tag:blogger.com,1999:blog-106143482023-11-30T03:10:31.875-08:00TGD diaryDaily musings, mostly about physics and consciousness, heavily biased by Topological Geometrodynamics background.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger2119125tag:blogger.com,1999:blog-10614348.post-86759812985447158392023-11-30T03:09:00.000-08:002023-11-30T03:09:31.385-08:00Pollack Effect and Some Anomalies of WaterIn the Pollack effect (PE) negatively charged exclusion zones (EZs) are induced at the boundary between the gel phase and water by an energy feed such as IR radiation. Pollack has introduced the notion of fourth phase of water, which obeys effective stoichiometry H<sub>1.5</sub>O and consists of hexagonal layers having therefore an ice-like structure. EZs e are able to clean up inpurities from their interior, which seems to be in conflict with the second law of thermodynamics. I have collected in the article <A HREF="https://tgdtheory.fi/public_html/articles/pollackwater.pdf">Pollack Effect and Some Anomalies of Water</A> examples of hydrodynamic anomalies, which might have an explanation in terms of the Pollack effect.
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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>.
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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-59736430487522578382023-11-29T19:58:00.000-08:002023-11-29T21:34:48.539-08:00Some facts about birational geometry
Birational geometry has as its morphisms birational maps: both the map and its inverse are expressible in terms of rational functions. The coefficients of polynomials appearing in rational functions are in the TGD framework rational. They map rationals to rationals and also numbers of given extension E of rationals to themselves (one can assign to each space-time region an extension defined by a polynomial).
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Therefore birational maps map cognitive representations, defined as discretizations of the space-time surface such that the points have physically/number theoretically preferred coordinates in E, to cognitive representations. They therefore respect cognitive representations and are morphisms of cognition. They are also number-theoretically universal, making sense for all p-adic number fields and their extensions induced by E. This makes birational maps extremely interesting from the TGD point of view.
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The following lists basic facts about birational geometry as I have understood them on the basis of Wikipedia articles about <A HREF="https://en.wikipedia.org/wiki/Birational_geometry"> birational geometry</A> and <A HREF ="https://en.wikipedia.org/wiki/Enriques Kodaira<sub>c</sub>lassification">Enriques-Kodaira classification</A>. I have added physics inspired associations with TGD.
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Birational geometries are one central approach to algebraic geometry.
<OL>
<LI> They provide classification of complex varieties to equivalence classes related by birational maps. The classification complex curves (real dimension 2) is best understood and reduces to the classification of projective curves of projective space CP<sub>n</sub> determined as zeros of a homogeneous polynomial. I had good luck since complex surfaces (real dimension 4) are of obvious interest in TGD: now however the notion of complex structure is generalized and one has Hamilton-Jacobi structure and Minkowski signature is allowed.
<LI> In TGD, a generalization of complex surfaces of complex dimension 2 in the embedding space H=M<sup>4</sup>× CP<sub>2</sub> of complex dimension 4 is considered. What is new is the presence of the Minkowski signature requiring a combination of hypercomplex and complex structures to the Hamilton-Jacobi structure. Note however the space-time surfaces also have counterparts in the Euclidean signature E<sup>4</sup>× CP<sub>2</sub>: whether this has a physical interpretation, remains an open question. Second representation is provided as 4-surfaces in the space M<sup>8</sup><sub>c</sub> of complexified octonions and an attractive idea is that M<sup>8</sup>-H duality corresponds to a birational mapping of cognitive representations to cognitive representations.
<LI> Every algebraic variety is birationally equivalent with a sub-variety of CP<sub>n</sub> so that their classification reduces to the classification of projective varieties of CP<sub>n</sub> defined in terms of homogeneous polynomials. n=2 (4 real dimensions) is of special relevance from the TGD point of view. A variety is said to be rational if it is birationally equivalent to some projective variety: for instance CP<sub>2</sub> is rational.
<LI> A concrete example of birational equivalence is provided by stereographic projections of quadric hypersurfaces in n+1-D linear space. Circle in plane is the simplest example. Let p be a point of quadric. The stereographic projection sends a point q of the quadric to the line going through p and q, that is a point of CP<sub>n</sub> in the complex case. One can select one point on the line as its representative. Another exammple is provided by Möbius transformations representing Lorentz group as transformations of complex plane.
