Could standard model have anomalies after all?

I heard very interesting news from LHC (see this). The title of the post at Restoration Monk is "CERN Detects First-Ever Quantum Gravity Clues from Proton Collisions".

The official narrative has been that the standard model works too well so that there are no signals serving as guide lines in attempts to extend the standard model. I have had difficulties with swallowing this story since this claim has been in conflict with what I have learned during years.

However, I learned now that over the past 10 years, deviations from both QCD and Standard Model physics, related to the supposed phase transition to quark gluon plasma, have been observed. The reports of these findings are scattered in literature. The article about these findings has been submitted for publication in The European Physical Journal.

The Google summary, which I obtained using the prompt "anomalous energy distributions in quark-gluon plasma events that deviate from predictions of both the Standard Model and supersymmetry" gives the following general data bits.

1. The LHC experiments have observed unusual patterns in the energy distribution of particles within the quark-gluon plasma, a state of matter believed to have existed shortly after the Big Bang.
2. There are deviations from Standard Model and Supersymmetry: These energy distribution patterns don't match predictions from either the Standard Model, which describes fundamental particles and forces, or supersymmetry, a theoretical framework extending the Standard Model.

The proposal mentioned in the popular article is that the observed anomalous effects could relate to quantum gravity. This would require that Newton's constant is renormalized to a very large value and looks to me unrealistic.

TGD inspired guess for the list of deviations

The above summary is very general and does not reveal any details. I have however worked with the problem of understanding the difference between TGD and standard model view for decades and it is relatively easy to fill in the details.

As a matter of fact, the deviations have been observed in what has been interpreted as a transition to quark plasma phase. They are familiar to me and they have emerged during a time period of about 20 years. I have discussed a large number of potential anomalies of the standard model from the TGD point of view (see this), in particular in the section "Still about quark gluon plasma and M₈₉ physics". TGD predicts a hierarchy of standard model physics and the ordinary M₁₀₇ hadron physics and M₈₉ hadron physics are only two examples of them. These standard model physics correspond to the hierarchy of color partial waves for quarks and leptons (see this, this and this).

The first deviations that I have commented on were reported by ALICE collaboration.

1. RHIC had already observed around 2005 in heavy ion collisions that the phase assumed to be quark gluon plasma at quantum criticality for the formation of quark gluon plasma behaved almost like a perfect fluid \cite{bpnu/surprise}. This was surprising. Around 2010 the same observation was made by LHC in proton-proton collisions.
2. The popular article "ALICE collaboration measures the size of the fireball in heavy-ion collisions" (see this) appeared in CERN Courier 2111. The fireball served as a meson source and had elongated shape in the direction of the collision axes rather than being a spherical object: this suggests that string-like or meson-like object was in question. TGD interpretation was as a meson of M₈₉ hadron physics.
3. The second popular article (see this) in CERN COURIER from year 2113 talks about the observation of alice suggesting an double ridge structure consisting of two peaks in momentum space corresponding to opposite longitudinal momenta (see this). Also this suggests a string-like or meson-like structure.

   The proposed TGD based interpretation was that the phase transition is not from hadron phase to quark gluon plasma but from ordinary M₁₀₇ hadrons to M₈₉ hadrons. In TGD, hadrons correspond to stringy objects made from monopole flux tubes and the stringy object could be a meson of M₈₉ hadron physics for which the proton mass is 512 the mass of the ordinary proton. The hadrons of this physics would be dark in the sense that they would have h_eff/h=512 so that the size of the dark proton would be that of the ordinary proton. This would make possible geometric resonance.

4. Also bumps were detected that were first interpreted in the framework of then fashionable SUSY. This interpretation failed and the bumps were forgotten. TGD suggested their interpretation as M₈₉ mesons and the estimate for their masses using naive scaling by a factor 512 gave encouraging results: see the sections "Scaled Variants of quarks and leptons" and "Scaled variants of hadron physics and electroweak physics" of \cite{allb}{TGDnewphys1}.

Some time ago I learned from an anomaly related to weak isospin (see this, discussed from the TGD point of view (see this this) in (see this). There are excellent reasons to expect that this anomaly belongs to the list of findings. The production rate for strange mesons is higher than for their charmed counterparts. This implies charge asymmetry, which is very difficult to understand in QCD since electroweak symmetries and color symmetry are completely uncorrelated.

In the TGD framework, leptons and quarks move in color partial waves and the color partial waves are different for different weak isospin values so that the charge asymmetry emerges at the fundamental level for color interactions.

The general TGD based view of standard model interactions

For years I have talked about the TGD based expansion of these findings but no one has listened. TGD predicts that the effects will appear in the TGD counterpart of the TGD counterpart of the transition to quark gluon plasma, which would in fact be the transition from M₁₀₇ hadron physics to M₈₉ hadron physics. In the recent TGD view of particle reactions (see this), the phase transition to the TGD analog of the quark gluon plasma without gluons occurs in any particle reaction and the reaction itself allows stringy description.

The general view of standard model interactions provided by TGD differs dramatically from the QCD view and also from the Standard Model picture and one might hope that the findings could provide convincing support for the TGD view.

1. Space-time at the fundamental level consists of 4-surfaces X⁴ in H=M⁴× CP₂ obeying holography= holomorphy principle (H-H), which reduces the field equations to local algebraic conditions. Theory is exactly solvable.
2. Color is not a spin-like quantum number as in QCD but analogous to orbital angular momentum in CP₂ and characterizes both leptons and quarks. Arbitrarily high color partial waves are possible.
3. All particles are bound states of fundamental fermions. Colored fermions as modes of Dirac equation in H have mass of order CP₂ mass (∼ 10^-4 M_Pl) but color singlet many quark states and leptons are light and correspond to the particles observed in the laboratory.
4. By H-H, the Dirac equation in X⁴ for the induced spinors in induced spinor structure allows massless quarks and leptons. This phase is the analog of the quark-gluon phase: gluons are not however present, just fundamental fermions. The interaction region for the collision of particles corresponding to 4-D space-time surfaces with the same generalized complex structure is the intersection of the space-time surfaces consisting of string world sheets so that a stringy description of interactions emerges. TGD generalizes the QCD type description of scattering to all interactions.
5. Color and electroweak interactions are very closely related since CP₂ isometries correspond to SU(3) and holonomies of CP₂ correspond to U(2) identifiable as a subgroup of SU(3). One can say that electroweak interactions are color interactions in electroweak spin degrees of freedom and color partial waves are analogous to angular momentum degrees of freedom. The prediction that color coupling strength is 9 times the electroweak coupling strenght is correct.

One proposed explanation for the findings made during 10 years in terms of gravitons might have some empirical justification. In the TGD framework, a natural counterpart of graviton would be emission of spin=2 meson of M₈₉ hadron physics.

Basic misunderstandings of TGD generated by large language models

One might think that for a scientific dissident the large language models are a God's gift making communications mere child's play. Unfortunately, this does not seem to be the case.

Quite recently we tested with Marko Manninen GPT (see this) by making prompts related to TGD and asking for killer arguments. The responses involve dramatic misunderstandings due to the conditioning of GPT to the standard model orthodoxy.

1. One wrong claim of GPT was that M₈₉ hadrons would have been observed long ago. This is of course not true: very special conditions are required to guarantee the quantum criticality for the transition to M₈₉ hadron physics.
2. Second claim was that cosmic strings, which in TGD are space-time surfaces with 2-D M⁴ projection. GPT confused TGD cosmic strings with GUT strings and they are indeed excluded empirically.
3. A third fatal mistake of GPT was that the TGDbased topological explanation of family replication phenomenon (see this) implies an infinite number of fermion families. There is a nice argument supporting the prediction of only 3 families.

See the article Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD or the chapter with the same title.

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

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

About mRNA folding, quenching, blackhole-like objects and universal genetic code

mRNA is single stranded but can fold back to itself and involves secondary structure related to base pairing and also 3-dimensional tertiary structures. Folding depends on mRNA sequence. mRNA sequence is charged since there is negative charge per every nucleotide. This causes self-repulsion. Local charge neutralization by ions can affect and control the folding. Also the interactions of mRNA with water are involved. This brings in the dependence on temperature and pH.

