Zero energy ontology and holography make possible memories by coding the quantum jump as a conscious event to the final state of the quantum jump

We have memories about the conscious experiences of the past. How are these memories formed? Zero energy ontology (ZEO) (see this) and this) suggests a rather concrete model for the representations of the memories in terms of the geometry of the space-time surface.

Consider first a brief summary of ZEO.

1. The basic notions of ZEO are causal diamond (CD), zero energy state, and state function reduction (SFR). There are two kinds of SFRs: "small" SFRs (SSFRs) and "big" SFRs (BSFRs).
2. A sequence of SSFRs is the TGD counterpart for a sequence of repeated measurements of the same observables: in wave mechanics they leave the state unaffected (Zeno effect). Already in quantum optics, one must loosen this assumption and one speaks of weak measurements. In the TGD framework, SSFRs give rise to a flow of consciousness, self.
3. BSFR is the counterpart of the ordinary SFR. In the BSFR the arrow of the geometric time changes and BSFR means the death of self and to a reincarnation with an opposite arrow of geometric time. Death and birth as reincarnation with an opposite arrow of time are universal notions in the TGD Universe.

Consider now this view in more detail.

1. Causal diamond CD=cd× CP₂ (see this) is the intersection of future and past directed light-cones of M⁴. In the simplest picture, cero energy states are pairs of 3-D many-fermion states at the opposite light-like boundaries of the CD.
2. Zero energy states are superpositions of space-time surfaces connecting the boundaries of CD. These space-time surfaces obey holography, which is almost deterministic. Holography = holomorphy principle allows their explicit construction as minimal surfaces and they are analogous to Bohr orbits when one interprets 3-surface as a generalization of a point-like particle. Already 2-D minimal surfaces fail to be completely deterministic (a given frame can span several minimal surfaces). This non-determinism forces ZEO: in absence of it one could have ordinary ontology with 3-D objects as basic geometric entities.

   The failure of complete determinism makes 4-dimensional Bohr orbits dynamical objects by giving them additional discrete degrees of freedom. They are absolutely essential for the understanding of memory and one can speak of a 4-dimensional brain.

3. The 3-D many-fermion states and the restriction of the wave function in WCW to a wave function to the space-of 3-surfaces as the ends of Bohr orbits at the passive boundary of CD are unaffected by the sequence of SSFRs. This is the counterpart for the Zeno effect. This requires that a given SSFR must correspond to a measurement of observables commuting with the observables which define the state basis at the passive boundary.

   The states at the opposite, active, boundary of CD are however affected in SSFRs and this gives rise to self and flow of consciousness. Also the size of CD increases in a statistical sense. The sequence of SSFRs gives rise to subjective time correlating with the increase of geometric time identifiable as the temporal distance between the tips of the CD. The arrow of time depends on which boundary of CD is passive and the time increases in the direction of the active boundary.

4. Ordinary SFRs correspond in TGD to BSFRs. Both BSFRs and SSFRs are possible in arbitrarily long scales since the h_eff hierarchy makes possible quantum coherence in arbitrary long scales.

   The new element is that the arrow of geometric time changes in BSFR since the roles of the active and passive boundaries of CD change. BSFR occurs when the set of observables measured at the active boundary no longer commutes with the set of observables associated with the passive boundary.

   The density matrix of the 3-D system characterizing the interaction of the 3-surface at the active boundary with its complement is a fundamental observable and if it ceases to commute with the observables at the active boundary, BSFR must take place.

Consider now what memory and memory recall could mean in this framework.

1. The view has been that active memory recall requires what might be regarded as communications with the geometric past. This requires sending a signal to the geometric past propagating in the non-standard time direction and absorbed by a system representing the memory (part of the brain or of its magnetic/field body). In the ZEO this is possible since BSFRs change the arrow of the geometric time.
2. The signal must be received by a system of geometric past representing the memory. This requires that 4-D space-time surfaces are not completely deterministic: Bohr orbits as 4-D minimal surfaces must have analogs of frames spanning the 2-D soap film, at which determinism fails. The seats of memories correspond to the seats of non-determinism as singularities of the space-time surface as a minimal surface.

3. How are the memories coded geometrically? This can be understood by asking what happens in SSFR. What happens is that from a set of 3-D final states at the active boundary some state is selected. This means a localization in the "world of classical worlds" (WCW) as the space of Bohr orbits. The zero energy state is localized to the outcome of quantum measurement. In ZEO the outcome therefore also represents the quantum transition to the final state! This is not possible in the standard ontology.

   The findings of Minev et al (see this and this) that in quantum optics quantum jumps correspond too smooth classical time evolutions leading from the initial state to the final state provide a direct support for this picture.

   ZEO therefore gives a geometric representation of a subjective experience associated with the SSFR. One obtains conscious information of this representation either by passive or active memory recall by waking up the locus of non-determinism assignable to the original conscious event. The slight failure of determinism for BSFRS is necessary for this. The sequence of SSFRs is coded to a sequence of geometric representations of memories about conscious events.

   This is how the Universe gradually develops representations of its earlier quantum jumps to its own state. Since the algebraic complexity of the Universe can only increase in a statistical sense the quantum hopping of the Universe in the quantum Platonic defined by the spinor fields of WCW implies evolution.

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

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

About the generalization of the holography = holomorphy ansatz to general analytic functions

The general ansatz works also for analytic functions with poles since (f₁=0,f₂=0) implies that the poles do not belong to the space-time surface. What is required is that the roots are not essential singularities. For rational functions R_i=P_i/Q_i the vanishing conditions reduce to those for the polynomials P_i.

The generalization Rieman zeta to polyzeta S_n(s₁,...,s_n) is s function of n complex variables (see this) and satisfies identities analogous to those satisfied by Riemann zeta. This generalization is extremely interesting from the point of view of physics of chaotic and quantum critical systems. Polyzeta S₄ with four complex arguments would define as its roots a 6-D analog of the twistor space of the space-time surface expected to have an infinite number of 6-D roots having interpretation as a generalization of zeros of Riemann zeta.

One could have f₁=S₄ so that its roots would correspond to 6-D zeros of polyzeta S₄(s₁,...,s₄) defining the counterparts of twistor surfaces! f₂=0 could define a map from the M⁴ twistor sphere S²₁ to CP₂ twistor sphere S²₂ characterized by a winding number or vice versa.

A further extremely nice feature is that the space-time surfaces form a number field in the sense that one can sum, multiply and divide the members of f_i and g_i of (f₁,f₂) and (g₁,g₂) elementwise. Also functional composition is possible. One could say that the space-time surface is a number. One can also consider polynomials and polynomials with prime order behave like multiplicative primes. It is also possible to identify prime polynomials with respect to functional composition (see this).

See the article TGD as it is towards end of 2024: part I 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.

Are supernovae induced by the transformation of M89 nuclei at the stellar surface to ordinary nuclei?

Supernovae as explosions of M₈₉ magnetic bubbles?

Could the explosions of the M₈₉ magnetic bubbles proposed to rise to the planets induce supernovae? The following vision suggests itself.

1. The flux tubes as M₈₉ super-nuclei split to ordinary M₁₀₇ nuclei and produce ordinary nuclear matter and liberate energy. This transition would give an additional contribution to the nuclear matter outside stars compensating for the missing contribution due to the missing ordinary nuclear matter inside stars.
2. The decay of giant M₈₉ nuclei defined by the monopole flux tubes would also create nuclei heavier than Fe, which are not produced in the stellar cores.
3. The pressure pulse created in this way leads to the formation of supernovae and blackhole-like objects? Various giant stars would be the outcome of these kinds of explosions of the M₈₉ surface layer?

One can check whether this hypothesis might make sense in the case of supernovae. I attach here a piece of text from the Wikipedia article about supernovae (see this) almost as such.

1. A supernova occurs during the last evolutionary stages of a massive star, or when a white dwarf is triggered into runaway nuclear fusion. The original object, progenitor, either collapses to a neutron star or black hole, or is completely destroyed to form a diffuse nebula. The peak optical luminosity of a supernova can be comparable to that of an entire galaxy before fading over several weeks or months.
2. Theoretical studies indicate that most supernovae are triggered by one of two basic mechanisms: the sudden re-ignition of nuclear fusion in a white dwarf, or the sudden gravitational collapse of a massive star's core.
3. In the re-ignition of a white dwarf, the object's temperature is raised enough to trigger runaway nuclear fusion, completely disrupting the star. Possible causes are an accumulation of material from a binary companion through accretion, or by a stellar merger.
4. In the case of a massive star's sudden implosion, the core of a massive star will undergo sudden collapse once it is unable to produce sufficient energy from fusion to counteract the star's own gravity, which must happen once the star begins fusing iron, but may happen during an earlier stage of metal fusion.
5. Supernovae can expel several solar masses of material at speeds up to several percent of the speed of light. This drives an expanding shock wave into the surrounding interstellar medium, sweeping up an expanding shell of gas and dust observed as a supernova remnant. Supernovae are a major source of elements in the interstellar medium from oxygen to rubidium. The expanding shock waves of supernovae can trigger the formation of new stars. Supernovae are a major source of cosmic rays. They might also produce gravitational waves.