</OL>
The notion of a minimal model is important.
<OL>
<LI> The basic observation is that it is possible to eliminate or add singularities by using birational maps of the space in which the surface is defined to some other spaces, which can have a higher dimension. Peaks and self-intersections are examples of singularities. The zeros of a birational map can be used to eliminate singularities of the algebraic surface of dimension n by blowups replacing the singularity with CP<sub>n</sub>. Poles in turn create singularities.
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The idea is to apply birational maps to find a birationally equivalent surface representation, which has no singularities. There is a very counter-intuitive formal description for this. For instance, complex curves of CP<sub>2</sub> have intersections since their sum of their real dimensions is 4. The same applies to 4-surfaces in H. My understanding is as follows: the blowup for CP<sub>2</sub> makes it possible to get rid of an intersection with intersection number 1. One can formally say that the blow up by gluing a CP<sub>1</sub> defines a curve which has negative intersection number -1.
<LI> In the TGD framework, wormhole contacts are Euclidian regions of space-time surface, which have the same metric and Kähler structure as CP<sub>2</sub> and light-like M<sup>4</sup> projection (or even H projection). They appear as blowups of singularities of 4-surfaces along a light-like curve of M<sup>8</sup>. The union of the quaternionic/associative normal spaces along the curve is not a line of CP<sub>2</sub> but CP<sub>2</sub> itself with two holes corresponding to the ends of the light-like curve. The 3-D normal spaces at the points of the light-like curve are not unique and form a local slicing of CP<sub>2</sub> by 3-D surfaces. This is a Minkowskian analog of a blow-up for a point and also an analog of cut of analytic function.
<LI> The Italian school of algebraic geometry has developed a rather detailed classification of these surfaces. The main result is that every complex surface X is birational either to a product CP<sup>1</sup>× C for some curve C or to a minimal surface Y. Preferred extremals are indeed minimal surfaces so that space-time surfaces might define minimal models. The absence of singularities (typically peaks or self-intersections) characterizing minimal models is indeed very natural since physically the peaks do not look acceptable.
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Mathematicians use invariants to characterize mathematical structures. In TGD birational invariants would be cognitive invariants. They would be extremely interesting physically if the 4-D generalization of holomorphy really to a fusion of complex and hypercomplex structrures make sense (see <A HREF="https://tgdtheory.fi/public_html/articles/wcwsymm.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>).
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There are several birationals invariants listed in the Wikipedia article. Many of them are rather technical in nature. The <A HREF="
https://en.wikipedia.org/wiki/Canonical_bundle">canonical bundle</A> K<sub>X</sub> for a variety of complex dimension n corresponds to n:th exterior power of complex cotangent bundle that is holomorphic n-forms. For space-time surfaces one would have n=2 and holomorphic 2-forms.
<OL>
<LI> Plurigenera corresponds to the dimensions for the vector space of global sections H<sub>0</sub>(X,K<sub>X</sub><sup>d</sup>) for smooth projective varieties and are birational invariants. The global sections define global coordinates, which define birational maps to a projective space of this dimension.
<LI> Kodaira dimension measures the complexity of the variety and characterizes how fast the plurigenera increase. It has values -∞,0,1,..n and has 4 values for space-time surfaces. The value -∞ corresponds to the simplest situation and for n=2 characterizes CP<sub>2</sub>, which is rational and has vanishing plurigenera.
<LI> The dimensions for the spaces of global sections of the tensor powers of complex cotangent bundle (holomorphic 1-forms) define birational invariants. In particular, holomorphic forms of type (p,0) are birational invariants unlike the more general forms having type (p,q). Betti numbers are not in general birational invariants.
<LI> Fundamental group is birational invariant as is obvious from the blowup construction. Other homotopy groups are not birational invariants.
<LI> <A HREF="https://en.wikipedia.org/wiki/Gromov Witten_invariant">Gromow-Witten</A> invariants are birational invariants. They are defined for pseudo-holomorphic curves (real dimension 2) in a symplectic manifold X. These invariants give the number of curves with a fixed genus and 2-homology class going through n marked points. Gromow-Witten invariants have also an interpretation as symplectic invariants characterizing the symplectic manifold X.
