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.

Nothing new under the Sun: really?: comments on the flux tube video of Sabine Hossenfelder

Sabine Hossenfelder was ranting in the Youtube video What is "gravitic propulsion" and could the US government hide it? (see this). Sabine has an excellent skill of humour and she tries to get the facts right but I don't like her aggressive attitude.

At this time, one theme was various exotic crackpot theories such as antigravity lacking mathematical foundations and physical motivations apart from some effects, which need not correspond to a genuine antigravity. I share Sabine's non-enthusiastic attitude here. Neither can I believe that existing scientific understanding would be hidden by the government except when the hiding is to maintain a technological competitive advantage.

The third theme was "Nothing new under the Sun". Particle physicists think like this, have been thinking so for half a century, that is, the time during which theoretical particle physics has not produced anything genuinely new. Sabine, who usually is not very empathetic towards particle theorists, shares this belief. The justification is that if there were some new physics, it would have already been observed. The problem is that Sabine, as a good reductionist, believes that all new physics must emerge in particle physics.

A couple of counterexamples. In my youth, fractals and solitons were invented. Suddenly, they were seen everywhere. A century ago, theorists told lay people that classical physics allowed us to understand everything. Then atomic physics and quantum physics came along and everything changed. The basic lesson here is that we only see what we believe is possible to see.

The enormous perspective bias of particle physicists is born out of reductionism: they believe that particle physics is the fundamental level from which everything follows. For a while, they even believed that all physics emerges from the physics of awe inspiring tiny strings at the Planck scale, but this led to a catastrophe: the theory was unable to predict anything and string theory is now perceived as an embarrassing topic of conversation.

At least Sabine admits that solving the fundamental problem of quantum measurement theory requires new physics. Or not new actually. Sabine believes that the world is deterministic as it was believed to be before the quantum revolution century ago. Such a return to the past is radical but not very inspiring.

At this point I have nothing to lose and I can safely predict that TGD is the next revolution and in fact will continue where the previous revolution left off when general relativity and quantum theory solidified into dogmas. The great narrative will change dramatically without being in conflict with what we observe now with our recent instruments and armed with the reductionistic belief system.

The belief system of particle physicists, astrophysicists, and cosmologists will experience the same fate as the belief system of classical physics more than a hundred years ago. Fractality will replace reductionism and already this changes everything. Even the standard model eill experience a revolution in the color sector leading to revolutions in hadron physics, nuclear physics, and even the physics of the Sun. At the level of observed particle physics the changes will be small. Cosmology and astrophysics are already in the grip of a revolution. Also biologist's and neuroscientist's belief systems share the same fate as a TGD-based view of consciousness and life will inevitably replace them. This is because logically inconsistent belief systems cannot survive the fight for memetic survival.

See for instance the articles at About the structure of Dirac propagator in TGD, About Dirac equation in H=M⁴×CP₂ assuming Kähler structure for M⁴, and Holography= holomorphy vision and a more precise view of 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 inflation really explain the very early super massive blackholes?

I visited Räsänen's blog (see this) and found a posting related to inflation theory.

The posting told about Jacopo Fumagalli's talk at the cosmology seminar of the Department of Physics of the University of Helsinki. The topic of the talk was the controversy between inflationary theorists that has lasted for years. I have already previously clarified for myself the analogies between inflationary theory and TGD (see this, this, andthis) and I will try to clarify my thoughts again.

First, a short, slightly edited summary that Google gives of inflationary theory. The cosmic inflation, producing a huge bubble containing the observable universe, lasted for a cosmic time about 10^-32 seconds, which is about 10¹¹ Planck times about 10^-43 seconds. At the end of cosmic inflation, the "bubbles" that form are incredibly large, with the observable universe contained within a single bubble. The universe's size is estimated to have increased by a factor of 10⁵⁰ during inflation. This means a region the size of a proton expanded to a size of 10¹⁹ light-years. The huge expansion meant that all gradients disappeared and this explains why CMB temperature is constant in precision of 10^-5.

Here is a list of the basic assumptions.

1. Cosmic inflation is characterized by an extremely rapid, exponential expansion of the very early universe.
2. Inflation doesn't end everywhere at once. Instead, it ends in patches, or "bubbles," within the larger inflating space.
3. The size of these bubbles at the end of inflation is enormous. According to the CMS Experiment, the universe went from the size of a proton to a vast expanse of 10¹⁹ light-years. UCLA Astronomy notes that even with this expansion, the observable universe is still relatively small compared to the overall size of the bubble.
4. The observable universe, which is what we can see and study, is just a tiny fraction of a single bubble.
5. The theory of eternal inflation suggests that inflation continues forever throughout much of the universe, creating an infinite multiverse of these bubbles, each potentially with its own physical laws.

Within the framework of the inflationary theory, attempts have also been made to understand dark matter by identifying dark matter as primordial black holes (see this), whose upper mass limit is from empirical facts of the order of 10^-18 solar masses and corresponds to a Schwartzschildt radius of about 10^-15 meters, or the Compton wavelength of a proton. This idea does not conform with the idea that the fluctuations of the mass density are Gaussian and approach to zero with an exponential rate during inflation.

When JWST found evidence for supermassive black holes in the very early universe, it was a natural attempt to identify them as an outcome of inflation (see this). Now the blackhole masses can be on the order of the Milky Way mass, or about 1.5× 10¹² solar masses. The radius of the Schwartzchild would be of the order of 4.5× 10¹⁵ km, which is of the order of 10³ light-years (ly=9.46× 10¹² km).

Such a black hole would be created by a quantum fluctuation in the energy density of the inflaton field due to a curvature fluctuation. The spatial size scale of these curvature fluctuations would be about 10³³ times the size of the fluctuations for the primordial blackholes proposed to explain primordial blackholes.

