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

Why the water on Earth is older than the 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

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 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 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 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 sea partons be dark?

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 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.

Summary of the TGD based view of mitosis and meiosis

I wrote roughly a year ago of the TGD view of mitosis and meiosis and proposed a solution to the the mystery of the allele dominance (a gene from either mother and father chromosome tends to dominate in the transcription of the DNA) based on the notion of dark DNA controlling ordinary DNA. Also dark mitosis and meiosis would occur. I noticed that a short section summarizing various considerations would be helpful for the reader.

The above considerations boil down to the following overall view of mitosis and meiosis in the TGD framework.

Consider first ordinary mitosis and meiosis.

1. In the ordinary mitosis two copies of chromosomes are formed. After this cell divides. The same could happen for the dark chromosomes. But this would leave allele dominance a mystery.
2. Ordinary meiosis involves replication of chromosomes of soma cells with chromosomes of father and mother. This is followed by recombination of the chromosomes followed by cell division so that two germ cells are obtained. After that both daughter cells with recombinant genomes split to germ cells giving four germ cells.

The TGD view of meiosis would be different. Dark meiosis and ordinary meiosis need not occur simultaneously and dark meiosis could occur before the ordinary one in some earlier mitosis.

1. Dark DNA can suffer at some cell replication dark meiosis involving recombination of dark DNAs for both chromosomes. The resulting dark DNA strands go to separate cells. The dark parts of the DNA would be analogous to that of gametes which would be different for the two daughter cells.

   Since dark DNA controls ordinary DNA, the dark gamete would by resonance mechanism select which allele dominates. One would have two kinds of cells with different allele dominances. One could say that the cells have different sex. This is a testable prediction.

2. If this replication occurs after some replication after the first replication, the dark gametes formed in the dark meiosis of different cells are different, and one can obtain a large number of different dark gametes. This number is not so large as for the ordinary meiosis since dark gametes do not change in the cell replications.
3. The dark gametes, which have formed by dark meiosis already in an earlier cell replication preceding meiosis, would determine the outcome of the recombination of ordinary DNA in the ordinary meiosis following dark meiosis after some cell replications. After this the dark gametes pair with ordinary DNA and give rise to an ordinary gamete.

See the article Mysteries related to gene expression and meiosis or the chapter ZEO, Adelic Physics, and Genes.

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

Does a Higgs-like particle decaying to electron-muon pairs exist?

It is a long time since I have written anything about particle physics for years. Now the LHC collaboration at CERN has represented evidence for the anomaly. Sabine Hossenfelder talks about the anomaly in popular terms in a Youtube video (see this). There is also a preprint about the anomaly (see this). The evidence is 2.5 sigmas (standard deviation) so that the anomaly is much below the minimum of 5 sigma for a discovery and could quite well disappear.

What has been studied is the possible occurrence of lepton flavor violating decays of Higgs bosons in proton-proton collisions at cm energy of 13 TeV has been analyzed using data from 2016-2018 period. The integrated luminosity is 136 fb^-1.

A small anomaly has been observed. It could be due to the flavor violating decay H→ e^+/- μ^-/+ of Higgs having mass 125 GeV. eμ pair could also come from the decay of a new boson, call it X, with mass assumed to be the range 110-160 GeV.

The dominant production modes for the Higgs boson are gluon fusion (ggH) and vector boson fusion (VBF). In both modes the interesting final state oppositely charged eμ pair. It would appear as a peak at mass m(H) or m(X) on top of a smoothly falling background due to the purely leptonic decays of tt^* and WW events, plus Drell-Yan events with a misidentified lepton. Monte Carlo fit indicates a 2.5 sigma bump 146 GeV.

Could TGD explain this anomaly? The TGD (see this) based topological explanation of the family replication phenomenon indeed predicts new exotic bosons (see this, this, and this).