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In TGD, the application would be to partonic 2-surfaces of given genus g and homology charge (Kähler magnetic charge) representatable as holomorphic surfaces in X=CP<sub>2</sub> containing n marked points of CP<sub>2</sub> identifiable as the loci of fermions at the partonic 2-surface. This number would be of genuine interest in the calculation of scattering amplitudes.
</OL>
What birational classification could mean in the TGD framework?
<OL>
<LI> Holomorphic ansatz gives the space-time surfaces as Bohr orbits. Birational maps give new solutions from a given solution. It would be natural to organize the Bohr orbits to birational equivalence classes, which might be called cognitive equivalence classes. This should induce similar organization at the level of M<sup>8</sup><sub>c</sub>.
<LI> An interesting possibility is that for certain space-time surfaces CP<sub>2</sub> coordinates can be expressed in terms of preferred M<sup>4</sup> coordinates using birational functions and vice versa. Cognitive representation in M<sup>4</sup> coordinates would be mapped to a cognitive representation in CP<sub>2</sub> coordinates.
<LI> The interpretation of M<sup>8</sup>-H duality as a generalization of momentum position duality suggests information theoretic interpretation and the possibility that it could be seen as a cognitive/birational correspondence. This is indeed the case M<sup>4</sup> when one considers linear M<sup>4</sup> coordinates at both sides.
<LI> An intriguing question is whether the pair of hypercomplex and complex coordinates associated with the Hamilton-Jacobi structure could be regarded as cognitively acceptable coordinates. If Hamilton-Jacobi coordinates are cognitively acceptable, they should relate to linear M<sup>4</sup> coordinates by a birational correspondence so that M<sup>8</sup>-H duality in its basic form could be replaced with its composition with a coordinate transformation from the linear M<sup>4</sup> coordinates to particular Hamilton-Jacobi coordinates. The color rotations in CP<sub>2</sub> in turn define birational correspondences between different choices of Eguchi-Hanson coordinates.
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If this picture makes sense, one could say that the entire holomorphic space-time surfaces, rather than only their intersections with mass shells H<sup>3</sup> and partonic orbits, correspond to cognitive explosions. This interpretation might make sense since holomorphy has a huge potential for generating information: it would make TGD exactly solvable.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/birational.pdf">Birational maps as morphisms of cognitive structures</A> or the chapter <a HREF= "https://tgdtheory.fi/public_html/articles/M8Hagain.pdf">New findings related to the number theoretical view of TGD</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>.
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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-8445317893403141732023-11-26T23:18:00.000-08:002023-11-28T00:23:59.840-08:00Cymatics, ringing bells, water memory, homeopathy, Pollack effect, turbulence
<B>Warning</B>: This post contains many words, which induce deep aggression in academic colleagues receiving a monthly salary: cymatics, the ringing bells of Buddhist monks, water memory, and homeopathy(!!). Pollack effect is perhaps not so aggression inducing and turbulence is quite neutral. All these words are linked: this is message that I try to communicate in the following.
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Cymatics (see <A HREF="https://en.wikipedia.org/wiki/Cymatics">this</A>) is a very interesting phenomenon. Thanks to Jukka Sarno for a post inspiring this comment. I lost the original link: Facebook has started to suddenly change the page content completely and this makes it very difficult to respond to the posts. Maybe some kind of virus is in question.
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I came across a related phenomenon recently. The ringing of Buddhist monks' bells by running the bell along its edge has strange effects. The water started to boil so that a strong transfer of energy had to happen to the water by sound. Energy was supplied to the system by the ringer of the bells. This energy could play a role of metabolic energy and help in the problems resulting from its local deficiency in the patient's body.
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Something analogous to turbulence also arises in cymatics. Turbulence and its generation are very interesting phenomena and poorly understood. Standard hydrodynamics, which was developed centuries ago, can't really cope with the challenges of the modern world: if only someone could tell this to the theoreticians working on it!
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I myself have built a model for turbulence and related phenomena (see <A HREF="https://tgdtheory.fi/public_html/articles/TGDhydro.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/freezing.pdf">this</A>). A core element of the model is the anomalous phenomenon observed by Pollack related to water. When water is irradiated in the presence of a gel phase with, for example, infrared light, negatively charged gel-like volumes are created in the water: Pollack talks about the fourth phase of water. Living matter is full of them: for instance cell interior is negatively charged as also DNA.