1. The  folded RNA strand should minimize energy. In the more general case (temperature above T=0 K) free energy F is minimized  instead of energy. F=E-TS  includes energy E as well as  -TS term from entropy. Energy minimization and entropy maximization compete.
2. In the models considered it is assumed that, as a good approximation, free energy is quadratic in observables, which include the orientation angles of the segments formed by two nucleotides in the mRNA chain.    The total energy contains the sum of energies that depend on the orientation angles between the nucleotide and its successor and predecessor. A further simplification is  to limit the strand to a plane.
3. What makes the situation non-trivial is that there can be segments in the mRNA strand that are  conjugates of mirror images of each other. Conjugation means the replacement  A↔U, C↔G. These segments tend to undergo base-pairing just like in the DNA double helix. This reduces the total energy and has a stabilizing effect. The first task is to identify such segment pairs and to process all possible configurations involving them to find the energetically most promising configuration and minimize the energy of the remaining part of the strand.
4. The   model considered is as simple as possible and quadratic in the observables, which include the orientation angles between the two nucleotides. One can of course ask whether codons can be treated as linear units of three nucleotides, i.e. codons would not bend.
5. The first step is to consider only planar configurations. The natural assumption is that the mRNA chain has no self intersections. In a plane, this assumption is very strong. One can also consider configurations which define closed 2-surfaces such as Platonic solids. Maximal symmetry is highly suggestive and an interesting possibility is provided by Hamiltonian cycles or paths at the sphere, which go through every vertex without intersections. Also torus topology allowing lattice-like structure is interesting and one can consider even knotted tori for both DNA, RNA and proteins.
6. In the 3-D case, one can imagine that the paired segments can even have portions, which are double helices like DNA (and also RNA). Protein folding gives some  hint of what might happen. Protein involves 3-D helical structures (1-D aperiodic lattices deformed to a helical shape, two-dimensional planar lattice-like pieces in which the protein travels back and forth in a single direction, plus random sequences. The inactive state of protein is essentially 3-dimensional cluster-like configuration. Parameters like temperature and pH determine which kind of structures appear.

How to calculate?

Although the model is in principle rather simple and computable, the actual calculation is difficult. Part of the reason is the large number of codons and the base-pairing. The situation is the same for proteins.

Quantum computing raises the hope that folding could be predicted even when the number of mRNA codons is large.

Quenching is the method used in the work that we discussed.

1. The basic observation is that the energy landscape of the system can be assumed to be fractal. There are potential wells inside potential wells. Spin glass is the standard term used for these kinds of systems.
2. The straightforward energy minimization by moving in the direction in which the energy decreases maximally leads to a lower well, which is hardly an absolute minimum. It is necessary to get out of it and therefore thermal energy must be fed into the system by using a suitable perturbation. After this one can try again. In this way, by gradually reducing the heating energy, it is hoped to end up to an absolute minimum.
3. The hardening of a scythe (I am a farmer's son) is a concrete example and is called quenching. First the scythe is forged and then cooled in a water tank. Then it is heated again and the same step is repeated. The amount of heating is reduced gradually. Finally, the energy minimum is obtained, which means the scythe is very hard.

The TGD analog for the mRNA folding problem

The mRNA folding problem has a very general counterpart in TGD (see this and this).

1. Now the folding and tangling occurs for monopole flux tubes (see this, this and this), and the many-sheeted space-time makes cross-bonds between flux tubes portions as analogs of base pairing possible. Also now modelling as a spin glass is natural and in ZEO one can ask whether classical action rather than energy is a more natural quantity to be minimized.
2. The slight failure of determinism in holography= holomorphy vision (see this, this, this and this) implies that spin glass property is extended to time direction in a discrete way. If the classical action becomes Kähler action, the non-determinism is huge.
3. The scale of the flux tube tangles varies from the elementary particle level (see this and this), through nuclear physics (see this), molecular physics, and biology (see this, this, this, this) to astrophysics and cosmology (see this).

The black hole, which in TGD generalizes to an entire hierarchy of black hole-like objects, serves as a good example.

1. For the TGD equivalent of a black hole, the flux tube tangle fills the entire volume (see this). The quantized thickness of the flux tube is the basic parameter labelling an entire hierarchy of blackhole-like objects. Even the solar core could be a blackhole-like object in this generalized sense. For the TGD counterpart of the ordinary black hole, the thickness would correspond to the Compton wavelength of a nucleon.
2. What is important is that a 3-D lattice structure can be attached to the system, each point of which corresponds to one neutron in the flux tube. If the flux tube cannot intersect itself, then it corresponds to a Hamiltonian path and to a Hamiltonian cycle when the path is closed. This means a huge reduction in the number of degrees of freedom but could be favored by energy minimization.
3. The first task is to determine all Hamiltonian paths/cycles. This is a purely geometric, well-known mathematical problem. One can find the cycle which minimizes the energy or free energy. The separation of energetics/thermodynamics from the geometry simplifies the situation dramatically.

From black holes to mRNA and universal genetic code

Hamiltonian paths/cycles could also be considered in the case of mRNA.

1. The size of the codon/nucleotide is constant so it is natural to assign a lattice to the system. Also now can find Hamiltonian paths/cycles by purely geometric arguments and the calculation is dramatically simplified.
2. Quite concretely, the simplification means that the orientation angle for two nucleotides/codons takes only a few values corresponding to the nearest neighbors. For a cubic lattice there are only 6. This prediction should be testable. Even if not exact energy minima, these configurations could be excellent approximations to them. Note however, that minima favor symmetries and lattice symmetry is this kind of symmetry.

As a matter of fact, Hamilton cycles on the icosahedron and tetrahedron, which are finite lattices on a sphere, are essential in the TGD-based model of the genetic code. An intereting possibility is that these cycles correspond physically to closed monopole flux tubes.

1. The essential thing is that icosa- and tetrahedral Hamilton cycles can be classified by using their symmetry group as a subgroup of the icosahedral or tetrahedral symmetries. Symmetry determines how many DNA codons code for a given amino acid and the model predicts correctly these numbers (see this and this). If the genetic code is universal, these symmetries might play an essential role even in systems with an astrophysical size.
2. TGD indeed predicts that genetic code is universal and based on the completely unique icosa tetrahedral tessellation of the hyperbolic 3-space (see this and this) playing a central role in TGD (mass shell, light-cone proper time constant surace). This tessellation would have tetrahedra, octahedra, and icosahedra, which are Platonic solids having triangles as faces, as basic building bricks. Does universality mean that both the notions of DNA, RNA and amino acids, or rather their dark variants realized in terms of flux tubes carrying dark nucleons, are universal?
3. TGD suggests a model for the Sun (see this) as a living system analogous to a cell or cell nucleus and perhaps realizing the universal genetic code. Could the Hamiltonian paths or cycles, defined by the monopole flux tube tangles and associated with the icosa tetrahedral tessellation, give rise to the analogs of DNA strands? If so, the Sun could be an extremely intelligent conscious entity, something totally different from a mere fusion reactor. In fact, the TGD view of the Sun proposes that the solar wind and solar radiation is produced at the surface layer of the Sun and that new physics predicted by TGD is involved.

See the chapter A Model for Protein Folding and Bio-catalysis.

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

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

Finally!

It is not an exaggeration to say that the 47 year lasting work to develop  the  basic vision behind   TGD to a mathematical theory with a precise physical interpretation  is in some sense finished. Because of the fractality, the emerging theory solves  numerous anomalies and  makes dramatic predictions  in all scales. The next step   is to transform the theory to a calculational apparatus but this requires a collective effort of both mathematicians and physicists.  

The last steps in the process  made transparent the amazing simplicity of the overall picture.

1. The study of the solution spectrum of Dirac equations in  the imbedding space H=M⁴×CP₂  and space-time surface X⁴ have led to a quite dramatic increase of the understanding of how TGD view of standard model physics and gravitation differs from standard view. All interactions reduce to the dynamics of 3-surfaces obeying holography = holomorphy principle and  by general coordinate invariance  only 4 H-coordinates define the primary dynamical variables at the fundamental level.

   Color confinement can be understood directly from the study of Dirac equation in H with M⁴ endowed with Kähler structure  and  electroweak and strong interactions can be seen as different aspects of  the same  interaction.  

2. Color partial waves in H are analogous to orbital angular momentum states and since the electroweak group can be regarded as a subgroup of SU(3),  electroweak quantum numbers can be regarded as  color quantum numbers   analogous to spin. "Strong-electroweak" is completely analogous "orbital angular momentum-spin".  
3. CP₂= SU(3)/U(2) states that also geometrically U(2) acts like a gauge group, whereas SU(3) as a whole is not a gauge group. This sharply distinguishes the standard model and its generalizations from TGD. In electroweak degrees of freedom confinement occurs only for SU(2) but not for electromagnetic U(1) and takes place by screening of electroweak isospin but pairs of left and right-handed neutrinos.
4. By holography= holomorphy (H-H) principle,  X⁴ can be seen as a generalization of a point-like particle and X⁴ spinor modes  are analogous to the spin states of a point-like particle.  The interaction of two space-time surfaces occurs in the intersection of the particle-like 4-surfaces, which for    identical H-J structures  consists of string world sheets. This is nothing but the analog for the interaction of point-like particles occurring only when they are at the same point.

