tag:blogger.com,1999:blog-106143482024-07-18T04:38:23.442-07:00TGD diaryDaily musings, mostly about physics and consciousness, heavily biased by Topological Geometrodynamics background.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger2219125tag:blogger.com,1999:blog-10614348.post-9677956531593048172024-07-14T21:10:00.000-07:002024-07-15T04:03:39.511-07:00Galaxy without stars
Galaxy without stars and containing only hydrogen gas is the newest strange finding of astronomers (see <A HREF="https://www.space.com/dark-primordial-galaxy-no-stars-green-bank-observatory">this</A>). The proposed explanation is that the galaxy-like structure is so young that the formation of stars has not yet begun.
</p><p>
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.
</p><p>
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.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/3pieces.pdf">About the recent TGD based view concerning cosmology and astrophysics</A> or the <A HREF="https://tgdtheory.fi/public_html/articles/3pieces.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-47900405635554120162024-07-14T00:07:00.000-07:002024-07-14T00:07:08.632-07:00New understanding about the energetics of muscle contraction
The FB post of Robert Stonjek told about a popular article in Phys Org (see <A HREF="https://phys.org/news/2024-07-physicists-imprint-previously-unseen-geometrical.html">this</A>) about the modelling of unexpected findings related to muscle contraction (see the <A HREF="https://www.nature.com/articles/s41567-024-02540-x">Nature article</A>). The article is very interesting from the point of view of TGD inspired quantum biology (see for instance <A HREF="https://tgdtheory.fi/public_hml/articles/watermorpho.pdf">this</A>).
</p><p>
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.
</p><p>
TGD suggests a very general new physics mechanism for how a biosystem can gain metabolic energy.
<OL>
<LI> 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.
<LI> 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<sub>eff</sub>>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.
<LI> At the next step h<sub>eff</sub> decreases and the connecting flux tube pair shortens. This liberates energy since the length of the flux tube pair increases with h<sub>eff</sub>. Quite generally the increase of h<sub>eff</sub> 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.
<LI> 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.
</OL>
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<sub>eff</sub>>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.
</p><p>
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
</p><p>
See for instance the article <A HREF="https://tgdtheory.fi/public_hml/articles/watermorpho.pdf">TGD view about water memory and the notion of morphogenetic field</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-51789567368473764162024-07-07T01:24:00.000-07:002024-07-07T20:16:44.872-07:00Do 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 P<sub>1</sub>,P<sub>2</sub> of polynomials of generalized complex coordinates of H=M<sup>4</sup>× CP<sub>2</sub> (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 S<sup>2</sup>.
</p><p>
One can also think of the space-time surface X<sup>4</sup> as a base space of a twistor surface X<sup>6</sup> in the product T(M<sup>4</sup>)× T(CP<sub>2</sub>) of the twistor spaces of M<sup>4</sup> and H. One can represent X<sup>4</sup> 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.
</p><p>
Could one generalize the notion of the Galois group so that one could speak of a Galois group acting on 4-surface X<sup>4</sup> 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 f<sub>1</sub>,f<sub>2</sub> 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.
</p><p>
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 X<sup>4</sup> algebraic values of X<sup>4</sup> coordinates and would be trivial for most points. Something different is needed.
</p><p>
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 S<sup>2</sup> complex coordinate of the analog of twistor bundle realized as a 6-surface in the product of twistor spaces of M<sup>4</sup> and CP<sub>2</sub>. This realization makes sense also for the P<sub>1</sub>,P<sub>2</sub> option.
</p><p>
The natural idea is that the Galois group acts as conformal transformations or even isometries of the twistor sphere S<sup>2</sup>. 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 II<sub>1</sub> 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 S<sup>2</sup> are expected to be physically very special so that the earlier intuitions seems to be correct.
</p><p>
General coordinate invariance allows any coordinates for the space-time surface X<sup>4</sup> as the base space of X<sup>6</sup> as the analog of twistor bundle and the complex coordinate z of S<sup>2</sup> 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.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024I.pdf">TGD as it is towards end of 2024: part I</A>
or a <A HREF="https://tgdtheory.fi/public_html/articles/TGD2024I.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-12863196867933615242024-07-06T23:48:00.000-07:002024-07-10T20:54:05.296-07:00The mystery of the magnetic field of the Moon
In <A HREF="https://bigthink.com/starts-with-a-bang/moon-two-faces-different/">Bighthink</A> 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.
</p><p>
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.
</p><p>
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.
</p><p>
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.
</p><p>
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.
</p><p>
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?
</p><p>
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<sub>M</sub>^3/R<sub>E</sub><sup>2</sup> ≈ R<sub>E</sub>/48 from R<sub>M</sub>≈ R<sub>E</sub>/4. This gives h≈ 130 km. The temperature of the recent Earth at this depth is around 1000 K (see <A HREF="https://www.sciencedirect.com/science/article/pii/S0012821X2200601X">this</A>). At the time of the formation of Moon, the temperature could have been considerably higher, and it could have been in molten magma state.
</p><p>
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.
</p><p>
Another mysterious observation is that Moon has apparentely turned itself inside out! The proposed mechanism indeed explains this. See the <A HREF="https://matpitka.blogspot.com/2024/05/did-moon-turn-itself-inside-out.html">blog post</A>.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/moonmysteries.pdf">Moon is mysterious</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/magnbubble1.pdf">Magnetic Bubbles in TGD Universe: Part I</A>.
</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-90500920372881206682024-06-28T01:29:00.000-07:002024-06-28T01:29:43.869-07:00TGD 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.</p><p>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 M<sup>8</sup>-H duality relating these two visions, to zero energy ontology (ZEO), and to a general view about scattering amplitudes.
</p><p>
Classical physics is coded either by the space-time surfaces of H or by 4-surfaces of M<sup>8</sup> with Euclidean signature having associative normal space, which is metrically M<sup>4</sup>. M<sup>8</sup>-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 M<sup>8</sup> is a pair of half-light-cones. M<sup>8</sup>-H duality maps the points of cognitive representations as momenta of fermions with fixed mass m in M<sup>8</sup> to hyperboloids of CD\subset H with light-cone proper time a= h<sub>eff</sub>/m.
</p><p>
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 M<sup>8</sup> the dynamics is determined by associativity of the normal space. </p><p>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.
</p><p>
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.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/TGD2024II.pdf">TGD as it is towards end of 2024: part II</A> or the <a HREF= "https://tgdtheory.fi/public_html/articles/TGD2024II.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-87390904425574785762024-06-28T01:28:00.000-07:002024-06-28T01:28:19.478-07:00TGD 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.
<OL>
<LI> The first view generalizes Einstein's program for the geometrization of physics. Space-time surfaces are 4-surfaces in H=M<sup>4</sup>× CP<sub>2</sub> 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.
<LI> 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.
<LI> 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.
</OL>
Second vision reduces physics to number theory.
<OL>
<LI> 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(o<sup>2</sup>) is metrically Minkowski space, having an interpretation as an analog of momentum space M<sup>8</sup> for particles identified as 3-surfaces of H, serving as the arena of number theoretical physics.
<LI> Classical physics is coded either by the space-time surfaces of H or by 4-surfaces of M<sup>8</sup> with Euclidean signature having associative normal space, which is metrically M<sup>4</sup>. M<sup>8</sup>-H duality as analog of momentum-position duality relates these views. The pre-image of CD at the level of M<sup>8</sup> is a pair of half-light-cones. M<sup>8</sup>-H duality maps the points of cognitive representations as momenta of fermions with fixed mass m in M<sup>8</sup> to hyperboloids of CD\subset H with light-cone proper time a= h<sub>eff</sub>/m.
</p><p>
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 M<sup>8</sup> 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.
<LI> 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.
</OL>
This summary was motivated by a progress in several aspects of TGD.
<OL>
<LI> 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.
<LI> Galois confinement at the level of M<sup>8</sup> 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.
<LI> 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.
</OL>
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 M<sup>8</sup>-H duality relating these two visions, to zero energy ontology (ZEO), and to a general view about scattering amplitudes.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/TGD2024I.pdf">TGD as it is towards end of 2024: part I</A> or the <a HREF= "https://tgdtheory.fi/public_html/articles/TGD2024I.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-66883319392162391082024-06-27T07:02:00.000-07:002024-07-10T20:55:40.799-07:00New support for the TGD based explanation for the origin of Moon
<B>The mystery of the magnetic field of the Moon</B>
</p><p>
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 <A HREF="https://tgdtheory.fi/public_html/articles/preCE.pdf">this</A>) 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.
</p><p>
The magnetic field of the Moon (see the <A HREF="https://en.wikipedia.org/wiki/Magnetic_field_of_the_Moon">Wikipedia article</A>) is mysterious. There are two ScienceAlert articles about the topic (see <A HREF="https://www.sciencealert.com/something-hidden-inside-the-moon-could-be-behind-its-mysterious-swirls-scientists-have-a-theory">this</A> and <A HREF="https://www.sciencealert.com/lunar-swirls-moon-magnetic-anomalies-subsurface-lava-tubes">this</A>). 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 <A HREF="https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2023JE008179">this</A>). 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 <A HREF="https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018JE005604">this</A>) considers a model for the origin local magnetic anomalies of the Moon manifesting themselves as lunar swirls.
</p><p>
<I> 1. The magnetic anomalies of the Moon</I>
<OL>
<LI> 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 <A HREF="https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018JE005604">HT</A> are of the same order of magnitude as the strength of the Earth's magnetic field with a nominal value of B<sub>E</sub>≈ .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.
<LI> 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<sup>th</sup> century. Reiner Gamma is a classical example of a lunar swirl illustrated by Fig 1. of <A HREF="https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018JE005604">this</A>. The origin of the swirlds is a mystery and several mechanisms have been proposed besides the crustal magnetism.
<LI> 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.
</OL>
The article <A HREF="https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018JE005604">HT</A> 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.
</p><p>
<OL>
<LI> 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.
<LI> 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<sup>-3</sup> Gauss were detected. A further analysis suggests the possibility of crustal fields of order 10<sup>-2</sup> Gauss to be compared with the Earth's magnetic field of .5 Gauss.
<LI> 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<sup>-2</sup> 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<sup>-2</sup> Gauss).
</p><p>
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.
<LI> 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.
</OL>
<I> 2. The TGD based model for the magnetic field of the Moon</I>
</p><p>
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.
</p><p>
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<sub>E</sub>/5 to the Earth's magnetic field which is topologically stable (see <A HREF="https://tgdtheory.fi/public_html/articles/Bmaintenance.pdf">this</A>). 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.
</p><p>
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.
</p><p>
<OL>
<LI> The TGD based model for the magnetic field of the Earth (see <A HREF="https://tgdtheory.fi/public_html/articles/Bmaintenance.pdf">this</A>) 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 CP<sub>2</sub>. 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.
<LI> 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.
</p><p>
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 <A HREF="https://tgdtheory.fi/public_html/articles/magnbubble1.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/magnbubble2.pdf">this</A>).
<LI> 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 <A HREF="https://tgdtheory.fi/public_html/articles/magnbubble2.pdf">this</A>) 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.
<LI> The formation of the Moon would have started with an explosion in which a magnetic bubble with thickness of about R<sub>E</sub>/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<sub>E</sub> 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.
</p><p>
<LI> 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.
<OL>
<LI> 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.
<LI> 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.
<LI> The energy liberated in the gravitational collapse melted the remaining fraction of the spherical disk as it fused to the proto Moon. From R<sub>M</sub>≈ R<sub>E</sub>/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<sub>E</sub>/4 and somewhat smaller than R<sub>M</sub>. 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.
</OL>
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 <A HREF="https://tgdtheory.fi/public_html/articles/magnbubble1.pdf">this</A>). Moons of other planets could have formed from ring-like structures by the gravitational collapse of a split ring.
<LI> The magnitude of the dark monopole flux for Earth is about B<sub>M</sub> =2B<sub>E</sub>/5 ≈ .2 Gauss for the nominal value B<sub>E</sub>=.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 Z<sup>0</sup> magnetic fields associated with hydrodynamic flows are possible and could be important in superfluidity (see <A HREF="https://tgdtheory.fi/public_html/articles/TGDhydro.pdf">this</A>).