These facts suggest that both in the case of white dwarfs and massive stars, the transformation of M₈₉ nuclei to ordinary nuclei triggers the supernova by creating a powerful pressure pulse towards the core of the star.

In the case of a supernova, the mass thrown out is measured using solar mass M_Sun as a unit. For the explosions producing planets, the mass M_E of the Earth is the natural mass unit. Can one understand this?

1. In the case of the Sun The magnetic bubble consists of M₈₉ monopole flux tubes forming a mass of about .005M_Sun. The baryons produced in the transition make mass of about 3ME at most and would compensate for the missing nuclear mass inside the star. A good guess is that the model for the solar M₈₉ bubble generalizes as such so that the fraction of M₈₉ mass scales like (R_star/R_Sun)².
2. For blue giants (see this ), the masses are in the range 10 -300 M_Sun and the radii vary in the range 10 -100 R_E as the table of the Wikipedia article shows. The amount of ordinary baryons produced would be in the range 10²-10⁴M_E at most and considerably smaller than M_Sun∼ 10⁶M_E.
3. In accordance with the expectations, the explosion should also throw out a considerable amount of ordinary nuclear matter. The huge inward directed pressure pulse produced by the transformation of the M₈₉ layer to M₁₀₇ nuclear matter would produce as a reaction a strong inward pulse and this in turn would induce an outward pulse throwing the ordinary nuclear matter out.
4. In the case of white dwarf the inward directed pressure pulse could heat the core and re-ignite a runaway nuclear fusion inducing a total disruption of the white dwarf. In the case of a massive star this could induce a gravitational collapse of the core leading to a blackhole-like object or a neutron star.

To sum up, the TGD based model would solve the problem due to the missing nuclear mass and provide a missing link to the model of supernova. The decay of the giant M₈₉ nuclei to ordinary nuclei would also explain the origin of the nuclei heavier than Fe.

See the article Some solar mysteries or the chapter with the same title.

A mechanism of photosynthesis which does not involve biomolecules

Standard biology teaches us that photosynthesis is needed to produce oxygen, which is the basic prerequisite of life. Besides complex biological apparatus this requires photons, which provide the needed energy. At the bottom of the ocean there is very dark and this might form a bottleneck for the evolution of life. Now it has been found that at the bottom of ocean mineral deposits known as polymetallic nodules can generate oxygen in absence of photons (see this). They contain combinations of cobalt, copper, lithium, and manganese and the size of the nodule can be that of a human hand. The initiation of electrolysis splitting water to hydrogen and oxygen needs only 1.5 eV voltage in seawater. This means that one has a battery. It was found that the nodules involve voltage as high as .95 eV.

The nodules could make possible electrolysis and splitting of water. They could make it possible to overcome the hen and egg problem due the fact that a complex biomolecular apparatus is needed for photosynthesis but this apparatus cannot exist in primordial biology.

In the TGD Universe, multicellular life would have evolved in underground oceans and bursted to the surface in the Cambrian explosion for about 450 million years ago (see for instance this), which in the TGD Universe was caused by the expansion of the Earth radius by a factor 2 in a rather short period of time. TGD indeed predicts that the cosmic expansion of astrophysical objects occurs as short bursts. This explains why the astrophysical objects comove in expansion but do not expand themselves .

A heavy objection against this vision is that there are no photons in underground oceans so that photosynthesis is not possible. I have proposed that the light arriving as dark photons - ordinary photons but with a large value of effective Planck constant h_eff - from the Earth's core (the temperature is nearly the same as in the solar corona) could have provided the metabolic energy. Also solar photons arriving as dark photons along monopole flux tubes could have provided the energy.

It seems that also the polymetallic nodules could generate photons and make possible the splitting of water. What could be the mechanism making this possible? It must be added that also electrolysis, thought to represent ancient physics, is not a well-understood phenomenon. Remarkably, "cold fusion" was discovered in electrolytes (for the TGD view see this and this) . The voltages used in electrolysis are in eV range and in atomic physics length scales they correspond to ridiculously weak electric fields. How can they cause the ionization essential for electrolysis?

1. In the Pollack effect (see this), the irradiation of water in the presence of the gel phase generates a voltage, and therefore produces a battery. This battery also makes possible electrolysis and the splitting of water producing oxygen. Pollack effect is not understood in the framework of standard chemistry.
2. The TGD explanation is that in the Pollack effect one fourth of the protons of water are transformed to dark photons and kicked to monopole flux tubes. This creates a negatively charged region called exclusion zone (EZ). This would generate a charge separation giving rise to the voltage. Photons would provide the needed energy to transform ordinary protons to dark protons with a larger value of h_eff and therefore larger energy.

   It has become gradually clear that what matters is energy. Therefore the Pollack effect can be realized in several ways. In particular, the formation of molecules as bound states of atoms can provide the needed energy: no photons would be needed (see this and this ).

   In particular, the reverse Pollack effect, that is dropping of dark protons from the monopole flux tubes back to ordinary protons, is also possible and would liberate ordinary photons needed in the splitting of water. This could also provide the photonic energy needed in photosynthesis and could provide a temporary storage of metabolic energy needed in photosynthesis and in the storage of energy to ATP (see this).

3. If this can happen in the nodules, the photosynthesis could have evolved in underground oceans via the fusion of atoms to molecules and completely without external light source.

See for instance the article Expanding Earth Hypothesis and Pre-Cambrian Earth 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.

Some solar mysteries

This article was inspired by the article "Is the Sun a Black Hole?" by Nassim Haramein. The article describes a collection of various anomalies related to the physics of the Sun, which I have also considered from the TGD point of view. The most important anomalies are the gamma ray anomalies and the missing nuclear matter of about 1500 Earth masses. The idea that the Sun could contain a blackhole led in the TGD framework to a refinement of the earlier model for blackhole-like objects (BHs) as maximally dense flux tube spaghettis predicting also their mass spectrum in terms of Mersenne primes and their Gaussian counterparts.

It however turned out that the TGD based model for the missing nuclear matter assigns the gamma ray anomalies to a magnetic bubble as a layer covering the surface of the Sun and consisting of closed monopole flux tube loops running in North-South direction and carrying M₈₉ nucleons with a mass which is 512 times the mass of the ordinary nucleon. This structure could be seen as a 2-D surface variant of the TGD counterpart of blackhole and under very natural assumptions its mass is the missing 1500 Earth masses of ordinary nuclear matter. This model conforms with the earlier model of the sunspot activity related to the reversal of the solar magnetic field. It also explains the gamma ray anomaly below 35 GeV.

A possible explanation for the TeV anomaly is in terms of M₇₉ nuclei generated in the TGD counterpart for the formation of quark gluon plasma, which in the TGD Universe would generate M₈₉ hadrons from M₁₀₇ hadrons. Now M₇₉ nuclei would be generated from M₈₉ hadrons in a process analogous to high energy nuclear collision, which would correspond to the collision of the M₈₉ flux tubes, whose distance would be larger than 2 Compton lengths of M₈₉ nucleons.

The model leads also to a proposal for the generation of the inner planets and Mars via explosion of the outer layer of the Sun consisting of M_k nucleons caused by the transformation of M_k nucleons to M₁₀₇ nucleons. M₈₉ would give the inner planets and cores of the outer planets, which would have got their gas envelopes by gravitational condensation.

See the article Some solar mysteries 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.

Galaxy without stars

Galaxy without stars and containing only hydrogen gas is the newest strange finding of astronomers (see this). The proposed explanation is that the galaxy-like structure is so young that the formation of stars has not yet begun.