But can we talk about quantum coherence and quantum fluctuations at this huge scale when even the theory of quantum gravitation is missing? It has been argued that fluctuations on a smaller scale destroy quantum coherence at much longer scales, which are truly enormous in relation to the size of primordial black holes (the size of a proton as the upper limit). Inflation theorists have argued about this for years, and according to Räsänen's posting, the view has now been reached that it does indeed work. The fact that these black hole-like objects seem to be real, certainly makes it easier to accept this view. The unpleasant alternative would be to abandon the entire inflation theory. In terms of career development this option is not attractive.

It is instructive to compare inflation theoretic narrative with the TGD view. The TGD view of cosmic evolution relies on the new view of space-time. Space-times are 4-D surfaces in H=M⁴× CP₂. Holography= holomorphy principle makes it possible to reduce the field equations to completely local algebraic equations (see this) and also the Dirac equation for fermions in H=M⁴× CP₂ can be solved exactly. If M⁴ is assumed to have a generalized K\"ahler structure, the field equations predict that colored fermions have mass of order of CP₂ mass, which is of order 10^-4 Planck masses. Also a mechanism, which allows the construction of massless color singlets, which get small mass by p-adic thermodynamics (see this), emerges.

The highly non-trivial prediction, in conflict with QCD picture, is that massless (and light) quarks and gluons are impossible. This means the model for the g-2 of muon must be based on data about hardons rather than lattice QCD so that the g-2 anomaly is actual (see this). TGD predicts the new physics which might explain the anomaly. It is clear that this picture challenges the views about cosmic evolution.

1. The starting point of also TGD based cosmology could have been the approximate constancy of the CMB. In inflationary cosmology the exponential expansion is believed to solve this problem.

   In TGD the solution is the possibility of quantum coherence in arbitrarily long scales. This follows the hierarchy of effective Planck constants predicted by the number-theoretic vision of physics complementary to the geometric vision. Exponential expansion is not needed in the TGD framework. The implications of this hierarchy are central also for the TGD view of consciousness and quantum biology.

2. Zero energy ontology (ZEO) (see this) makes it possible to solve the basic mystery of quantum measurement theory without interpreting. ZEO predicts that in the ordinary state function reduction the arrow of time changes. This could have dramatic implications also for the evolution of galaxies. Living forth and back in geometric time could have given rise to a very rapid galactic evolution and could explain stars and galaxies older than the Universe.
3. TGD view of space-time predicts that cosmic strings as 4-D surfaces with string world sheet as M⁴ projection and complex 2-surface as CP₂ projection are possible. The very early cosmology would be cosmic string dominated. Einsteinian space-time with 4-D M⁴ projection would have emerged rather early, maybe at the same time as inflation would have ended.

   The cosmic strings could explain how it is possible to see the objects in the very early Universe. Cosmic strings/flux tubes would form an analog of a communication network along which photons with large h_eff behaving like dark photons would propagate in a precisely targeted way and without dissipation.

4. The transition to radiation dominated cosmology would have been due to the instability of the 2-dimensional M⁴ projection and the collisions of cosmic strings would have led to the liberation of their dark energy as ordinary matter as the cosmic strings thickened to monopole flux tubes and formed tangles along long cosmic strings identifiable as galaxies. This does not require exponential increase of the thickness of the cosmic strings. The magnetic fields of monopole flux tubes are possible with currents and could explain the stability of magnetic fields in cosmic scales and also that of the Earth's magnetic field. Importantly, gravitational condensation of ordinary matter would not have created galaxies and stars. The process would have proceeded from long to short scales and eventually generated ordinary matter.
5. Eventually this process would have led to the formation of quasars, galaxies and blackhole and whitehole like objects with opposite arrow of time could be naturally associated with the galactic nuclei. These objects would tangles of monopole flux tubes filling the entire volume rather than singularities of the theory. This would have occurred much later. Cosmic strings precedessors of the galaxies would have been present already in the primordial cosmology.

   The recent finding that the origin of CMB might relate to the rapid formation of the very early large galaxies forces us to reconsider the standard narrative about cosmic evolution. I have discussed this from the TGD perspective in (see this and this). TGD also challenges the standard view about QCD, hadron physics, nuclear physics and the physics of the Sun (see this and this).

See the article About the TGD counterpart of the inflationary cosmology 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.

Strange correlation between the strength of the Earth's magnetic field and the atmospheric oxygen content

Sabine Hossenfelder (see this) talked about the recently discover strong correlation between the strength of the Earth's magnetic field and O₂ content the atmosphere (see this).

This is an extremely interesting finding from the TGD point of view. TGD is a theory of everything but unlike its competitors, it inspires a quantum theory of consciousness and of biology. The new view about magnetic fields differing from the Maxwellian view leads to the notion of field body/magnetic body accompanying any system, also the Earth. It predicts that the biosphere very probably behaves quantum coherently at the level of the magnetic body in the scale of Earth and even at very long scales.

In the TGD framework, space-time is identified as a 4-surface in H=M⁴× CP₂. This leads to a new view of classical, in particular electromagnetic fields differing in many respects from the Maxwellian view. One can assign a field body to a given physical system. Field bodies are carriers of phases of ordinary matter with non-standard value of effective Planck constant of h_eff, which can have very large values implying quantum coherence in even astrophysical scales. The field body is a key notion in the TGD based view of living matter.

The homology of CP₂ is non-trivial and this implies the existence of closed monopole flux tubes carrying monopole magnetic flux although no monopole charges are predicted. The monopole magnetic fields need no current as a source and are therefore stable unlike ordinary magnetic fields which disappear when the current generating them dissipates. This explains the stability of the Earth's magnetic field (see this) and also the existence of magnetic fields in cosmological scales. The monopole magnetic fields are ideal from the point of view of biology (see this, this, this and this).

It is known that the changes in the magnetic field strength and its orientation have had strong effects on biology and consciousness. The local weakening of the magnetic field strength and Schumann resonance have been assigned also with disorders of societies by Callahan (see this and this). TGD suggests a model for the reversal of the magnetic field (see this and this).