See the article Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD or the chapter chapter with the same title.

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

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

Unitarity constraint and the construction of S-matrix in the TGD framework

The recent TGD based view of particle reactions (see this) replaces QCD type approach with its stringy version and allows the construction of S-matrix for arbitrary initial and final states.

1. The construction of S-matrix in elementary particle degrees of freedom reduces to that for fundamental fermions. There are two levels involved. External particles are constructed as bound states of fundamental fermions giving rise to hadrons, leptons, gauge bosons, and gravitons. Number theoretic vision, in particular Galois confinement (see this and this) plays a key role in the construction of the bound states.

   The fundamental fermions correspond to the modes of the Dirac equation in H, being massless in the 8-D sense. If M⁴ has hypercomplex Kähler structure the Dirac equation in H allows massless light color singlet states as many-fermion states (see this).

   The analog of the quark phase corresponds to modes of the X⁴ Dirac operator for fundamental fermions, which are massless in 4-D sense: color triplets can be understood in terms of CP₂ geometry. The oscillator operators for X⁴ modes are expressible in terms of those for H modes (see this).

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

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

2. The S-matrix is determined by the overlap of these two fermionic state bases and the unitary matrix describing the scattering in the quark phase. Fermion pair creation in the induced classical fields is the basic vertex and reduces to a defect of the standard smooth structure: these defects give rise to an exotic smooth structure (see this, this and this). In the vertex, fermion current fails to be conserved for the standard smooth structure but is proposed to be conserved for the exotic smooth structure (see this, this, this and this). The non-vanishing divergence at the defect determines various vertices.
3. Besides the fermionic degrees of freedom, also the geometric degrees of freedom of WCW are included. Holography = holomorphy vision (H-H) (see this, this, this and this) implies that the path integral disappears and there is only a functional integral over 3-surfaces X³ and the sum over the Bohr orbits for each X³. Does the role of the functional integral become trivial with respect to unitarity? Locality in WCW suggests that this is the case. Let us assume in the following that this is indeed the case.

Unitarity is a strong constraint in the construction of S-matrix and will be considered in the sequel.

Two T-matrices corresponding to hadronic phase in H and quark phase in X⁴

How could the T-matrix for hadronic phase relate to the T-matrix for the quark phase, call it briefly t?

1. t would be related to scattering in the string phase, where the quarks would be free or rather at the boundary lines of string world sheets at light-like partonic orbits. The phase would consist only of conformally massless quarks and leptons at the fermionic lines. H-H would determine the space-time surfaces X⁴ and fermionic modes.
2. We can start from unitarity. In the hadron phase, the scattering amplitude satisfies the conditionT-T^† = TT^†. Unitarity would also hold for t in the quark phase. In the forward direction, a cut for T in the forward direction essentially gives the total cross section.
3. The scattering would correspond to two "big" state function reductions (BSFRs) changing the arrow of time (see this and this). T would be between the hadron phases and T^† between their time reversals. The same applies to t. This suggests a concrete interpretation of unitarity. T and T^† would correspond to opposite time directions. Analogously, t and t^† would be associated with a sequence of SSFRs in opposite time directions, increasing the size of the CD as a correlate for the geometric time. This would give a concrete geometric meaning for the unitary conditions.
4. T would decompose into a product of three operators. The first one would be the operator O, which would project from the hadron phase to the quark phase. It could, and actually should, be a 1-1 map. The second operator would be t or t^†, which would describe the scattering operator in the quark phase. The third would be the inverse operation of O. It should be possible to identify it uniquely, but if O is not 1-1, then there might be problems.
5. H-H gives strong conditions. t would correspond to a sequence of SSFRs and classical non-determinism would determine t. The creation of quark pairs is the basic process created by t, and here exotic smooth structures would come into play (see this)/masterformula,insectform}.

Could the unitarity for T reduce to unitarity for t?

1. O projects the hadronic state into a state consisting of quarks and the latter evolves according to t. After that, the quark state would to a hadronic state and the inverse of O would be included. The reduction T→ t from the hadronic level to the quark level takes place if an inverse of O exists.
2. If quark states can be mapped in 1-1 way to hadronic states, then the classical non-determinism, which can be interpreted as a cognitive non-determinism, would completely determine t. Everything would be discrete and extremely simple at the quark level. Note however that quark pair production occurs and the defect of the standard smooth structure as a classical correlate.

   The transition involves the usual quantum physical non-determinism, which naturally to O and its inverse. O would be completely determined by the overlap of the spinor modes of H and X⁴ determined by H-H.

Can the matrix O be invertible?

Can O define an isometry between two different state spaces? The analog of a projection from the hadron phase to the quark phase is in question, and it need not be an isometry. The analog of projection, or rather, the map, of O from the hadron phase to the quark phase is well-defined. Can O have a unique inverse? Light-likeness in H and light-likeness in X⁴ are very different notions physically: is a 1-1 correspondence between hadronic and quark states possible?

1. Could the additional degrees of freedom in the quark phase come from the fact that X⁴ is not closed like CP₂ and CD is finite? Conformal modes would diverge in H but not in X⁴ and increase the number of the fermion modes. The argument does not seem convincing to me.
2. Classical non-determinism (see this)/memorytgd} brings in additional degrees of freedom identified as cognitive degrees of freedom. Could this make isometry possible?
3. Could additional degrees of freedom in the quark phase emerge from an improved measurement resolution needed to "see" the quarks. This would correspond to a larger extension to rationals and that in turn to cognitive non-determinism so that this option is equivalent with the third option.

About the role of hyperfinite factors (HFFs)?

1. HFF (see this, this and this) is a fractal and contains hierarchies of subalgebras isomorphic with HFF itself. The number-theoretic vision assigns such hierarchies as hierarchies of algebraic extensions of rationals. Also measurement accuracy can be defined in terms of algebraic complexity.
2. The concept of inclusion is central. A subfactor corresponds to a subalgebra of the factor. Inclusion is not a 1-1 correspondence nor isometry. For a factor, the trace of the unitary operator is Tr(Id)=1 and for a sub-factor, the trace of the projector to it is Tr(P)= q≤ 1. q is quantized. There is a close connection with quantum groups and related concepts. The concept of HFF is particularly natural for fermions, so that it nicely fits into TGD.
3. Does the quark phase correspond to a subfactor of the hadron phase? Could classical non-determinism increase the value of q to unity and make the correspondence an isometric embedding of the quark operator algebra to hadronic operator algebra?

See the article Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD or the chapter chapter with the same title.

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

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

Does quantum criticality quite generally imply Einstein's equations in TGD?

Jacobsen has argued that Einstein's equations follow from thermodynamic arguments (see this. Empty space Einstein's equations would follow from the vanishing of the second variation of volume. I have discussed this from the TGD point of view in (see this).

This is very interesting from the point of view of TGD for the following reasons.

1. Quantum criticality is the basic guiding principle of TGD. In the same way that holomorphy determines the dynamics of 2-D quantum critical systems, its 4-D generalization would determine the dynamics of the space-time surfaces. Holography in turn follows from the condition that the definition of the geometry of the "world of classical worlds" (WCW) consisting of 3-surfaces realizes 4-D general coordinate invariance. Quantum classical correspondence is realized if one can assign to a given 3-surface almost unique space-time surface as its "Bohr orbit" identifiable as a preferred extremal of a classical action. It indeed turns out that there is a slight failure of determinism.

   This gives rise to holography =holomorphy vision (see this and this) predicting that space-time surfaces are holomorphic surfaces and therefore minimal surfaces. This is actually true for any classical action which is general coordinate invariant and constructible in terms of the induced geometry.

2. The details of the classical action action would be seen in the vacuum functional since the classical action defines the Kähler function of the "world of classical worlds" (WCW)(see this. They could also be seen via the boundary conditions at partonic surfaces serving as interfaces of regions with Minkowskian and Euclidean signature of the induced metric (see this and this) and stating that conserved classical charges are indeed conserved. The dream is that also the boundary conditions following holography= holomorphy vision are universally satisfied.
3. Note that the number theoretical vision suggests another way to fix the classical action. Number theoretical vision strongly suggests that the exponential of the action defining the vacuum functional is a number theoretic invariant and I have considered some natural candidates for it (see this).

Could one understand, or rather, generalize the finding of Jacobsen in the TGD framework? Could it be possible to find an analog of Einstein's equations at the fundamental level allowing an improved understanding of how the replacement of the many-sheeted space-time with a metrically deformed M⁴ gives Einstein's equations. The following considerations show that this naive idea fails but that the second variations of the boundary conditions of field equations with respect to zero modes could give rise to equations determining the extrema of the Kähler function of WCW.