The hydrogen galaxy might be also seen as a support for the TGD based view of the formation of galaxies and stars. The basic objects would be cosmic strings (actually 4-D objects as surfaces in M^4xCP_2 having 2-D M^4 projection) dominating the primordial cosmology. Cosmic strings would carry energy as analog of dark energy and would give rise to the TGD counterpart of galactic dark matter predicting the flat velocity spectrum of distance stars around the galaxy. Cosmic strings are unstable against thickening producing flux tube tangles. The reduction of string tension in the thickening liberates energy giving rise to the visible galactic matter, in particular stars. This process would be the TGD counterpart of inflation and produce galaxies and stars. Quasars would be formed first.

One can however consider a situation in which there is only hydrogen gas but no cosmic strings. If the hydrogen "galaxy" has this interpretation, the standard view of the formation of galaxies as gravitational condensation could be wrong. Galaxy formation would proceed from short to long length scales rather than vice versa.

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. .

New understanding about the energetics of muscle contraction

The FB post of Robert Stonjek told about a popular article in Phys Org (see this) about the modelling of unexpected findings related to muscle contraction (see the Nature article). The article is very interesting from the point of view of TGD inspired quantum biology (see for instance this).

Muscle contraction requires energy. From the article one learns that the contraction is not actually well-understood. The interesting finding is that the rate of muscle contraction correlates with the rate of water flow through the muscle. As if the water flow would provide the energy needed by the contraction. How? This is not actually well-understood. This is only one example of the many failures of naive reductionism in recent biology.

TGD suggests a very general new physics mechanism for how a biosystem can gain metabolic energy.

1. One can start from biocatalysis, whose extremely rapid rate is a complete mystery in the framework of standard biochemistry. The energy wall which reactants must overcome makes the reactions extremely slow. A general mechanism of energy liberation allowing us to get over the wall, should exist. The reactants should also find each other in the molecular crowd.
2. The first problem is that one does not understand how reactants find each other. The magnetic monopole flux tubes, carrying phases of ordinary matter with effective Planck constant h_eff>h behaving like dark matter, make the living system a fractal network with molecules, cells, etc at the nodes. The U-shaped flux tubes acting as tentacles allow the reactant molecules to find each other: a resonance occur when the U-shaped flux tubes touching each other have same magnetic value of magnetic field and same thickness, a cyclotron resonance occurs, they reconnect to form a pair of flux tubes connecting the molecules. Molecules have found each other.
3. At the next step h_eff decreases and the connecting flux tube pair shortens. This liberates energy since the length of the flux tube pair increases with h_eff. Quite generally the increase of h_eff requires energy feed, and in biosystems this means metabolic energy feed. The liberated energy makes it possible to overcome the energy barrier making the reaction slow.
4. This mechanism applied to the monopole flux tubes associated with water clusters and bioactive molecules is a basic mechanism of the immune system and allows the organism to find bioactive molecules which do not belong to the system normally. Cyclotron frequency spectrum of the biomolecule serves as the fingerprint of the molecule. This is also the basic mechanism of water memory.

In muscle contraction, the flow of water involving these contracting flux tubes would liberate the energy needed by contraction and the process would be very fast. The water flowing through the muscle is a fuel carrying energy at its monopole flux tubs with h_eff>h. The energy is used and water becomes ordinary. The rate of the flow correlates with the rate of contraction and with the rate of the needed metabolic energy feed.

The interesting question is whether this mechanism reduces to the usual ATP-ADP mechanism in some sense or whether ATP-ADP mechanism is a special case of this mechanism

See for instance the article TGD view about water memory and the notion of morphogenetic field.

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.

Do local Galois group and ramified primes make sense as general coordinate invariant notions?

In TGD, space-time surface can be regarded as a 4-D root for a pair P₁,P₂ of polynomials of generalized complex coordinates of H=M⁴× CP₂ (of of the coordinates is generalized complex coordinates varying along light-like curves). Each pair gives rise to a 6-D surface proposed to be identifiable as analog of twistor space and their intersection defines space-time surface as a common base of these twistor spaces as S².

One can also think of the space-time surface X⁴ as a base space of a twistor surface X⁶ in the product T(M⁴)× T(CP₂) of the twistor spaces of M⁴ and H. One can represent X⁴ as a section of this twistor space as a root of a single polynomial P. The number roots of a polynomial does not depend on the point chosen. One considers polynomials with rational coefficients but also analytic functions can be considered and general coordinate invariance would suggest that they should be allowed.

Could one generalize the notion of the Galois group so that one could speak of a Galois group acting on 4-surface X⁴ permuting its sheets as roots of the polynomial? Could one speak of a local Galois group with local groups Gal(x) assigned with each point x of the space-time surface. Could one have a general coordinate invariant definition for the generalized Galois group, perhaps working even when one considers analytic functions f₁,f₂ instead of polynomials. Also a general coordinate invariant definition of ramified primes identifiable as p-adic primes defining the p-adic length scales would be desirable.

The required view of the Galois group would be nearer to the original view of Galois group as permutations of the roots of a polynomial whereas the standard definition identifies it as a group acting as an automorphism in the extension of the base number field induced by the roots of the polynomial and leaving the base number field. The local variant of the ordinary Galois group would be defined for the points of X⁴ algebraic values of X⁴ coordinates and would be trivial for most points. Something different is needed.

In the TGD framework, a geometric realization for the action of the Galois group permutings space-time regions as roots of a polynomial equation is natural and the localization of the Galois group is natural. I have earlier considered a realization as a discrete subgroup of a braid group which is a covering group of the permutation group. The twistor approach leads to an elegant realization as discrete permutations of the roots of the polynomial as values of the S² complex coordinate of the analog of twistor bundle realized as a 6-surface in the product of twistor spaces of M⁴ and CP₂. This realization makes sense also for the P₁,P₂ option.

The natural idea is that the Galois group acts as conformal transformations or even isometries of the twistor sphere S². The isometry option leads to a connection with the McKay correspondence. Only the Galois groups appearing in the hierarchy finite subgroups of rotation groups appearing in the hierarchy of Jones inclusions of hyper-finite factors of type II₁ are realized as isometries and only the isometry group of the cube is a full permutation group. For the conformal transformations the situation is different. In any case, Galois groups representable as isometries of S² are expected to be physically very special so that the earlier intuitions seems to be correct.

General coordinate invariance allows any coordinates for the space-time surface X⁴ as the base space of X⁶ as the analog of twistor bundle and the complex coordinate z of S² is determined apart from linear holomorphies z → az+b, which do not affect the ramimifed primes as factors of the discriminant defined by the product of the root differences.

See the article TGD as it is towards end of 2024: part I or a 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 mystery of the magnetic field of the Moon

In Bighthink there was an interesting story telling about the strange finding related to the faces of the Moon. The finding is that the faces of the Moon are very different. Moon and Earth are in rotational resonance meaning that the we see always the same face of the Moon. In 1959 the first spacecraft flew around the Moon and it was found that the two sides of the Moon are very different.

The near side is heavily cratered and the lighter areas are in general more cratered that the dark areas known as maria. Craters have a fractal structure: craters within craters. Dark areas have different decomposition. At the far side there are relatively few dark maria and the dark side is thoroughly cratered and "rays" appear to radiate out from them.

The "obvious" explanation for the difference between the two sides is that there is a massive bombardment by heavy towards the far side whereas Earth has shielded the near side. This explanation fails quantitatively: the number of collisions at the near side should be only 1 per cent smaller at the far side. The far side is about 30 per cent more heavily cratered than the near side. There is no explanation for the size and abundance difference of the maria.

The article discusses the explanation in terms of Theia hypothesis stating that Moon was formed as a debris resulting from a collision of Mars size planet with Earth. If the Earth was very hot, certain elements would have been depleted from the surface of the Moon and chemical gradients would have changed its chemical decomposition. The very strong tidal forces when the Moon and Earth were near to each other would have led to a tidal locking. If the near side has thinner crust, Maria could be understood as resulting from molten lava flows into great basins and lowlands of the near side. If the maria solidified much later than the highlands one can understand why the number of craters is much lower. The impact did not leave any scars. The hot Earth near the Moon also explain the difference in crustal thickness.

TGD suggests a different explanation consistent with the Theia hypothesis. TGD predicts that cosmic expansion consists of a sequence of rapid expansions. This explains why the astrophysical objects participate in cosmic expansion but do not seem to expand themselves. The prediction is that astrophysical objects have experienced expansions. The latest expansion would have occurred .5 billion years ago and increased the radius of Earth by a factor 2. These epansion can be also explosions throwing away a layer of matter. Sun would created planets in this kind of explosions by the gravitational condensation of the resulting spherical layers to form the planet. Also Moon could have emerged in an explosion of Earth throwing out a thin expanding spherical layer. This would explains why the composition of Moon is similar to that of Earth.

