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.

Technical problems of the holography= holomorphy vision

The realization of holography= holomorphy vision has 3 problems.

1. Hyper complex conjugation u↔ v for the hypercomplex coordinates, which are real, might pose serious interpretational problems. Suppose that the roots of the generalized analytic maps f=(f₁,f₂)(u,w,ξ₁,ξ₂): H→ C² define the space-time surfaces.

   If u↔ v represents hypercomplex conjugation, the functions f_i and their generalized complex conjugates involving the replacement of hypercomplex coordinate u with v need not define the same surface. Their intersection is in general a 3-dimensional surface X³ with u=v. Should one fuse these surfaces so that hypercomplex conjugation by geometric symmetry? What is the physical interpretation of the two regions?

2. It is far from obvious whether CP₂ type extremals and their deformation allow a realization in terms of holography= holomorphy vision. It turns out Wick rotation provides a solution to the problem.
3. The surfaces of u-type and v-type do not allow light-like partonic orbits at which the induced metric changes the signature. It seems that the space-time surfaces must have regions in which the dynamic embedding space coordinates depend on both u and v. Also in this case Wick rotation solves the problem.

1. Definition of hypercomplex conjugation

What does one mean with the generalization of the complex conjugation when applied to the argument of f? Could it correspond a) to (u,w,ξ₁,ξ₂)→ (u,w ,ξ₁, ξ₂ so that there is no hypercomplex conjugation or b) to (v,w,ξ₁,ξ₂)→ (u,w, ξ₁, ξ₂) so that there is hypercomplex conjugation.

1. For option a), the roots of f and f represent the same surface. For the roots of f the contribution of complex coordinates to g_uv and g_vw is vanishing but the components g_uw and there is only the contribution of M⁴ metric to g_uv. Partonic orbits are not possible.
2. For option b), the roots of the conjugate f do not coincide with the roots of f unless symmetries exist. Since one can transform the hypercomplex and complex cases to each other by a Wick rotation, it seems necessary to assume that the union of the u-type and v-type regions defines the space-time surface. Hypercomplex conjugation would be a non-local symmetry transforming to each other two parts of the space-time surface. The 3-surface u=v would be a 3-dimensional surface along which the two space-time regions would be glued together,

Consider the option b) in more detail.

1. How to identify the u- and v-type regions? In the model for elementary particles, Euclidian regions as deformations of CP₂ extremals connect two Minkowskian space-time sheets, which are extremely near to each other having a distance of order CP₂ radius. Could the two Minkowskian space-time sheets correspond to u- and v-type regions and could generalized complex conjugation (u,w,ξ₁,ξ₂)↔ (v,w, ξ₁, ξ₂) transform then to each other.
2. Could the 3-surface X³ with u=v correspond to a surface in the interior of CP₂ extremal which along which the sheets are glued together? The condition u=v makes the two conditions equivalent as ordinary complex conjugates of each other. For the simplest option u=m⁰+m³, v= m⁰-m³ the condition u=v gives m³=0 and so that the intersection of the u and v-type regions would be 3-D surface inside the wormhole contact and analogous to a particle at rest.
3. In complex analysis, the counterpart of the 3-surface X³ defined by the u=v condition is the real axis. Could u- and v type solutions represent an analog of 2-valued analytic functions, such as z^1/2 having a cut discontinuity for the imaginary part along the positive real axis, effectively replacing the complex plane with its 2-fold covering.

   Now the cut would be associated with the values of the dynamical embedding space coordinates and the two sides of X³ would correspond to the two Minkowskian space-time sheets. At X³ the u- and v-type time evolutions would be glued together. Discontinuity for dynamical H coordinates would mean that both sheets haave a hole and are actually separate. If only derivatives are discontinuous, X³ represents a 3-D edge.

4. Could X³ could be interpreted in terms of an exotic smooth structure allowing an interpretation as the standard smooth structure with defects? The u- lines would transform to v-lines at X³ and give rise to edges violating the standard smoothness.

   Also the partonic orbits could define analogous defects since the u- resp. v-lines could have an edge. The identification of fermion lines as these kinds of lines allow the interpretation of defects as vertices for the creation of fermion-antifermion pair as turning of fermion line backwards in time (see this and this)?