<LI> 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.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/moonmysteries.pdf">Moon is mysterious</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/magnbubble1.pdf">Magnetic Bubbles in TGD Universe: Part I</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-18195781874833106272024-06-10T00:38:00.000-07:002024-06-26T01:31:26.545-07:00Holography=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 X<sup>4</sup>⊂ H=M<sup>4</sup>× CP<sub>2</sub>. For the first option the space-time surfaces are roots of two generalized analytic functions P<sub>1</sub>,P<sub>2</sub> defined in H . For the second option single analytic generalized analytic function defines X<sup>4</sup> as its root and as the base space of 6-D twistor twistor-surface X<sup>6</sup> in the twistor bundle T(H)=T(M<sup>4</sup>)× TCP<sub>2</sub>) identified as a zero section.
</p><p>
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.
</p><p>
M<sup>8</sup>-H duality is a second key principle of TGD. M<sup>8</sup>-H duality can be seen a number theoretic analog for momentum-position duality and brings in mind Langlands duality. M<sup>8</sup> can be identified as octonions when the number-theoretic Minkowski norm is defined as Re(o<sup>2</sup>). The quaternionic normal space N(y) of y∈ Y<sup>4</sup>⊂ M<sup>8</sup> having a 2-D commutative complex sub-space is mapped to a point of CP<sub>2</sub>. Y<sup>4</sup> has Euclidian signature with respect to Re(o<sup>2</sup>). The points y∈ Y<sup>4</sup> are lifted by a multiplication with a co-quaternionic unit to points of the quaternionic normal space N(y) and mapped to M<sup>4</sup>⊂ H inversion.
</p><p>
This article discusses the relationship of the holography = holomorphy vision with the number theoretic vision predicting a hierarchy h<sub>eff</sub>=nh<sub>0</sub> 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 M<sup>8</sup>-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.
</p><p>
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.
</p><p>
See the artice <a HREF= "https://tgdtheory.fi/public_html/articles/holoholonumber.pdf">Holography = holomorphy vision in relation to quantum criticality, hierarchy of Planck constants, and M<sup>8</sup>-H duality</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/holoholonumber.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-67436975079351447902024-06-04T22:56:00.000-07:002024-06-12T21:07:39.687-07:00About the origin of multicellularity in the TGD UniverseA 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?</p><p>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. </p><p>Could one understand this by using the TGD based spacetime concept. There are two cases to be considered. The general option is that f<sub>i</sub> are analytic functions of 3 complex coordinates and 1 hypercomplex (light-like) coordinate of H and (f<sub>1</sub>,f<sub>2</sub>)=(0,0) defines the space-time surface. </p><p>A simpler option is that f<sub>i</sub> are polynomials P<sub>i</sub> with rational or even algebraic coefficients. Evolution as an increase of number theoretic complexity (see <A HREF="https://tgdtheory.fi/public_html/articles/adelephysics.pdf">this</A>) suggest that polynomials with rational coefficients emerged first in the evolution.
<OL>
<LI> For the general option (f<sub>1</sub>,f<sub>2</sub>), the extension of rationals could emerge as follows. Assume 2-D singularity X<sup>2</sup><sub>i</sub> at a particular light-like partonic orbit (m<sub>i</sub> such orbits for f<sub>i</sub>) defining a X<sup>2</sup><sub>i</sub> as a root of f<sub>i</sub>. If f<sub>2</sub> (f<sub>1</sub> ) is restricted to X<sup>2</sup><sub>1</sub> <I> resp.</I> X<sup>2</sup><sub>2</sub> is a polynomial P<sup>2</sup><sub>i</sub> with algebraic coefficients, it has m<sub>2</sub> <I> resp.</I> m<sub>1</sub> discrete roots, which are in an algebraic extension of rationals with dimension m<sub>2</sub> <I> resp.</I> m<sub>1</sub>.
Note that m<sub>2</sub> can depend on X<sup>2</sup><sub>i</sub>. Only a single extension appears for a given root and can depend on it. The identification of h<sub>eff</sub>=n<sub>i</sub>h<sub>0</sub> looks natural and would mean that h<sub>eff</sub> is a local property characterizing a particular interaction vertex. Note that it is possible that the coefficients of the resulting polynomial are algebraic numbers. </p><p>For the polynomial option (f<sub>1</sub>,f<sub>2</sub>)=(P<sub>1</sub>,P<sub>2</sub>), the argument is essentially the same except that now the number of roots of P<sub>1</sub> <I> resp.</I> P<sub>2</sub> does not depend on X<sup>2</sup><sub>2</sub> <I> resp.</I> X<sup>2</sup><sub>1</sub>. The dimension n<sub>1</sub> resp. n<sub>2</sub> of the extension however depends on X<sup>2</sup><sub>2</sub> <I> resp.</I> X<sup>2</sup><sub>1</sub> since the coefficients of P<sub>1</sub> <I> resp.</I> P<sub>2</sub> depend on it.
<LI> The proposal of the number theoretic vision of TGD is that the effective Planck constant is given by h<sub>eff</sub>=nh<sub>0</sub>, h<sub>0</sub><h is the minimal value of h<sub>eff</sub> 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=m<sub>1</sub>m<sub>2</sub> 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=m<sub>1</sub>m<sub>2</sub> can be also considered. For the general option, the degree of the polynomial P<sub>1</sub> can depend on a particular root X<sup>2</sup><sub>2</sub> of f<sub>2</sub> .
<LI> The dimension n<sub>E</sub> 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<sub>m</sub> it has m! elements. If it is a cyclic group Z<sub>m</sub>, it has m elements.
</OL>
For the original view of M<sup>8</sup>-H duality, single polynomial P of complex variable with rational coefficients determined the boundary data of associative holography (see <A HREF="https://tgdtheory.fi/public_html/articles/M8H1.pdf">this</A>, (see <A HREF="https://tgdtheory.fi/public_html/articles/M8H2.pdf">this</A>, and <A HREF="https://tgdtheory.fi/public_html/articles/cM8Hagain.pdf">this</A>). The iteration of P was proposed as an evolutionary process leading to chaos (see <A HREF="https://tgdtheory.fi/public_html/articles/chaostgd.pdf">this</A>) and led to an exponential increase of the degree of the iterated polynomial as powers m<sup>k</sup> of the degree m of P and to a similar increases of the dimension of its algebraic extension. </p><p>This might generalize to the recent situation (see <A HREF="https://tgdtheory.fi/public_html/articles/holoholonumer.pdf">this</A>) if the iteration of polynomials P<sub>1</sub> <I> resp.</I> P<sub>2</sub> at the partonic 2-surface X<sup>2</sup><sub>2</sub> <I> resp.</I> X<sup>2</sup><sub>1</sub> defining holographic data makes sense and therefore induces a similar evolutionary process by holography. This could give rise to a transition to chaos at X<sup>2</sup><sub>i</sub> making itself manifest as the exponential increase in the number of roots and degree of extension of rationals and h<sub>eff</sub>.
</OL>
One can consider the situation also from a more restricted point of view provided by the structure of H.
<OL>
<LI> The space-time surface in H=M<sup>4</sup>× CP<sub>2</sub> can be many-sheeted in the sense that CP<sub>2</sub> coordinates are m<sub>1</sub>-valued functions of M<sup>4</sup> coordinates. Already this means deviation from the standard quantum field theories. This generates a m<sub>1</sub>-sheeted quantum coherent structure not encountered in QFTs.
Anyons could be the basic example in condensed matter physics (see <A HREF="https://tgdtheory.fi/public_html/articles/anyontgd.pdf">this</A>). m<sub>1</sub> is not very large in this case since CP<sub>2</sub> has extremely small size (about 10<sup>4</sup> Planck lengths) and one would expect that the number of sheets cannot be too large.
<LI> M<sup>4</sup> and CP<sub>2</sub> can change the roles: M<sup>4</sup> coordinates define the fields and CP<sub>2</sub> takes the role of the space-time. M<sup>4</sup> coordinates could be m<sub>2</sub> valued functions of CP<sub>2</sub> coordinates: this would give a quantum coherent system acting as a unit consisting of a <I> very</I> large number m<sub>2</sub> of <I> almost</I> identical copies at different positions in M<sup>4</sup>. The reason is that there is a lot of room in M<sup>4</sup>. These regions could correspond to monopole flux tubes forming a bundle and also to almost identical basic units.
</p><p>
If m<sub>i</sub> corresponds to the degree of a polynomial, quite high degrees are required. The iteration of polynomials would mean an exponential increase in powers d<sup>k</sup> 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<sup>k</sup>.
<LI> 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 <A HREF="https://tgdtheory.fi/public_html/articles/TIH.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/tessellationH3.pdf">this</A>). This tessellation could define a universal genetic code extending far beyond the chemical life and having several realizations also in ordinary biology.
<LI> The number of neurons in the brain is estimated to be about 86 billions: 10<sup>12</sup>≈ 2<sup>40</sup>. 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 M<sup>4</sup> 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.
<LI> If n=h<sub>eff</sub>/h<sub>0</sub> corresponds to the dimension n<sub>E</sub> of the extension, it could be of the order 10<sup>14</sup> 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).
</OL>
Could this give a recipe for building geometric and topological models for living organisms? Take sufficiently high degree polynomials f<sub>1</sub> and f<sub>2</sub> 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.</p><p>See the article <a HREF= "https://tgdtheory.fi/public_html/articles/watermorpho.pdf">TGD view about water memory and the notion of morphogenetic field</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/watermorpho.pdf">chapter</A> with the same title.</p><p>For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.</p><p>For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/watermorpho.pdf">TGD view about water memory and the notion of morphogenetic field</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/watermorpho.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.</p><p>For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-21330387381972712432024-06-04T20:53:00.000-07:002024-06-04T20:53:08.780-07:00About the generation of matter-antimatter asymmetry in the TGD Universe?
I have developed a rather detailed view of interaction vertices (see <A HREF="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">this</A>). 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.
</p><p>
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=M<sup>4</sup>/ti,esCP<sub>2</sub>.
</p><p>
Let's take two such functions, f<sub>1</sub> and f<sub>2</sub>, 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.
</p><p>
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 CP<sub>2</sub> complex coordinates could be conjugated. </p><p>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.
</p><p>
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.
</p><p>
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.
</p><p>
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?
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">What gravitons are and could one detect them in TGD Universe?</A> or the <A HREF="https://tgdtheory.fi/pdfpool/whatgravitons.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-82170949774602597792024-06-03T04:51:00.000-07:002024-06-03T22:55:04.820-07:00Comparing TGD- and QFT based descriptions of particle interactionsMarko 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 <A HREF ="https://tgdtheory.fi/public_html/articles/TGDcritics.pdf">this</A>, <A HREF ="https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>, <A HREF ="https://tgdtheory.fi/public_html/articles/WCWsymm.pdf">this</A>, <A HREF ="https://tgdtheory.fi/public_html/articles/intsectform.pdf">this</A>, <A HREF ="https://tgdtheory.fi/public_html/articles/SW.pdf">this</A>, and <A HREF ="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">this</A>).
</p><p>
<B>Differences between QFT and quantum TGD</B>
</p><p>
Several key ideas related to quantum TGD distinguish between TGD and QFTs.
<OL>
<LI> 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.
</p><p>
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.
</p><p>
In TGD, the quantum field Ψ(x) is replaced by a formally <I>classical</I> 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). </p><p>
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.
<LI> 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.
</p><p>
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 <A HREF ="https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>). 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 M<sup>4</sup>×CP<sub>2</sub> defined as roots of two generalized complex functions. The space of these 4-D Bohr orbits gives the WCW (see <A HREF ="https://tgdtheory.fi/public_html/articles/WCWsymm.pdf">this</A>), which corresponds to the configuration space of an electron in ordinary wave mechanics.
<LI> 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.
</p><p>
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.
<LI> 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.
</p><p>
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.
<LI> 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.
</p><p>
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?
</OL>
</p><p>
<B>Description of interactions in TGD</B>
</p><p>
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).
<OL>
<LI> 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.
</p><p>
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.
</p><p>
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.
</p><p>
At singularities, the field equations of the <I>whole</I> 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.
</p><p>
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<sup>k</sup> 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!
</p><p>
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.
