sum rule assuming vanishing strange quark contribution and testing the spin structure of the proton. Bjorken sum rule was found to be satisfied reasonably well. Ellis-Yaffe sum rules related to the spin structure of the proton were violated.

It was found that the contributions of u quarks were positive and those of s quarks (assuming that they are present) and d quarks negative and the sum almost vanished when the presence of s was assumed. The Gell-Mann quark model predicts that u-quarks contribute spin 2/3 and d-duarks -1/6 units (ℏ) to the proton spin. For the fit allowing besides u, d contributions, also s contributions, the contributions were found to be 0.373, -0.254 and -0.113. The sum was 0.006 and nearly zero. For protons the contribution is roughly one half of Gell-Mann prediction. For d quark the magnitude of the contribution is considerably larger than the Gell-Mann prediction -1/6≈-.16.

The Wikipedia article creates the impression that the proton spin crisis has been solved: the orbital angular momentum would significantly contribute to the spin of the proton. Also sea partons, in particular gluon helicity polarization would contribute to the proton spin. This might well be the case.

4.2 Dark sea partons and proton spin crisis

I have considered possible TGD inspired solutions of the proton spin crisis already earlier. One can however also consider a new version involving dark sea quarks.

1. The possibility that sea partons are dark in the TGD sense, forces us to ask what was really measured in the EMC experiment leading to the discovery of the proton spin crisis. If sea partons are dark, only the quark distribution functions corresponding to quarks with ordinary value of h_eff appearing in the coupling to muon would contribute? This should be the case in all experiments in which incoming particles are leptons.

   Assuming that also valence quarks can be part of time strange, the results of the EMC experiment assume that most of the proton spin could reside at the polarized dark sea. Note however that also orbital angular momentum can explain the finding and in the TGD framework color magnetic flux tubes could carry "stringy" angular momentum.

2. For this option one could identify the measured cross section in terms of scattering from quarks with h_eff=h. It has been proposed that valence quarks are large scale structures (low energy limit) and sea quarks are small scale structures (high energies) inside valence quarks.

   In the TGD framework, this suggests that valence quarks correspond to a larger p-adic prime than sea quarks. This does not imply that valence quarks have large h_eff. Large h_eff for the sea partons would increase their size so that, contrary to the expectations from the Uncertainty Principle, they could contribute to hadron-hadron scattering with large momentum transfer in long length scales.

The idea that the average spin of valence quarks in the baryons vanishes is attractive. What comes to mind is the following idea.

1. >The valence quarks have an ordinary value of h_eff and the perturbation series does not converge. One should have a concrete realization for the transfer of color interactions at the level of valence quark to the level of the sea quarks with large h_eff. If only dark gluons exist, the color interactions take place at the level of the color MB, and one the perturbation theoretic coupling would be α_s= β₀/4π.

   The physical mechanism in question should map valence quarks to dark valence quarks at the MB. Also color confinement could take place at the level of the color MB and induce it at the valence quark level. The ordinary electroweak interactions should take place between valence quarks but also a dark variant of ew interactions between dark quarks is possible and indeed assumed in TGD inspired quantum biology. Could the mechanism be as follows?

2. Consider a free hadron. The color MB contains dark sea quark and antiquark with opposite charges and spins such that dark antiquark combines with a valence quark to form an entangled color singlet meson-like spin singlet.

   The second dark quark with opposite color and electroweak quantum numbers would carry the spin of the valence quark. Quark quantum numbers would be transferred by entanglement to the color MB! Color confinement would take place at the level of MB and induce color confinement at the level of valence quarks.

3. Ordinary electroweak interactions would take place at the level of valence quarks. Electroweak interactions cannot measure color charges so that the color entanglement between valence quark and dark sea quark would be preserved.

   What happens when a quark changes to another quark with different charge in the ordinary electroweak mediated by W boson exchange? Entanglement would be now between different charge states, say between valence u and dark d^*. In the ground states of hadron this cannot be the case. This suggests that the exchange of dark W boson transforms dark d^*u state to u^*u state. Dark W bosons could correspond to a lower mass scale than ordinary gauge bosons.

   What about spontaneous exchange of dark W boson transforming dark u^* u state to d^*u state? This would transform u^* pair to uk ud^*, which is not possible in equilibrium. The emission of ordinary W boson could transform d to d^* and one would have beta decay induced by dark beta decay.

   The more general question is how the physics of ordinary matter can be seen as a shadow dynamics controlled by the dark matter at the magnetic body. The proposed pairing could provide the needed mechanism.

See the article About the TGD based views of family replication phenomenon and color confinement or the chapter with the same title.

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