The hypothesis resembles the Theia hypothesis. The hypothesis however suggests that the Moon should consist of a material originating from both Theia and Earth. The compositions of Earth and Moon are however similar. Why Theia and Earth would have had similar compositions?

This spherical layer was unstable against gravitational condensation to form the Moon. If the condensation was such that there was no radial mixing, the layer's inner side remained towards the Earth. This together with the tidal locking could allow to understand the differences between the near and far sides of the Moon. The chemical composition of the near side would correspond to that in the Earth's interior at certain depth h. One can estimate the thickness h of the layer as h= R_M^3/R_E² ≈ R_E/48 from R_M≈ R_E/4. This gives h≈ 130 km. The temperature of the recent Earth at this depth is around 1000 K (see this). At the time of the formation of Moon, the temperature could have been considerably higher, and it could have been in molten magma state.

Orbital locking would rely on the same mechanism as in Theia model. The half-molten state would have favored the development of the locking. The far side would represent the very early Earth affected by the meteoric bombardment or some other mechanism creating the craters.

Another mysterious observation is that Moon has apparentely turned itself inside out! The proposed mechanism indeed explains this. See the blog post.

See the article Moon is mysterious or the chapter Magnetic Bubbles in TGD Universe: Part I.

TGD as it is towards end of 2024: part II

This article is the second part of the article trying to give a rough overall view about Topological Geometrodynamics (TGD) as it is towards the end of 2024. Various views about TGD and their relationship are discussed at the general level. In the first part of the article the geometric and number theoretic visions of TGD were discussed.

In the first part of the article the two visions of TGD: physics as geometry and physics as number theory were discussed. The second part is devoted to the details of M⁸-H duality relating these two visions, to zero energy ontology (ZEO), and to a general view about scattering amplitudes.

Classical physics is coded either by the space-time surfaces of H or by 4-surfaces of M⁸ with Euclidean signature having associative normal space, which is metrically M⁴. M⁸-H duality as the analog of momentum-position duality relates geometric and number theoretic views. The pre-image of causal diamond cd, identified as the intersection of oppositely directed light-cones, at the level of M⁸ is a pair of half-light-cones. M⁸-H duality maps the points of cognitive representations as momenta of fermions with fixed mass m in M⁸ to hyperboloids of CD\subset H with light-cone proper time a= h_eff/m.

Holography can be realized in terms of 3-D data in both cases. In H the holographic dynamics is determined by generalized holomorphy leading to an explicit general expression for the preferred extremals, which are analogs of Bohr orbits for particles interpreted as 3-surfaces. At the level of M⁸ the dynamics is determined by associativity of the normal space.

Zero energy ontology (ZEO) emerges from the holography and means that instead of 3-surfaces as counterparts of particles their 4-D Bohr orbits, which are not completely deterministic, are the basic dynamical entities. Quantum states would be superpositions of these and this leads to a solution of the basic problem of the quantum measurement theory. It also leads also to a generalization of quantum measurement theory predicting that in the TGD counterpart of the ordinary state function reduction, the arrow of time changes.

A rather detailed connection with the number theoretic vision predicting a hierarchy of Planck constants labelling phases of the ordinary matter behaving like dark matter and ramified primes associated with polynomials determining space-time regions as labels of p-adic length scales. There has been progress also in the understanding of the scattering amplitudes and it is now possible to identify particle creation vertices as singularities of minimal surfaces associated with the partonic orbits and fermion lines at them. Also a connection with exotic smooth structures identifiable as the standard smooth structure with defects identified as vertices emerges.

See the article TGD as it is towards end of 2024: part II 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.

TGD as it is towards end of 2024: part I

This article is the first part of the article, which tries to give a rough overall view about Topological Geometrodynamics (TGD) as it is towards the end of 2024. Various views about TGD and their relationship are discussed at the general level.

1. The first view generalizes Einstein's program for the geometrization of physics. Space-time surfaces are 4-surfaces in H=M⁴× CP₂ and general coordinate invariance leads to their identification as preferred extremals of an action principle satisfying holography. This implies zero energy ontology (ZEO) allowing to solve the basic paradox of quantum measurement theory.
2. Holography = holomorphy principle makes it possible to construct the general solution of field equations in terms of generalized analytic functions. This leads to two different views of the construction of space-time surfaces in H, which seem to be mutually consistent.
3. The entire quantum physics is geometrized in terms of the notion of "world of classical worlds" (WCW), which by its infinite dimension has a unique K\"ahler geometry. Holography = holomorphy vision leads to an explicit general solution of field equations in terms of generalized holomorphy and has induced a dramatic progress in the understanding of TGD.

Second vision reduces physics to number theory.

1. Classical number fields (reals, complex numbers, quaternions, and octonions) are central as also p-adic number fields and extensions of rationals. Octonions with number theoretic norm RE(o²) is metrically Minkowski space, having an interpretation as an analog of momentum space M⁸ for particles identified as 3-surfaces of H, serving as the arena of number theoretical physics.
2. Classical physics is coded either by the space-time surfaces of H or by 4-surfaces of M⁸ with Euclidean signature having associative normal space, which is metrically M⁴. M⁸-H duality as analog of momentum-position duality relates these views. The pre-image of CD at the level of M⁸ is a pair of half-light-cones. M⁸-H duality maps the points of cognitive representations as momenta of fermions with fixed mass m in M⁸ to hyperboloids of CD\subset H with light-cone proper time a= h_eff/m.

   Holography can be realized in terms of 3-D data in both cases. In H the holographic dynamics is determined by generalized holomorphy leading to an explicit general expression for the preferred extremals, which are analogs of Bohr orbits for particles interpreted as 3-surfaces. At the level of M⁸ the dynamics is determined by associativity. The 4-D analog of holomorphy implies a deep analogy with analytic functions of complex variables for which holography means that analytic function can be constructed using the data associated with its poles and cuts. Cuts are replaced by fermion lines defining the boundaries of string world sheets as counterparts of cuts.

3. Number theoretical physics means also p-adicization and adelization. This is possible in the number theoretical discretization of both the space-time surface and WCW implying an evolutionary hierarchy in which effective Planck constant identifiable in terms of the dimension of algebraic extension of the base field appearing in the coefficients of polynomials is central.

This summary was motivated by a progress in several aspects of TGD.

1. The notion of causal diamond (CD), central to zero energy ontology (ZEO), emerges as a prediction at the level of H. The moduli space of CDs has emerged as a new notion.
2. Galois confinement at the level of M⁸ is understood at the level of momentum space and is found to be necessary. Galois confinement implies that fermion momenta in suitable units are algebraic integers but integers for Galois singlets just as in the ordinary quantization for a particle in a box replaced by CD. Galois confinement could provide a universal mechanism for the formation of all bound states.
3. There has been progress in the understanding of the quantum measurement theory based on ZEO. From the point of view of cognition BSFRs would be like heureka moments and the sequence of SSFRs could correspond to an analysis, possibly having the decay of 3-surface to smaller 3-surfaces as a correlate.

In the first part of the article the two visions of TGD: physics as geometry and physics as number theory are discussed. The second part is devoted to M⁸-H duality relating these two visions, to zero energy ontology (ZEO), and to a general view about scattering amplitudes.

See the article TGD as it is towards end of 2024: part I 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.

New support for the TGD based explanation for the origin of Moon

The mystery of the magnetic field of the Moon

I have learned that the Moon is a rather mysterious object. The origin of the Moon is a mystery although the fact that its composition is the same as that of Earth gives hints; Moon is receding from us (cosmic recession velocity is 78 per cent of this velocity, which suggests that surplus recession velocity is due to the explosion) (see this) it seems that the Moon has effectively turned inside out; the faces of the Moon are very different; the latest mystery that I learned of, are the magnetic anomalies of the Moon. The TGD based view of the origin of the Moon combined with the TGD view of magnetic fields generalizing the Maxwellian view explains all these mysterious looking findings.

The magnetic field of the Moon (see the Wikipedia article) is mysterious. There are two ScienceAlert articles about the topic (see this and this). There is an article by Krawzynksi et al with the title "Possibility of Lunar Crustal Magnatism Producing Strong Crustal Magnetism" to be referred as Ketal (see this). The article by Hemingway and Tikoo with the title "Lunar Swirl Morphology Constrains the Geometry, Magnetization, and Origins of Lunar Magnetic Anomalies" to be referred as HT (see this) considers a model for the origin local magnetic anomalies of the Moon manifesting themselves as lunar swirls.