</p><p>
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<sup>k</sup> is there non-vanishing and infinite.
</OL>
</p><p>
<B>Description of the interaction vertices</B>
</p><p>
<OL>
<LI> How to get the TGD counterparts of the QFT vertices?
</p><p>
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?
</p><p>
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.
<LI> The modified Dirac action should give elementary particle vertices for a given Bohr trajectory.
</p><p>
There are two options:
<OL>
<LI> 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.
</p><p>
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.
<LI> 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.
<OL>
<LI> In 2-D vertices, the generalized acceleration field H<sup>k</sup> 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
M<sup>4</sup> are obtained. The failure of the generalized holomorphy is absolutely essential.
<LI> 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.
<LI> Generalized Brownian motion gives the vertices. One obtains the equivalents of Einstein's and Newton's equations at the vertices. The M<sup>4</sup> part M<sup>k</sup> of the generalized acceleration is related to the gravitons and the CP<sub>2</sub> part S<sup>k</sup> 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<sup>k</sup>, which is S=1.
</OL>
<LI> Consider now the description of fermion pair creation.
<OL>
<LI> 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.
<LI> 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 CP<sub>2</sub> part S<sup>k</sup> of the generalized acceleration H<sup>k</sup>. The Higgs vacuum expectation is only at the vertices. But this is exactly what is actually wanted! No separate symmetry breaking mechanism is needed!
<LI> 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.
<LI> 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 <A HREF ="https://tgdtheory.fi/public_html/articles/TGDcritics.pdf">this</A>).
<LI> 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 <A HREF ="https://tgdtheory.fi/public_html/articles/intsectform.pdf">this</A> and <A HREF ="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">this</A> ).
</OL>
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-80622679201434629852024-05-31T22:07:00.000-07:002024-05-31T22:07:41.520-07:00In what sense the early Universe could contain dark matter or energy as primordial blackholes?Are blackholes possible in the early Universe? Is the energy density in the early Universe so high that the gravitation collapses matter to blackholes? Could primordial blackholes explain the dark
matter (see <A HREF= "https://www.livescience.com/space/black-holes/scientists-may-have-finally-solved-the-problem-of-the-universes-missing-black-holes">this</A>)?
</p><p>
Before trying to cook up answers to these questions one should ask whether these questions are physically meaningful? I believe that a more meaningful question concerns the reality of blackholes. They represent singularities, at which general relativity fails. How should one modify general relativity to get rid of a system carrying the entire mass of the star in a single point? Perhaps this is the correct question.
</p><p>
TGD provides this modification. It solves the basic problem of GRT due the loss of the classical conservation laws and which also predicts the standard model symmetries and classical fields. In TGD, blackholes are replaced by blackhole-like objects, which can be regarded as tangles of monopole flux tubes filling the entire volume below the Schwartschild radius.
</p><p>
This leads to a new view of the very early Universe. Cosmic strings with 2-D M^4 projection and 2-D CP_2 projection dominate in the very early Universe. Cosmic strings are unstable against the thickening of M^4 projection and this gives to quasars as blackhole-like objects, or rather, to white-hole-like objects feeding energy into environment as the dark energy of the cosmic string transforms to ordinary matter as it thickens to monopole flux tube.
</p><p>
One might say that these primordial blackhole-like objects evaporate and produces ordinary matter. One can also say that this process is the TGD counterpart of inflation. The exponential expansion is not needed in TGD since quantum coherence in the scales made possible by the presence of arbitrarily long cosmic strings with monopole flux making them stable against splitting implies the approximate constancy of CMB temperature.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/3pieces.pdf">About the recent TGD based view concerning cosmology and astrophysics</A> or the <A HREF="https://tgdtheory.fi/pdfpool/3pieces.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-48699013176280989312024-05-30T23:02:00.000-07:002024-05-30T23:41:48.248-07:00Why the electric currents that should accompany magnetic substorms in the magnetotail are missing?
I found an interesting popular article (see <A HREF="https://www.space.com/mms-magnetic-substorms
">this</A>) telling about the surprising findings associated with the sub-storms of magnetic storms accompanying sunspots in the magnetotail of the Earth. The reconnections were observed and Maxwell's electrodynamics also predicts electric currents associated with them. However, there was no evidence for them.
</p><p>
TGD based view of electromagnetic fields predicts deviations from the Maxwellian view. In TGD, the magnetic field decomposes into two parts. The TGD counterpart of Maxwellian magnetic fields and the monopole flux part is not present in the Maxwellian theory.
<OL>
<LI> The Maxwellian part consists of flux tubes with a cross section which has a boundary, say disk. The flux tubes correspond to space-time regions, or space-time sheets as I call them. The Maxwellian part requires currents to create it. At the quantum field theory (QFT) limit of TGD this gives rise to the Maxwellian magnetic fields.
<LI> The monopole part consists of closed monopole flux tubes, which have a closed 2-surface as cross section and the Maxwellian flux tubes with, say, disk-like cross section. These are not possible in field theories in Minkowski space. Monopole flux part would contribute roughly 2/5 to the total magnetic field strength of Earth at the QFT limit.
</p><p>
What is important is that the monopole part does not require currents to create it. The monopole part is topologically stable and explains the puzzling existence of the magnetic fields in even cosmic scales and also the maintenance of the Earth's magnetic field. The Maxwellian part decays since the currents creating it dissipate (see <A HREF="https://tgdtheory.fi/public_html/articles/Bmaintenance.pdf">this</A>) .
</OL>
Monopole flux tubes carry h<sub>eff</sub>>h phases of ordinary matter behaving like dark matter.
<OL>
<LI> These phases solve the missing baryon problem and the increasing fraction of missing baryons during cosmic evolution. The loss of baryons would be due to the gradual generation of effectively dark phases of nucleons (and other particles) with increasing values of h<sub>eff</sub>. h<sub>eff</sub> has an interpretation as a measure for an algebraic complexity of the space-time region measured by the dimension of the algebraic extension defined by the two polynomials associated with the region of space-time surface considered. A given polynomial with integer or rational coefficients defines an extension of rationals and the extensions associated with two polynomials define an extension containing both extensions. Mathematically, this increase is completely analogous to the unavoidable increase of entropy. This increase of complexity would give to evolution, also biological evolution. Dark matter in this sense plays a key role in the TGD inspired quantum biology.
<LI> Notice that in TGD, the galactic dark matter is actually dark energy of cosmic strings (extremely thin monopole flux tubes) and of the monopole flux tubes to which they thicken as extremely thin flux tubes. Therefore one should speak of galactic dark energy. The recent discovery of what looks like MOND type gravitational anomaly for distant stars of binaries
gives strong support for this view (see <A HREF="https://tgdtheory.fi/public_html/articles/MONDTGD.pdf">this</A>).
</OL>
Consider now the mystery of the missing currents. No electric currents associated with storm were observed also the signatures of reconnections were observed. Could the magnetopause be dominated by the monopole flux tubes carrying the h<sub>eff</sub>>h phases of ordinary mater behaving like dark matter. The existence of the associated electric currents is not needed to create the monopole magnetic fields. Are electric currents very weak or are they only apparently absent since they are dark? How does magnetotail relate to this? Is it only because the reconnections occur here.
</p><p>
See the article at <A HREF="https://tgdtheory.fi/public_html/articles/magnbubble2.pdf">Magnetic Bubbles in TGD Universe: part II</A> or the <A HREF="https://tgdtheory.fi/pdfpool/magnbubble2.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-6026084819304910882024-05-29T22:45:00.000-07:002024-05-30T05:48:49.797-07:00 Could the TGD view of galactic dark matter make same predictions as MOND?I learned about a very interesting findingso of Kyu-Hyun Chae related to the dynamics of binaries of widely separated stars (<A HREF=" https://phys.org/news/2023-08-smoking-gun-evidence-gravity-gaia-wide.html">this</A>) . The dynamics seems to violate Newtonian gravitation for low accelerations, which naturally emerge at large separations and the violations are roughly consistent with the MOND hypothesis. This raises the question whether the TGD based explanation of flat velocity spectra associated with galaxies could be consistent with the <A HREF ="https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics">MOND hypothesis</A>).
</p><p>
The TGD based model for the binary system involving the monopole flux tubes associated with the stars of the binary leads to a prediction for the critical acceleration which is of the same magnitude as the galactic critical accelerations. This result generalizes if the scaling law T<sup>2</sup>(m)/m= constant for the system with mass m associated with a long monopole flux tube with string tension T(m) holds true.
</p><p>
See <A HREF="https://tgdtheory.fi/public_html/articles/MONDTGD.pdf">Could the TGD view of galactic dark matter make same predictions as MOND?</A> and the chapter A HREF="https://tgdtheory.fi/pdfpool/3pieces.pdf">About the recent TGD based view concerning cosmology and astrophysics</A>
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-7406862050542576112024-05-23T03:41:00.000-07:002024-05-23T04:15:34.003-07:00Intersection forms, exotic smooth structures, and particle vertices in the TGD frameworkGary Ehlenberg sent an email telling about his discussion with GPT related to exotic smooth structures. The timing was perfect. I was just yesterday evening pondering what the exotic smooth structures as ordinary smooth structures with defects could really mean and how to get a concrete grasp of them.
</p><p>
Here are some facts about the exotic smooth structures. I do not count myself as a real mathematician but the results give a very useful perspective.
</p><p>
<B> Summary of the basic findings about exotic smooth structures</B>
</p><p>
The study of exotic R<sup>4</sup>'s has led to numerous significant mathematical developments, particularly in the fields of differential topology, gauge theory, and 4-manifold theory. Here are some key developments:
<OL>
<LI>Donaldson's Theorems
</p><p>
Simon Donaldson's groundbreaking work in the early 1980s revolutionized the study of smooth 4-manifolds. His theorems provided new invariants, known as Donaldson polynomials, which distinguish between different smooth structures on 4-manifolds.
</p><p>
Donaldson's Diagonalization Theorem: This theorem states that the intersection form of a smooth, simply connected 4-manifold must be diagonalizable over the integers, provided the manifold admits a smooth structure. This result was crucial in showing that some topological 4-manifolds cannot have a smooth structure.
</p><p>
Donaldson s Polynomial Invariants: These invariants help classify and distinguish different smooth structures on 4-manifolds, particularly those with definite intersection forms.
<LI> Freedman's Classification of Topological 4-Manifolds
</p><p>
Michael Freedman's work, which earned him a Fields Medal in 1986, provided a complete classification of simply connected topological 4-manifolds. His results showed that every such manifold is determined by its intersection form up to homeomorphism.
</p><p>
h-Cobordism and the Disk Embedding Theorem: Freedman's proof of the h-cobordism theorem in dimension 4 and the disk embedding theorem were instrumental in his classification scheme.
<LI> Seiberg-Witten Theory
</p><p>
The development of Seiberg-Witten invariants provided a new set of tools for studying smooth structures on 4-manifolds, complementing and sometimes simplifying the methods introduced by Donaldson.
</p><p>
Seiberg-Witten Invariants: These invariants are simpler to compute than Donaldson invariants and have been used to prove the existence of exotic smooth structures on 4-manifolds.
<LI> Gauge Theory and 4-Manifolds
</p><p>
Gauge theory, particularly through the study of solutions to the Yang-Mills equations, has provided deep insights into the structure of 4-manifolds.
</p><p>
Instantons: The study of instantons (solutions to the self-dual Yang-Mills equations) has been crucial in understanding the differential topology of 4-manifolds. Instantons and their moduli spaces have been used to define Donaldson and Seiberg-Witten invariants.
<LI> Symplectic and Complex Geometry
</p><p>
The interaction between symplectic and complex geometry with 4-manifold theory has led to new discoveries and techniques.
</p><p>
Gompf's Construction of Symplectic 4-Manifolds: Robert Gompf's work on constructing symplectic 4-manifolds provided new examples of exotic smooth structures. His techniques often involve surgeries and handle decompositions that preserve symplectic structures.
</p><p>
Symplectic Surgeries: Techniques such as symplectic sum and Luttinger surgery have been used to construct new examples of 4-manifolds with exotic smooth structures.
<LI> Floer Homology
</p><p>
Floer homology, originally developed in the context of 3-manifolds, has been extended to 4-manifolds and provides a powerful tool for studying their smooth structures.