In Jacobsen's case the vanishing of the second variation of volume in special space-time coordinates extremizing it gives rise to vacuum Einstein's equations. Now space-time is a 4-surface and the variation could be with respect to a subset of its embedding space coordinates. By holography= holomorphy principle, the space-time surface is a minimal surface. Hamilton Jacobi structure (see this) defines natural holomorphic coordinates but it is natural to require manifest general coordinate invariance.

One can consider the variation of 4-volume with respect to the local H-J coordinates of the space-time surface as an analogy for what Jacobson did.

1. General coordinate invariance implies that only the variation of the boundaries or interfaces between Minkowskian and Euclidean regions defining the holographic data matter. This conforms with the universality of H-H vision. The variation would be in the direction of the normal of the partonic orbits as interfaces of Minkowskian and Euclidean regions. This is like varying the length of a string requiring extremum.
2. A possible interpretation would be as a procedure finding extremum of WCW Kähler function with respect to the zero modes which do not appear in its line element. These maxima are of special importance in the functional integral (see this and this) and indeed critical.
3. This would give a single field equation for the H coordinate in the normal variation. Since the field equations depend on the classical action only at these boundaries, this option could in very general sense give rise to the analogs of Einstein's equations: gravitational field would have as a source the matter assigned with the partonic orbits. This would conform with the physical picture: matter at the partonic orbits affects the fields in the interior by boundary conditions.
4. The second variation would be for the normal components of the canonical momentum currents (or isometry currents) defined by the classical action. They would depend only on the first derivatives of H coordinates only and would give rise to second order partial differential equations.

   If the action involves a boundary term (such as Chern-Simons term allowed by light-likeness) (see this and this), one can obtain field equations coupling the boundary dynamics to the normal currents. The equations are very different from Einstein's equations but the physical idea is the same: vacuum Einstein's equations outside the matter are replaced with analogs of massless field equations solved by H-H vision.

See the chapter TGD and Possible Gravitational Anomalies.

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

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

The observation of non-standard arrow of time in systems characterized by Oxygen-redox electrochemistry

I learned of very interesting empirical findings (see this) demonstrating the existence of a non-standard arrow of time in systems characterized by Oxygen-redox (OR) chemistry. These kinds of findings fit very nicely with the general TGD based view of living systems in which the change of the arrow of time occurs in long scales and with the proposed vision about their generalization to systems which could be seen as living computers. In this view, electrochemistry would rely on new physics effects predicted by TGD.

Here is the abstract of the article,

Structural disorder within materials gives rise to fascinating phenomena, attributed to the intricate interplay of their thermodynamic and electrochemical properties. Oxygen-redox (OR) electrochemistry offers a breakthrough in capacity limits, while inducing structural disorder with reduced electrochemical reversibility. The conventional explanation for the thermal expansion of solids relies on the Grüneisen relationship, linking the expansion coefficient to the anharmonicity of the crystal lattice6. However, this paradigm may not be applicable to OR materials due to the unexplored dynamic disorder order transition in such systems . Here we reveal the presence of negative thermal expansion with a large coefficient value of -14.4(2) × 10^{-6 o}C^-1 in OR active materials, attributing this to thermally driven disorder order transitions.

The modulation of OR behaviour not only enables precise control over the thermal expansion coefficient of materials, but also establishes a pragmatic framework for the design of functional materials with zero thermal expansion. Furthermore, we demonstrate that the reinstatement of structural disorder within the material can also be accomplished through the electrochemical driving force. By adjusting the cut-off voltages, evaluation of the discharge voltage change indicates a potential for nearly 100 percent structure recovery. This finding offers a pathway for restoring OR active materials to their pristine state through operando electrochemical processes, presenting a new mitigation strategy to address the persistent challenge of voltage decay.

Zero energy ontology (ZEO) (see this and this) solves the quantum measurement problem in the TGD framework and predicts that in the TGD counterparts of the ordinary state function reductions (SFRs) associated with quantum measurements the arrow of time changes. I call these reductions "big" SFRs. In "small" SFRs (SSFRs) corresponding to repeated measurements of the same observables the arrow would not change but a "self measurement" inducing a small change would occur and give rise to self as a conscious entity.

TGD also predicts a hierarchy of effective Planck constants h_eff, which makes possible quantum coherence, BSFRs and SSFRs, and the non-standard arrow of time in arbitrarily long scales. This predicts exotic effects on all scales. In living matter these effects would be of special importance but appear also in astrophysical and perhaps even in cosmological scales. Even in the particle reactions a pair of BSFRs would occur (see this and this).

The phase of matter with a reversed arrow of time would look for an observer with the standard arrow of time just like the phase of matter reported here. The laws of thermodynamics would hold true but with a reversed arrow of time (see this, this, this). This was a general description for what might be in question. One can however look at the situation at a much more detailed level.

1. In Oxygen-redox (OR) reactions electrons are transferred from oxygen to the acceptor or vice versa. In the TGD based quantum biology, a fundamental role is played by the Pollack effect (see this) induced by irradiation using light in IR, visible and UV range. This induced negatively charged exclusion zones (EZs), which behave as if they had a reversed arrow of time.
2. The TGD based explanation of Pollack effect (see this, this this, this, this, this) is that protons from -OH groups (of say water) are kicked to to the field body of the system, where they become dark protons with a large value of h_eff. The arrow of time for the field body of EZ changes in this process. Since the field body controls the dynamics of EZ, this induces effective change of the arrow of time of EZ. The transfer process OH→ O^- + dark proton could correspond to a reversal of a topological qubit and this could make DNA a topological quantum computer.
3. Pollack effect generalizes (see this) and would take place in electrolysis and for instance give rise to the pH of water. What is fascinating is that the generalized Pollack effect could quite generally take place in systems involving cold plasmas. Computers could be such systems (see this) and one can consider Gallium based liquid computer, which would be a hybrid of ordinary and quantum computer giving rise to a life form (see this).
4. Also in the OR system described in the abstract, a generalization of Pollack effect creating negatively charged regions could be responsible for the change of the arrow of time.

See the article TGD and condensed matter or the chapter with the same title.

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

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

A more detailed vision of the TGD counterpart of the standard model stimulated by the analysis of LLM session

Recently Marko Manninen performed a LLM session using OpenAI's O3 language model using prompts related to the geometric aspects of TGD: the results can be found in the article by Marko and me presented in the article by Marko Manninen and me (see this) paper. Due to its "education", there were also grave misunderstandings and the model tended to hallucinate in its responses at the level of detail. Included were prompts requesting killer tests and asking whether these kinds of tests were already carried out. The fact that the responses were based on misunderstandings of what TGD is, forced to direct attention to the details of the related areas of TGD landscape and this had a very fruitful outcome.

Three kinds of questions related to the interpretation of TGD

The analysis created three kinds of questions related to the interpretation of TGD.

1. The idea (see this) about the phase transition between phases described in terms of Dirac equation in H resp. X⁴ as a generalization of the notion of the deconfinement phase transition resp. hadronization replaces the QCD type description with a stringy description in which the intersection of the space-time surfaces of colliding particles consisting of 2-D string worlds sheets determines the scattering amplitudes. In ZEO, this phase transition would involve two "big" state function reductions reversing the arrow of time and the time.
2. From the beginning it has been clear that color SU(3) is isometry group rather than gauge group and that its subgroup U(2) identifiable as a holonomy group acting on H spinors corresponds to a gauge group. The very definition of CP₂ as coset space states this geometrically.
   1. Could this mean the reduction of color confinement at the level of spinor quantum numbers to SU(2)_L confinement (see this)? Photons would not be confined, or screened by the pairs of right- and left handed neutrinos screening also the color of leptonic color partial waves (see this).
   2. Gluons do not appear as couplings of H spinors. Do gluons exist at all and is the identification of classical gluons as projections of Killing vectors wrong? Or do gluons correspond to electroweak gauge potentials in CP₂ spin degrees of freedom and would therefore correspond to electroweak interactions? But is this consistent with the fact that strong interactions are indeed strong?
3. A further stimulus came from the claim of GPT that already the existing data excludes copies of hadron physics labelled by Mersenne primes and their Gaussian variants. Is this really the case and are the earlier indications about bumps (see this and this) wrong?
   1. Under what conditions does the phase transition between M₁₀₇ and M₈₉ hadron physics occur with a significant rate?
   2. Is quantum criticality, forcing the Compton scales of ordinary hadrons and dark M₈₉ hadrons to be identical, necessary? This is indeed assumed in the model for the bumps as M₈₉ mesons reported at LHC. If so, the transition from M₁₀₇ H phase to X⁴ phase would occur in the first BSFR and the transition from the X⁴ phases to X⁴ phase to M₈₉ H phase would take place in the second BSFR. Just as in TGD inspired biology, the increase of the h_eff by factor 512 would require "metabolic" energy feed increasing the quark energies proportional to h_efff by this factor. This energy would come from the collision energy of colliding heavy nuclei. The decay of M₈₉ hadrons to M₁₀₇ hadrons would occur spontaneously. This kind of decay at the surfaces of the Sun is proposed to be responsible for the generation of solar wind and solar energy (see this).
   3. Is the assumption about the labelling of scaled variants of hadron physics by nuclear p-adic length scales too restricted since hadrons (say pions) are labelled also by other p-adic length scales than that of nucleon?
   4. Could the hierarchy of hadron physics correspond to the hierarchy color representations for quarks and leptons in 1-1 correspondence and labelled by single integer k appearing in the solution spectrum of the Dirac equation in H. If so, hadrons and leptons for a given value of k could correspond to several p-adic primes?