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Some of the water's protons disappear somewhere: in the TGD world they would go to the magnetic body of the water and form dark matter there precisely because we cannot detect them with standard methods. This dark matter would be a phase of ordinary matter with a nonstandard, and often very large value of effective Planck constant. This would make it quantum coherent in much longer scales than ordinary matter.
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Pollack's fourth phase resembles ice and very recently it has been discovered that there is a thin ice-like layer at the interface between water and air (see <A HREF="https://tgdtheory.fi/public_html/articles/TGDhydro.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/freezing.pdf">this</A>). Could it be Pollack's fourth phase? The energy input is essential. In cymatics and in the case of bells the energy feeder would be sound rather than light. In homeopathy (one of the most hated phenomena of physics besides water memory; I have never understood why it generates so deep a hatred), the shaking of the homeopathic preparation would supply the energy. A fourth phase of water would be created and the water would become "living" as its magnetic body would "wake up" and start to control ordinary matter.
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Homeopathy is one of the most hated phenomena of physics besides water memory; I have never understood why it generates so deep hatred), the shaking of the homeopathic preparation would supply the energy. A fourth phase of water would be created and the water would become "living" as its magnetic body would "wake up" and start to control ordinary matter.
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In homeopathy, shaking would provide the energy making it possible to create magnetic organisms consisting of flux tubes associated with water molecule clusters connected by hydrogen bonds. Their cyclotron frequency spectrum would mimic the corresponding spectrum of the molecules dissolved in water. Water would magnetically mimic the intruder molecule and from the perspective of biology this would be enough for water memory explaining homeopathic effects. This should be trivial for scientists living in the computer age but some kind of primitive regression makes it impossible for colleagues to stay calm and rational when they hear the word "homeopathy".
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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>.
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.com1tag:blogger.com,1999:blog-10614348.post-33521123181707059372023-11-26T01:52:00.000-08:002023-11-29T21:31:23.801-08:00Birational maps as morphisms of cognitive structures
Birational maps and their inverses are defined in terms of rational functions. They are very special in the sense that they map algebraic numbers in a given extension E of rationals to E itself. In the TGD framework, E defines a unique discretization of the space-time surface if the preferred coordinates of the allowed points belong to E. I refer to this discretization as cognitive representation. Birational maps map points in E to points in E so that they define what might be called cognitive morphism.
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M<sup>8</sup>-H duality duality (H=M<sup>4</sup>× CP<sub>2</sub>) relates the number vision of TGD to the geometric vision. M<sup>8</sup>-H duality maps the 4-surfaces in M<sup>8</sup><sub>c</sub> to space-time surfaces in H: a natural condition is that in some sense it maps E to E and cognitive representations to cognitive representations. There are special surfaces in M<sup>8</sup><sub>c</sub> that allow cognitive explosion in the number-theotically preferred coordinates. M<sup>4</sup> and hyperbolic spaces H<sup>3</sup> (mass shells), which contain 3-surfaces defining holographic data, are examples of these surfaces. Also the 3-D light-like partonic orbits defining holographic data. Possibly also string world sheets define holographic data. Does cognitive explosion happen also in these cases?
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In M<sup>8</sup><sub>c</sub> octonionic structure allows to identify natural preferred coordinates. In H, in particular M<sup>4</sup>, the preferred coordinates are not so unique but should be related by birational mappings. So called Hamilton-Jacobi structures define candidates for preferred coordinates: could different Hamilton-Jacobi structures relate to the each other by birational maps? In this article these questions are discussed.
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See the article <a HREF= "https://tgdtheory.fi/public_html/articles/birational.pdf">Birational maps as morphisms of cognitive structures</A> or the chapter <a HREF= "https://tgdtheory.fi/public_html/articles/M8Hagain.pdf">New findings related to the number theoretical view of TGD</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-63095262071737964192023-11-24T04:39:00.000-08:002023-11-24T04:39:20.008-08:00Boundary conditions at partonic orbits and holography
TGD reduces coupling constant evolution to a number theoretical evolution of the coupling parameters of the action identified as Kähler function for WCW. An interesting question is how the 3-D holographic data at the partonic orbits relates to the corresponding 3-D data at the ends of space-time surfaces at the boundary of CD, and how it relates to coupling constant evolution.