1. The magnetic anomalies of the Moon

1. The Moon has no global magnetic field but there are local rather strong magnetic fields. What puts bells ringing is that their ancient strengths according to HT are of the same order of magnitude as the strength of the Earth's magnetic field with a nominal value of B_E≈ .5 Gauss. Note that also Mars lacks long range magnetic field but has similar local anomalies so that Martian auroras are possible. The mechanism causing these fields might be the same.
2. The crustal fields are a surface phenomenon and it is implausible that they could be caused by the rotation of plasma in the core of the Moon. The crustal magnetic fields seem to be associated with the lunar swirls, which are light-colored and therefore reflecting regions observed already at the 16^th century. Reiner Gamma is a classical example of a lunar swirl illustrated by Fig 1. of this. The origin of the swirlds is a mystery and several mechanisms have been proposed besides the crustal magnetism.
3. Since Moon does not have a global magnetic field shielding it from the solar wind and cosmic rays, weathering is expected to occur and change the chemistry of the surface so that it becomes dark colored and ceases to be reflective. In lunar maria this darkening has been indeed observed. The lunar swirls are an exception and a possible explanation is that they involve a relatively strong local magnetic field, which does the same as the magnetic field of Earth, and shields them from the weathering effects. It is known that the swirls are accompanied by magnetic fields much stronger than might be expected. What is interesting is that the opposite face of the Moon is mostly light-colored. Does this mean that there is a global magnetic field taking care of the shielding.

The article HT discusses a mechanism for how exceptionally strong magnetization could be associated with the vertical lava tubes and what are called dikes. The name indicates that the dikes are parallel to the surface.

1. The radar evidence indicates that the surface of the Moon once contained a molten rock. This suggest a period of high temperature and volcanic activity billions of years ago. Using a model of lava cooling rates Krawczynski and his colleagues have examined how a titanium-iron oxide, a mineral known as ilmenite - abundant on the Moon and commonly found in volcanic rock - could have produced a magnetization. Their experiments demonstrate that under the right conditions, the slow cooling of ilmenite can stimulate grains of metallic iron and iron nickel alloys within the Moon's crust and upper mantle to produce a powerful magnetic field explaining the swirls.
2. The paleomagnetic analysis of the Apollo samples suggests that there was a global magnetic field during period ≈ 3.85-3.56 Ga (the conjectured Theia event would have occurred ≈ 4.5 Ga ago), which would have reached intensities .78+/- .43 Gauss. The order of magnitude for this field is the same as that for the Earth's recent magnetic field. At the landing site of Apollo 16 magnetic fields as strong as .327 × 10^-3 Gauss were detected. A further analysis suggests the possibility of crustal fields of order 10^-2 Gauss to be compared with the Earth's magnetic field of .5 Gauss.
3. The lunar swirls consist of bright and dark surface markings alternating in a scale of 1-5 km. If their origin is magnetic, also the crustal magnetic fields must vary in the same scale. The associated source structures, modellable as magnetic dipoles, should have the same length scale. The restricted volume of the source bodies should imply strong magnetization. 300 nT crustal fields (.3 × 10^-2 Gauss) are necessary to produce the swirl markings. The required rock magnetization would be higher than .5 A/m (note that 1 A/m corresponds to about 1.25× 10^-2 Gauss).

   The model assumes that below the surface there are vertical magnetic dipoles serving as sources of the local magnetic field. The swirls as light regions would be above the dipoles generating a vertical magnetic field. In the dark regions, the magnetic field would be weak and approximately tangential due the absence of magnetization.

4. A mechanism is needed to enhance the magnetization carrying capacity of the rocks. The proposal is that a heating associated with the magmatic activity would have thermodynamically altered the host rocks making possible magnetizations, which are by an order of magnitude stronger than those associated with the lunar mare basalts (the existence of which suggets that the surface was once in a magma state). The slow cooling would have enhanced the metal content of the rocks and magnetization would have formed a stable record of the ancient global magnetic field of the Moon.

2. The TGD based model for the magnetic field of the Moon

The above picture would conform with the TGD based model in which the face of the Moon opposite to us corresponds to the bottom of the ancient Earth's crust. It could have been at high enough temperature at the time of the explosion producing the Moon. The volcanic activity would have occurred in the Earth's crust and magnetization would be inherited from that period.

One can however wonder how the magnetized structures could have survived for such a long time. The magnetic fields generated by macroscopic currents in the core are unstable and their maintenance in the standard electrodynamics is a mystery to which TGD suggests a solution in terms of the monopole flux contribution of about 2B_E/5 to the Earth's magnetic field which is topologically stable (see this). If the TGD explanation for the origin of the Moon is correct, these stable monopole fluxes assignable with the ancient crust of the Earth should be present also in the recent Moon and could cause a strong magnetization.

The mysterious findings could be indeed understood in the TGD based model for the birth of the Moon as being due to an explosion throwing out the crust of Earth as a spherical shell which condensed to form the Moon.

1. The TGD based model for the magnetic field of the Earth (see this) predicts that the Earth's magnetic field is the sum of a Maxwellian contribution and monopole contribution, which is topologically stable. This part corresponds to monopole flux tubes reflecting the nontrivial topology of CP₂. The monopole flux tubes have a closed 2-surface as a cross section and, unlike ordinary Maxwellian magnetic fields, the monopole part requires no currents to generate it. This explains why the Earth's magnetic field is stable in conflict with prediction that it should decay rather rapidly. Also an explanation for magnetic fields in cosmic scales emerges.
2. The Moon's magnetic field is known to be a surface phenomenon and very probably does originate from the rotation of the Moon's core as the Earth's magnetic field is believed to originate. In TGD, the stable monopole part would induce the flow of charged matter generating Maxwellian magnetic field and magnetization would also take place.

   If the Moon was born in the explosion throwing out the crust of Earth, the recent magnetic field should correspond to the part of the Earth's magnetic field associated with the monopole magnetic flux tubes in the crust. The flux tubes must be closed, which suggests that the loops run along the outer boundaries of the crust somewhat like dipole flux and return back along the inner boundaries of the crust. Therefore they formed a magnetic bubble. I have proposed that the explosions of magnetic bubbles of this kind generated in the explosions of the Sun gave rise to the planets (see this and this).

3. After the explosion throwing out the expanding magnetic bubble, the closed monopole flux tubes could have suffered reconnections changing the topology. I have considered a model for the Sunspot cycle (see this) in terms of a decay and reversal of the magnetic field of Sun based on the mechanism in monopole flux tube loops forming a a magnetic bubble at the surface of the Sun split by reconnection to shorter monopole flux loops for which the reversal occurs easily and is followed by a reconnection back to long loops with opposite direction of the flux. This process is like death followed by decay and reincarnation and corresponds to a pair of "big" state function reductions (BSFRs) in the scale of the Sun. Actually biological death could involve a similar decay of the monopole flux tubes associated with the magnetic body of the organism and meaning reduction of quantum coherence.
4. The formation of the Moon would have started with an explosion in which a magnetic bubble with thickness of about R_E/20 ≈ 100 km, presumably the crust of the Earth, was thrown out. A hole in the bubble was formed and after that the bubble developed to a disk at a surface of possibly expanding sphere, which contracted in the tangential direction to form the Moon. The monopole flux tubes of the shell followed matter in the process. In the first approximation, the Moon would have been a disk. The radius of Moon is less than one third of that for the Earth so that monopole flux tube loops of the crust with length of 2π R_E had to contract by a factor of about 1/3 to give rise to similar flux tubes of Moon. This would have increased the density by a factor of order 9 if the Moon were a disk, which of course does not make sense.