2. How to represent CP₂ type extremals and their deformations?

CP₂ type extremals represent basic solutions of field equations. For them the M⁴ projection is a light-like curve and does not contribute to the induced metric. But how to represent this surface in holography= holomorphy vision. What is required is that the curve parameter u of the light-like curve is a function of a single real CP₂ coordinate. For instance, the function f₁= g(ξ₁)+u would formally give either u=g(ξ₁), which makes no sense. The second option is Im(g(ξ₁))=0, which violates holomorphy and reduces the dimension of the CP₂ type extremal to 3.

Here Wick rotation suggests an elegant solution.

1. One can replace the hypercomplex coordinate u and its conjugate v with a complex coordinate z and its conjugate z. For instance, for (u,v)= (m⁰+m³,m⁰-m³) this would change m³ to -m³ and if one uses m⁰+im³ and m⁰-im³ as Wick rotate coordinates (z,z) this corresponds to complex conjugation. One can solve the roots of f_i for their Wick rotated form and perform Wick rotation to the roots to get the solution. The problem posed by the CP₂ type extremals disappears.

   Note that one can also interpret the metric of M² for complex coordinates (z,z) as a number theoretic metric introduced in M⁸ in the context of M⁸-H duality (see this). The metric in (u,v) ((m⁰,m³)) coordinates corresponds to the imaginary (real ) part of z².

2. Wick rotation predicts that the solved embedding space complex coordinates depend on both u and v in some region, in which the metric is Euclidean. It transforms to Minkowskian metric at a 3-D light-like interface identifiable as partonic orbit. This is just what is wanted. The reason is that for pure u and v type regions with 4-D M⁴ projection the component g_uv of the induced metric receives no contribution from CP₂ and corresponds to the metric of the empty Minkowski spaces. Partonic surfaces would not be possible. u- resp. v-type regions correspond to regions, where it is possible to regard u resp. v as a parameter appearing in f_i rather than a dynamical variable to be solved.
3. Outside the partonic orbit assignable to a given Minkowskian space-time sheet, one has a u- or v-type solution. Wick rotation implies that in the Euclidean region the metric receives a contribution from M⁴. This in turn makes possible the presence of a light-like 3-D interface at which the 4-metric becomes degenerate and actually metrically 2-dimensional so that it can be glued to the induced metric of a Minkowskian space-time sheet as u- or v-type solution.

It seems that the pairs of space-time sheets connected by wormhole contacts represent a basic solution type for holography= holomorphy vision. The wormhole contacts generalize also tothe solutions which represent cosmic strings and their deformations. Even the vertices for the creation of fermion-antifermion pairs seem to emerge as defects of exotic smooth structures.

This picture would relate several key ideas of TGD: holography= holomorphy vision involving hypercomplex numbers, the notion of light-like partonic orbit, the idea that exotic smooth structures make possible non-trivial scattering theory in 4 dimensional space-time. One can compare this picture with the intuitive phenomenological picture.

1. The doubling and partonic seems to be an inherent property of the holography= holomorphy vision and of hypercomplex analyticity. u-v pairing is true also in CP₂-type regions. The intersection of u and v regions has a well-defined and in general non-vanishing g_uv, which does not reduce to mere Minkowskian contribution to it. The condition g_uv=0 is true at the partonic orbit defining the interface between Euclidean wormhole contact as a piece of CP₂ type extremal and Minkowskian space-time sheets.
2. Could the u- and v-type regions correspond to a pair of Minkowskian space-time and also Euclidean space-time regions? At the partonic orbit the u- and v-sheets intersect. This does not conform with the intuitive view about the wormhole contacts. Could this mean that there is no wormhole contact such that its throats carry opposite homology charges? This does not conform with the physical intuitions. If one wants to keep the view about parallel space-time sheets, both Minkowskian space-time sheets must be u-v pairs and both wormhole throats must be intersections of the u and v sheets?

See the article Holography= holomorphy vision and a more precise view of partonic orbits or the chapter Holography= holomorphy vision: analogues of elliptic curves and partonic orbits .

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 M4 Kähler force have observable effects?