<OL>
<LI> The twistor lift of TGD strongly favours 6-D Kähler action, which dimensionally reduces to Kähler action plus volume term plus topological ∫ J∧ J term reducing to Chern Simons-Kähler action. The coefficients of these terms are proposed to be expressible in terms of number theoretical invariants characterizing the algebraic extensions of rationals and polynomials determining the space-time surfaces by M<sup>8</sup>-H duality.
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Number theoretical coupling constant evolution would be discrete. Each extension of rationals would give rise to its own coupling parameters involving also the ramified primes characterizing the polynomials involved and identified as p-adic length scales.
<LI> The time evolution of the partonic orbit would be non-deterministic but subject to the light-likeness constraint and boundary conditions guaranteeing conservation laws. The natural expectation is that the boundary/interface conditions for a given action cannot be satisfied for all partonic orbits (and other singularities). The deformation of the partonic orbit requiring that boundary conditions are satisfied, does not affect X<sup>3</sup> but the time derivatives ∂<sub>t</sub> h<sup>k</sup> at X<sup>3</sup> are affected since the form of the holomorphic functions defining the space-time surface would change. The interpretation would be in terms of duality of the holographic data associated with the partonic orbits <I> resp.</I> X<sup>3</sup>.
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There can of course exist deformations, which require the change of the coupling parameters of the action to satisfy the boundary conditions. One can consider an analog of renormalization group equations in which the deformation corresponds to a modification of the coupling parameters of the action, most plausibly determined by the twistor lift. Coupling parameters would label different regions of WCW and the space-time surfaces possible for two different sets of coupling parameters would define interfaces between these regions.
</OL>
In order to build a more detailed view one must fix the details related to the action whose value defines the WCW Kähler function.
<OL>
<LI> If Kähler action is identified as Kähler action, the identification is unique. There is however the possibility that the imaginary exponent of the instanton term or the contribution from the Euclidean region is not included in the definition of Kähler function. For instance instanton term could be interpreted as a phase of quantum state and would not contribute.
<LI> Both Minkowskian and Euclidean regions are involved and the Euclidean signature poses problems. The definition of the determinant as (-g<sub>4</sub>)<sup>1/2</sup> is natural in Minkowskian regions but gives an imaginary contribution in Euclidean regions. (|g<sub>4</sub>|)<sup>1/2</sup> is real in both regions. i(g<sub>4</sub>)<sup>1/2</sup> is real in Minkowskian regions but imaginary in the Euclidean regions.
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There is also a problem related to the instanton term, which does not depend on the metric determinant at all. In QFT context the instanton term is imaginary and this is important for instance in QCD in the definition of CP breaking vacuum functional. Should one include only the 4-D or possibly only Minkowskian contribution to the Kähler function imaginary coefficient for the instanton/Euclidian term would be possible?
<LI> Boundary conditions guaranteeing the conservation laws at the partonic orbits must be satisfied. Consider the |g<sub>4</sub>| case. Charge transfer between Euclidean and Minkowskian regions. If the C-S-K term is real, also the charge transfer between partonic orbit and 4-D regions is possible. The boundary conditions at the partonic orbit fix it to a high degree and also affect the time derivatives ∂<sub>t</sub>h<sup>k</sup> at X<sup>3</sup>. This option looks physically rather attractive because classical conserved charges would be real.
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If the C-S-K term is imaginary it behaves like a free particle since charge exchange with Minkowskian and Euclidean regions is not possible. A possible interpretation of the possible M<sup>4</sup> contribution to momentum could be in terms of decay width. The symplectic charges do not however involve momentum. The imaginary contribution to momentum could therefore come only from the Euclidean region.
<LI> If the Euclidean contribution is imaginary, it seems that it cannot be included in the Kähler function. Since in M<sup>8</sup> picture the momenta of virtual fermions are in general complex, one could consider the possibility that Euclidean contribution to the momentum is imaginary and allows an interpretation as a decay width.
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/wcwsymm.pdf">Symmetries and Geometry of the "World of Classical Worlds"</A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/wcwnew.pdf">Recent View about K\"ahler Geometry and Spin Structure of "World of Classical Worlds"</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-28197631919792798202023-11-23T20:26:00.000-08:002023-11-23T22:11:37.258-08:00Why the water flowing out of bathtub rotates always in the same direction?