Progress in the understanding TGD view of the relation between electroweak and strong interactions

TGD view predicts at the fundamental level strong correlations between electroweak and strong interactions. But the precise understanding of these correlations has developed rather slowly. The writing of the comments to the GPT prompts was a rather exhaustive process but it was not a waste of time. It led to considerable progress in this respect. Gluon couplings do not appear in Dirac equations and in (see this) the possibility that there are no gluon vertices at the fundamental level was discussed so that somehow electroweak couplings also describe strong interactions. The recent general view of interactions allows to make these considerations much more detailed.

1. Also for X⁴ Dirac equation one obtains quark color and it would correspond to conformal modes proportional to (ξ₁,ξ₂,1) possible for the induced Dirac equation and perhaps having interpretation as reduction of color triplet to U(2) doublet plus singlet. The triplet corresponds to different coordinate patches of CP₂ to which the three Z₃ poles can be assigned. Therefore one obtains annihilation to quark pairs in this sense. Conformal invariance could make higher modes gauge degress of freedom.
2. As noticed, a long standing puzzle has been the fact that electroweak U(2) has a holonomy group of CP₂ is the maximal compact subgroup of SU(3). Could one see electroweak interactions as an aspect of color interactions or vice versa? Could one say that there is a symmetry breaking reducing isometry group SU(3) to its subgroup U(2) identifiable as holonomy group and an electroweak gauge group? Could CP₂= SU(3)/U(2) realize the gauge group nature of U(2) geometrically. Could electroweak confinement by the pairs of left and right-handed neutrinos screening the weak isospin correspond to SU(2)_L⊂ SU(3) confinement in spin degrees of freedom. There would be no color confinement for photons associated with U(1). Full color confinement would take place for the light states formed from the H spinor modes.
3. Why are strong interactions strong? The annihilation rate to quark pairs by the proposed vertices is sum of three pairs and the rate is 9 times higher than for the annihilation to leptons. The electroweak coupling strength is of order α_em=1/137 so that the rate for quark pair production corresponds to α_s= 9α_em∼ .1. This would give a correct order of magnitude estimate!
4. Old-fashioned hadron physics talked about conserved vector currents (CVC) and partially conserved axial currents (PCAC). These notions emerged from the observations that hadronic reaction rates can be expressed in terms of correlations of electroweak currents. This raises the question whether the strong interaction could reduce to electroweak interactions in some sense (see this).
5. What happens to the scaled up variants of hadron and electroweak physics if strong and electroweak physics fuse to whatever one might call it (unified physics?)? The only way to understand why the range of strong interactions is given by the hadronic length scale is that strong interactions would correspond to electroweak interactions in p-adic length scales, which correspond to hadrons and possibly also quarks. Weak bosons should correspond to a much longer Compton scale. Nucleons would correspond to the p-adic length scale L(107) and pions to M(113). The original view of weak bosons was that weak interactions correspond to the scale L(89) corresponding to Mersenne prime. Weak boson mass scales turned out to correspond to L(91) However, the original view is rather attractive and would fit with the view that M₈₉ hadron physics fuses with ordinary electroweak physics and several p-adic length scales are involved with a given copy. The copies of this unified physics in turn could correspond to color partial waves for Dirac equation in H. Electro-weak bosons would be special kinds of mesons in the sense that they are superpositions of both quark and lepton pairs. Photon would be even more special in that SU(2)⊂ SU(3) confinement would not apply to it because U(1) is abelian.

The scaling hypothesis, stating that the mass scales of mesons are scaled by a factor 512 in the transition M₁₀₇→ M₈₉, is probably too strong but gives testable predictions to start with.

1. One key question concerns the M₁₀₇ counterparts of weak bosons. They would correspond to genus g=0 (u and d quarks). A naive scaling of masses by factor 1/512 would give a mass scale near 500 MeV. There is no report about the observation of these bosons. For ρ meson the mass scale without QCD hyperfinite splitting induced by color magnetism is around 500 MeV. Are these weak bosons separate from ρ assumed to involve only quark pairs or do they correspond to ρ? For the latter option their decays to leptons should reveal this.
2. What about pseudoscalar π accompanying ρ? Standard model does not predict pseudoscalar electroweak boson. Its counterpart for M₈₉ should exist. Evidence is reported for the existence of a pseudoscalar at the intermediate boson mass scale about 80 GeV. For k=113, assignable to the Mersenne prime of the nucleus, one obtains the mass estimate 20 MeV. There is strong evidence for Xboson with mass around 17 MeV and I have considered the interpretation as a weak boson.
3. What about M₁₀₇ counterpart of Higgs scalar with mass of 125 GeV? By a naive scaling, it should have mass about 250 MeV. The are many candidates candidates for scalar mesons (see this) but they have masses above the mass 500 MeV of sigma boson whose existence is still not confirmed. σ is a very broad Breit-Wigner type resonance, which does not support interpretation as a scaled down Higgs boson. For k=113 the mass should be around 32 MeV.

See the article About Dirac equation in H=M⁴×CP₂ assuming Kähler structure for M⁴ or the chapter with the same title.

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

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

Could large language models be useful in theory development?

OpenAI's flagship ChatGPT O3 model (GPT in the sequel, see this) used here through the standard ChatGPT web interface underpins the research presented in the article by Marko Manninen and me (see this) paper. All questions were prompted in a single continuous session by Marko Manminen (see this) so that the model's internal chain-of-thought engine could preserve context and build upon earlier reasoning steps. Whenever its pre-training knowledge proved insufficient, GPT launched its integrated browser to retrieve citable sources and anchor each claim in publicly available data. The first goal was to see how realistic answers GPT can give nowadays compared to the answers we got two and half years ago, when ChatGPT 3.5 was released. At that time, there was not much to report since the language models were at their early age without grounding. The second goal was to see whether GPT could be useful from the point of view of TGD. Notably, the TGD view of physics as number theory was not considered in this investigation as we thought it would definitely be too hard for any meaningful inference. 7 prompts were used. The first 3 prompts were questions related to the basic mathematical notions of TGD (see this and this) in the physics as geometry vision.

1. Explain in detail how the M⁴ \times CP₂ geometry is induced to the spacetime surface in TGD and how the field equations are solved?
2. What does the holography= holomorphy (H-H) hypothesis mean in TGD?
3. What do induced geometry and induced spinor structure mean? What does the Dirac equation mean in TGD (use the latest material)

There were also 2 prompts related to the relation of TGD to other theories.

1. How does TGD differ from general relativity? How do TGD-inspired cosmology and astrophysics differ from what GRT predicts?
2. How does the particle physics predicted by TGD differ from that predicted by the Standard Model?

The last 2 prompts asked for criticism and tests of TGD and whether this kind of tests have been already carried out.

1. How should we stress test and attack this concept, be sceptic about?
2. Which of those tests have been already carried out?

The general conclusion was that the lack of real understanding and the learned attitudes leads to hallucinatory behavior and one cannot take responses of GPT seriously. However, GPT allows a bird's eye view of large theoretic structures like TGD, developed over a long period of time. Although the objections represented by GPT turned out to be wrong, they forced a detailed study of the related parts of TGD landscape. This led to a considerable sharpening of the recent view of TGD, which has developed very rapidly during recent years and one can even say that TGD is now able to give the counterparts of Feynman rules. One can say that GPT does not lead to new discoveries but makes it possible to fill in the details. This GPT session is discussed in the article (see this).

Questions inspired by the analysis of the GPT session

The analysis created three kinds of questions related to the interpretation of TGD.