</p><p>
Instanton Floer Homology: This theory associates a homology group to a 3-manifold, which can be used to study the 4-manifolds that bound them. It has applications in understanding the exotic smooth structures on 4-manifolds.
<LI> Exotic Structures and Topological Quantum Field Theory (TQFT)
</p><p>
The study of exotic R<sup>4</sup>'s has also influenced developments in TQFT, where the smooth structure of 4-manifolds plays a crucial role. TQFTs are sensitive to the smooth structures of the underlying manifolds, and exotic R<sup>4</sup>'s provide interesting examples for testing and developing these theories.
</OL>
</p><p>
To sum up, the exploration of exotic R<sup>4</sup>'s has led to significant advances across various areas of mathematics, particularly in the understanding of smooth structures on 4-manifolds. Key developments include Donaldson and Seiberg-Witten invariants, Freedman s topological classification, advancements in gauge theory, symplectic and complex geometry, Floer homology, and topological quantum field theory. These contributions have profoundly deepened our understanding of the unique and complex nature of 4-dimensional manifolds.
</p><p>
<B>How exotic smooth structures appear in TGD</B>
</p><p>
The recent TGD view of particle vertices relies on exotic smooth structures emerging in D=4. For a background see <A HREF= "https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">this</A> , and <A HREF="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">this</A> .
<OL>
<LI> In TGD string world sheets are replaced with 4-surfaces in H=M<sup>4</sup>xCP<sub>2</sub> which allow generalized complex structure as also M<sup>4</sup> and H.
</p><p>
<LI> The notion of generalized complex structure.
</p><p>
The generalized complex structure is introduced for M<sup>4</sup>, for H=M<sup>4</sup>× CP<sub>2</sub> and for the space-time surface X<sup>4</sup> ⊂ H.
<OL>
<LI> The generalized complex structure of M<sup>4</sup> is a fusion of hypercomplex structure and complex structure involving slicing of M<sup>4</sup> by string world sheets and partonic 2-surfaces transversal to each other. String world sheets allow hypercomplex structure and partonic 2-surface complex structure. Hypercomplex coordinates of M<sup>4</sup> consist of a pair of light-like coordinates as a generalization of a light-coordinate of M<sup>2</sup> and complex coordinate as a generalization of a complex coordinate for E<sup>2</sup>.
<LI> One obtains a generalized complex structure for H=M<sup>4</sup>×CP<sub>2</sub> with 1 hypercomplex coordinate and 3 complex coordinates.
<LI> One can use a suitably selected hypercomplex coordinate and a complex coordinate of H as generalized complex coordinates for X<sup>4</sup> in regions where the induced metric is Minkowskian. In regions where it is Euclidean one has two complex coordinates for X<sup>4</sup>.
</OL>
</p><p>
<LI> Holography= generalized holomorphy
</p><p>
This conjecture gives a general solution of classical field equations. Space-time surface X<sup>4</sup> is defined as a zero locus for two functions of generalized complex coordinates of H, which are generalized-holomorphic and thus depend on 3 complex coordinates and one light-like coordinate. X<sup>4</sup> is a minimal surface apart from singularities at which the minimal surface property fails. This irrespective of action assuming that it is constructed in terms of the induced geometry. X<sup>4</sup> generalizes the complex submanifold of algebraic geometry.
</p><p>
At X<sup>4</sup> the trace of the second fundamental form, H<sup>k</sup>, vanishes. Physically this means that the generalized acceleration for a 3-D particle vanishes i.e one has free massless particle. Equivalently, one has a geometrization of a massless field. This means particle-field duality.
<LI> What happens at the interfaces between Euclidean and Minkowskian regions of X<sup>4</sup> are light-like 3-surfaces X<sup>3</sup>?
</p><p>
The light-like surface X<sup>3</sup> is topologically 3-D but metrically 2-D and corresponds to a light-like orbit of a partonic 2-surface at which the induced metric of X<sup>4</sup> changes its signature from Minkowskian to Euclidean. At X<sup>3</sup> a generalized complex structure of X<sup>4</sup> changes from Minkowskian to its Euclidean variant.
</p><p>
If the embedding is generalized-holomorphic, the induced metric of X<sup>4</sup> degenerates to an effective 2-D metric at at X<sup>3</sup> so that the topologically 4-D tangent space is effectively 2-D metrically.
<LI> Identification of the 2-D singularities (vertices) as regions at which the minimal surface property fails.
</p><p>
At 2-D singularities X<sup>2</sup>, which I propose to be counterparts of 4-D smooth structure, the minimal surface property fails. X<sup>2</sup> is a hypercomplex analog of a pole of complex functions and 2-D. It is analogous to a source of a massless field.
</p><p>
At X<sup>2</sup> the generalized complex structure fails such that the trace of the second fundamental form generalizing acceleration for a point-like particle develops a delta function like singularity. This singularity develops for the hypercomplex part of the generalized complex structure and one has as an analog a pole of analytic function at which analyticity fails. At X<sup>2</sup> the tangent space is 4-D rather than 2-D as elsewhere at the partonic orbit.
</p><p>
At X<sup>2</sup> there is an infinite generalized acceleration. This generalizes Brownian motion of a point-like particle as a piecewise free motion. The partonic orbits could perform Brownian motion and the 2-D singularities correspond to vertices for particle reactions.
</p><p>
At least the creation of a fermion-antifermion pair occurs at this kind of singularity. Fermion turns backwards in time. Without these singularities fermion and antifermion number would be separately conserved and TGD would be trivial as a physical theory.
<LI> One can identify the singularity X<sup>2</sup> as a defect of the ordinary smooth structure.
</p><p>
This is the conjecture that I would like to understand better and here my limitations as a mathematician are the problem.
</p><p>
I can only ask questions inspired by the result that the intersection form I (X<sup>4</sup>) for 2-D homologically non-trivial surfaces of X<sup>4</sup> detects the defects of the ordinary smooth structure, which should correspond to surfaces X<sup>2</sup>, i.e. vertices for a pair creation.
<OL>
<LI> CP<sub>2</sub> has an intersection form corresponding to the homologically non-trivial 2-surfaces for which minimal intersection corresponds to a single point. The value of intersection form for 2 2-surfaces is essentially the product of integers characterizing their homology equivalence classes. If each wormhole contact contributes a single CP<sub>2</sub> summand to the total intersection form, there would be two summands per elementary particle as monopole flux tube.
<LI> 2-D singularity gives rise to a creation of an elementary particle and would therefore add two CP<sub>2</sub> summands to the intersection form. The creation of a fermion-antifermion pair has an interpretation in terms of a closed monopole flux tube. A closed monopole flux tube having wormhole contacts at its "ends" splits into two by reconnection.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/whatgravitons.pdf"> What gravitons are and could one detect them in TGD Universe?</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/whatgravitons.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-2881137449731222172024-05-23T03:35:00.000-07:002024-05-23T03:35:57.757-07:00How to handle the interfaces between Minkowskian and Euclidean regions of space-time surface?
The treatment of the dynamics at the interfaces X<sup>3</sup> between Minkowskian and Euclidean regions X<sup>3</sup> of the space-time surface identified as light-like partonic orbits has turned out to be a difficult technical problem. By holomorphy as a realization of generalized holography, the 4-metric at X<sup>3</sup> degenerates to 2-D effective Euclidean metric apart from 2-D delta function singularities X<sup>2</sup> at which the holomorphy fails but the metric is 4-D.
</p><p>
One must treat both the bosonic and fermionic situations.
There are two options for the treatment of the interface dynamics.
<OL>
<LI> The interface X<sup>3</sup> is regarded as an independent dynamic unit. The earlier approaches rely on this assumption. By the light-likeness of X<sup>3</sup>, C-S-K action is the only possible option. The problem with U(1) gauge invariance disappears if C-S-K action is identified as a total divergence emerging from the instanton term for Kähler action.
</p><p>
One can assign to the instanton term a corresponding contribution to the modified Dirac action at X<sup>3</sup>. It however seems that the instanton term associated with the 4-D modified Dirac action does not reduce to a total divergence allowing to localize it a X<sup>3</sup>.
</p><p>
In this approach, conservation laws require that the normal components of the canonical momentum currents from the Minkowskian and Euclidean sides add up to the divergence of the canonical momentum currents associated with the C-S-K action.
<LI> Since the interface is not a genuine boundary, one can argue that one should treat the situation as 4-dimensional. This approach is adopted in this article. In the bosonic degrees of freedom, the C-S-K term is present also for this option could determine the bosonic dynamics of the boundary apart from a 2-D delta function type singularities coming from the violation of the minimal surface property and of the generalized holomorphy. At vertices involving fermion pair creation this violation would occur.
</OL>
In the 4-dimensional treatment there are no analogs of the boundary conditions at the interface.
<OL>
<LI> It is essential that the 3-D light-like orbit X<sup>3</sup> is a 2-sided surface between Minkowskian and Euclidean domains. The variation of the C-S-K term emerging from a total divergence could determine the dynamics of the interface except possibly at the singularities X<sup>3</sup>, where the interior contributions from the 2 sides give rise to a 2-D delta function term.
<LI> The contravariant metric diverges at X<sup>3</sup> since by holography one has g<sub>uv</sub>=0 at X<sup>3</sup> outside X<sup>2</sup>. The condition J<sub>uv</sub>= 0 could guarantee that the contribution of the Kähler action remains finite. The contribution from Kähler action to field equations could be even reduced to the divergence of the instanton term at X<sup>3</sup> by what I have called electric-magnetic duality proposed years ago (see <A HREF="https://tgdtheory.fi/pdfpool/prext.pdf">this</A>). At X<sup>3</sup>, the dynamics would be effectively reduced to 2-D Euclidean degrees of freedom outside X<sup>2</sup>. Everything would be finite as far as Kähler action is considered.
<LI> Since the metric at X<sup>3</sup> is effectively 2-D, the induced gamma matrices are proportional to 2-D delta function and by J<sub>uv</sub>=0 condition the contribution of the volume term to the modified gamma matrices dominates over the finite contribution of the Kähler action. This holds true outside the 2-D singularities X<sup>2</sup>. In this sense the idea that only induced gamma matrices matter at the interfaces, makes sense.
</p><p>
In order to obtain the counterpart of Einstein's equations the metric must be effectively 2-D also at X<sup>2</sup> so that det(g<sub>2</sub>)=0 is true although holomorphy fails. It seems that one must assume induced, rather than modified, gamma matrices (effectively reducing to the induced ones at X<sup>3</sup> outside X<sup>2</sup>) since for the latter option the gravitational vertex would vanish by the field equations.
</p><p>
The situation is very delicate and I cannot claim that I understand it sufficiently. It seems that the edge of the partonic orbit due to the turning of the fermion line and involving hypercomplex conjugation is essential.
<LI> For the modified Dirac equation to make sense, the vanishing of the covariant derivatives with respect to light-like coordinates seems necessary. One would have D<sub>u</sub>Ψ=0 and D<sub>v</sub>Ψ=0 in X<sup>3</sup> except at the 2-D singularities X<sup>2</sup>, where the induced metric would have diagonal components g<sub>uu</sub> and g<sub>vv</sub>. This would give rise to the gauge boson vertices involving emission of fermion-antifermion pairs.
</p><p>
<LI> By the generalized holomorphy, the second fundamental form H<sup>k</sup> vanishes outside X<sup>2</sup>. At X<sup>2</sup>, H<sup>k</sup> is proportional to a 2-D delta function and also the Kähler contribution can be of comparable size This should give the TGD counterpart of Einstein's equations and Newtonian equations of motion and to the graviton vertex.
</p><p>
The orientations of the tangent spaces at the two sides are different. The induced metric at the Minkowskian side would become 4-D. At the Euclidean side it could be Euclidean and even metrically 2-D.
</OL>
The following overview of the symmetry breaking through the generation of 2-D singularities is suggestive. Masslessess and holomorphy are violated via the generation of the analog of Higgs expectation at the vertices. The use of the induced gamma matrices violates supersymmetry guaranteed by the use of the modified gamma matrices but only at the vertices.