In FB Wes Johnson wondered whether Coriolis force could explain why the water flowing out of bathtub forms a vortex with direction which is opposite at Northern and Southern hemispheres.
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Coriolis effect is a coordinate force proportional to ω× v, where ω is the angular velocity of Earth directed to Noth and v is the velocity of the object. For bathtub v would be downwards, that is in the direction of Earth radius. At the equator Coriolis force is along the equator and non-vanishing. On the other hand, the force causing rotation of water in the bathtub is of opposite sign below and above equator and therefore vanishes at equator. Therefore Coriolis force is excluded as an explanation.
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My own view is that this is a hydrodynamical effect and new physics might be involved. Turbulence is involved and vortex is generated. The direction of the rotation of the vortex should be understood. The selection of a specific direction violates parity symmetry and this gives in the TGD framework strong guidelines.
<OL>
<LI> The vortex is in the direction of the Earth's gravitational force. In the TGD framework, gravitational interaction is mediated by monopole flux tubes in the direction of the gravitational field. Quantum gravitation is involved and it is quite possible that the gravitational magnetic body (MB) induces the effect since quite generally MB plays a control role, in particular in living matter.
<LI> The induced Kähler field contributes to both electromagnetic and classical (weak) Z<sup>0</sup> field: since the matter is em neutral but not Z<sup>0</sup> neutral, it seems that Z<sup>0</sup> field must be in question. Could the gravitational MB of Earth consist of Z<sup>0</sup> monopole flux tubes?
</p><p>
If this is the case, a macroscopic quantum effect involving a very large value ℏ<sub>gr</sub>=GMm/β<sub>0</sub> of gravitational Planck constant of the pair formed by Earth mass and particle must be in question since ordinary Z<sup>0</sup> has extremely short range. The gravitational Compton length Λ<sub>gr</sub> = ℏ<sub>gr</sub>/m= GM/β<sub>0</sub>= r_S/2β<sub>0</sub> does not depend on particle mass and Z<sup>0</sup> is about .5 cm, one half of the Schwartschild radius of the Earth, for the favored β<sub>0</sub>=v<sub>0</sub>/c=1.
<LI> In the classical Z<sup>0</sup> field, particles with Z<sup>0</sup> charges rotate around the axis of the field and since magnetic flux is approximately dipole field, the flux lines are radial but are upwards/downwards above/below the equator. This would explain why the rotation directions of the vortex are opposite and Northern and Southern hemispheres. The presence of the classical Z<sup>0</sup> field, which violates parity symmetry, would also conform with the parity breaking and would be essential for the understanding of the mystery of chiral selection in biomatter.
</OL>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
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-57207429825657291282023-11-22T22:32:00.000-08:002023-11-24T19:22:10.590-08:00Mysterious lift of drill in downwards water flowI learned of a very interesting and paradoxical looking phenomenon. Thanks for Shamoon Ahmed for the link. A drill with a helical geometry raises in a downwards fluid flow (see <A HREF="https://www.facebook.com/watch?v=671753375096778">this</A>) This is in conflict with the naive expectations.
<OL>
<LI> Suppose first that momentum is conserved. By momentum conservation water must get downwards directed momentum if the drill obtains upwards directed momentum. If there is no slipping, just the opposite should happen. Therefore the situation could be like in a turbulent flow: the water and the drill do not directly touch each other. There is indeed turbulence as one can see.
</p><p>
But what makes possible the slipping? It has been quite recently learned that the surface of water in air has thin ice-like layer for which TGD suggests and explanation (see <A HREF="https://tgdtheory.fi/public_html/articles/freezing.pdf">this</A>). The surface between drill and water would be covered by a very thin ice layer so that slipping would take place naturally. Drill is like a skater. Also the boundary layer in the water (liquid) flow past a body could be a thin ice-sheet. Second analogy is as a screw penetrating upstream.
<LI> But is the momentum really conserved? Water is accelerated in the gravitational field: this gives it momentum. Water is rotating already before the addition of the drill. The downwards kinematic pressure, which increases downwards, pushes the drill having a helical geometry. If there is no friction fixing the drill to water flow, the drill has no other option than raise. The constraint due to helicality forces the drill to rotate.