1. The idea (see this) about the phase transition between phases described in terms of Dirac equation in H resp. X⁴ as a generalization of the notion of the deconfinement phase transition resp. hadronization replaces the QCD type description with a stringy description in which the intersection of the space-time surfaces of colliding particles consisting of 2-D string worlds sheets determines the scattering amplitudes. In ZEO, this phase transition would involve two "big" state function reductions reversing the arrow of time and the time.
2. From the beginning it has been clear that color SU(3) is isometry group rather than gauge group and that its subgroup U(2) identifiable as a holonomy group acting on H spinors corresponds to a gauge group. The very definition of CP₂ as coset space states this geometrically.
   1. Could this mean the reduction of color confinement at the level of spinor quantum numbers to SU(2)_L confinement (see this)? Photons would not be confined, or screened by the pairs of right- and left handed neutrinos screening also the color of leptonic color partial waves (see this).
   2. Gluons do not appear as couplings of H spinors. Do gluons exist at all and is the identification of classical gluons as projections of Killing vectors wrong? Or do gluons correspond to electroweak gauge potentials in CP₂ spin degrees of freedom and would therefore correspond to electroweak interactions? But is this consistent with the fact that strong interactions are indeed strong?
3. A further stimulus came from the claim of GPT that already the existing data excludes copies of hadron physics labelled by Mersenne primes and their Gaussian variants. Is this really the case and are the earlier indications about bumps (see this and this) wrong?
   1. Under what conditions does the phase transition between M₁₀₇ and M₈₉ hadron physics occur with a significant rate?
   2. Is quantum criticality, forcing the Compton scales of ordinary hadrons and dark M₈₉ hadrons to be identical, necessary? This is indeed assumed in the model for the bumps as M₈₉ mesons reported at LHC. If so, the transition from M₁₀₇ H phase to X⁴ phase would occur in the first BSFR and the transition from the X⁴ phases to X⁴ phase to M₈₉ H phase would take place in the second BSFR. Just as in TGD inspired biology, the increase of the h_eff by factor 512 would require "metabolic" energy feed increasing the quark energies proportional to h_efff by this factor. This energy would come from the collision energy of colliding heavy nuclei. The decay of M₈₉ hadrons to M₁₀₇ hadrons would occur spontaneously. This kind of decay at the surfaces of the Sun is proposed to be responsible for the generation of solar wind and solar energy (see this).
   3. Is the assumption about the labelling of scaled variants of hadron physics by nuclear p-adic length scales too restricted since hadrons (say pions) are labelled also by other p-adic length scales than that of nucleon?
   4. Could the hierarchy of hadron physics correspond to the hierarchy color representations for quarks and leptons in 1-1 correspondence and labelled by single integer k appearing in the solution spectrum of the Dirac equation in H. If so, hadrons and leptons for a given value of k could correspond to several p-adic primes?

Progress in the understanding TGD view of the relation between electroweak and strong interactions

TGD view predicts at the fundamental level strong correlations between electroweak and strong interactions. But the precise understanding of these correlations has developed rather slowly. The writing of the comments to the GPT prompts was a rather exhaustive process but it was not a waste of time. It led to considerable progress in this respect. Gluon couplings do not appear in Dirac equations and in (see this) the possibility that there are no gluon vertices at the fundamental level was discussed so that somehow electroweak couplings also describe strong interactions. The recent general view of interactions allows to make these considerations much more detailed.

1. Also for X⁴ Dirac equation one obtains quark color and it would correspond to conformal modes proportional to (ξ₁,ξ₂,1) possible for the induced Dirac equation and perhaps having interpretation as reduction of color triplet to U(2) doublet plus singlet. The triplet corresponds to different coordinate patches of CP₂ to which the three Z₃ poles can be assigned. Therefore one obtains annihilation to quark pairs in this sense. Conformal invariance could make higher modes gauge degress of freedom.
2. As noticed, a long standing puzzle has been the fact that electroweak U(2) has a holonomy group of CP₂ is the maximal compact subgroup of SU(3). Could one see electroweak interactions as an aspect of color interactions or vice versa? Could one say that there is a symmetry breaking reducing isometry group SU(3) to its subgroup U(2) identifiable as holonomy group and an electroweak gauge group? Could CP₂= SU(3)/U(2) realize the gauge group nature of U(2) geometrically. Could electroweak confinement by the pairs of left and right-handed neutrinos screening the weak isospin correspond to SU(2)_L⊂ SU(3) confinement in spin degrees of freedom. There would be no color confinement for photons associated with U(1). Full color confinement would take place for the light states formed from the H spinor modes.
3. Why are strong interactions strong? The annihilation rate to quark pairs by the proposed vertices is sum of three pairs and the rate is 9 times higher than for the annihilation to leptons. The electroweak coupling strength is of order α_em=1/137 so that the rate for quark pair production corresponds to α_s= 9α_em∼ .1. This would give a correct order of magnitude estimate!
4. Old-fashioned hadron physics talked about conserved vector currents (CVC) and partially conserved axial currents (PCAC). These notions emerged from the observations that hadronic reaction rates can be expressed in terms of correlations of electroweak currents. This raises the question whether the strong interaction could reduce to electroweak interactions in some sense (see this).
5. What happens to the scaled up variants of hadron and electroweak physics if strong and electroweak physics fuse to whatever one might call it (unified physics?)? The only way to understand why the range of strong interactions is given by the hadronic length scale is that strong interactions would correspond to electroweak interactions in p-adic length scales, which correspond to hadrons and possibly also quarks. Weak bosons should correspond to a much longer Compton scale. Nucleons would correspond to the p-adic length scale L(107) and pions to M(113). The original view of weak bosons was that weak interactions correspond to the scale L(89) corresponding to Mersenne prime. Weak boson mass scales turned out to correspond to L(91) However, the original view is rather attractive and would fit with the view that M₈₉ hadron physics fuses with ordinary electroweak physics and several p-adic length scales are involved with a given copy. The copies of this unified physics in turn could correspond to color partial waves for Dirac equation in H. Electro-weak bosons would be special kinds of mesons in the sense that they are superpositions of both quark and lepton pairs. Photon would be even more special in that SU(2)⊂ SU(3) confinement would not apply to it because U(1) is abelian.

The scaling hypothesis, stating that the mass scales of mesons are scaled by a factor 512 in the transition M₁₀₇→ M₈₉, is probably too strong but gives testable predictions to start with.

1. One key question concerns the M₁₀₇ counterparts of weak bosons. They would correspond to genus g=0 (u and d quarks). A naive scaling of masses by factor 1/512 would give a mass scale near 500 MeV. There is no report about the observation of these bosons. For ρ meson the mass scale without QCD hyperfinite splitting induced by color magnetism is around 500 MeV. Are these weak bosons separate from ρ assumed to involve only quark pairs or do they correspond to ρ? For the latter option their decays to leptons should reveal this.
2. What about pseudoscalar π accompanying ρ? Standard model does not predict pseudoscalar electroweak boson. Its counterpart for M₈₉ should exist. Evidence is reported for the existence of a pseudoscalar at the intermediate boson mass scale about 80 GeV. For k=113, assignable to the Mersenne prime of the nucleus, one obtains the mass estimate 20 MeV. There is strong evidence for Xboson with mass around 17 MeV and I have considered the interpretation as a weak boson.
3. What about M₁₀₇ counterpart of Higgs scalar with mass of 125 GeV? By a naive scaling, it should have mass about 250 MeV. The are many candidates candidates for scalar mesons (see this) but they have masses above the mass 500 MeV of sigma boson whose existence is still not confirmed. σ is a very broad Breit-Wigner type resonance, which does not support interpretation as a scaled down Higgs boson. For k=113 the mass should be around 32 MeV.

See the article Could large language models be useful in theory development? by Marko Manninen and M. Pitkänen or the chapter with the same title.

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

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

How could the transitions between hadronic and quark phases occur in the TGD framework?

The solutions of the ordinary Dirac equation in H with M⁴ Kähler structure have masses of order CP₂ and light states are color singlets whereas the solutions of the induced/modified Dirac equation for quarks in X⁴ are massless. In the case of quarks this suggests an interpretation in terms of hadrons and massless quarks. This picture also applies to leptons.

The QCD description of hadronic reactions is statistical and is in terms of quark and gluon distribution functions characterizing hadrons and fragmentation functions to hadrons for quarks and gluons. What could the TGD counterparts of these functions be and could an analogous description at quantum level be possible? What happens in the transitions hadron phase and free quark phase and how to describe this in TGD?

1. Hadron phase ↔ quark phase transition as a transition between phases characterized by 8-D and 4-D masslessness

In the transition to the X⁴ phase with free massless quarks, the colored H spinor modes are replaced with holomorphic X⁴ spinor modes. The opposite transition takes place in hadronization. X⁴→ H transition is analogous with the Higgs mechanism in which transition occurs from a massless phase to a massive phase (in M⁴ sense). Transition is also between deconfined and confined phases. This description applies also to leptons which also move in H spinor partial waves.