</p><p>
There is however an objection. The use of the induced gammas in the modified Dirac equation seems necessary although the non-vanishing of H<sup>k</sup> seems to violate the hermiticity at the vertices. Can the turning of the fermion line and the exotic smooth structure allow to get rid of this problem?
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/whatgravitons.pdf"> What gravitons are and could one detect them in TGD Universe?</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/whatgravitons.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-17395151953871133332024-05-22T19:08:00.000-07:002024-05-25T22:29:04.285-07:00Direct evidence for a mesoscale quantum coherence in living matterThis posting was inspired by Sabine Hossenfelder's video (see <A HREF= "https://youtu.be/R6G1D2UQ3gg?si=W3i6cLznyDiIKKg3">this</A>) telling about the recently observed evidence for quantum coherence in mesoscales by Babcock et al (see <A HREF = "https://pubs.acs.org/doi/10.1021/acs.jpcb.3c07936">this</A>).
</p><p>
<B>Experimental evidence for the mesoscale quantum coherence of living matter</B>
</p><p>
The abstract to the article of Babcock et al summarizes the findings.
</p><p>
<I> Networks of tryptophan (Trp) an aromatic amino acid with strong fluorescence response are ubiquitous in biological systems, forming diverse architectures in transmembrane proteins, cytoskeletal filaments, sub-neuronal elements, photoreceptor complexes, virion capsids, and other cellular structures.
<BR>
We analyze the cooperative effects induced by ultraviolet (UV) excitation of several biologically relevant Trp mega-networks, thus giving insights into novel mechanisms for cellular signaling and control.
<BR>
Our theoretical analysis in the single-excitation manifold predicts the formation of strongly superradiant states due to collective interactions among organized arrangements of up to > 10<sup>5</sup> Trp UV-excited transition dipoles in microtubule (MT) architectures, which leads to an enhancement of the fluorescence quantum yield (QY) that is confirmed by our experiments.
<BR>
We demonstrate the observed consequences of this superradiant behavior in the fluorescence QY for hierarchically organized tubulin structures, which increases in different geometric regimes at thermal equilibrium before saturation, highlighting the effect s persistence in the presence of disorder.<BR>
Our work thus showcases the many orders of magnitude across which the brightest (hundreds of femtoseconds) and darkest (tens of seconds) states can coexist in these Trp lattices.
</I>
</p><p>
From the article it is clear that the observed phenomenon is expected to be very common and not only related to MTs. From <A HREF = "https://en.wikipedia.org/wiki/Tryptophan">Wikipedia</A> one learns that tryptophan is an amino acid needed for normal growth in infants and for the production and maintenance of the body's proteins, muscles, enzymes, and neurotransmitters. Trp is an essential amino acid, which means that the body cannot produce it, so one must get it from the diet.
</p><p>
Tryptophan (Trp) is important throughout biology and forms lattice-like structures. From the article I learned that Trp plays an essential role in terms of communications. There is a connection between Trp and biophotons as well. Trp's response to UV radiation is particularly strong and also to radiation up to red wavelengths.
</p><p>
What is studied is the UV excitation of the Trp network in the case of MTs. The total number of Trp molecules involved varies up to 10<sup>5</sup>. The scales studied are mesoscales: from the scale of a cell down to the scales of molecular machines. The wavelengths at which the response has been studied start at about 300 nm (4.1 eV, UV) and extend to 800 nm (1.55 eV, red light) and are significantly longer than tubulin's scale of 10 nm. This indicates that a network of this size scale is being activated. The range of time scales for the radiant states spans an enormous range.
</p><p>
UV excitation generates a superradiance meaning that the fluorescence is much more intense than it would be if the Trps were not a quantum-coherent system. The naive view is that the response is proportional to N<sup>2</sup> rather than N, where N is the number N of Trp molecules. Super-radiance is possible even in thermal equilibrium, which does not fit the assumptions of standard quantum theory and suggests that quantum coherence does not take place at the level of the ordinary biomatter.
</p><p>
In standard quantum physics, the origin of the mesoscale coherence is difficult to understand. Quantum coherence would be the natural explanation but the value of Planck constant is far too small and so are the quantum coherence lengths. The authors predict superradiance, but it is not clear what assumptions are involved. Is quantum coherence postulated or derived (very likely not).
</p><p>
<B> TGD based interpretation</B>
</p><p>
I have considered MTs in several articles (see for instance <A HREF="https://tgdtheory.fi/public_html/articles/mt.pdf">this</A>, <A HREF="https://tgdtheory.fi/pdfpool/nervepulse.pdf">this</A> and <A HREF="https://tgdtheory.fi/pdfpool/np2023.pdf">this</A>).
</p><p>
In TGD, the obvious interpretation would be that the UV stimulus induces a sensory input communicated to the magnetic body of the Trp network, analogous to the EEG, which in turn produces superradiance as a "motor" reaction. The idea about MT as a quantum antenna is one of the oldest ideas of TGD inspired quantum biology (see <A HREF="https://tgdtheory.fi/pdfpool/tubuc.pdf">this</A>). The communication would be based on dark photons involved also with the communications of cell membrane to the MB of the brain and with DNA to its MB.
</p><p>
The Trp network could correspond to some kind of lattice structure or be associated with such a structure at the magnetic body of the system. The notion of bioharmony (see <A HREF="https://tgdtheory.fi/articles/public_html/harmonytheory.pdf">this</A> and <A HREF = "https://tgdtheory.fi/articles/public_html/bioharmony2022.pdf">this</A>) leads to a model of these communications based on the universal realization of the genetic code in terms of icosa tetrahedral tessellation of hyperbolic space H<sup>3</sup>.
</p><p>
The icosa tetrahedral tessellation (see <A HREF="https://tgdtheory.fi/articles/public_html/TIH.pdf">this</A> and <A HREF="https://tgdtheory.fi/articles/public_html/tesssellationH3.pdf">this</A>) is completely unique in that it has tetrahedrons, octahedrons, and icosahedrons as basic objects: usually only one platonic solid is possible. This tessellation predicts correctly the basic numbers of the genetic code and I have proposed that it could provide a realization of a universal genetic code not limited to mere biosystems. Could the cells of the Trp lattice correspond to the basic units of such a tessellation?
</p><p>
The work of Bandyopadhyay et al (see for instance <A RHEF="https://cutt.ly/CaYbCzY">this</A>) gives support for the hypothesis that there is hierarchy of frequency scales coming as powers of 10<sup>3</sup> (10 octaves for hearing in the case of humans) ranging from 1 Hz (cyclotron frequency of DNA) and extending to UV.
</p><p>
This hierarchy could correspond to a hierarchy of magnetic bodies. Gravitational magnetic bodies assignable to astrophysical objects (see <A HREF = "https://tgdtheory.fi/articles/public_html/penrose.pdf">this</A> and <A HREF = "https://tgdtheory.fi/articles/public_html/precns.pdf">this</A>) and electric field bodies to systems with large scale electric fields (see <A HREF="https://tgdtheory.fi/articles/public_html/hem.pdf">this</A> see <A HREF="https://tgdtheory.fi/articles/public_html/BB.pdf">this</A>) can be considered. They possess a very large value of the gravitational/electric Planck constant giving rise to a long length scale quantum coherence.
</p><p>
Gravitational magnetic bodies have a cyclotron energy spectrum, which by Equivalence principle is independent of the mass of the charged particle. The discrete spectrum for the strengths of the endogenous magnetic field postulated by Blackman and identified as the non-Maxwellian monopole flux tube part of the magnetic field having minimal value of 2B<sub>E</sub>/5=.2 Gauss would realize 12-note spectrum for the bioharmony. The spectrum of Josephson energies assignable to cell membrane is independent of h<sub>eff</sub> (see <A HREF="https://tgdtheory.fi/articles/public_html/np2023.pdf">this</A>).
</p><p>
Both frequency spectra are inversely proportional to the mass of the charged particle, which makes them ideal for communication between ordinary biomatter and dark matter. Frequency modulated signals from say cell membrane to the magnetic body and coding the sensory input would propagate as dark Josephson photons to the magnetic body and generate a sequence of resonance pulses as a reaction, which in turn can induce nerve pulses or something analogous to them in the ordinary biomatter. In a rough sense, this would be a transformation of analog to digital.
</p><p>
Authors also propose that superradiance could involve a shielding effect, analogous to what happens in the Earth's magnetic field and might be based on a similar mechanism.
<OL>
<LI> In the standard description, the Earth's magnetic field catches the incoming cosmic rays, such as UV photons, to the field lines, and thus prevents the arrival of the radiation to the surface of Earth. Van del Allen radiation belts are of special importance.
<LI> In the TGD description, a considerable fraction of incoming high energy photons and maybe also other higher energy particles would be transformed to their dark variants at the magnetic monopole flux tubes of the MB of the Earth with a field strength estimated to be B<sub>end</sub>=2B<sub>E</sub>/5, where B<sub>E</sub>=.5 Gauss is the nominal value of the Earth's magnetic field. This mechanism would transform the high energy photons to low energy dark photons with much longer wavelengths which have very weak interactions with the ordinary biomatter. These in turn would be radiated away as ordinary photons and in this way become neutralized. The scaling factor for the wavelength would be ℏ<sub>gr</sub>/h if the gravitational MB of the Earth is involved.
</p><p>
Something similar would take place in biological systems at cellular level. The UV photons would be transformed to dark photons with much longer wavelengths and radiated away as ordinary photons.
</OL>
Can one identify a range of biological scales perhaps labelled by the values of ℏ<sub>eff</sub>/ℏ coming as powers of 10<sup>3</sup>.
<OL>
<LI> The findings of Cyril Smith related to the phenomenon of water memory suggest that in living matter a scaling of photon frequency can take place with a scaling factor 2× 10<sup>11</sup> or is inverse. In the TGD framework, I christened this mechanism as "scaling law of homeopathy" (sounds suicidal in the ears of a mainstream colleague, see <A HREF="https://tgdtheory.fi/pdfpool/homeoc.pdf">this</A>). For a UV radiation with λ=300 nm frequency f=1.24× 10<sup>15</sup> Hz this would mean scaling down of frequency to 6.8 kHz and scaling up of wavelength to .4× 10<sup>5</sup>.
<LI> The kHz scale is one of the preferred scales suggested by the work of Bandyopadhyay, suggesting also a hierarchy of the scaling factors 2× 10<sup>11-3x</sup>, x=-1,0,2,...
Could there exist a hierarchy of biological scales differing by powers of 10<sup>3</sub>? Could these scaling factors correspond to various values of h<sub>eff</sub>/h<sub>0</sub>?
<LI> In the TGD inspired quantum biology, the Earth's gravitational magnetic body plays a key role. Could one assign the length scale with x=-1 with the Earth's gravitational magnetic body having gravitational Planck constant equal to ℏ<sub>gr</sub>= GM<sub>E</sub>m/β<sub>0</sub>, β<sub>0</sub>=v<sub>0</sub>/c≈ 1, where M<sub>E</sub> is the mass of Earth? By the Equivalence Principle, the gravitational Compton length is independent of mass m of the particle and for Earth is about .5 cm, the size scale of a snowflake.
<LI> The scaling hierarchy in powers of 10<sup>3</sup> would predict besides .5 cm, the length scale 5 μm of cell nucleus, the length scale 5 nm characterizing the thickness of the lipid layer of cell membrane and of the DNA double strand, and the scale 5 × 10<sup>-12</sup> m to be compared with the Compton length 2.4 × 10<sup>-12</sup> m of electron. The scaling hierarchy would be naturally associated with the electron naturally. The wavelength scale corresponding to x=-2 is λ=.4× 10<sup>8</sup> m, which is equal to the circumference of Earth 2π R<sub>E</sub>≈ .4× 10<sup>8</sup> m defining the lowest Schumann resonance frequency!
<LI> If β<sub>0</sub>=v<sub>0</sub>/c ≤ 1 is true, the scales with x=0,1,... cannot correspond to the values ℏ<sub>gr</sub> for β<sub>0</sub> coming as positive powers of 10<sup>3</sup> and its difficult to imagine hierarchy of masses as powers of 10<sup>3</sup>.