</p><p>
Water in the vortex and drill would rotate in opposite directions and helicality constraint would transform the rotational motion of the drill to a translational motion and force the rotation of drill to gain upwards directed momentum.
<LI> This raises some questions.
<OL>
<LI> Could there be a connection with the fact that in the Northern/Southern hemisphere water flowing in a water tub rotates in a unique direction (kind of parity breaking)?
<LI> What is the role of the handedness of the drill? One would expect that the drill with an opposite handedness rotate in an opposite direction? What if the handedness of the drill does not favor the natural rotation direction for the vortex? Do these effects tend to cancel.
</OL>
</OL>
There might be a connection with the "ordinary" hydrodynamics. The drill raising in the fluid flow is analogous to a propeller. Could also ordinary propeller involve the same basic mechanism and act like a skater and in this way minimize dissipative energy losses? It is known that propellers induce cavitation as evaporation of water and there is anecdotal evidence from power plants that more energy is liberated in the process than one would expect. Recently it was found that the mere irradiation of water by light leads to its evaporation as a generation of droplets, which would have ice-like surface layer consisting of the fourth phase of water (this requires energy): Pollack effect again! Could dark photons with a non-standard value of Planck constant provide the energy needed for the cavitation creating a vapour phase with a larger total area of fourth phase of water?
</p><p>
Runcel D. Arcaya informed me of the work of a brilliant experimentalist and inventor <A HREF="https://infinityturbine.com/viktor-schauberger.html">Victor Schauberger</A> related to the strange properties of flowing water. This work relates in an interesting manner to the effect discussed. I have written about Schauberger's findings about to the ability of fishes too swim "too" easily upstream. Gravitation is involved also now. Could the bodily posture of the fish generate the counterpart of the helical geometry? Could the fish as a living organism help to generate the fourth phase of water in the water bounding their skin by Pollack effect, which requires the presence of a gel phase besides energy source (IR radiation for instance) to transform part of protons of water molecules to dark photons with a higher energy.
</p><p>
Schauberger also invented a method of water purification using vortex flow: the reason for why the method works remained unclear. In Pollack effect, the negatively charged exclusion zones (EZs) spontaneously purify themselves. This conflicts with the thermodynamical intuitions. The TGD explanation is in terms of reversed arrow of time which explains the purification process as normal diffusion leading to the decay of gradients but taking place with an opposite arrow of time. Could the purification of in vortex flow be caused by the Pollack effect creating the surface layers consisting of the fourth phase of water (EZs)?
</p><p>
Schauberger developed the notion of living water and believed that spring water is somehow very special in this respect. In TGD water is regarded as a multiphase system involving magnetic body with layers labelled by the values of effective Planck constant h<sub>eff</sub>. The larger the value of the h<sub>eff</sub>, the higher the (basically algebraic complexity) and "IQ" of the system. Gravitational magnetic body has the largest value of effective Planck constant. Spring water is pure and could be this kind of highly complex system. Also systems involving turbulence and vortices are very complex.
</p><p>
See the article <A HREF=https://tgdtheory.fi/public_html/articles/freezing.pdf">TGD Inspired Model for Freezing in Nano Scales</A> and the chapter <A HREF=https://tgdtheory.fi/pdfpool/TGDhydro.pdf">TGD and Quantum Hydrodynamics</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-47881480883824705902023-11-22T00:17:00.000-08:002023-11-24T04:07:09.373-08:00About the universality of the holomorphic solution ansatz
The explicit solution of field equations in terms of the generalized holomorphy is now known. Also the emergence of supersymplectic symmetry is understood: it emerges as symmetries of Chern-Simons-Kähler action at the 3-D partonic orbits defining part of 3-D holographic data.
</p><p>
The solution ansatz is independent of action as long it is general coordinate invariance depending only on the induced geometric structures. Space-time surfaces would be minimal surfaces apart from lower-dimensional singular surfaces at which the field equations involve the entire action. Only the singularities, classical charges and positions of topological interaction vertices depend on the choice of the action (see <A HREF="https://tgdtheory.fi/public_html/articles/wcwsymm.pdf">this</A>). Kähler action plus volume term is the choice of action forced by twistor lift making the choice of H unique.