M⁴ Kähler potential should be felt also by covariantly constant right-handed neutrino so that right-handed neutrino would not completely decouple from gauge interactions. TGD predicts that both quarks and leptons, in particular right- and left-handed neutrinos have an infinite number of color partial waves with CP₂ mass scale. As found, there is a mechanism neutralizing color partial waves of leptons and giving rise to massless neutrinos, which become massive by p-adic thermodynamics. Right-handed covariantly constant neutrinos would already be color singlets and massless so that this mechanism would not be needed. There would however be coupling to the induced M⁴ gauge potential. Could this coupling relate to the poorly understood massivation of neutrinos involving the mixing of right-handed and left-handed neutrinos?

The following simple model makes it possible to estimate the size of the effect of M⁴ Kähler force for elementary fermions at space-time level. Induced Dirac equation is assumed.

1. Both nucleons and leptons create a classical induced M⁴ Kähler potential, which contributes to the U(1) part of the induced electroweak gauge potentials in the background space-time assignable to the nucleus.
2. The gauge forces are felt at the light-like fermion lines at 3-D light-like partonic orbits. A string world sheet connecting say electron and nucleon could mediate the interaction.
3. Consider 1-D light-like fermion line at the partonic orbit of a fermion. Idealize the fermion line as a light-like geodesic line in M⁴× S¹, where S¹⊂ CP₂ is a geodesic circle. 8-D masslessness implies p²- R²ω²=0 (see this), where ω is expected to be the order of the particle mass and characterizes the rotation velocity associated with S¹. A physically motivated guess is that ω is a geometric correlate for the Compton time of the fermion so that fermion can be said to have an internal clock.
4. Consider M4 and CP2 contributions to the Kähler potential. Denote by u the CP2 coordinate serving as a coordinate for the fermion line at the partonic orbit as the interface between Euclidean CP2 type region identifiable as a wormhole contact connecting two Minkowskian space-time sheets and Minkowskian region. The CP2 part of the induced Kähler potential is of order ACP2u ∼ 1/R, where R is CP2 radius. The M4 part of the induced Kähler potential is AM4k∂ mk/∂u ∼ ω ∼ m. For electrons, the ratio of the two contributions is ω R ∼ me/m(CP2) ∼ 10-17 and therefore extremely small. This guarantees that the induced M4 Kähler form has negligible effects.

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.

Calcium anomaly as evidence for a new boson with mass in the range 10 eV to 10 MeV

I learned about findings giving support for the view about a new interaction implying that the energies of electrons depend on the neutron number of the atom in a way, which is not explainable in the standard model (see this). A new interaction mediated by a scalar boson with mass in the range 10 eV-10 MeV is proposed as an explanation for the findings. There are many other anomalies, which a boson with a mass ∼ 17 MeV could explain.

The following gives the abstract of the article published in Phys Rev Letters.

Nonlinearities in King plots (KP) of isotope shifts (IS) can reveal the existence of beyond-standard-model (BSM) interactions that couple electrons and neutrons. However, it is crucial to distinguish higher-order standard model (SM) effects from BSM physics. We measure the IS of the transitions ³P₀→ ³P₁ in Ca¹⁴⁺ and ²S_1/2 → ²D_5/2 in Ca⁺ with sub-Hz precision as well as the nuclear mass ratios with relative uncertainties below 4× 10^-11 for the five stable, even isotopes of calcium (^{40,42,44,46,48}Ca).
Combined, these measurements yield a calcium KP nonlinearity with a significance of ∼ 10³σ. Precision calculations show that the nonlinearity cannot be fully accounted for by the expected largest higher-order SM effect, the second-order mass shift, and identify the little-studied nuclear polarization as the only remaining SM contribution that may be large enough to explain it. Despite the observed nonlinearity, we improve existing KP-based constraints on a hypothetical Yukawa interaction for most of the new boson masses between 10 eV/c² and 10⁷ eV/c².

My understanding of what has been done is as follows.