</p><p>
Could the electric Planck constants as counterparts of gravitational Planck constants (see <A HREF="https://tgdtheory.fi/public_html/articles/hem.pdf">this</A>, and <A HREF="https://tgdtheory.fi/public_html/articles/BB.pdf">this</A>) defined as ℏ<sub>em</sub>= Qe<sup>2</sup>/β<sub>0</sub>, where Q is the charge of a system analogous to the electrode of a capacitor, give these scales as electric Compton length for electron? This would conform with the fact that cell interior and DNA are negatively charged.
</OL>
There are good reasons to believe that these findings will be noticed by the people fighting with the problems related to quantum computers caused by the extreme fragility of quantum coherence in standard quantum theory. One might even hope that the basic assumptions of quantum theory could be questioned. The TGD based generalization of quantum theory could pave the way for building quantum computers and also raises the question whether ordinary computers could become in some sense living systems under suitable conditions (see <A HREF="https://tgdtheory.fi/public_html/articles/GPT.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/TGDdeeplearn.pdf">this</A>, and <A HREF="https://tgdtheory.fi/public_html/articles/tgdcomp.pdf">this</A>). S ee also
<A HREF="https://youtu.be/R6G1D2UQ3gg">this</A> about the recently observed evidence for quantum coherence in mesoscales by Babcock et al that motivated these considerations.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/mt.pdf">New Results about Microtubules as Quantum Systems</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/mt.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-46605748496341460202024-05-20T22:39:00.000-07:002024-05-20T22:39:40.899-07:00Intersection forms, exotic smooth structures, and particle vertices in the TGD frameworkGary Ehlenberg sent an email telling about his discussion with GPT related to exotic smooth structures. The timing was perfect. I was just yesterday evening pondering what the exotic smooth structures as ordinary smooth structures with defects could really mean and how to get a concrete grasp of them.
</p><p>
Here are some facts about the exotic smooth structures. I do not count myself as a real mathematician but the results give a very useful perspective.
</p><p>
<B> Summary of the basic findings about exotic smooth structures</B>
</p><p>
The study of exotic R<sup>4</sup>'s has led to numerous significant mathematical developments, particularly in the fields of differential topology, gauge theory, and 4-manifold theory. Here are some key developments:
<OL>
<LI>Donaldson's Theorems
</p><p>
Simon Donaldson's groundbreaking work in the early 1980s revolutionized the study of smooth 4-manifolds. His theorems provided new invariants, known as Donaldson polynomials, which distinguish between different smooth structures on 4-manifolds.
</p><p>
Donaldson's Diagonalization Theorem: This theorem states that the intersection form of a smooth, simply connected 4-manifold must be diagonalizable over the integers, provided the manifold admits a smooth structure. This result was crucial in showing that some topological 4-manifolds cannot have a smooth structure.
</p><p>
Donaldson s Polynomial Invariants: These invariants help classify and distinguish different smooth structures on 4-manifolds, particularly those with definite intersection forms.
<LI> Freedman's Classification of Topological 4-Manifolds
</p><p>
Michael Freedman's work, which earned him a Fields Medal in 1986, provided a complete classification of simply connected topological 4-manifolds. His results showed that every such manifold is determined by its intersection form up to homeomorphism.
</p><p>
h-Cobordism and the Disk Embedding Theorem: Freedman's proof of the h-cobordism theorem in dimension 4 and the disk embedding theorem were instrumental in his classification scheme.
<LI> Seiberg-Witten Theory
</p><p>
The development of Seiberg-Witten invariants provided a new set of tools for studying smooth structures on 4-manifolds, complementing and sometimes simplifying the methods introduced by Donaldson.
</p><p>
Seiberg-Witten Invariants: These invariants are simpler to compute than Donaldson invariants and have been used to prove the existence of exotic smooth structures on 4-manifolds.
<LI> Gauge Theory and 4-Manifolds
</p><p>
Gauge theory, particularly through the study of solutions to the Yang-Mills equations, has provided deep insights into the structure of 4-manifolds.
</p><p>
Instantons: The study of instantons (solutions to the self-dual Yang-Mills equations) has been crucial in understanding the differential topology of 4-manifolds. Instantons and their moduli spaces have been used to define Donaldson and Seiberg-Witten invariants.
<LI> Symplectic and Complex Geometry
</p><p>
The interaction between symplectic and complex geometry with 4-manifold theory has led to new discoveries and techniques.
</p><p>
Gompf's Construction of Symplectic 4-Manifolds: Robert Gompf's work on constructing symplectic 4-manifolds provided new examples of exotic smooth structures. His techniques often involve surgeries and handle decompositions that preserve symplectic structures.
</p><p>
Symplectic Surgeries: Techniques such as symplectic sum and Luttinger surgery have been used to construct new examples of 4-manifolds with exotic smooth structures.
<LI> Floer Homology
</p><p>
Floer homology, originally developed in the context of 3-manifolds, has been extended to 4-manifolds and provides a powerful tool for studying their smooth structures.
</p><p>
Instanton Floer Homology: This theory associates a homology group to a 3-manifold, which can be used to study the 4-manifolds that bound them. It has applications in understanding the exotic smooth structures on 4-manifolds.
<LI> Exotic Structures and Topological Quantum Field Theory (TQFT)
</p><p>
The study of exotic R<sup>4</sup>'s has also influenced developments in TQFT, where the smooth structure of 4-manifolds plays a crucial role. TQFTs are sensitive to the smooth structures of the underlying manifolds, and exotic R<sup>4</sup>'s provide interesting examples for testing and developing these theories.
</OL>
</p><p>
To sum up, the exploration of exotic R<sup>4</sup>'s has led to significant advances across various areas of mathematics, particularly in the understanding of smooth structures on 4-manifolds. Key developments include Donaldson and Seiberg-Witten invariants, Freedman s topological classification, advancements in gauge theory, symplectic and complex geometry, Floer homology, and topological quantum field theory. These contributions have profoundly deepened our understanding of the unique and complex nature of 4-dimensional manifolds.
</p><p>
<B>How exotic smooth structures appear in TGD</B>
</p><p>
The recent TGD view of particle vertices relies on exotic smooth structures emerging in D=4. For a background see <A HREF= "https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">this</A> , and <A HREF="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">this</A> .
<OL>
<LI> In TGD string world sheets are replaced with 4-surfaces in H=M<sup>4</sup>xCP<sub>2</sub> which allow generalized complex structure as also M<sup>4</sup> and H.
</p><p>
<LI> The notion of generalized complex structure.
</p><p>
The generalized complex structure is introduced for M<sup>4</sup>, for H=M<sup>4</sup>× CP<sub>2</sub> and for the space-time surface X<sup>4</sup> ⊂ H.
<OL>
<LI> The generalized complex structure of M<sup>4</sup> is a fusion of hypercomplex structure and complex structure involving slicing of M<sup>4</sup> by string world sheets and partonic 2-surfaces transversal to each other. String world sheets allow hypercomplex structure and partonic 2-surface complex structure. Hypercomplex coordinates of M<sup>4</sup> consist of a pair of light-like coordinates as a generalization of a light-coordinate of M<sup>2</sup> and complex coordinate as a generalization of a complex coordinate for E<sup>2</sup>.
<LI> One obtains a generalized complex structure for H=M<sup>4</sup>×CP<sub>2</sub> with 1 hypercomplex coordinate and 3 complex coordinates.
<LI> One can use a suitably selected hypercomplex coordinate and a complex coordinate of H as generalized complex coordinates for X<sup>4</sup> in regions where the induced metric is Minkowskian. In regions where it is Euclidean one has two complex coordinates for X<sup>4</sup>.
</OL>
</p><p>
<LI> Holography= generalized holomorphy
</p><p>
This conjecture gives a general solution of classical field equations. Space-time surface X<sup>4</sup> is defined as a zero locus for two functions of generalized complex coordinates of H, which are generalized-holomorphic and thus depend on 3 complex coordinates and one light-like coordinate. X<sup>4</sup> is a minimal surface apart from singularities at which the minimal surface property fails. This irrespective of action assuming that it is constructed in terms of the induced geometry. X<sup>4</sup> generalizes the complex submanifold of algebraic geometry.
</p><p>
At X<sup>4</sup> the trace of the second fundamental form, H<sup>k</sup>, vanishes. Physically this means that the generalized acceleration for a 3-D particle vanishes i.e one has free massless particle. Equivalently, one has a geometrization of a massless field. This means particle-field duality.
<LI> What happens at the interfaces between Euclidean and Minkowskian regions of X<sup>4</sup> are light-like 3-surfaces X<sup>3</sup>?
</p><p>
The light-like surface X<sup>3</sup> is topologically 3-D but metrically 2-D and corresponds to a light-like orbit of a partonic 2-surface at which the induced metric of X<sup>4</sup> changes its signature from Minkowskian to Euclidean. At X<sup>3</sup> a generalized complex structure of X<sup>4</sup> changes from Minkowskian to its Euclidean variant.
</p><p>
If the embedding is generalized-holomorphic, the induced metric of X<sup>4</sup> degenerates to an effective 2-D metric at at X<sup>3</sup> so that the topologically 4-D tangent space is effectively 2-D metrically.
<LI> Identification of the 2-D singularities (vertices) as regions at which the minimal surface property fails.
</p><p>
At 2-D singularities X<sup>2</sup>, which I propose to be counterparts of 4-D smooth structure, the minimal surface property fails. X<sup>2</sup> is a hypercomplex analog of a pole of complex functions and 2-D. It is analogous to a source of a massless field.
</p><p>
At X<sup>2</sup> the generalized complex structure fails such that the trace of the second fundamental form generalizing acceleration for a point-like particle develops a delta function like singularity. This singularity develops for the hypercomplex part of the generalized complex structure and one has as an analog a pole of analytic function at which analyticity fails. At X<sup>2</sup> the tangent space is 4-D rather than 2-D as elsewhere at the partonic orbit.
</p><p>
At X<sup>2</sup> there is an infinite generalized acceleration. This generalizes Brownian motion of a point-like particle as a piecewise free motion. The partonic orbits could perform Brownian motion and the 2-D singularities correspond to vertices for particle reactions.
</p><p>
At least the creation of a fermion-antifermion pair occurs at this kind of singularity. Fermion turns backwards in time. Without these singularities fermion and antifermion number would be separately conserved and TGD would be trivial as a physical theory.
<LI> One can identify the singularity X<sup>2</sup> as a defect of the ordinary smooth structure.
</p><p>
This is the conjecture that I would like to understand better and here my limitations as a mathematician are the problem.
</p><p>
I can only ask questions inspired by the result that the intersection form I (X<sup>4</sup>) for 2-D homologically non-trivial surfaces of X<sup>4</sup> detects the defects of the ordinary smooth structure, which should correspond to surfaces X<sup>2</sup>, i.e. vertices for a pair creation.
<OL>
<LI> In homology, the defect should correspond to an intersection point of homologically non-trivial 2-surfaces identifiable as wormhole throats, which correspond to homologically non-trivial 2-surfaces of CP<sub>2</sub>. This suggests that I(X<sup>4</sup><sub>1</sub>) for X<sup>4</sup><sub>1</sub> containing the singularity/vertex differs from I(X<sup>4</sup><sub>2</sub>) when X<sup>4</sup> does not contain the vertex.
<LI> Singularities contribute to the intersection form. The creation of fermion-antifermion pair has an interpretation in terms of closed monopole flux tubes. A closed monopole flux tube with wormhole contacts at its "ends" splits into two by reconnection. The vertex at which the particle is created, should contribute to the intersection form: the fermion-antifermion vertex as the intersection point?
</OL>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-10656446745525209072024-05-19T23:35:00.000-07:002024-05-20T00:45:59.584-07:00Antipodal duality from the TGD point of view: answer to a question by Avi Shrikumar
Avi Shrikumar asked about the antipodal duality (see <A HREF="https://www.wired.com/story/particle-physicists-puzzle-over-a-new-duality/">this</A>), which has been discovered in QCD but whose origin is not well-understood.
</p><p>
Antipodal duality implies connections between strong and electroweak interactions, which look mysterious since in the standard model these interactions are apparently independent. This kind of connections were discovered long before QCD and expressed in terms of the conserved vector current hypothesis (CVC) and partially conserved axial current PCAC hypothesis for the current algebra.