About 500 million years ago, the Cambrian Explosion occurred and meant the mysterious appearance of highly evolved multicellular organisms. Where did they emerge from? In the TGD based view of cosmology (this and this), the cosmic expansion takes place as rapid jerks for astrophysical objects, including planets and the Earth. This suggests that this kind of rapid increase of the radius of the Earth by factor 2 took place about 500 million years ago and led to the burst of highly evolved multicellular life from the underground oceans to the surface. Oceans were formed and the photosynthesizing multicellular life forms oxygenated the oceans and also the atmosphere. There is indeed evidence for life in underground oceasn able to perform photosynthesis and TGD leads to an explanation for how this is possible (see for instance this and this).

As the figure 1 of the article (see this) about the correlation between magnetic field strength and O₂ percent of the atmosphere shows, both the oxygen percent in atmosphere and the strength of the magnetic field characterized by virtual geometric axial dipole moment started to grow about 500 My ago and is maximum about 300 My ago. TGD view of Cambrian Explosion suggests that the strengthening of the magnetic field, perhaps by the emergence of monopole flux tubes, implied a rapid evolution of the oxygen based life forms in the oceans created by the rapid expansion and caused oxygenation of the atmosphere.

See the article Empirical support for the Expanding Earth hypothesis or the chapter Expanding Earth Hypothesis and Pre-Cambrian Earth.

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.

Have we misidentified the origin of CMB and what implications this might have?

Sabine Hossenfelder talked about a highly interesting recent theoretical finding related to the origin of the cosmic microwave background (CMB) (see this). The Youtube video tells about the article of Gjergo and Kroup (see this) raising the question that the so called early-type galaxies (ETGs) found by James Webb telescope, could give to CMB an additional contribution, which according to the most conservative estimate is 1.4 per cent and can even dominate of the ordinary contribution if present. This could mean a revolution in cosmology and is therefore extremely interesting from the TGD point of view.

Consider first some background.

1. Consider first the standard model for the origin of CMB. The standard cosmology assumes plasma phase. In the very early stages quarks and gluons were free. The nucleosynthesis took place and eventually the formation of atoms became possible as the temperature of plasma consisting mostly of hydrogen was low enough.

   Thermal radiation decoupled from thermal equilibrium and the universe became opaque. The radiation temperature started to decrease like 1/a, a is the scale factor of the Universe, which in TGD is identifiable as light-cone proper time for causal diamond (CD). The age of the Universe neutralization was about t∼ .379 My. Later a reheating occured and ionized the atoms and the Universe became transparent. This was due to the formation of stars which generated radiation and the solar wind.

   Some numbers are in order. The recent age of the universe is about t= 1.4× 10⁴ My. The temperature in the decoupling was 3000 K so that a₀/a(t)= (3/2.75)× 10³∼ 10³. t₀/t ∼ 1.4/.379 × 10⁴.

2. Very massive early-type galaxies (ETG) were studied theoretically by using the data provided by James Webb telescope. a₀/a(t(ETG))= 1+z, z was in the range. They produced dust and radiation in thermal equilibrium with it. When the age of the Universe was was roughly t(ETG)∼ 500 My (considerably shorter than t= 1.4× 10⁴ My) the radiation ecoupled from the thermal equilibrium and gave an additional contribution to CMB. The lower bound for the contribution is 1.4 per cent but it could be even of order one and could even dominate.

   LambdaCDM view of dark is assumed in the theoretical considerations of the article (see this) so one must be cautious with comparison with the TGD view. The vision is that rapid star formation generated dust and radiation, which was thermalized. Decoupling from matter occurred and the analog of CMB was generated.

3. This finding does not challenge the Big Bang but can challenge the narrative about how stars and galaxies emerged. This finding could in fact change the entire cosmology of the time before these very rapidly forming galaxies appeared.

   This together with the TGD view of cosmic evolution (see this), forces to challenge the narrative about the cosmic evolution before the nucleosynthesis and even after that the plasma, formed from hydrogen atoms and light nuclei need not have been present in considerable amounts. The assumption that the gravitational condensation of hydrogen and other atoms give rise to the formation of stars and galaxies, might be wrong.

   Was there any plasma phase? Was there any primordial nucleosynthesis? Was there any CMB in the standard sense? Was there any gravitational condensation of the ordinary matter to form stars?

TGD indeed suggests a completely different cosmology and astrophysics before the formation of these strange galaxies (see this, this, this, this, this, and this).

1. In the TGD framework, the decay of cosmic strings by forming tangles and thickening would produce ordinary particles as liberated energy giving rise to stars and galaxies. The long cosmic strings would thicken and produce ordinary matter in a way similar to the decay of the vacuum expectations of inflationary fields to ordinary matter. Galaxies and even stars need not form as ordinary matter undergoes gravitational condensation.

   This mechanism together with the zero energy ontology (ZEO) allowing time reversal in ordinary state function reductions, could explain the rapid formation of early-type galaxies. The decay of the cosmic strings could have produced ordinary matter and also stars and galaxies. An elegant explanation for the galactic dark matter and predictions for the flat velocity spectrum of distant stars around galaxies emerges. It is not clear whether the primordial plasma, formed from hydrogen atoms and light nuclei, has been present in considerable amounts.

2. Dirac equation for H=M⁴× CP₂, assuming that M⁴ has K\"ahler structure predicts, that colored states, in particular quarks and gluons cannot exist as light particles. Only hadrons and leptons are possible and also their heavier counterparts (see this).

   This distinguishes dramatically between the standard model and TGD. The infinite hierarchy of color partial waves of quarks and leptons gives rise to corresponding hierarchies of massless hadrons and leptons, which generate thermal mass squared by p-adic thermodynamics. There would be no "desert" predicted by GUTs. Quark gluon plasma has not been present in the early Universe. Instead, cosmic strings would have dominated and colored states would have been present only at temperatures was very near to Hagedorn temperature of order CP₂ mass assignable to cosmic strings, 4-D objects with 2-D string world sheet as M⁴ projection, which dominated the mass density. Einsteinian space-time with 4-D M⁴ projection did not yet exist and was generated in the transition to radiation dominated phase.