5. If the mass density did not change appreciably, the spherical shell with a hole had to transform to a structure filling the volume of the Moon. One can try to imagine how this happened.
   1. The basic assumption is that the far side corresponds to the surface of the ancient Earth. Near side could correspond to the lower boundary of its crust. A weaker condition is that the near side and a large part of the interior correspond to magma formed in the explosion and in the gravitational collapse to form the Moon. There is indeed evidence that the near side of the Moon has been in a molten magma state. This suggests that the crust divided into a solid part and magma in the explosion, which liberated a lot of energy and heated the lower boundary of the crust.
   2. Part of the solid outer part of the disk gave rise to the far side of the Moon. When the spherical disk collapsed under its own gravitational attraction, some fraction of the solid outer part, which could not contract, formed an outwards directed spherical bulge whereas the magma formed an inwards directed bulge.
   3. The energy liberated in the gravitational collapse melted the remaining fraction of the spherical disk as it fused to the proto Moon. From R_M≈ R_E/3, the area of the far side of the Moon is roughly by a factor 1/18 smaller than the area of the spherical disk, which means that the radius of the part of disk forming the far side is about R_E/4 and somewhat smaller than R_M. Most of the spherical disk had to melt in the gravitational collapse. The thin crust of the near side was formed in the cooling process.
   This model applies also to the formation of planets. The proposal indeed is that the planets formed by a collapse of a spherical disk produced in the explosion of Sun (see this). Moons of other planets could have formed from ring-like structures by the gravitational collapse of a split ring.
6. The magnitude of the dark monopole flux for Earth is about B_M =2B_E/5 ≈ .2 Gauss for the nominal value B_E=.5 Gauss. The monopole flux for the long loops is tangential but if reconnection occurs there are portions with length ΔR  inside  which the flux is vertical and connects the upper and lower boundaries of the  layer. Note  that in the TGD inspired quantum hydrodynamics  also dark Z⁰ magnetic fields associated with hydrodynamic flows  are possible and could be important in superfluidity (see this).
7. As already noticed, the far side of the Moon, which would correspond to the surface of the ancient Earth, is light-colored, which suggests that the monopole magnetic fields might be global and tangential at the far side. If so, the reconnection of the monopole flux tubes have not taken place at the far side. If magnetic anomalies are absent at the far side, the monopole part of the magnetic field should have taken care of the shielding by capturing the ions of the solar wind and cosmic rays as I have proposed. The dark monopole flux tubes play a key role in the TGD based model for the terrestrial life and this raises the question whether life could be possible also in the Moon, perhaps in its interior.

See the article Moon is mysterious or the chapter Magnetic Bubbles in TGD Universe: Part I.

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 in relation to quantum criticality, hierarchy of Planck constants, and M8-H duality

Holography = holomorphy vision generalizes the realization of quantum criticality in terms of conformal invariance. Holography = holomorphy vision provides a general explicit solution to the field equations determining space-time surfaces as minimal surfaces X⁴⊂ H=M⁴× CP₂. For the first option the space-time surfaces are roots of two generalized analytic functions P₁,P₂ defined in H . For the second option single analytic generalized analytic function defines X⁴ as its root and as the base space of 6-D twistor twistor-surface X⁶ in the twistor bundle T(H)=T(M⁴)× TCP₂) identified as a zero section.

By holography, the space-time surfaces correspond to not completely deterministic orbits of particles as 3-surfaces and are thus analogous to Bohr orbits. This implies zero energy ontology (ZEO) and to the view of quantum TGD as wave mechanics in the space of these Bohr orbits located inside a causal diamond (CD), which form a causal hierarchy. Also the consruction of vertices for particle reactions has evolved dramatically during the last year and one can assign the vertices to partonic 2-surfaces.

M⁸-H duality is a second key principle of TGD. M⁸-H duality can be seen a number theoretic analog for momentum-position duality and brings in mind Langlands duality. M⁸ can be identified as octonions when the number-theoretic Minkowski norm is defined as Re(o²). The quaternionic normal space N(y) of y∈ Y⁴⊂ M⁸ having a 2-D commutative complex sub-space is mapped to a point of CP₂. Y⁴ has Euclidian signature with respect to Re(o²). The points y∈ Y⁴ are lifted by a multiplication with a co-quaternionic unit to points of the quaternionic normal space N(y) and mapped to M⁴⊂ H inversion.

This article discusses the relationship of the holography = holomorphy vision with the number theoretic vision predicting a hierarchy h_eff=nh₀ of effective Planck constants such that n corresponds to the dimension for an extension rationals (or extension F of rationals). How could this hierarchy follow from the recent view of M⁸-H duality? Both realizations of holography = holomorphy vision assume that the polynomials involved have coefficients in an extension F of rationals Partonic 2-surfaces would represent a stronger form of quantum criticality than the generalized holomorphy: one could say islands of algebraic extensions F from the ocean of complex numbers are selected. For the P option, the fermionic lines would be roots of P and dP/dz inducing an extension of F in the twistor sphere. Adelic physics would emerge at quantum criticality and scattering amplitudes would become number-theoretically universal. In particular, the hierarchy of Planck constants and the identification of p-adic primes as ramified primes would emerge as a prediction.

Also a generalization of the theory of analytic functions to the 4-D situation is suggestive. The poles of cuts of analytic functions would correspond to the 2-D partonic surfaces as vertices at which holomorphy fails and 2-D string worlds sheets could correspond to the cuts. This provides a general view of the breaking of the generalized conformal symmetries and their super counterparts as a necessary condition for the non-triviality of the scattering amplitudes.

See the artice Holography = holomorphy vision in relation to quantum criticality, hierarchy of Planck constants, and M⁸-H duality or the chapter with the same title.

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

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

About the origin of multicellularity in the TGD Universe

A living organism consists of cells that are almost identical and contain DNA that is the same for all of them but expresses itself in different ways. This genetic holography is a fundamental property of living organisms. Where does it originate?

Dark DNA associated with magnetic flux tubes is one or the basic predictions of the TGD inspired biology. One can say that the magnetic body controls the ordinary biomatter and dictates its development. Could one have a structure that would consist of a huge number of almost identical copies of dark DNA forming a quantum coherent unit inducing the coherence of ordinary biomatter? Could this structure induce the self-organization of the ordinary DNA and the cell containing it.

Could one understand this by using the TGD based spacetime concept. There are two cases to be considered. The general option is that f_i are analytic functions of 3 complex coordinates and 1 hypercomplex (light-like) coordinate of H and (f₁,f₂)=(0,0) defines the space-time surface.

A simpler option is that f_i are polynomials P_i with rational or even algebraic coefficients. Evolution as an increase of number theoretic complexity (see this) suggest that polynomials with rational coefficients emerged first in the evolution.

1. For the general option (f₁,f₂), the extension of rationals could emerge as follows. Assume 2-D singularity X²_i at a particular light-like partonic orbit (m_i such orbits for f_i) defining a X²_i as a root of f_i. If f₂ (f₁ ) is restricted to X²₁ resp. X²₂ is a polynomial P²_i with algebraic coefficients, it has m₂ resp. m₁ discrete roots, which are in an algebraic extension of rationals with dimension m₂ resp. m₁. Note that m₂ can depend on X²_i. Only a single extension appears for a given root and can depend on it. The identification of h_eff=n_ih₀ looks natural and would mean that h_eff is a local property characterizing a particular interaction vertex. Note that it is possible that the coefficients of the resulting polynomial are algebraic numbers.

   For the polynomial option (f₁,f₂)=(P₁,P₂), the argument is essentially the same except that now the number of roots of P₁ resp. P₂ does not depend on X²₂ resp. X²₁. The dimension n₁ resp. n₂ of the extension however depends on X²₂ resp. X²₁ since the coefficients of P₁ resp. P₂ depend on it.

2. The proposal of the number theoretic vision of TGD is that the effective Planck constant is given by h_eff=nh₀, h₀<h is the minimal value of h_eff and n corresponds to the dimension of the algebraic extension of rationals. As noticed, n would depend on the roots considered and in principle m=m₁m₂ values are possible. This identification looks natural since the field of rationals is replaced with its extension and n defines an algebraic dimension of the extension. n=m₁m₂ can be also considered. For the general option, the degree of the polynomial P₁ can depend on a particular root X²₂ of f₂ .
3. The dimension n_E of the extension depends on the polynomial and typically seems to increase with an exponential rate with the degree of the polynomials. If the Galois group is the permutation group S_m it has m! elements. If it is a cyclic group Z_m, it has m elements.

For the original view of M⁸-H duality, single polynomial P of complex variable with rational coefficients determined the boundary data of associative holography (see this, (see this, and this). The iteration of P was proposed as an evolutionary process leading to chaos (see this) and led to an exponential increase of the degree of the iterated polynomial as powers m^k of the degree m of P and to a similar increases of the dimension of its algebraic extension.

This might generalize to the recent situation (see this) if the iteration of polynomials P₁ resp. P₂ at the partonic 2-surface X²₂ resp. X²₁ defining holographic data makes sense and therefore induces a similar evolutionary process by holography. This could give rise to a transition to chaos at X²_i making itself manifest as the exponential increase in the number of roots and degree of extension of rationals and h_eff. One can consider the situation also from a more restricted point of view provided by the structure of H.