1. Fundamental fermions would in TGD framework correspond to partonic 2-surfaces, whose orbits define light-like 3-surfaces identifiable ad boundaries between Minkowskian and Euclidean space-time regions. The Euclidean regions correspond to deformations of what I call CP₂ type extremals. Orientable 2-surfaces are characterized by the genus g defined as the number of handles attached to a 2-sphere to obtain the topology in question.
2. TGD predicts that 3 lowest genera are special in the sense that they allow global Z₂ symmetry as a conformal symmetry unlike higher generations (see this). This raises the 3 lowest genera in a special position. The handles behave like particles and the higher genera would not form bound states of handles and have a mass continuum characteristic for free many-particle states unlike the lowest ones corresponding to g=0,1,2. This boils down to the assumption that only 2 handles can form a bound state.
3. The fundamental fermion would correspond to a partonic 2-surface carrying a point-like fermion and would serve as building bricks of both fermions as bosons as elementary particles. Elementary particles would correspond to closed monopole flux tube structures connecting two Euclidean wormhole contacts so that the monopole flux loop would run along the first Minkowskian space-time sheet and return along the other.

Group theoretically, the 3 fermion generations behave like an SU(3)_g triplet, completely analogous to the (u,d,s) triplet introduced by Gell-Mann. This combinatorial symmetry could define an approximate dynamical symmetry involving SU(3)_g→ U(2)_g symmetry breaking, analogous to that in the case of Gell-Mann's SU(3).

1. Each electroweak gauge boson and gluon would form an SU(3)_g octet analogous to (π,K,η) and SU(3)_g singlet analogous to η'.
2. Ordinary gauge bosons would SU(3)_g singlets analogous to η'. Their couplings to fermion families would be identical and thus obey fermion universality. These states would be superpositions of pairs with g=0,1,2.
3. Besides this, 2 additional SU(3)states with vanishing SU(3)_g quantum number analogous to π₀ and η are predicted. Their couplings to fermions induce a violation of fermion universality coming from the coupling to both gluons and weak bosons.

   There are some indications for this violation from the earlier experiments (see this) and the p-adic mass scales of the higher boson families as analogs of π₀ and η correspond to p-adic length scales assignable to Mersennes or Gaussian Mersennes. The couplings of these states to fermionic loops imply deviations from the predictions of the standard model and might explain the reported anomalies.

   Here one would have a deviation from the expectations suggested by the analogy with the Gell-Mann's SU(3), which would suggest that the ordinary weak bosons are more massive than the exotic ones: this would not be the case.

4. Also non-diagonal bosons with non-vanishing SU(3)_g quantum numbers, being analogous to π^+/- and 2 kaon doublets, are predicted. I have earlier assumed (see this) that these states are much more massive than the SU(3)_g neutral states.

   If one takes the recent finding at the face value, the situation would not be this. The analogy with the Gell-Mann's SU(3) suggests that one has a weakly broken U(1)×U(1)⊂ U(2)_g ⊂ SU(3)_g symmetry such that the two lowest generations correspond to u and d. Both gluons and electroweak gauge bosons, including Higgs, would have additional states decaying to oppositely charged eμ pairs and thus violate lepton universality. Also counterparts of kaons as pairs involving g=2 partonic 2-surfaces are predicted.

5. The simplest interpretation for X would be in terms of a Higgs like states analogous to π^+/-. The U(2)_g symmetry would be violated if the mass of X is 146 GeV: one would have Δ m/< m>= 2(m(X)-m(H))/(m(X)+m(H) ≈ 15 %.

This picture raises questions related to the CKM mixing as mixing topologies of partonic 2-surfaces (see this).

1. It is assumed to be due to topology changing time evolution for partonic 2-surfaces: a kind of dispersion in the "world of classical worlds'' (see this), or more precisely, in the moduli space of conformal equivalences of 2-surfaces consisting of Teichmüller spaces for various genera, would be in question.
2. Could the exchanges of SU(3)_g octet bosons between both fermions and bosons induce the mixing dynamically or at least contribute to the mixing. This mixing is not a single particle phenomenon. It conserves SU(3)_g "isospin" and "hypercharge" and essentially this means conservation of total genus as sum of signed genera, which are opposite for fermions and antifermions. If SU(3)_g octet has masses above M₈₉ mass scale assignable to Higgs, this mixing is expected to be rather small and an effect comparable to weak interactions.
3. The mass scale of SU(3)_g photon octet must be large, say M₈₉ mass scale: otherwise one would lose approximate conservation of various lepton numbers and a bad failure of the Universality. Color confinement would allow a light SU(3)_g gluon octet. What implications could the additional light gluons have?