3. p-Adically scaled versions of hadron physics are predicted. They correspond to light colorless hadrons formed from fermion modes corresponding to different color partial waves (see this and this). This could completely revolutionize the nuclear physics of the Sun (see this).This could also revolutionize the physics of the early Universe, at least before the stabilization of atoms, because quarks and glums would not exist except at temperatures of order CP₂ mass scale, which is of order 10^-4 Planck masses. This could revolutionize cosmology even after that if the plasma, consisting of protons and light nuclei, is actually created as galaxies and stars were born as tangles of cosmic strings.
4. The decay of cosmic strings to ordinary matter by a step-wise p-adic cooling from Hagedorn temperature determined by CP₂ mass scale (see this and this). Last year, I wrote an article considering the possibility that the nuclear physics of the Sun could differ dramatically from the standard view. At the solar surface, the M₈₉ hadrons with a mass scale, which is 512 the mass scale of ordinary hadrons, associated with monopole flux tubes connecting Sun to the galactic nucleus would decay into ordinary hadrons and produce solar radiation and the solar wind. The interior of the Sun would be something completely different from what has been assumed, being analogous to the cell nucleus.

   This decay, occurring by p-adic cooling (see this), could produce a plasma consisting of hydrogen atoms and light atoms as galaxies and stars were formed. This plasma would be created much later than has been assumed and would not be primordial! Weinberg's classic "The first 3 minutes" would become a historical curiosity!

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.

Holography= holomorphy vision and a more precise view of partonic orbits

Partonic orbits are a central piece of the TGD view of elementary particles. In the sequel a more precise identification of these surfaces is considered.

1. The roles of fermionic and geometric degrees of freedom

It is useful to clarify some basic aspects of dynamics in the TGD Universe.

1. There are two kinds of degrees of freedom in TGD: geometric, i.e. degrees of freedom of the space-time surface, and fermionic. All elementary particles are made up of fermions and antifermions: bosons emerge. There are no bosonic primary quantum fields.
2. The basic result from the solution of the Dirac equation for H spinor fields, assuming that M⁴ has a non-trivial Kähler structure (see this), is that the mass scale of colored partial waves of fermions is given by CP₂ mass scale and there are no free massless gluons or quarks. However, assless color singlets for which the difference in the numbers of quarks and antiquarks is a multiple of three, are possible. This gives baryons and mesons.

   Here comes a crucial difference between QCD and TGD. In lattice QCD there would be no g-2 anomaly whereas the approach based on the information given by physical hadrons imply the anomaly. In TGD, the anomaly would be real and the new physics TGD predicts it. For example, copies of hadron physics at larger mass scales are predicted. Also the higher color partial waves give rise to new hadrons and also leptons. It will be exciting to see whether QCD or TGD is right.

3. The arguments of the n-point functions of the second quantized free fermion fields of H (scattering amplitudes) are points of the spacetime surface so that the dynamics of the spacetime surface affects the scattering amplitudes. Effectively, the spacetime surface defines the classical background in terms of the induced fields: induced metric, spinor connection, etc...

A particle can be seen in two ways:

1. Particle as a 3-surface and its Bohr orbit as a four-surface X⁴.
2. Particle as a fermion and its orbit, the fermion line is a light-like curve, maybe even a geodesic line in M⁴× CP₂.

The spacetime surface has an anatomy.

1. X⁴ has internal structure and the 3-D partonic orbits define light-like surfaces X³ at which the Minkoski signature of the surface becomes Euclidean so that the metric determinant vanishes.
2. A fermion line would be an intersection of 2-D string world sheet and a 3-D light-like partonic orbit. A string world sheet can naturally be obtained as the intersection of two spacetime surfaces if they have the same Hamilton-Jacobi structure, i.e. the same H coordinates u,w, ξ₁, ξ₂ and their conjugates (uv).

   One can ask whether the mutual interactions of particles as space-time surfaces occur only when they have the same Hamilton-Jacobi structure. If so the interactions can be described in terms of their intersections consisting of string world sheets and fermion lines at their boundaries. If so, a strong analogy with string models would emerge.

   Could also the self-interactions be described by considering infinitesimal deformation of the space-time surface preserving H-J structure and finding the string world sheets in this case?

3. The genus of the parton surface is an important topological quantum number. The genera g=0,1,2 corresponds to the observed fermion generations. g=2 allows a bound state for the handles of the sphere that are like particles. This is because g ≤ 2 allows global conformal symmetry. In the g\ge 2 topology, g handles are like particles in a multiparticle state, and the mass spectrum of the states is continuous, unlike for elementary particles.

   Also the homological charge of the partonic 2-surface, identifiable as Kähler magnetic charge of the space-time surface is an important topological quantum number.

2. How to find the 3-D light-like trajectories of parton surfaces

The challenge is to find partonic orbits as boundaries of Minkowskian and Euclidean space-time regions and it is enough to study the Minkowskian region of the space-time surface. In the Euclidean regions, identifiable as CP₂ type extremals, the (f₁,f₂)=(0,0) ansatz fails. Holography= holomorphy hypothesis is however satisfied and this is enough.

The trajectories of partonic 2-surfaces are singularities at, the Euclidean induced 4-geometry transforms into Minkowskian. The light-like dimension implies |det(g)|^1/2=0. The challenge is to derive the partonic orbits from this.

What conditions are used.

1. The space-time surface X⁴ is defined by the conditions (f₁,f₂)=(0,0), where f₁ and f₂ are analytic functions H= M⁴× CP₂→ C² depending only on the hypercomplex coordinate u (or v) with light-like coordinate curves and complex coordinates w, ξ₁ and ξ₂ of H but not on the coordinates v as hypercomplex conjugate of u (or u) and the conjugates w, ξ₁, ξ₂.

   As a special case, f_i are polynomials or rational functions. Additional restrictions can be posed on the coefficients of the polynomials. The conditions (f₁,f₂)=(0,0) have been studied in some cases (see this).