1. Nonlinear isotope shift (IS) in KP for Ca isotopes A=42,44,46,48 relative to the isotope A=40 observed. Note that or ³P₀→ ³P₁ in Ca¹⁴⁺ 14-fold electronic ionization so that the electronic configuration is [He]2s² 2p².
2. What is measured are the differences δ ν^A₅₇₀ and δ ν^A₇₂₉ of the frequencies (equivalently energies) of the initial and final electronic configuration for these two transitions as function of A ∈ {10,42,44,46,48}. From these shifts the differences δ ν^A,40₅₇₀=δ ν^A₅₇₀-δ ν⁴⁰₅₇₀ and δ ν^A,40₇₂₉ = δ ν^A₇₂₉- δ ν⁴⁰₇₂₉ of these shifts for δ ν^A,40₅₇₀=δ ν^A₅₇₀-δ ν⁴⁰₅₇₀ with A ∈{42,44,46,48} are deduced.
3. If the effects of the neutron number on the electron energies equals to that predicted by standard model, δ ν^A,40₇₂₉ should be a linear function of δ ν^A,40₅₇₀. In the graphical representation the linearity allows to replaced the shifts with δ ν^A,40₅₇₀ → δ ν^A,40₅₇₀ -452 [GHz amu]==X and δ ν^A,40₇₂₉ → δ ν^A,40₇₂₉- 2327 [GHz amu]==Y are performed. This gives the King plot representing Y as function of X.
4. Fig 1. of the article gives the shifts for Ca isotopes for A∈{42,44,46,48} and from the 4 boxes magnifying the graph for the isotope shifts for these values of A show a small non-linearity: the red ellipses are not located at the blue vertical lines. For A= 42,44,48 the red ellipse is shifted to the right but for A=46 it is shifted to the left.

A Yukava scalar with mass in range 10 eV to 10⁷ eV proposed as an explanation. I am not able to conclude whether the scalar property is essential or whether also pseudoscalar is possible. The coupling to the boson affects the binding energies of electrons so that they have additional dependence on the neutron number. If the King plot were linear, the difference would be proportional to the neutron number implying proportional to A-40. The slope of the curve would be 45 degrees. Note that from the table I the differences are in the range .1 meV to 1 meV about δ E/E ∼ 10^-4. One neutron pair corresponds to an energy difference of order .1 meV.

One can consider two options in the TGD framework.

1. The upper bound for the boson mass is about 10 MeV and this suggests 17 MeV pseudoscalar which could explain several earlier nuclear physics anomalies (see this and this) and for which I have proposed a TGD inspired model (see this). In particular, X boson explains Yb anomaly for which also non-linearity of the King plot was observed. This anomaly to the deformations of nuclei caused by adding neutrons.
2. In the TGD framework one can consider also a second option, which is M⁴ Kähler force as a new interaction. M⁴ Kähler potential contributes to electroweak U(1) force if total Kähler potential replaces CP₂ Kähler potential in classical U(1) gauge potential. Could M⁴ Kähler potential give a contribution of the required size to the neutron-electron interaction? I have discussed this contribution in (see this). A simple model shows that the effects are extremely small. This implies that the new interaction does not imply any obvious anomalies. At the level of the embedding space Dirac equation, the effects are dramatic. The basic implication is that colored states of fermions have mass of order CP₂ mass and only color singlets can be light. One implication is that the g-2 anomaly is real since the calculation using hadronic data as input rather than lattice QCD gives the anomaly (see this).

See the article X boson as evidence for nuclear string model or the chapter Nuclear String Hypothesis.

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 to avoid Babelian confusion in theoretical physics?

Avril Emil wondered in discussion group of The Finnish Society for Natural Philosophy, how it is possible to deduce explanations from so different premises (see this). The discussion was related to the deepening crisis of cosmology caused by the findings of James Webb space telescope and suggesting that the big cosmic narrative is entirely wrong: even the origin of the CMB is challenged by FWST. I glue below my response.

Principles are needed, a mathematician would talk about an axiomatic approach. Otherwise, the result is a confusion of languages at Babel.

1. If we demand that the description of gravity and also other interactions be geometrized and that the classical conservation laws hold true as a consequence of Noether's theorem, we end up to H=M⁴×CP₂ if we demand the symmetries of the standard model.
2. If we also demand a number-theoretic description complementary to the geometric one (the equivalent of Langlands duality), we end up with M⁸-H duality and classical number systems are an essential part of the theory. M⁸ corresponds to octonions. The dynamics in M⁸ are also fixed by the quaternionicity/associativity requirement. The symmetries of the standard model correspond to the number-theoretic symmetries of octonions.
3. If we demand a generalization of 2-D conformal symmetry to 4-dimensionality, we end up with holography= holomorphism vision. The dynamics of spacetime surfaces is unique everywhere except at singularities, regardless of the action principle, if it is general coordinate invariant and constructible using induced geometry. Spacetime surfaces are minimal surfaces (analogous to solutions of massless field equations) and the field equations reduce to purely algebraic local conditions. The theory is classically exactly solvable.
4. One can claim that the theory is uniquely determined simply because it exists mathematically. The requirement for the existence of a twistor gradient in the theory leads to H=M⁴×CP₂. Only these two 4-spaces in H have a twistor space with the Kähler structure needed to define the classical theory.