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.

Do the reversals of the Earth's magnetic field induce evolutionary leaps?

Do the reversals of the Earth's magnetic field induce evolutionary leaps?

I received from Zakaria Ameziane a highly interesting question related to the TGD inspired theory of consciousness and quantum biology, in particular self hierarchy and the notion of quantum jump according to TGD, and the role of the Earth's magnetic field in quantum biology. The question went roughly as follows.

"There is an interesting hypothesis which demonstrates that the DMT, by its affinity with UV-B rays, could be produced significantly, endogenously when the electromagnetic fields are reversed. If this hypothesis would prove to be true, could it trigger a new quantum jump?"

The question involve a link to a discussion in DMT Quest discussion group (DMT Quest is an organization, which supports DMT research) in Twitter (see this). The link is warmly recommended. The discussion was related to the the so-called Stoned Ape Theory of evolution claims that that the transition from Homo erectus to Homo sapiens and the cognitive revolution was caused by the addition of psilocybin mushrooms, specifically the mushroom Psilocybe cubensis, into the human diet around 100,000 years ago. One can also consider alternative forms of this idea.

From the discussion one can pick up the following facts.

1. DMT is often assigned with pineal gland, "third eye" and the seat of the soul, according to Descartes but according to recent views it is present in the entire brain. DMT (is reported to induce a growth of neurons (see this) (I have discussed DMT from the TGD point of view here and here).

   By its affinity with UV-B rays, DMT could be produced significantly endogenously as magnetic field reversal occurs and the shield provided by the Earth's magnetic field against UV rays is temporarily lost.

2. The latest magnetic reversal occurred 40,000 years ago in the so-called Laschamp event (see this). Interestingly, Neanderthals disappeared at this time.
3. 40,000 years also corresponds to a time when a large change in the shape of human brain took place (see this). The following excerpt is from the abstract of the article.

   ".... Our data show that, 300,000 years ago, brain size in early H. sapiens already fell within the range of present-day humans.

   Brain shape, however, evolved gradually within the H. sapiens lineage, reaching present-day human variation between about 100,000 and 35,000 years ago. This process started only after other key features of craniofacial morphology appeared modern and paralleled the emergence of behavioral modernity as seen from the archeological record.

   Our findings are consistent with important genetic changes affecting early brain development within the H. sapiens lineage since the origin of the species and before the transition to the Later Stone Age and the Upper Paleolithic that mark full behavioral modernity."

4. Relatively recent research indicates that changes in the geomagnetic field of the earth causes genetic and metabolic changes in plants indicating the potential to be a driver of evolution (see this).

These observations inspire the question whether the magnetic reversal could have induced not only a significant growth of neurons in human brains but also an evolutionary jump?

1. Could this effect have occurred at the level of genes, at the level of epigenesis or both? The amazing findings of Levin \cite{bbio/Levin1,Levin2,Levin3,Levinnohead} (see for instance this), discussed from the TGD point of view from the TGD point of view here, suggest that besides genes, also electromagnetic field patterns assignable to cell groups (not only neuron groups), determine the outcome of morphogenesis via epigenesis and that modifications of these patterns during the embryo stage can dramatically modify the outcome of morphogenesis without any change at the level of genes. What is remarkable is that these changes are inherited.
2. Could the magnetic reversal have induced an inheritable change of the shape and the electromagnetic structure of the brains of developing embryos? Could the increased amount of DMT during the reversal be behind this change? If only a permanent epigenetic change is in question, it might be induced by DMT.

The following summarizes roughly my reply to the question by Zakaria Ameziane. The reply describes first very briefly what self hierarchy and quantum jumps mean inthe TGD framework.

1. Selves can fuse to larger selves by entangling stably. This could occur in both "small" and "big" statefunction reductions (SFRs). In a pair of BSFRs (BSFRs change the arrow of time) and a TGD counterpart of quantum tunnelling takes place this kind of fusion could occur. This would mean an extension of consciousness. Perhaps this happens as the person gradually wakes up. Also the fusion of say visual fields to single visual field could occur in this way. Right and left brain, or rather their magnetic bodies, could also fuse in this way.
2. DMT is assigned with pineal gland, I would tend to see its presence as a prerequisite for a connection to a rather high level of hierarchy of selves, magnetic body corresponding to a rather long length and time scales.