A more general view is based on conformal symmetry breaking. In hadronization 4-D light-likeness replaced with 8-D light-likeness in H. Propagation takes place along the space-time surface and propagator is determined by the induced/modified Dirac operator. What is of crucial importance is that fermionic oscillator operators for inducd spinors fields are expressed in terms of those for the H spinor field.

What about the description of color in the X⁴ phase? Does one obtain color triplets in the holomorphic basis? Could the color partial waves {ξ₁,ξ₂,1} proportional form a counterpart of color triplet? Does the color triplet correspond to the 3 coordinate patches for the complex structure of CP₂ as a complex projective space? Why color triplets are special for quarks and color singlets for leptons. Does this relate to conformal invariance making higher partial waves gauge degrees of freedom? What about Kac-Moody type gauge invariance? Could only the lowest modes matter. Fixed H spinor modes as ground states for Kac-Moody representations.

2. Quantum measurement theory in ZEO as a guideline

Quantum measurement can be seen as a Hilbert space projection.Could this projection be induced by a geometric projection from H to the space-time surface for the spinor modes. The modes of the X⁴ Dirac operator have a fixed M⁴ chirality and this is the signature of masslessness. Apart from the covariantly constant right-handed neutrino, H modes have only a fixed H chirality and are therefore massive. Therefore also M⁴ chirality would be measured in the transition to the quark phase. Note that also projections to lower dimensional surfaces, such as partonic orbits, string world sheets and fermion lines make sense if this interpretation is correct.

In this picture, the overlap between H modes and X⁴ modes would characterize the transition from hadrons to quarks and vice versa. The ZEO based description of any particle reaction involves a pair of BSFRs. In the case of hadronic reactions this would involve the transition of hadrons to quarks in BSFR, time evolution with opposite arrow of time, and second BSFR leading from quark phase to hadron phase.

1. In ZEO, the deconfinement phase transition H→ X⁴ from hadron to quark phase would involve a localization from H to X⁴. This also means a localization in the "world of classical worlds" (WCW). In the deconfined state localized to single X⁴, one would have an analog of QFT in a fixed background space-time. Note however that every 3-surface defines its own space-time surface as its Bohr orbit, which is however not quite unique, which in fact forces ZEO. Therefore one has a superposition of scattering amplitudes over the space-time surfaces satisfying holography= holomorphy principle.
2. Hadronization as a transition X⁴→ H would in turn mean a delocalization in WCW and could be interpreted as a localization in the analog of momentum space for WCW. The observables measured would be quantum numbers of WCW spinor modes. This includes measurement of H quantum numbers but the light states are color singlet many fermion states. Color partial waves have the CP₂ mass scale.

3. What  does the interaction of particles as space-time surfaces mean?

What does the interaction of particles as space-time surfaces obeying holography= holomorphy principle mean?   When do  the particle interactions lead to the transition to the phase corresponding to a localization in WCW? In strong interactions this kind of interaction requires a high collision energy implying that the interactions occur in a scale smaller than the geometric size scale of the colliding particles so that the internal geometric structure of the particle become visible. In the TGD framework, these details naturally correspond to lower dimensional structure consisting of the light-like parton orbits and string world sheets having their boundaries at the parton orbits. Note that this picture might apply to to all interactions. Topological considerations allow to make this picture rather concrete (see this).

1. For topological reasons, the intersection of the generic space-time surfaces is  a discrete set of points.  The systems  should fuse somehow and form a quantum coherent interaction region. If the H-J structures of the space-time surfaces are identical meaning that in the interaction region both space-time surfaces have the same coordinates (u,v, w, ξ₁, ξ₂), the intersection is 2-D string world sheet,  containing point-like fermions as fermion lines at its  boundaries assignable to light-like 3-D parton orbit (see this). This makes possible a string model type description for  the interactions  of the  fundamental fermions. By the hypercomplex holomorphy, the description would be rather simple  since  the second light-like coordinate of the string world sheet is non-dynamical.
2. Only fermions and their bound states appear as  fundamental quantum  objects in  the TGD framework. If they emerge in the formation of states delocalized in WCW they would correspond to hadrons, leptons and electroweak bosons.  In particular, bosons as incoming and outgoing  are identified as bound states of fermions and antifermions.  The stringy view of  the interactions implies that  bosons need not  appear at all in the   deconfined phase.

   If so,    there would be no gluons and the fundamental vertex would correspond to a creation  or annihilation of a fermion pair  from "vacuum" and the classical induced gauge fields would define the vertices.  This would take place when string world sheets fuse or split and a pair of fermion lines at separate string world sheets is created or disappears.

3. The notion of exotic smooth structure (see this, this, and this) possible only in 4-D space-time and reducing to the standard smooth structure apart from defects identifiable as this kind of singularities  allows these kinds of  edges (see this, this, and this). This allows also to consider scattering events in which the fermion line has an edge serving as vertex giving rise to momentum exchange.  These edges would correspond to failure of holomorphy at a single point.

4. The relationship between the oscillator operators of spinor modes in H and X⁴

It is possible to express X⁴ oscillator operators in terms of H oscillator operators (see this). Induction means the restriction of the mode expansion of the second quantized H spinor field to the space-time surface X⁴. Similar expansion for X⁴ spinor field in terms of conformal modes makes sense. The two representations must be identical. This implies that the oscillator operators at X⁴ are expressible as inner products of conformal modes and H spinor field. H oscillator operators are fundamental and no separate second quantization at X⁴ is needed.

The inner products between the spinor modes of X⁴ and H involve an integration over the space-time surface or a lower-dimensional space-time region. By the 8-D chiral symmetry the matrix element must involve gamma matrices and reduce to an integral of an inner product of the conformal mode of the induced Dirac operator with the fermionic super current over the parton orbit. The 3-D intersection of the space-time surface with the light-like boundary of CD cannot be excluded. The integral over the parton orbit is natural since the transversal hypercomplex coordinate for the associated string world sheet is not dynamical. These integrals characterize the transition between the two phases and its reversal and would replace the parton distribution functions and fragmentation functions in TGD. The conservation of color quantum numbers and corresponding M⁴ quantum numbers in holomorphic basis in which X⁴ complex coordinates correspond to those of H.

What about propagators in the quark phase? The propagation would be restricted to X⁴ rather than occurring in H. X⁴ spinor field would be defined as the sum over its conformal modes and the Dirac propagator would be defined as a two point function, which can be calculated because oscillator operators are expressible in terms of H oscillator operators.

5. Description of hadron reactions in ZEO

As found, zero energy ontology and holomorphy= holography vision suggest a universal description of all particle reactions. The particle reaction involves a temporary time reversal involving two BSFRs.

1. In the first BSFR a projection from the space of hadron states in H to free many-quark states in X⁴ would occur. This localization in WCW would also involve a measurement of M⁴ chirality by an external observer. The resulting state would consist of free massless quarks in X⁴ and evolve by SSFRs backwards in geometric time. The interactions would be mediated by string world sheets having fermion lines at their boundaries and the notion of exotic smooth structure would be essential making possible fermion scattering and pair creation in the absence of fundamental bosonic quantum fields.
2. After that a second BSFR would occur inducing a delocalization in WCW and a hadronic state would emerge and evolve by SSFRs. One can say that the states delocalized in WCW correspond to hadrons (and quite generally color singlet states). WCW observables, which include the observables associated with H, would be measured. Concerning the calculation of the scattering amplitudes, this means that the quark oscillator oscillator operators would be expressed in terms of H oscillator operators and a Hilbert space projection to a state of hadrons would take place.

See the article About Dirac equation in H= M⁴ × CP₂ assuming Kähler structure for M⁴ or the chapter with the same title.

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

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

Massless quarks as modes of the Dirac equation for the induced spinors at the space-time surface

I wrote some time ago an article describing the results from solving the Dirac equation in H= M⁴×CP₂ assuming that M⁴ has an analog of Kähler structure. Apart from covariantly constant right handed neutrino (covariantly constant in CP₂) the color partial waves have huge masses with mass scale given by CP₂ mass scale. It is however possible to obtain massless color singlet many-quark states with the difference of quark and antiquark numbers equal to a multiple of 3. These would develop p-adic thermal mass squared. The conclusion was that only hadrons are possible in this framework.

There is however an objection against this view. The successes of QCD suggests that also the description in terms of massless quarks should make sense and should correspond to a phase different from the hadronic phase.