   The 4-dimensionality of spacetime surfaces follows in several ways: as an extension of conformal invariance from 2 to 4 dimensions and also from the requirement that, assuming free fermion fields in H, one obtains a vertex on the spacetime surface geometrically corresponding to the creation of a fermion pair. The requirement that a free theory gives interactions sounds impossible to implement, but a special feature of 4-D spacetimes is the exotic diff structures, which are standard diff structures with defects corresponding to vertices. The creation of a fermion pair intuitively corresponds to the turning of a fermion line back in time and the edge associated with this turning corresponds to the defect, the vertex.

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.

Can one understand the transparency of the early Universe without a thorough revolution in cosmology?

There is a highly interesting post by Ethan Siegel in Bigh-Think talking about the somewhat mysterious transparency of the Early Universe to radiation (see (see this). The views are especially interesting also from the point of view of TGD narrative about cosmology (see this and this).

If the primordial plasma is neutralized and forms atoms, the radiation from the very early Universe in the energy range of atoms would not reach us. The neutralization process would have meant the generation of cosmic microwave background (CMB) since the photons would have decoupled from the thermal equilibrium.

This raises a question: How does the radiation from the early Universe reach us? The findings of JWST have made the problem even worse than it was before JWST.

One can imagine several explanations.

1. Reionization took place by some mechanism. This is not a well-understood problem. The formation of stars and galaxies should have made this possible somehow. Ions did not absorb and propagation became possible.
2. A more radical explanation explaining how JWST was able to observed very early galaxies, considered by Ethan Siegel in Big-Think (see this), is that there was no dust consisting of neutral atoms so that no absorption occurred! But what about CMB? If there was no neutral matter, there should have been no CMB generated in its formation!

   Very interestingly, the recent findings of JWST suggest that the CMB might have an origin different from what has been assumed in the standard cosmology. JWST has identified very early large galaxies and stars, whose formation is not understood in the standard cosmology. They could have generated dust and radiation in thermal equilibrium with it. The radiation would have decoupled from the thermal equilibrium and given rise to the observed CMB.

   This option forces us to completely reconsider the cosmological narrative before this event. Was there any primordial plasma? Was there any formation of hadrons from quarks? Were nuclei produced by cosmic nucleosynthesis? Were they able to form a considerable amount of atoms? Was there any need for reionization? Could the narrative of the standard cosmology be completely wrong?

What is the TGD based narrative? The newest piece in this story is the observation that the origin of cosmic microwave background need not be what it is though to be, that is the decoupling of radiation from matter as ions formed neutral atoms (see this).

A very brief summary of the TGD view of cosmology (see this) is first in order.

1. The primordial phase would have been dominated by cosmic strings, which are 4-surfaces with 2-D M⁴ and CP₂ projections. This phase could have been in Hagedorn temperature of the order of CP₂ mass defining the mass scale of color partial waves of quarks and leptons.
2. Galaxies and stars would have been produced as cosmic strings collided, thickened and liberated matter giving rise to the ordinary matter. This process would have served as the TGD counterpart for inflation and would have lasted much longer than 10^-32 seconds (see this and this). Therefore it might be better to talk about the TGD counterpart of eternal inflation. Cosmic string tangles decaying to ordinary would correspond to the bubbles of the inflationary scenario.

This view allows us to consider two basic options explaining the transparency.

1. The formation of very early large galaxies and stars generated ions as solar wind. The stars would have produced ions as solar wind. Was this enough to preserve the charged plasma state and prevent neutralization leading to a loss of transparency? Did this give rise to charged plasma so that the radiation could propagate freely in this plasma?

   Note however that if there was no neutral matter (dust) present before this event, the Universe was transparent also before it.

2. The second option is that the propagation took place along a network of monopole flux tubes as dark photons. The network would have acted like a communication network making precisely targeted propagation without dissipative losses and without 1/r² weakening of the signal associated with 3-D propagation.

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