</p><p>
I looked at the antipodal duality as I learned of it (see <A HREF="https://tgdtheory.fi/public_html/articles/antipodalTGD.pdf">this</A>) but did not find any obvious explanation in TGD at that time. After that I however managed to develop a rather detailed understanding of how the scattering amplitudes emerge in the TGD framework. The basic ideas about the construction of vertices (see <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">this</A>) are very helpful in the sequel.
<OL>
<LI> In TGD, classical gravitational fields, color fields, electroweak fields are very closely related, being expressed in terms of CP<sub>2</sub> coordinates and their gradients, which define the basic field like variables when space-time surface 4-D M<sup>4</sup> projection. TGD predicts that also M<sup>4</sup> possesses Kähler structure and gives rise to the electroweak U(1) gauge field. It might give an additional contribution to the electroweak U(1) field or define an independent U(1) field.
</p><p>
There is also a Higgs emission vertex and the CP<sub>2</sub> part for the trace of the second fundamental fundamental form behaves like the Higgs group theoretically. This trace can be regarded as a generalized acceleration and satisfies the analog of Newton' s equation and Einstein's equations. M<sup>4</sup> part as generalized M<sup>4</sup> acceeration would naturally define graviton emission vertex and CP<sub>2</sub> part Higgs emission vertex.
</p><p>
This picture is bound to imply very strong connections between strong and weak interactions and also gravitation.
<LI> The construction of the vertices led to the outcome that all gauge theory vertices reduce to the electroweak vertices. Only the emission vertex corresponding to Kähler gauge potential and photon are vectorial and can contribute to gluon emission vertices so that strong interactions might involve only the Kähler gauge potentials of CP<sub>2</sub> and M<sup>4</sup> (something new).
<LI> The vertices involving gluons can involve only electroweak parity conserving vertices since color is not a spin-like quantum number in TGD but corresponds to partial waves in CP<sub>2</sub>. This implies very strong connections between electroweak vertices and vertices involving gluon emission. One might perhaps say that one starts the U(1) electroweak vertex and its M<sup>4</sup> counterpart and assigns to the final state particles as a center of mass motion in CP<sub>2</sub>.
</p><p>
If this view is correct, then the standard model would reflect the underlying much deeper connection between electroweak, color and gravitational interactions implied by the geometrization of the standard model fields and gravitational fields.
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/antipodalTGD.pdf">Antipodal duality and TGD</A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/twisttgd.pdf">About TGD counterparts of twistor amplitudes</A> .
</p><p>
For a summary of earlier postings see <A HREF="https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-5554011997463794182024-05-19T23:20:00.000-07:002024-05-19T23:20:09.161-07:00Comparison of string model and TGD: answer to the question of Harekhrisna AcharayaHarekhrisna Acharaya asked how TGD compares with string theory. In the following a short answer.
</p><p>
TGD could be also seen as a generalization of string models. Strings replace point-like particles and in TGD 3-surfaces replace them.
</p><p>
<B> A. Symmetries</B>
</p><p>
<OL>
<LI> In string models 2-D conformal symmetry and related symmetries are in key roles. They have a generalization to TGD. There is generalization of 2-D conformal invariance to space-time level in terms of Hamilton-Jacobi structure. This also implies a generalization of Kac-Moody type symmetries. There are also supersymplectic symmetries generalizing assignable to δ M<sup>4</sup><sub>+</sub>×CP<sub>2</sub> and reflecting the generalized symplectic structure for the light-cone M<sup>4</sup><sub>+</sub> and symplectic structure for CP<sub>2</sub>. These symmetries act as Noether symmetries in the "world of classical worlds" (WCW).
<LI> In string models 2-D conformal invariance solves field equations for strings. This generalizes to the TGD framework.
<OL>
<LI> One replaces string world sheets with 4-D surfaces as orbits of 3-D particles replacing strings as particles. The 2-D conformal invariance is replaced with its 4-D generalization. The 2-D complex structure is replaced with its 4-D analog: I call it Hamilton-Jacobi structure. For Minkowski space M<sup>4</sup> this means composite of 2-D complex structure and 2-D hypercomplex structure. See <A HREF="https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A> .
<LI> This allows a general solution to the field equations defining space-time in H=M<sup>4</sup>×CP<sub>2</sub> realizing holography as generalized holomorphy. Space-time surfaces are analogous to Bohr orbits. Path integral is replaced with sum over Bohr orbits assignable to given 3-surface.
</p><p>
Space-time surfaces are roots of two generalized holomorphic functions of 1 hypercomplex (light-like) coordinate and 3 complex coordinates of H. Space-time surfaces are minimal surfaces irrespective of action as long as it is expressible in terms of the induced geometry.
<LI> There are singularities analogous to poles (and cuts) at which generalized holomorphy and minimal surface property fails and they correspond to vertices for particle reactions. There is also a highly suggestive connection with exotic smooth structures possible only in 4-D. This gives rise to a geometric realization of field particle duality. Minimal surface property corresponds to the massless d'Alembert equation and free theory. The singularities correspond to sources and vertices. The minimal surface as the orbit of a 3-surface corresponds to a particle picture.
</OL>
</OL>
</p><p>
<B> B. Uniqueness as a TOE</B>
</p><p>
The hope was that string models would give rise to a unique TOE. In string models branes or spontaneous compactification are needed to obtain 4-D or effectively 4-D space-time. This forced to give up hopes for a unique string theory and the outcome was landscape catastrophe.
<OL>
<LI> In TGD, space-time surfaces are 4-D and the embedding space is fixed to H=M<sup>4</sup>×CP<sub>2</sub> by standard model symmetries. No compactification is needed and the space-time is 4-D and dynamical at the fundamental level.
</p><p>
The space-time of general relativity emerges at QFT limit when the sheets of many-sheeted space-time are replaced with single region of M<sup>4</sup> made slightly curved and carryin gauge potentials sum of those associated with space-time sheets.
<LI> How to uniquely fix H: this is the basic question. There are many ways to achieve this.
<OL>
<LI> Freed found that loop spaces have a unique geometry from the existence of Riemann connection. The existence of the Kahler geometry of WCW is an equally powerful constraint and also it requires maximal isometries for WCW so that it is analogous to a union of symmetric spaces. The conjecture is that this works only for H=M<sup>4</sup>×CP<sub>2</sub>. Physics is unique from its geometric existence.
<LI> The existence of the induced twistor structure allows for the twistor lift replacing space-time surfaces with 6-D surfaces as S<sup>2</sup> bundles as twistor spaces for H=M<sup>4</sup>×CP<sub>2</sub> only. Only the twistor spaces of M<sup>4</sup> and CP<sub>2</sub> have Kaehler structure and this makes possible the twistor lift of TGD.
<LI> Number theoretic vision, something new as compared to string models, leads to M<sup>8</sup>-H duality as an analog of momentum position duality for point-like particles replaced by 3-surface. Also this duality requires H=M<sup>4</sup>×CP<sub>2</sub>. M<sup>8</sup>-H duality is strongly reminiscent of Langlands duality.
</p><p>
Although M<sup>8</sup>-H duality is purely number theoretic and corresponds to momentum position duality and does not make H dynamical, it brings to mind the spontaneous compactification of M<sup>10</sup> to M<sup>4</sup>×S .
</OL>
</p><p>
<B> C. Connection with empiria</B>
</p><p>
String theory was not very successful concerning predictions and the connection with empirical reality. TGD is much more successful: after all it started directly from standard model symmetries.
<OL>
<LI> TGD predicts so called massless extremals as counterparts of classical massless fields. They are analogous to laser light rays. Superposition for massless modes with the same direction of momentum is possible and propagation is dispersion free.
<LI> TGD predicts geometric counterparts of elementary particles as wormhole contacts, that is space-time regions of Euclidean signature connecting 2 Minkowskian space-time sheets and having roughly the size of CP<sub>2</sub> and in good approximation having geometry of CP<sub>2</sub>. MEs are ideal for precisely targeted communications.
<LI> TGD predicts string-like objects (cosmic strings) as 4-D surfaces. They play a key role in TGD in all scales and represent deviation from general relativity in the sense that they do not have 4-D M<sup>4</sup> projection and are not Einsteinian space-times. The primordial cosmology is cosmic string dominated and the thickening of cosmic strings gives rise to quasars and galaxies. Monopole flux tubes are fundamental also in particle, nuclear and even atomic and molecular physics, biology and astrophysics. See for instance <A HREF="https://tgdtheory.fi/public_html/articles/3pieces.pdf">this</A> .
<LI> An important deviation of TGD from string models is the notion of field body. The Maxwellian/gauge theoretic view of fields is replaced with the notion of a field body having flux sheets and flux tubes as body parts. Magnetic monopoles flux tubes require no currents to maintain the associated magnetic fields. This explains the existence of magnetic fields in cosmic scales and of huge cosmic structures. Also the stability of the Earth's magnetic field finds an explanation.
</p><p>
The dark energy of cosmic strings explains the flat velocity spectrum of stars around galacxies and therefore galactic dark matter.
<LI> Number theoretic vision predicts a hierarchy of space-time surfaces defined as roots of pairs of polynomials with increasing degree. This gives rise to an evolutionary hierarchy of extensions of rationals and also behind biological evolution.
</p><p>
The dimensions of extensions correspond to a hierarchy of effective Planck constants h<sub>eff</sub>=nh<sub>0</sub> serving as measure of algebraic complexity and giving rise to a hierarchy of increasing quantum coherence scales. Ordinary particles with h<sub>eff</sub>>h behave like dark matter. The identification is not as galactic dark matter but as dark phases residing at field bodies and controlling ordinary matter (h<sub>eff</sub> serves as a measure for intelligence). They explain the missing baryonic matter.
</OL>
For a summary of earlier postings see <A HREF="https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-54649946087642764552024-05-19T01:12:00.000-07:002024-05-19T01:12:42.869-07:00An audiofile by Tuomas Sorakivi about TGD view of Biefeld Brown effectTuomas Sorakivi prepared an audio file with text about the model of the Biefeld Brown effect in the TGD framework. In the recent experiments of Charles Buhler related to Biefeld Brown effect (emdrive represents earlier similar experiment) are carried out in a vacuum chamber and using a casing of the electrodes of the asymmetric capacitor-like system to prevent the leakage currents. Maximum acceleration of 1 g was detected and the effect increases with the strength of the electric field. Electron currents rather than ionic currents seem to be responsible for the effect.
</p><p>
This strongly suggests new physics. Either the law of momentum fails or there is some third, unidentified, party with which the capacitor-like system exchanges momentum and energy.
</p><p>
In the TGD Universe this third party would be the field body, presumably electric field body (EB). Instead of the ordinary Planck constant, the electric Planck constant at the EB of a single electrode would characterize the electrons. Its value is rather large and makes possible quantum coherence in the scale of the smaller electrode. Generalized Pollack effect would transfer electrons to dark electrons at EBs and its reversal would return them back so a net momentum would be left to the EB.
</p><p>
See the audiofile <A HREF="https://www.youtube.com/watch?v=4tK15XLN_ug">Topological Geometrodynamics view of Biefeld Brown effect</A>
</p><p>
or the article <a HREF= "https://tgdtheory.fi/public_html/articles/BB.pdf">About Biefeld Brown effect</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/hem.pdf">About long range electromagnetic quantum coherence in TGD Universe</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-60223100628439437352024-05-18T22:37:00.000-07:002024-05-18T22:43:06.896-07:00The essay of Marko Manninen about the geometric aspects of TGD
Marko Manninen wrote a very nice essay about the geometric aspects of TGD. This has involved a lot of inspiring discussions during a couple of years, which have also helped me to articulate TGD more precisely. Below is Marko's summary of his essay.
</p><p>
It is now official. My previous research as a citizen scientist on gamma rays, peer-reviewed and published in 2021, has been followed by a new study, this time in the field of theoretical fundamental physics. It is often said that experiments and empirical data are groping in the dark without theories. In this context, without a unified theory of spacetime, quantum phenomena, and elementary particles, our understanding and applications remain incomplete.
</p><p>
In my new nearly 150-page English essay-research, published by Holistic Science Publications, I aim to present the early history and geometric foundations of the Topological Geometrodynamics (TGD) theory, which Dr. Matti Pitkänen began developing in the 1970s. The text includes accessible introductory material to help a broader audience grasp the basics and motivations of the TGD theory. For specialists, there is in-depth content to engage with.