2. (det(g)^1/2=0 gives an additional condition and gives a 3-D light-like partonic orbit X³.
3. The rows of the induced metric g can be written as a matrix in the general case in the form

   (g_uu, g_uv , g_uw, g_uw)

   (g_vu, g_vv , g_vw, g_vw)

   (g_wu, g_wv , g_ww, g_ww)

   (g_wwu, g_wv , g_ww, g_ww)

   Holomorphy implying that the embedding space metric and induced metric are tensors of type (1,1) implies the vanishing of a large fraction of elements. This gives

   (0,g_uv , 0, g_uw)

   (g_vu,0 , g_vw, 0)

   (0,g_wv ,0, g_ww)

   (g_wu,0 , g_ww, 0)

   The symmetry g_αβ=g_αβ leaves only 4 independent matrix elements. g_uv, g_uw, g_vw, g_ww.

   The determinant det(g) is obtained by expanding the first row in the relation.

   det(g)= -g_uvcof_uv- g_uwcof_uw .

   For example, cof_uv is obtained by dropping the row and column passing through uv from the original matrix, resulting in a 3x3 matrix. cof_uv is its determinant. cof_uv is calculated with the same algorithm. This is all elementary matrix algebra.

   The vanishing condition for the determinant is as follows:

   det(g)= -g_uvcof_uv- g_uwcof_ww=0 .

   This gives one additional real condition defining the 3-D surface as the light-like trajectory of the partonic 2-surface.

3. det(g)=0 conditions as a generalization of Virasoro conditions

The determinant condition has an interpretation as a generalization of the Virasoro conditions of string models to the 4-D context.

1. If the situation were 2-dimensional instead of 4-D, the det(g)=0 condition would give a light-like curve and the light-likeness would give rise to the Virasoro conditions. This was actually one of the first observations as I discovered CP₂ extremals, whose M⁴ projection is a light-like curve for the Kähler action (see this). The conditions as such are not Virasoro conditions. It is the derivative of the conditions with respect to the curve parameter, which gives the Virasoro conditions. By taking Fourier transform one obtains the standard form of the Virasoro conditions.

   The Virasoro conditions can fail at discrete points and these singularities have an interpretation as vertices and also as points at which the generalized holomorphy fails. The poles and zeros of the ordinary analytic function are analogs for this.

2. For the 4-D generalization, the light-like curve is replaced by a 3-D light-like parton trajectory. The analogs of Virasoro conditions would be very natural also now because 2-D conformal invariance is generalized to 4-dimensional one. The Virasoro conditions have one integer, the conformal weight. Now the Fourier transform with respect to the coordinates of X⁴, say u and w gives conditions labelled by two integers having interpretation as conformal weights.

   This suggests that conditions can be seen as analogs of Virasoro conditions. Their generalization gives rise to analogs of the corresponding gauge conditions for the Kac-Moody algebra, just like in the string model. A lot of physics would be involved.

3. A new element brought by TGD is that algebras would have non-negative conformal weights meaning that an entire fractal hierarchy of isomorphic algebras is predicted such that subalgebra and its commutator with the entire algebra annihilate the physical states (see this). This makes possible a hierarchy of gauge symmetry breakings in which a subspace of the entire algebra transforms from a gauge algebra to a dynamical algebra.

4. How to solve the det(g)=0 condition?

1. We need to solve the induced metric. This means moving from algebraic geometry to differential geometry because the induced metric is of the form

   g_αβ = h_kl ∂_αh^k ∂_βh^l .

   Here α and β refer to u,v,w,w and k and l refer to u,v,w,w, ξ₁,ξ₂. The metric of H in these coordinates can be written easily. From this, we need to calculate the induced metric.

2. Analyticity drops some of the derivatives because u, w, ξ₁, ξ₂ is a function only of the coordinates u,w whereas v, w, ξ₁,ξ₂ is a function only of the coordinates v,w.

   If u,w can serve as coordinates of X⁴, we only obtain the trivial conditions u=u and w=w, but ξ₁=ξ₁(u,w) and ξ₂=ξ₂(u,w) require an analytical solution for f₁=f₂=0. Of course, we also have to calculate the partial derivatives of the conjugate variables, but they are obtained by conjugating the already calculated ones.

   If f_i are polynomials of degree n<5 with respect to w, analytic expressions for ξ_i(u,w) are possible and the analytic calculation of the partial derivatives can be considered. Otherwise, we have to use numerical methods. One could hope that a symbolic program for calculating partial derivatives could be found .

3. Numerical calculation of partial derivatives requires that the variables h^k are examined at nearby points u,w and the difference quotient is calculated. If the discretization is sufficiently dense, the partial derivatives can be estimated using neighboring points.
4. Then we just have to calculate the components of the induced metric and from these det(g) using the formula given above and find the points |det(g)|=0, i.e. the partonic orbit, by minimizing |det(g)|.
5. In this way, we get from each point of the discretized space-time surface X⁴ to a new point with a smaller value of |det(g)|. Is it necessary to choose a sufficiently large, 3-dimensional discrete subset of X⁴ and proceed in this way.

The calculation would boil down to a repetition of the following steps to get |det(g)|=0 in a given accuracy.

1. Calculate f₁=f₂=0 giving a 4-D surface X⁴.
2. Calculate the partial derivatives at the point of X⁴. If the discretization is dense enough, there is no need for a deformation.
3. Calculate the induced metric at each point.
4. Calculate |det(g)| for each point.
5. Go the neighboring point at which the decrease of |det(g)| is largest.

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 the Pollack effect make possible liquid metal analogs of semiconductors?

Could the Pollack effect allow us to build effective Ga semiconductors and even transistor-like elements? Electrons and holes are essential for semiconductors. In n (p) type regions electrons doping is by atoms for which the number of valence electrons is larger (smaller) than atoms or molecules considered. In p type regions, doping is by atoms for which the number of valence electrons is smaller. Ga(OH)₃, which is in gel phase, is an excellent candidate for the semiconductor of this kind.

Pollack effect creating O^-+ dark proton from OH creates negatively charged exclusion zones (EZs). The delocalization of the negative charges of O^- ions as conduction electrons could give rise to an analog of n doping. In the presence of electric fields , these electrons can be removed from the EZ.