Concerning the finding that something dramatic took place in the evolution of the human brain about 40,000 years ago when also magnetic reversal took place. Catastrophes induce quantum criticality in long scales which in turn could induce evolutionary jumps.

1. I have just developed a model for the change of the magnetic polarity (see this and this): the change of the polarity would be associated both in the case of Sun and Earth to a BSFR changing the arrow of time. This process would be like death followed by reincarnation with the opposite arrow of time at the level of the magnetic body (MB). The sequences of reversals would define the analog of a sleep-wakeup cycle on a large scale.
2. BSFR corresponds to quantum criticality: the monopole flux loops of the magnetic body of Earth decay into pieces, change direction and fuse again as required by the magnetic reversal. MB is the boss and this universal mechanism would also induce biological decay after death and re-organization of molecules to a living organism. It would also be behind catabolism and anabolism at molecular level.
3. During the period of BSFR associated with the reversal, the UV radiation from outer space can enter the Earth's surface and induce large genetic and also other kinds of biological changes. A BSFR at the level of MB of Earth inducing the magnetic reversal could have induced a cascade of BSFRs at shorter scales possibly inducing dramatic evolutionary changes.

   In the TGD Universe, the genes do not dictate everything. Also electromagnetic field patterns at the cellular level, both for neurons and ordinary cells, are in a central role in dictating the development of embryos, as Levin's findings demonstrate. Their change would involve epigenetic change (see this). This point was already discussed.

4. For instance, these BSFRS inducing large changes at the MB of the brain could have increased the probability of the fusion of MBs of say left and right hemispheres to a larger unit, the MB of the entire brain. This would have induced a stronger interaction of right and left hemispheres. The periods of time in an entangled, "whole-brainy" state would have significantly increased.

   This might relate to the hypothesis that bicamerality in which right and left hemispheres behaved like independent selves (schizophrenics and young children might be bicamerals) transformed to modern consciousness in which the brain hemisphere tends to behave like a single coherent entity.

5. There is evidence that the magnetic field of Earth is changing right now (this). Could it mean that polarity reversal of the Earth's magnetic field might happen in the not so distant future. An interesting question is what this could mean for our species.
6. The magnetic bodies of Sun and Earth interact and in TGD framework both MBs play a key role in the quantum biology (see this and this) based on gravitational quantum coherence prevailing in astrophysical scales.

   An interesting question is whether the solar 11+11 year "sleep-awake" cycle of the solar MB could induce periodicies in human behavior, say in social structures. Maybe statisticians could have something to say about this.

See the article A TGD Inspired Model for Solar Flares or the chapter Magnetic Bubbles in TGD Universe: Part II.

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

Dark matter in the TGD sense can be detected as absence of the ordinary matter!

I received a link to a highly interesting popular article with title "A Breakthrough Experiment Unlocking the Mystery of Unconventional Superconductivity" (see this). The article told about the work of Sarah Hirthe et al reported in the article "Magnetically mediated hole pairing in fermionic ladders of ultracold atoms" published in Nature (see this).

The TGD based view of unconventional superconductivity and biosuperconductivity (see for instance this, this, and this) is based on new view of quantum physics provided by new space-time concept and number theoretic vision predicting phases of ordinary matter behaving like dark matter and labelled by effective Planck constant h_eff=nh₀, which can be very large as compared to the ordinary Planck constant h. This the case for the gravitational Planck constant introduced originally by Nottale. This implies quantum coherence in long scales essential for superconductivity.

This view suggests that hole pairs are formed when the electron pairs are transferred to the magnetic flux tubes and become dark and therefore have a non-standard value of effective Planck constant. This creates hole pairs at the level of the ordinary matter and the motion of the dark electron pair corresponds to that for the hole pair. The electron pair goes to a pair of magnetic flux tubes and transversal fluctuations in the shape of flux tubes are essential in the transition to superconductivity. This picture is consistent with the reported findings.

The really important message from the TGD point of view is that dark matter in TGD sense can be detected as the absence of ordinary matter! Hole pair is a shadow Cooper pair of dark electrons.

See the article TGD and Condensed Matter Physics or the chapter with the same title.

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