Saturday, July 20, 2024

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 M_{107} 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.

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.

Sunday, July 14, 2024

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 heff>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 heff decreases and the connecting flux tube pair shortens. This liberates energy since the length of the flux tube pair increases with heff. Quite generally the increase of heff 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 heff>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.

Sunday, July 07, 2024

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.

Saturday, July 06, 2024

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= RM^3/RE2 ≈ RE/48 from RM≈ RE/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.

Friday, June 28, 2024

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= heff/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= heff/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.

Thursday, June 27, 2024

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 BE≈ .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 16th 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 2BE/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 RE/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 RE 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 RM≈ RE/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 RE/4 and somewhat smaller than RM. 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 BM =2BE/5 ≈ .2 Gauss for the nominal value BE=.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.

Monday, June 10, 2024

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 heff=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.