The dropping of the dark protons back to ordinary protons giving rise to O⁺ ions would give rise to p-type doping. In the case of water this would create OH₃⁺ ions responsible for the pH of water. This might give rise to np type junction and one can even imagine analogs of npn and pnp type transistors. These transistors would be dynamical and the ordinary bits and OH-O^-+ p qubits would be very closely related.

See the article Could computers be living and move? or the chapter Quartz crystals as a life form and ordinary computers as an interface between quartz life and ordinary life?.

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 the new ANITA anomaly be due to dark cosmic rays (in TGD sense)?

ANITA, a balloon-borne radio detector flying over Antarctica was designed to detect neutrinos. Recently, it has however detected something totally unexpected: strange radio pulses rising from beneath the ice (see this). The strange radio waves detected by ANITA came from way below the ice, at angles so steep -about 30 degrees - that they should have traveled through thousands of kilometers of solid rock. Standard physics does not allow this. Pierre Auger Collaboration has carried out a search for the counterparts of events similar to those detected fy ANITA (see this).

The first particle physics based guess would be that the radio wave pulses originated from a collision of ultrahigh energy neutrinos propagating through the Earth. The neutrino would have interacted with the condensed matter creating relativistic particles, which give rise coherent Cerenkov radiation (see this) at radio wave frequencies. A backwards directed cone at which the emission is maximal would be created. Sonic boom occurring as an object moves with a velocity larger than the sound velocity of the medium is a good analogy.

The Cerenkov radiation is created in condensed matter at energies, which correspond to the frequencies associated with core electronic transitions in condensed matter since the refractive index n is smaller than 1 below these frequencies so that the phase velocity v_ph= c/n is smaller than c and therefore below the velocity of the particle. These frequencies correspond to radio frequencies so that the primary signals need not be at radio frequencies.

The interpretation of the events in terms of UHE neutrinos fails. The distance travelled by the neutrino inside the Earth should be 6000-7000 km. The interpretation in terms of ultra heavy neutrinos with energies in the range of .2 EeV (.2 × 10¹⁸ eV) requires that the neutrino should have travelled 10-12 interaction lengths so that the probability of the events creating the shower by the resulting tau leptons is quite too small. New physics seems to be involved. Particle physicists would propose new extremely weakly interacting particles, perhaps dark matter particles decaying to ordinary particles.

TGD (see for instance this and this) predicts the existence of a hierarchy of phases of ordinary matter with non-standard value of Planck constant h_eff, which can be very large so that these phases are quantum coherent in long length scales. These phases behave like dark matter and would reside at the field/magnetic bodies, which are the TGD counterpart for classical fields.

These new phases need not have anything to do with the galactic dark matter in the TGD framework: galactic dark matter would be analogous to dark energy and correspond to magnetic and volume energy associated with what I call cosmic strings (see this). The observed disappearance of baryonic matter during the cosmic evolution could correspond to a gradual transformation of ordinary protons to dark protons at the field bodies. The h_eff>h phases, in particular dark protons and dark photons, are the key players in the TGD inspired quantum biology (see this, this and this).

These (effectively) dark particles could propagate along the field (magnetic) body of the Earth and would have a scaled up interaction length proportional to h_eff/h>1. Their transformation to ordinary particles with h_eff=h would generate the shower. Also the transformation of dark photons to ordinary photons could create pairs of charged particles and lead to a generation of showers.

The identification of dark particles as dark variants of cosmic rays could also explain the unexpected finding of James Webb telescope of very distant galaxies (see this). In standard cosmology, these galaxies should not be visible. Could the dark radiation arrive along monopole flux tubes connecting stars to the galactic center or even galactic blackhole?

This explanation is of course only the first guess and a lot of work is needed to check whether it works at a quantitative level.

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.

g-2 two anomaly of muon's magnetic moment in the TGD framework

g-2 anomaly for muons magnetic moment is a possible indication of new physics. There are two approaches to the estimation of the g-2 in the existing physics.

1. The first one is based on the experimental input from hadron physics and the second one is based on QCD lattice calculations and relies on quarks and gluons (see this. The QCD prediction conforms with the most recent experimental result (2025).
2. The calculation using empirical data from hadronic vacuum polarization, which predicts that the anomalous magnetic moment of muon is larger than the standard model prediction by factor of order 10^-9. TGD supports this approach.

The TGD view of hadrons differs from the QCD view since the TGD view of color is very different. The basic predictions are as follows and follow from Dirac equation for free fermions in H=M⁴×CP₂. The two H-chiralities correspond to quarks and leptons and the different couplings to CP₂ Kähler predict correctly the charge spectrum and electroweak couplings.

1. The Dirac equation in H=M⁴×CP₂ has two variants. First variant assumes just the usual M⁴ geometry without Kähler form whereas the second option assumes that M⁴ has self-dual Kähler form strongly suggested by twistorialization. 8-D masslessness predicts that the mass squared spectra (eigenvalues of the Dirac operator squared) for M⁴ and CP₂ must be same. Mass squared contains scalar d'Alembertian contribution depending on the color partial wave and spin term which does not depend on color partial wave. For properly chosen unit of mass squared, both the d'Alembertian - and spin contribution modulo 3 equals to 1 for quarks and 0 for leptons. It is possible to satisfy M⁴ masslessness condition.
2. Without M⁴ Kähler form 8-D masslessness this gives no additional conditions and one obtains infinite number of color partial waves with mass scale given by CP₂ mass of about 10^-4 Planck masses except for right-handed neutrino which is massless.
3. If Kähler form is assumed, the mass squared spectra for leptons having H chirality +1 as product of M⁴ and CP₂ chiralities is still integer valued for both M⁴ and CP₂ and it is possible to satisfy 8-D masslessness since leptons couple to 3-multiple of both Kähler form of CP₂ and M⁴.
4. The proposed mechanism to produce massless states has been that there must be negative contributions to mass squared identifiable as conformal weight which can be used to reduce the mass squared to zero. p-Adic thermodynamics would give the light masses as thermodynamic mass squared.