1. The induction of the spinor structure to the space-time surface is a fundamental piece of TGD. This gives a induced/modified Dirac equation at the space-time surface X⁴ and the generalized holomorphic solutions of this equation are massless in the sense that the square of the modified Dirac operator annihilates them (see this and this). The conjugates of the holomorphic gamma matrices annihilate these modes and implies that the spin term involving the induced Kähler form vanishes and does not give rise to mass squared term. Somehow I failed to realize that the modes of this Dirac equation represent massless quarks. One can speak of a phase dual to the hadronic phase.
2. The induction of spinor structure (see this) by restricting the H modes to the space-time surface however requires a generalized holomorphic solution basis for H, which makes sense only in finite regions of M⁴ and CP₂ inside which the holomorphic modes remain finite. It is not clear whether this basis is locally orthogonal to the solution basis of ordinary Dirac equation in H. These modes must remain finite in X⁴. Since space-time surfaces are enclosed inside CDs with a finite size scale and CP₂ type Euclidean regions connecting two Minkowskian space-time sheets (see this and this) have holes as 3-D light-like partonic orbits, these modes can remain finite.
3. If the notion of the induced/modified spinor structure really makes sense, one can speak of two phases: free quarks and gluons and hadrons. The hadronic phase corresponds to the modes of the Dirac operator of H massless in 8-D sense but extremely massive in M⁴ sense. The holomorphic modes of the X⁴ Dirac operator correspond to massless quarks and gluons and also leptons. These descriptions should be dual to each other. The challenge is to understand this phase transition, which means breaking of conformal invariance and can be seen as a generalization of the phase transition from Higgs=0 phase to a phase with non-vanishing Higgs expectation.

See the article About Dirac equation in H=M⁴×CP₂ assuming Kähler structure for M⁴ or the chapter with the same title.

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

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

The empirical evidence for self-interacting dark matter as support for the TGD view of galactic dark matter

Sabine Hossenfelder talks in Youtube (see this about the evidence accumulating for the notion of self-interacting dark matter. Self-interactions are needed to explain unexpectedly strong clustering of red dwarf galaxies. Both LambdaCDM and MOND fail to explain the clustering since absence of self-interactions does not favour the correlations reflected by the strong clustering. The article of Zhang et al is titled "Unexpected clustering pattern in dwarf galaxies challenges formation models" (see this). There are also other pieces of evidence for the self-interactions.

The TGD counterpart of the self-interacting dark matter would be cosmic strings, which are 4-D space-time surfaces in H=M⁴× CP₂ having string world sheet as M⁴ projection and a complex 2-surface, such as homologically non-trivial geodesic sphere, as a CP₂ projection. Cosmic strings would dominate in the primordial cosmology and then a transition to radiation dominated phase would occur as an analog of the inflationary period in which strings would thicken to flux tubes with 3-D E³ projection. No exponential expansion is needed since the predicted gravitational quantum coherence in arbitrarily long scales explains the constancy of CMB temperature.

Galactic dark matter would be classical magnetic and volume energy of the cosmic string and dark energy would be a better term. Self-interaction guarantees strong correlations between the galaxies associated with the string as tangles of the cosmic string for which the string thickens to a monopole flux tube and liberates energy as ordinary particles. These tangles would contain stars as sub-tangles. These tangles can be formed in the collisions of cosmic strings. The velocity spectrum for distant stars is predicted to be flat for a single long cosmic string.

See for instance the article About the recent TGD based view concerning cosmology and astrophysics.

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

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

Ring Nebula as evidence for the TGD view of planets and stars and their formation

Ethan Siegel posted to BigThink a highly interesting article "Did JWST catch the Ring Nebula forming new planets?" (see this). Planets are observed in the nebula.

I glue here the description of the article almost as such.

1. The standard view is that when hydrogen depletes in the core of the Sun, it will expand to a red giant. Mercury, Venus, and likely also Earth will be devoured. The Oort cloud, Kuiper belt, and possibly even Neptune and Uranus. Therefore the presence of planets in the Ring Nebula is surprising. Finally a white dwarf will form and ionizes the previous ejecta.
2. The observations of JWST of Ring Nebula at a distance about 2000 ly however suggest that the story continues. Ring Nebula possesses a ring, lobes and inner and outer halos. Inside many different chemical elements can be detected. Polar flows of CO⁺ ions inside a barrel shaped material are observed. The dying star's remnant is centrally located but a long suspected companion star remains elusive. JWST research, focusing on the Ring Nebula s interior and central regions, is vitally important. The central star is surrounded by a compact dust cloud, revealed at long wavelengths (above ∼ 5 microns). These dusty features resemble young protoplanetary and dusty debris disks.

   The formation of planets in this way does not conform with the standard view that planets are formed from a proto-disk. This may mark a new, unforeseen planet-forming phase. Perhaps white dwarf systems spawn new planets, even after dying.

In the TGD based cosmology, the smooth cosmic expansion is replaced with fast explosive events, mini bigbangs, in with the size of the astrophysical objects suddenly increases or it throws out a layer to which a magnetic bubble consisting of a network of monopole flux tubes is formed. This view revolutionizes the view about the formation of planets and smaller structures.

1. The ring nebula discussed in the article having several layers brings to mind the TGD based proposal for the formation of planets. The central star would suffer an explosion throwing out spherical shells from its surface and these shells could (not necessarily) later condense to rings and these in turn would form planets. This mechanism could replace the standard model for the formation of planets as a gravitational condensation of protodisk.

   For magnetic bubbles see this and this. For solar anomalies see this and this.

   Vega is a star with proto disk-like structure but, contrary to the expectations, has no planets (see this).

2. Even the planets could explode and create moons and rings in this way. Moon and Deimos and Phobos, the moons of Mars, could have formed in this kind of explosion (see this, this and this).
3. Cambrian Explosion for Earth would have caused expansion of radius of Eartg by factor 2 and led to the bursts of underground oceans containing highly evolved multicellulars to the surface of the Earth (see this and this).

How could this vision relate to the findings of JWST? It is good to first describe briefly some aspect of the TGD view of astrophysics described in the article "Some solar mysteries" (see the this).

1. The article relies on new hadron- and nuclear physics predicted by TGD. In particular, scaled up copies of hadron physics are predicted and M₈₉ hadron physics have a mass scale which is 512 times the mass scale of ordinary nucleons.
2. Also involved is zero energy ontology (ZEO), which solves the basic problem of quantum measurement theory and predicts that the arrow of time changes in "big" state function reductions. This would happen even in astrophysical scales.
3. The number theoretic view of physics (see this, this, this, this and this) in turn predicts that quantum coherence is possible even in astrophysical scales. Nottale proposed that the notion of gravitational Planck constant ℏ_gr makes sense for classical long range gravitational fields and considered a model of the planetary system as an analog of atom. The value of ℏ_gr value is fixed by the Equivalence Principle apart from a dimensionless velocity parameter β₀ = v₀/c, which for Sun is about 2^-11. In the TGD framework, ℏ_gr is proposed to be a genuine Planck constant (see this, this, this) assignable to phases of the ordinary matter located ad field bodies and behaving like dark matter but not identifiable as galactic dark matter which is more like dark energy associated with cosmic strings in TGD. The proposal generalizes to long range electric fields (see this).

The key observation is the following numerical coincidence. White dwarf is a very dense object with a radius of about Earth radius and mass of the order of the mass of the Sun. What could this mean?

1. In the TGD based model of the Sun (see the this) gravitational Compton length of the Sun, assuming Nottale's hypothesis for gravitational Planck constant, is very near to the the radius of the Earth. Could white dwarf be seen as a gravitationally dark object with a gravitational Compton length near to the Earth radius, an analog of an elementary particle?
2. In this model, the Sun would receive metabolic energy as M₈₉ hadrons identifiable as scaled up copies of ordinary hadrons from the galactic center, possibly from the TGD counterpart of the galactic blackhole and these M₈₉ hadrons would decay to ordinary hadrons and produce solar wind and solar radiation. The solar core would be something totally different, perhaps analogous to a cell nucleus.

   Are stars living, metabolizing systems that are born, flourish, and die and whether the remnants of a star can give rise to a reincarnation of the star generating its own planetary system by these explosions as TGD counterparts for a smooth cosmic expansion? Do they form networks analogous to multicellular systems communicating using the signals propagating parallel to the monopole flux tubes?

3. In this framework the stragen observations about white dwarfs combined with the TGD view of the Sun and of the formation of planets inspires several questions. Did the predecessor of the Sun "die" and "reincarnate" as a white dwarf and produce outer planets in its explosion? Did the white dwarf explode and produce the recent Sun and the inner planets?

See for instance the article ANITA anomaly, JWST observation challenging the interpretation of CMB, and star formation in the remnant of a star or the chapter About the recent TGD based view concerning cosmology and astrophysics.

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

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