1. The space-time surface in H=M⁴× CP₂ can be many-sheeted in the sense that CP₂ coordinates are m₁-valued functions of M⁴ coordinates. Already this means deviation from the standard quantum field theories. This generates a m₁-sheeted quantum coherent structure not encountered in QFTs. Anyons could be the basic example in condensed matter physics (see this). m₁ is not very large in this case since CP₂ has extremely small size (about 10⁴ Planck lengths) and one would expect that the number of sheets cannot be too large.
2. M⁴ and CP₂ can change the roles: M⁴ coordinates define the fields and CP₂ takes the role of the space-time. M⁴ coordinates could be m₂ valued functions of CP₂ coordinates: this would give a quantum coherent system acting as a unit consisting of a very large number m₂ of almost identical copies at different positions in M⁴. The reason is that there is a lot of room in M⁴. These regions could correspond to monopole flux tubes forming a bundle and also to almost identical basic units.

   If m_i corresponds to the degree of a polynomial, quite high degrees are required. The iteration of polynomials would mean an exponential increase in powers d^k of the degree d of the iterated polynomial P and a transition to chaos. For a polynomial of degree d=2 one would obtain a hierarchy m=2^k.

3. Lattice like systems would be a basic candidate for this kind of system with repeating units. The lattice could be also realized at the level of the field body (magnetic body) as a hyperbolic tessellation. The fundamental realization of the genetic code would rely on a completely unique hyperbolic tessellation known as icosa tetrahedral tessellation involving tetrahedron, octahedron and icosahedron as the basic units (see this and this). This tessellation could define a universal genetic code extending far beyond the chemical life and having several realizations also in ordinary biology.
4. The number of neurons in the brain is estimated to be about 86 billions: 10¹²≈ 2⁴⁰. If cell replications correspond to an iteration of a polynomial of degree 2, morphogenesis involves 40 replications. Human fetal cells replicate 50-70 times. Could the m almost copies of the basic system define a region of M⁴ corresponding to genes and cells? Could our body and brain be this kind of quantum coherent system with a very large number of almost copies of the same basic system. The basic units would be analogs of monads of Leibniz and form a polymonad. They could quantum entangle and interact.
5. If n=h_eff/h₀ corresponds to the dimension n_E of the extension, it could be of the order 10¹⁴ or even larger for the gravitational magnetic body (MB). The MB could be associated with the Earth or even of the Sun: the characteristic Compton length would be about .5 cm for the Earth and half of the Earth radius for the Sun).

Could this give a recipe for building geometric and topological models for living organisms? Take sufficiently high degree polynomials f₁ and f₂ and find the corresponding 4-surface from the condition that they vanish. Holography=holomorphy vision would also give a model for the classical time evolution of this system as classical, and not completely deterministic realization of behaviors and functions. Also a quantum variant of computationalistic view emerges.

See the article TGD view about water memory and the notion of morphogenetic field 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.

See the article TGD view about water memory and the notion of morphogenetic field or the chapter with the same title.

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

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

About the generation of matter-antimatter asymmetry in the TGD Universe?

I have developed a rather detailed view of interaction vertices (see this). Everything boils down to the question of what the creation of a fermion-antifermion pair is in TGD. Since bosonic fields are not primary fields (bosons are bound states of fermions and antifermions), the usual view about generation of fermion antifermion pairs does not work as such and the naive conclusion seems to be that fermions and antifermions are separately conserved.

Holography=holomorphy identification leading to an explicit general solution of field equations defining space-time surfaces as minimal surfaces with 2-D singularities at which the minimal surface property fails, is the starting point. A generalized holomorphism, which maps H to itself, is characterized by a generalized analyticity, in particular by a hyper-complex analyticity. The analytic function from H to H in the generalized sense depends on the light-like coordinate or its dual ( say -t+z and t+z in the simplest case) and the 3 remaining complex coordinates of H=M⁴/ti,esCP₂.

Let's take two such functions, f₁ and f₂, and set them to zero. We get a 4-D space-time surface that is a holomorphic minimal surface with 2-D singularities at which the minimal surface property and holomorphy fails. Singularities are analogs of poles. Also the analogs of cuts can be considered and would look like string world sheets: they would be analogous to a positive real axis along which complex function z^(i/n) has discontinuity unless one replaces the complex plane with its n-fold covering. The singularities correspond to vertices. and the fundamental vertex corresponds to a creation of fermion-antifermion pair.

There are at least two types of holomorphy in the hypercomplete sense, corresponding to analyticity with respect to -t+z or t+z as a light-like coordinate defining the analogs of complex coordinates z and its conjugate. Also CP₂ complex coordinates could be conjugated.

These two kinds of analyticities would naturally correspond to fermions and to antifermions identified as time-reflected (CP reflected) fermions. This time reflection transforms fermion to antifermion. This is not the reversal of the arrow of time occurring in a "big" state function reduction (BSFR) as TGD counterpart of what occurs in quantum measurement, which corresponds to interchange of the roles of the fermionic creation and annihilation operators.

When a fermion pair, which can also form a boson as a bound state, is created, the partonic 2-surface to which the fermion line is assigned, turns back in time. At the vertex, where this occurs, neither of these two analyticities applies: holomorphy and the minimal surface property are violated because at the vertex the type of analyticity changes.

Now comes the crucial observation: the number theoretic vision of TGD predicts that quantum coherence is possible in macroscopic and even astrophysical and cosmological scales and corresponds to the existence of arbitrarily large connected space-time regions acting as quantum coherence regions: field bodies as counterparts of Maxwellian fields can indeed be arbitrarily large.

For a given region of this kind one must choose the same kind of generalized analyticity, say -t+z or t+z even at very long scales. Only fermions or antifermions but not both are possible for this kind of space-time sheets! Does this solve the mystery of matter-antimatter asymmetry and does its presence demonstrate that quantum coherence is possible even in cosmological scales?

See the article What gravitons are and could one detect them in TGD Universe? 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.

Comparing TGD- and QFT based descriptions of particle interactions

Marko Manninen made interesting questions related to the relationship between TGD and quantum field theories (QFTs). In the following, I will try to summarize an overview of this relationship in the recent view about quantum TGD. I have developed the latest view of quantum TGD in various articles (see this, this, this, this, this, and this).

Differences between QFT and quantum TGD

Several key ideas related to quantum TGD distinguish between TGD and QFTs.

1. The basic problem of QFT is that it involves only an algebraic description of particles. An explicit geometric and topological description is missing but is implicitly present since the algebraic structure of QFTs expresses the point-like character of the particles via commutation and anticommutation relations for the quantum fields assigned to the particles.

   In the string models, the point-like particle is replaced by a string, and in the string field theory, the quantum field Ψ(x) is replaced by the stringy quantum field Ψ(string), where the "string" corresponds a point in the infinite-D space of string configurations.

   In TGD, the quantum field Ψ(x) is replaced by a formally classical spinor field Ψ (Bohr orbit). The 4-D Bohr orbits are preferred extremals of classical action satisfying holography forced by general coordinate invariance without path integral and represent points of the "world of classical worlds" (WCW). The components of Ψ correspond to multi-fermion states, which are pairs of ordinary 3-D many-fermion states at the boundaries of causal diamond (CD).

   The gamma matrices of the WCW spinor structure are linear combinations of fermionic oscillator operators for the second quantized free spinor field of H. They anticommute to the WCW metric, which is uniquely determined by the maximal isometries for WCW guaranteeing the existence of the spinor connection. Physics is unique from its existence, as implied also by the twistor lift and number theoretic vision and of course, by the standard model symmetries and fields.

2. In TGD, the notion of a classical particle as a 3-surface moving along 4-D "Bohr orbit" as the counterpart of world-line and string world sheet is an exact aspect of quantum theory at the fundamental level. The notions of classical 3-space and particle are unified. This is not the case in QFT and the notion of a Bohr orbit does not exist in QFTs. TGD view of course conforms with the empirical reality: particle physics is much more than measuring of the correlation functions for quantum fields.

   Quantum TGD is a generalization of wave mechanics defined in the space of Bohr orbits. The Bohr orbit corresponds to holography realized as a generalized holomorphy generalizing 2-D complex structure to its 4-D counterpart, which I call Hamilton-Jacobi structures (see this). Classical physics becomes an exact part of quantum physics in the sense that Bohr orbits are solutions of classical field equations as analogs of complex 4-surfaces in complex M⁴×CP₂ defined as roots of two generalized complex functions. The space of these 4-D Bohr orbits gives the WCW (see this), which corresponds to the configuration space of an electron in ordinary wave mechanics.

3. The spinor fields of H are needed to define the spinor structure in WCW. The spinor fields of H are the free spinor fields in H coupling to its spinor connection of H. The Dirac equation can be solved exactly and second quantization is trivial.