How to obtain massless states in M⁴ sense and what theses massless states are? For colored spinor modes they are massless in 8-D sense but massless states in M⁴ sense are required. Several proposals can be considered.

1. The proposal is that the generalized superconformal analogs of Kac-Moody algebras and super symplectic algebras should be used to construct states from the ground states assignable to the modes of the Dirac equation for which states are massless in 8-D sense and have CP₂ mass scale if the mode is colored. A possible exception is covariantly constant right-handed neutrino, which might be tachyonic. Assume that at the fundamental level, the mass squared identifiable as a conformal weight is additive for states of several fundamental fermions.

   For super-conformal generators mass squared correspond to a conformal weight and their action on the fermionic ground states generates a non-negative integer valued mass squared spectrum and mass squared corresponds to a conformal weight with CP₂ mass scale.

   For the 4-D generalization of superconformal algebra hypercomplex and complex degrees of freedom give rise to corresponding conformal weights as longitudinal and transversal conformal weights and the total conformal weight is the difference of these two. This difference could be also negative.

2. Massless Dirac equation requires 8-D masslessness for the fundamental fermions defining the ground states of generalized super-conformal representations. Could it be possible to have negative integer values of M⁴ mass squared for covariantly constant right-handed neutrino. If so, these states are off mass shell states in 8-D sense. The addition of a tachyonic right-handed covariantly constant neutrinos is analogous to a supersymmetry. Could these tachyonic contributions to the positive mass squared coming from the superconformal degrees of freedom make possible M⁴ masslessness? Or could also two superconformal contributions sum up to negative contribution. Also this allow to build states with vanishing M⁴ mass squared. If the addition of neutrino-pairs correspond to the action of a tachyonic super-conformal generator reducing the mass squared, these intuitive views would be equivalent.
3. There is also a second way to see the problem. M⁸-H duality (see this and this) predicts that M⁴ ⊂ H corresponds to some quaternionic normal space M⁴ of a four-surface Y⁴ ⊂ M⁸ with Euclidian signature of number theoretically induced metric. Fermions correspond to discrete points of Y⁴ and the deformation of Y⁴ rotate the quaternionic normal space M⁴ locally so that 8-D massless states are massless in M⁴ sense. In other words, the 8-momentum is in the direction of the normal space. 8-D masslessness corresponds to M⁴ masslessness. The coordinate system of M⁸ could be regarded as analogous to a system in which the transverse part of light-like momentum is vanishing.
4. What does this kind of deformation of Y⁴ mean? Could it correspond to a local G₂ automorphism respecting quaternionicity. This automorphism modifies color representations. At the level this would suggest that the color representations of leptons and quarks combinbe to irreducible representations of G₂ with different values of M⁴ mass squared and that one can obtain also vanishing mass squared value. One can however argue that local G₂ transformation can have no physical effect.

   However, TGD predicts that conformal algebras have non-negative conformal weights and define a hierarchy of isomorphic sub-algebras with conformal weights coming as integer multiples of the weights of the full algebra. The gauge action of the sub-space of A spanned by generators with conformal weights h≤ n would transform to dynamical symmetries and only the generators A_nk and their commutators with A would annihilate the physical states. Could these local G₂ deformations transform in this way to dynamical symmetries. This transmutation from gauge - to dynamical symmetries might correspond physically to the addition of pairs of tachyonic right handed neutrinos and left handed neutrinos? This would also give electroweak screening and the reduction of color so that massless color singlets for leptons are obtained.

To sum up, the basic prediction following from mere Dirac equations in H with M⁴ Kähler form is that baryons and mesons rather than quarks and gluons are the basic dynamical units at low energies and colored fundamental fermions appear as dynamical units only in the CP₂ mass scales. This has a direct relevance for the understanding of muon's anomalous g-2 anomaly. This means that the g-2 must be calculated by using baryons as basic units and therefore hadronic data. p-Adic length scale hypothesis and also the infinite number of color partial waves predicts a hierarchy of scaled up hadron physics and electroweak physics. If this picture is correct, the g-2 anomaly can be seen as a support for new physics. The scaled up hadron physics and possible scaled variants of weak bosons could give rise to the g-2 anomaly but TGD does not have the machinery to estimate it precisely enough. In any case, the situation is extremely interesting from the TGD point of view.

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 and the generalized holomorphic solutions of this equation are massless in the sense that the square of the modified Dirac operator annihilates them. The conjugates of the holomorphic gamma matrices annihilate these modes and implies that the spin term involving the induced K\"ahler form vanishes and does not give rise to mass squared term.
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) 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 work of Lee Cronin et al related to iCHELLs

In the earlier post "Could Gallium make possible liquid metal life" (see this) I discussed the recent discovery of Chinese scientists and mentioned also the earlier work of Lee Cronin's group related to the possibility of metal life (see this or this). Here is the abstract of an article published in 2010 (see this:

"Self-assembly has proven a powerful means of preparing structurally intricate nanomaterials, but the mechanism is often masked by the common one-pot mixing procedure. We employed a flow system to study the steps underlying assembly of a previously characterized molybdenum oxide wheel 3.6 nanometers in diameter. We observed crystallization of an intermediate structure in which a central Mo36 cluster appears to template the assembly of the surrounding Mo150 wheel. The transient nature of the template is demonstrated by its ejection after the wheel is reduced to its final electronic state. The template’s role in the self-assembly mechanism is further confirmed by the deliberate addition of the template to the reaction mixture, which greatly accelerates the assembly time of the Mo150 wheel and increases the yield."

The following short abstract (see this) summarizes the work the second article of Cronin et al (see this). Unfortunately, the article is behind the paywall.

"Interfacial membrane formation by cation exchange of polyoxometalates produces modular inorganic chemical cells with tunable morphology, properties, and composition (see picture). These inorganic chemical cells (iCHELLs), which show redox activity, chirality, as well as selective permeability towards small molecules, can be nested within one another, potentially allowing stepwise reactions to occur in sequence within the cell."

To understand the work of it is good to list some basic concepts.