</p><p>
Current mainstream fundamental physics theories assume elementary particles are geometrically point-like entities. This simplification works when studying phenomena in isolation. However, when attempting to create a unified representation of spacetime, quantum mechanics, and elementary particles, we have been stuck for over 50 years. The problematic concept of time and its nature has also been difficult to resolve.
</p><p>
According to TGD, these issues are overcome by treating elementary particles not as points or even strings, as in string theories, but as 3-surfaces in an eight-dimensional hyperspace. Through a geometric induction process, the required symmetries related to the conservation laws of physics are transferred from the static hyperspace to the dynamic 3-surfaces of the real world. Plato's allegory of the cave is a fitting analogy here: the experienced world with its elementary particles and dynamic laws is a shadowy reflection of higher-dimensional symmetrical mathematical structures. Regarding time, we must also include experienced time and integrate human conscious experience into the unified theory framework, as done in TGD.
</p><p>
These proposals have been surprisingly radical within the community. Despite recognizing the open problems, solutions rarely make it through peer review. This challenge has now been overcome, and we eagerly await to see if new interested researchers will engage with and perhaps apply this work over the years.
</p><p>
My major effort is now behind me, and we can enjoy the fruits of my labor. My most significant long-term endeavor began about four years ago when I first heard about TGD. My interest was piqued by TGD's holistic approach, addressing profound topics without neglecting humanistic and mind-philosophical dimensions. My independent research culminated in a six-month writing marathon, completed at the turn of 2023-24, under Dr. Pitkänen's patient tutorship.
</p><p>
Thanks also go to Antti Savinainen, a physics teacher at Kuopio Lyceum, who thoroughly reviewed and commented on my text. Ville-Veli Einari Saari, Rode Majakka, and Tuomas Sorakivi from our regular Zoom group meetings have been excellent sounding boards for discussions. Dr. Ari J. Tervashonka, who has a Ph.D. in the history of science and ether theories, has been a crucial academic link, guide, and support during the publication process. Heartfelt thanks and humble apologies also go to my loved ones who have often heard these perhaps incomprehensible ideas as I processed the theory aloud.
</p><p>
We would be very grateful if you share the link to my publication and mention it in suitable contexts. Feel free to comment and ask questions; we promise to respond diligently. You can find the essay <A HREF ="https://www.holistic-science-publications.com/book-series/">here</A> or <A HREF = "https://drive.google.com/file/d/18oNxyRqjWyJ3I8ZcXlIzDOJTpONDeGjq/view">here</A>.
</p><p>Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-76600612920075427722024-05-09T23:47:00.000-07:002024-05-09T23:47:18.219-07:00Could the model of Biefeld Brown effect apply to rotating magnetic systems?
Could model of Biefeld Brown be also applied to a rather massive rotating magnetic system studied by Russian researchers Godin and Roschin (see <A HREF="
http://www.rexresearch.com/roschin/roschin.htm/">this</A>), which I have tried to understand during years (see <a HREF= "https://tgdtheory.fi/pdfpool/Faraday.pdf">this</A>).
<OL>
<LI> The system consists of a stator and rollers rotating around it. Also the effect of a radial electric field was studied. The high voltage between stator and electrodes outside the rollers varied in a range 0-20 kV. Therefore a capacitor-like system is in question. Positive potential was associated with the stator so that the force experienced by electrons was towards the electrodes. This generates a strong radial electric field and there is an ionization of air around the rotating magnet, which could be caused by high energy electrons from the surface of the rotor as in coronal discharge.
<LI> What happens is that the system begins to accelerate spontaneously as the rotation frequency approaches 10 Hz, the alpha frequency of EEG. Rather dramatic weight reduction of 35 per cent and a generation of cylindrical magnetic walls with B=.05 Tesla parallel to the rotation direction are reported. The sign of the effect depends on the direction of rotation.
</OL>
The situation resembles in many respects to that in the Biefeld Brown effect.
<OL>
<LI> Could the Pollack effect feed electrons to the magnetic and/or electric FB of the system. The electrons would also leave some of their angular momentum to the FB and drop back. Otherwise the rotors develop a positive charge Q= ω BS proportional to the rotation frequency ω, magnetic field B and the area S of the vertical boundary of the cylinder, as in the Faraday effect.
</p><p>
The pumping of electrons to the FB would generate both the momentum and angular momentum as a recoil effect. Now the vertical components of momentum and angular momentum in z-direction would be involved. In the first approximation, the magnetic field can be modelled as a dipole field in Maxwellian theory.
<LI> Rollers are rotating magnets. What is interesting is that in the Faraday effect a rotating magnet develops a radial voltage proportional to the rotating frequency and magnetic field. One expects that the same occurs for the rollers. This cannot be understood in Maxwell's theory as induction since the motion is not linear and the calculation of the voltage using the same formula requires a generation of a charge density. In TGD, the assumption that the vector potential of the magnetic field rotates with the magnet, explains the effect. Could this charge density be due to a transfer of electrons to the FB of the system? Positive charge density would be generated and create a force opposite to the direction of the Earth's gravitational acceleration so that the Faraday effect for the rollers cannot explain the findings.
<LI> One expects that the vector potentials for the magnetic fields of rollers rotate as in the Faraday effect. Also the magnetic fields associated with the rollers or rather, their flux tubes should rotate. This could lead to a twisting of the flux tubes. The twisting would suggest that the flux tubes of FBs of the rollers are helical monopole flux tubes (by rotation) emerging from the top and retung back at the bottom of the roller system. There is an obvious analogy with the solar magnetic field.
</p><p>
Could this generate momentum and angular momentum recoils? The two ends of the rollers should generate different recoils. The only asymmetry between the top and bottom is that the Earth surface bounds the system at the bottom. Could this give rise to a higher degree of quantum coherence at the upper ends of the rollers, which could give rise to a non-vanishing net acceleration and angular acceleration.
<LI> The observed magnetic walls could correspond to the return flux associated with the magnetic field of the rollers. That they are walls suggests that the flux tubes from the rollers fuse to a single flux wall and this gives rise to a quantum coherence. That the return flux consists of several magnetic walls rather than a single one suggests that the magnetic wall emerging from the roller system decomposes to these walls and the scale of quantum coherence is reduced. If the fluxes of walls return separately to the lower ends of rollers the degree of quantum coherence would be lower and this could give rise to a net effect.
<LI> Where could the energy of rotation and lift come from? Does it come from some external source, say the MB of the Earth? This could relate to as the 10 Hz cyclotron resonance assignable to the Fe ions in the "endogenous" magnetic field B<sub>end</sub>= 2B<sub>E</sub>/5 assigned to the monopole flux tubes as the model for the findings of Blackman suggests?
</p><p>
Does the energy come from the internal magnetic energy of the stator magnet or of rollers? Or does the energy come from the electrostatic energy associated with the horizontal electric field between electrodes and rollers as in the Biefeld Brown effect. This voltage should gradually reduce if this is the case.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/BB.pdf">About Biefeld Brown effect</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/hem.pdf">About long range electromagnetic quantum coherence in TGD Universe</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-17107589913527951842024-05-07T22:46:00.000-07:002024-05-08T20:37:20.413-07:00Biefeld Brown effect in TGD UniverseBiefeld Brown effect is one of the effects studied by "free energy" researchers. What happens is that an asymmetry capacitor for which the electrodes are of different size starts to move in the direction of the smaller electrode. The so called emdrive could be also based on this effect. Recently I learned of the experiments carried out by Buhler's team. An acceleration of 1 g is achieved for a capacitor-like system in vacuum and the effect increases rapidly with the strength of the electric field between the electrodes. This raises the question whether new physics is involved: either as a failure of the momentum conservation or as a presence of an unidentified system with which a momentum transfer takes place. In this article I consider the TGD basic model in which the third system is identified as the electric field body associated with the system.
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In the TGD basic model, the third system is identified as the electric field body (FB) associated with the system. The key idea is that electronic momentum is pumped from the electrodes to their FBs: an electron is transferred to the FB, leaves some of its momentum to FB and drops back and in this way gives rise to a recoil. For the smaller electrode the quantum coherence is higher and the pumping is more effective. This gives rise to the Biefeld Brown effect, perhaps even in the situation when the dielectric is present. There is also a net transfer of electrons momentum to the positive electrode, which reduces the voltage while keeping the system neutral and provides in this way electrostatic energy to the kicked electrons. This explains why the effect is stronger when the smaller electrode is positively charged.
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See the article <a HREF= "https://tgdtheory.fi/public_html/articles/BB.pdf">About Biefeld Brown effect</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/hem.pdf">About long range electromagnetic quantum coherence in TGD Universe</A>.
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For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-10707730164075729582024-05-06T22:49:00.000-07:002024-05-06T22:50:23.271-07:00Could entanglement entropy have a role similar to that of thermodynamical entropy?Gary Ehlenberg sent a link to a popular article (see <A HREF="https://phys.org/news/2024-05-scientists-entropy-quantum-entanglement.html">this</A>) telling about the work of Bartosz Regula and Ludovico Lami published as an article with title "Reversibility of quantum resources through probabilistic protocols" in Nature (see <A HREF="https://www.nature.com/articles/s41467-024-47243-2">this</A>).
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Quantum entanglement gives rise to a density matrix analogous to that of a thermodynamic system. One can assign to it entropy by a standard formula. In thermodynamics entropy characterizes the system besides other state variables. Could entanglement entropy have a role similar to that of thermodynamic entropy and allow us to classify entangled systems?
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<LI> In thermodynamics there are transformations of thermodynamic state, which in the adiabatic case preserve entropy. There is also a theorem giving an upper bound for the efficiency of a thermal engine transforming heat to work, which is ordered energy. Could one consider a similar theorem? Could thermodynamics generalize to a science of entropy manipulation?
<LI> Could adiabatic transformations preserving entanglement entropy be possible between two systems with the same entanglement entropy? Could the second law stating the increase of entropy generalize and state that transformations decreasing the entanglement entropy are not possible?
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Suppose that a system A defined as an equivalence class of systems with the same density matrix can be transformed B. Can one transform B to A in this kind of situation? This would be a counterpart of thermodynamic irreversibility stating that adiabatic time evolutions are reversible.
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<LI> It has been indeed proposed that it is possible to connect any two entangled systems with the same entanglement entropy by a transformation preserving the trace of the density matrix and keeping the eigenvalues positive. This transformation generalizes unitary transformations, which preserve the eigenvalues of the density matrix having probability interpretation. This kind of transformation would consist of basic physical transformations: I must confess that I do not quite understand what this means. If the conjecture is true one could classify entangled systems in terms of the entanglement entropy.
<LI> There are however systems for which the conjecture fails. A weaker condition would be that this kind of transformation exists in a probabilistic sense: the analog of adiabatic transformation would fail for some system pairs. One can apply the transformations of a specified set O of transformations to an ensemble formed by copies of A. Intuitively it would seem that the number of transformations in the set of O transforming A to B adiabatically divided by the total number of transformations gives a measure for the success. I am not quite sure whether this definition is used.
<LI> It is also stated the relative entropy for the probability distributions defined by the density matrices for systems A and B would in turn serve as an entanglement measure. Each fixed system B with fixed density matrix (or A) would define such a measure.
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This could have application to TGD inspired theory of consciousness.
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<LI> In TGD inspired theory of consciousness, one can assign to any system a number theoretic negentropy as a sum of p-adic entanglement: here the sum is over the ramified primes of an algebraic extension of rationals considered. The p-adic negentropies obey a formula similar to that for the ordinary entanglement negentropy. p-Adic negentropies can be however positive unlike the ordinary entanglement negentropy as a negative of entanglement entropy. The sum of p-adic negentropies measures the information of entanglement unlike ordinary entropy which measures the loss of information about either entangled state caused by the entanglement.
<LI> The number theoretic vision of TGD predicts that the entanglement negentropy is bound to increase in statistical sense in the number theoretic evolution and that this increase forces the increase of the ordinary entanglement entropy. Could the basic theorems of thermodynamics generalize also to this case and provide a mathematical way to understand the evolution of intelligent systems?
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For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0