   This determines the fermionic propagators in H and induces them at the space-time surfaces. The propagation of fermions is thus trivialized. All that remains is to identify the vertices. But there is also a problem: how to avoid the separate conservation of fermion and antifermion numbers. This will be discussed below.

4. At the fermion level, all elementary particles, including bosons, can be said to be made up of fermions and antifermions, which at the basic level correspond to light-like world lines on 3-D parton trajectories, which are the light-like 3-D interfaces of Minkowski spacetime sheets and the wormhole contacts connecting them.

   The light-like world lines of fermions are boundaries of 2-D string world sheets and they connect the 3-D light-like partonic orbits bounding different 4-D wormhole contacts to each other. The 2-D surfaces are analogues of the strings of the string models.

5. In TGD, classical boson fields are induced fields and no attempt is made to quantize them. Bosons as elementary particles are bound states of fermions and antifermions. This is extraordinarily elegant since the expressions of the induced gauge fields in terms of embedding space coordinates and their gradients are extremely non-linear as also the action principle. This makes standard quantization of classical boson fields using path integral or operator formalism a hopeless task.

   There is however a problem: how to describe the creation of a pair of fermions and, in a special case, the corresponding bosons, when there are no primary boson fields? Can one avoid the separate conservation of the fermion and the antifermion numbers?

Description of interactions in TGD

Many-particle interactions have two aspects: the classical geometric description, which QFTs do not allow, and the description in terms of fermions (bosons do not appear as primary quantum fields in TGD).

1. At the classical level, particle reactions correspond to topological reactions, where the 3-surface breaks, for example, into two. This is exactly what we see in particle experiments quite concretely. For instance, a closed monopole flux tube representing an elementary particle decomposes to two in a 3-particle vertex.

   There is field-particle duality realized geometrically. The minimal surface as a holomorphic solution of the field equations defines the generalization of the light-like world line of a massless particle as a Bohr orbit as a 4-surface. The equations of the minimal surface in turn state the vanishing of the generalized acceleration of a 3-D particle identified as 3-surface.

   At the field level, minimal surfaces satisfy the analogs of the field equations of a massless free field. They are valid everywhere except at 2-D singularities associated with 3-D light-like parton trajectories. At singularities the minimal surface equation fails since the generalized acceleration becomes infinite rather than vanishing. The analog of the Brownian particle experiences acceleration: there is an "edge" on the track.

   At singularities, the field equations of the whole action are valid, but are not separately true for various parts of the action. Generalized holomorphy breaks down. These 2-D singularities are completely analogous to the poles of an analytic function in 2-D case and there is analogy with the 2-D electrostatics, where the poles of analytic function correspond to point charges and cuts to line charges.

   This gives the TGD counterparts of Einstein's equations, analogs of geodesic equations, and also the analogy Newton's F=ma. Everything interesting is localized at 2-D singularities defining the vertices. The generalized 8-D acceleration H^k defined by the trace of the second fundamental form, is localized on these 2-D parton surfaces, vertices. One has a generalization of Brownian motion for a particle-like object defined by a partonic 2-surface or equivalently for a particle as 3-surface. Intriguingly, Brownian motion has been known for a century and Einstein wrote his first paper after his thesis about Brownian motion!

   Singularities correspond to sources of fermion fields and are associated with various conserved fermion currents: just like in QFTs. For a given spacetime surface, the source- vertex - is a discrete set of 2-D partonic surface just as charges correspond to poles of analytic function in 2-D electrostatics.

   At the classical level, the 2-D singularities of the minimal surfaces therefore correspond to vertices and are localized to the light-like paths of parton surfaces where the generalized holomorphy breaks down and the generalized acceleration H^k is there non-vanishing and infinite.

Description of the interaction vertices

1. How to get the TGD counterparts of the QFT vertices?

   Vertices typically contain a fermion and an antifermion and the gauge potential, which is second quantized. Now, classical gauge potentials are not second quantized. How to obtain the basic gauge theory vertices?

   This is where the standard approximation of QFTs helps intuition: replace the quantized boson field with a classical one. This gives the vertex corresponding to the creation of a pair of fermions. Thanks to that, only the fermion and the sum of the antifermion numbers are conserved and the theory does not reduce to a free field theory. One should be able to do the same now. However, the precise formulation of this vision is far from trivial.

2. The modified Dirac action should give elementary particle vertices for a given Bohr trajectory.

   There are two options:

   1. Modified gammas are defined as contractions of ordinary gamma matrices of H with the canonical momentum currents associated with the classical action defining the space-time surface. Supersymmetry is now exact: besides color and Poincare super generators there is an infinite number of conserved super symplectic generators and infinitesimal generalized superholomorphisms.

      This option does not work: the modified Dirac equation implies that the Dirac action and also vertices vanish identically. Although one has partonic 2-surfaces as singularities of minimal surfaces defining vertices, the theory is trivial because the usual perturbation theory does not work.

   2. Modified gamma matrices are replaced by the induced gamma matrices defined by the volume term (cosmological term of the classical action). Supersymmetry is broken but only at the 2-D vertices. The anticommutator of the induced gammas gives the induced metric. This is not true for the modified gammas defined by the entire action: in this case the anticommutators are rather complex, being bilinear in the canonical momentum currents. Is it possible to have a non-trivial theory despite the breaking of supersymmetry at vertices or or does the supersymmetry breaking make possible a non-trivial theory? This seems to be the case.
      1. In 2-D vertices, the generalized acceleration field H^k is proportional to the 2-D delta function and gives rise to the graviton and Higgs vertices. One obtains also the vertices related to gauge bosons from the coupling of the induced spinor field to induced spinor connection. Only the couplings to electroweak gauge potentials and U(1) K&aum;hler gauge potential of M⁴ are obtained. The failure of the generalized holomorphy is absolutely essential.
      2. Color degrees of freedom are completely analogous to translational degrees of freedom since color quantum numbers are not spin-like in TGD. Strong interactions are vectorial and correspond to Kähler gauge potentials.
      3. Generalized Brownian motion gives the vertices. One obtains the equivalents of Einstein's and Newton's equations at the vertices. The M⁴ part M^k of the generalized acceleration is related to the gravitons and the CP₂ part S^k to the Higgs field. Spin J=2 for graviton is due to the rotational motion of the closed monopole flux tube associated with the gravitation giving an additional unit of spin besides the spin of H^k, which is S=1.
   3. Consider now the description of fermion pair creation.
      1. Intuitively, the creation of a fermion pair (and thus also a boson) corresponds to the fermion turning backwards in time. At the level of the geometry of the space-time surface, this corresponds to the partonic 2-surface turning backwards in time, and the same happens to the corresponding fermion line. Turning back in time means that effectively the fermion current is not conserved: if one does not take into account that the parton surface turns in the other direction of time, the fermion disappears effectively and the current must has a singular divergence. This is what the divergence of the generalized acceleration means.
      2. This implies that the separate conservation is lost for fermion and antifermion numbers. This means breaking of supersymmetry, of masslessness, of generalized holomorphy and also the generation of the analog of Higgs vacuum excitation as CP₂ part S^k of the generalized acceleration H^k. The Higgs vacuum expectation is only at the vertices. But this is exactly what is actually wanted! No separate symmetry breaking mechanism is needed!
      3. The failure of the generalized holomorphy at the 2-D vertex means that the holomorphic partonic orbit turns at the singularity to an antiholomorphic one. For the annihilation vertex it could occur only for the hypercomplex part of the generalized complex structure.
      4. Remarkably, the states associated with connected 4-surfaces consist of either fermions or antifermions but not both. This explains matter antimatter asymmetry if quantum coherence is possible in arbitrarily long scales. In TGD, space-time surfaces decompose to regions containing either matter or antimatter and, by the presence of quantum coherence even in cosmological scales, these regions can be very large. The quantum coherence in large scales is implied by the number theoretic vision predicting a hierarchy of Planck constants labelling phases of ordinary matter behaving like dark matter (see for instance this).
      5. What is the precise mathematical formulation of this vision? This is where a completely unique feature of 4-dimensional manifolds comes in: they allow exotic smooth structures. Exotic smooth structure is the standard smooth structure with lower-dimensional defects. In TGD, the defects correspond in TGD to 2-D parton vertices as "edges" of Brownian motion. In the exotic smooth structure, the edge disappears and everything is soft. Pair creation and non-trivial theory is possible only in dimension D=4 (see this and this ).

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

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