1. Transition metals (see this, which are in periods 4,...,7 of the periodic table, are used. Molybdenum (Mo) is the one used in the first work.
2. Metallates (see this are compounds involving metal bound to several ions, which are negatively charged oxygen ions so that one talks of polyoxometalates. Examples of oxometalates are MnO₄^-,CrO₄^2-, VO₃^- or VO₄^3-, WO₄^2-. Also thio-,seleno-, telluro,- cyano-,... etc metallates are possible. Oxometallates have oxyanions (see this) as building blocks. Polyoxometalates (see this) consisting of several oxyanyons for which the general formula is A_xO^z-_y . Their protonation produces oxyacid HA_xO^z_y.

   An interesting question, inspired by the notion of topological OH-O^- + dark proton qubit is whether this transition and its reverse can also have variants in which a proton of the oxyacid is transformed to a dark proton at the field body or vice versa.

3. Phosphates PO₄^3-, playing a key role in biology, are analogs of oxometallate. P is not a metal but can have besides the naively expected oxidation state -3 (3 missing valence electrons) also oxidation states +3 and +5 so that it behaves like a metal. Transition metals have typically oxidation state +3.

Cronin et al introduce the notion of iCHELL as an analog of cell membrane.

1. iCHELL is formed in aqueous environment in presence of two kinds of salts. The first salt is formed from (oxyanions), which are large negative ions of transition metals such as tungsten W, usually belonging to group 6 and light positively charged ions such as H⁺ and Na⁺, which both behave like metal in this situation.

   The second kind of salt is formed from large positively charged organic ions and light negatively charged ions such as Cl^-. The organic ion could be phosphorus, which can behave like a metal and become positively charged.

2. When the solutions of these salts are mixed, self-organization takes place and the salts exchange parts so that large metal oxides pair with the large organic ions. This new salt is insoluble in water: it precipitates as a shell, iCHELL, around the injected solution. For instance, salt formed from a large negatively charged oxyanion and large positively charged organic ion and light ions Na⁺ Cl^- can emerge. iCHELLs have a metal oxide backbone. An analog of cell membrane isolating its interior from the exterior is in question. Membrane potential characterizes it.

The experience with ordinary biology raises questions.

1. Could one imagine cell organelles: iCHELLs within iCHELLs?
2. Is a selective transfer of chemicals through iCHELLs possible: this would allow a control of chemial reactions. It is indeed possible to generate holes in membrane acting as ion channels. There are also some indications that proton pump transferring protons through the membrane is possible.
3. What about photosynthesis: is the splitting of water into hydrogen ions, electrons, and oxygen, the first step of photosynthesis, possible? Light-sensitive ties linked to metal oxide molecules as analogs of photoreceptors.
4. What about DNA and genetic code?
5. Evolution and pH dependent survival of fittest? TGD suggets that pH coulda actually correspond to the density of dark protons.
6. Is inorganic metallic life based on the same principles as the ordinary life possible?

Could the TGD based quantum model of living systems relying on water serve as a guideline for speculations?

1. Water is involved also now and could have an important role. The basic form of Pollack effect occurs in the presence of a gel phase negatively charged regions of water (exclusion zones (EZs) able to remove impurities inside them). Oxyanyons can be transformed to oxyacids by the reversal of the Pollack effect (see this)/pollackwater,pollackphoto,photosynth}.
2. The system can be regarded as cold plasma and cold plasmas are in a key role in TGD view of the role of the TGD counterparts of classical electric, magnetic, and gravitational fields in quantum biology (see this and this). The generalization of the Pollack effect in which the binding energy liberated in the formation of organic or other molecules leads to self-organization creating new more complex molecules by driving protons to dark protons at the field body of the system. Could this kind of mechanism explain the formation of iCHELLs?
3. Could OH-O^- + dark p give rise to a topological qubit (see this)? Could the energy difference between these two states of qubits correspond to a voltage and could external voltage pulses modify this voltage so that Pollack effect or its reversal become possible and allow the flip the qubit?

   Could the oxyanion side of the membrane give rise to 2-D structure consisting of bits and associated qubits?

4. Can one imagine a counterpart for DNA and genetic code? TGD suggests that genetic code has a universal realization in terms of a completely unique tessellation of hyperbolic 3-space (mass shell or cosmic time constant hyperboloid of CD), which involves 3 platonic solids instead of ne (tetrahedron, octahedron, and icosahedron having triangular faces)(see this).

   This tessellation can induce besides 1-D realizations also 2-D and even 3-D realizations also at the level of cell membrane as a 2-D realization. Could the OH-O^-+p qubits assignable to the oxyanyon backbone provide a dynamical 2-D realization of the genetic code in the same same way as OH-O^-+p qubits they might do in the case of ordinary DNA and perhaps also ordinary cell membrane.

5. What is the role of positively charged organic ions? It is needed to create the analog of membrane potential. Could it also play a role similar to that of gel phase in the Pollack effect? Cells and also DNA are negatively charged. If negatively charged ions are in the interior of the membrane, one might say that this is the case now. On the other hand, DNA is negatively charged at the outer surface (phosphate ions). Perhaps, a more plausible option is that the water generates negatively charged EZs in the Pollack effect creating the dark protons at the field body.
6. Could the TGD based quantum model of neuronal and cell membrane (see this) as a generalized Josephson junction with dark protons and ions forming Cooperpairs, serve as a guideline? In this model, proton pump involves Pollack effect and its reversal. The communications of the cell membrane to the magnetic body of the system would occur by Josephson radiation, whose frequency is proportional to the harmonic of the membrane potential (f= eV/h_eff). The huge value of the effectively Planck constant h_eff makes possible very low frequencies, such as EEG frequencies. The membrane potential and therefore also the Josephson frequency is modulated by the environment. Josephson radiation induces cyclotron transitions at the field body when the Josephson frequency equals the cyclotron frequency and analogs of nerve pulse sequences are generated giving possibly a response to the information sent to the field body.

See the article Can living computers move? or the chapter Quartz crystals as a life form and ordinary computers as an interface between quartz life and ordinary life?.

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.