</p><p>
The universality has a very intriguing implication. One can assign to any action of this kind conserved Noether currents and their fermionic counterparts (also super counterparts). One would have a huge algebra of conserved currents characterizing the space-time geometry. The corresponding charges need not be conserved since the conservation conditions at the partonic orbits and other singularities depend on the action. The discussion of the symplectic symmetries leads to the conclusion that they give rise to conserved charges at the partonic 3-surfaces obeying Chern-Simons-Kähler dynamics, which is non-deterministic.
</p><p>
Partonic 3-surfaces could be in the same role as space-like 3-surfaces as initial data: the time coordinate for this time evolution would be dual to the light-like coordinate of the partonic orbit. Could one say that the measurement localizing the partonic orbit leads to a phase characterized by a particular action? The classical conserved quantities are determined by the action. The WCW K\"ahler function should correspond to this action and different actions would correspond to different regions of WCW. Could phase transition between these regions take place when the 4-surface determined by the partonic orbit belongs to regions corresponding to two different effective actions. The twistor lift suggests that action must be the sum of the Kähler action and volume term so that only Kähler couplings strength, the coefficient of instanton term and the dynamically determined cosmological constant would vary.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/wcwsymm.pdf">Symmetries and Geometry of the "World of Classical Worlds"</A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/wcwnew.pdf">Recent View about K\"ahler Geometry and Spin Structure of "World of Classical Worlds"</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-12167453327968069222023-11-21T01:46:00.000-08:002023-11-21T22:09:42.858-08:00Some comments about the identification of leptons and matter-antimatter asymmetry
The mathematical formulation of TGD has now reached a stage in which one can seriously consider fixing the details of the physical interpretation of the theory. The discussion of the detailed physical interpretation in articles (see <A HREF="https://tgdtheory.fi/public_html/articles/nuclatomplato.pdf">this</A>), inspired by what I called Platonization, led to a proposal for a unification of hadron, nuclear, atomic, and molecular physics in terms of the notion of Hamiltonian cycles defined by monopole flux tubes at Platonic solids. This generated quite unexpected insights and killer predictions.
</p><p>
In (see <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">this</A>) a construction of strong, electroweak and gravitational interaction vertices, reducing them to partly topological 2-vertex describing a creation of fermion-antifermion pair in a classical induced electroweak gauge potentials, led to very concrete predictions relating also the topological explanation of family replication phenomenon and its correlation with homology charge of the partonic 2-surface.
</p><p>
In the articles (see <A HREF="https://tgdtheory.fi/public_html/articles/wcwsymm.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>) the identification of the isometries of WCW were considered and explicit realizations of symplectic and holomorphic isometry generators demonstrated that the original intuitive view is almost correct. The new aspects were related to the holography suggesting also a duality between symplectic and holomorphic isometry charges and supercharges. Also the relationship of holography, apparently in conflict with path integral approach, was understood. The dynamics of light-like partonic orbits is almost topological and not completely deterministic, which implies that the finite sum over partonic orbits can be approximated with path integral at QFT limit.
</p><p>
The emergence of all these constraints raises the hope that one could fix the interpretation of the theory at the level of details. In this article, the identification of leptons and matter-antimatter asymmetry are reconsidered in light of the new understanding.
<h3>About two competing identifications for leptons</h3>
In the TGD Universe, one can imagine two competing identifications of leptons.
<OL>
<LI> Leptons and quarks correspond to different chiralities of spinors of H=M<sup>4</sup>× CP<sub>2</sub>.
<LI> Only quarks are fundamental fermions and leptons are anti-baryon like objects.
</OL>
<h4>Option A: Are both leptons and quarks fundamental fermions?</h4>
</p><p>
The first option means that both lepton and quark chiralities appear in the modified Dirac action fixed by hermicity once the action fixing space-time surfaces or their lower-dimensional submanifolds such as string world sheets and partonic orbits is known. In accordance with the experimental facts, lepton and quark numbers are conserved separately for this option. This is the original proposal and seems to be the most realistic option although the geometry of "world of classical worlds" (WCW) in terms of anticommutators of WCW gamma matrices, expressible as super generators of symmetries of H inducing isometries of WCW, seems to require only a single fermionic chirality.
</p><p>
The challenge is to explain why both chiralities are needed. It seems now clear that all elementary particles should be assignable to 2-sheeted monopole flux tubes with the fermion lines at wormhole throats (partonic 2-surfaces) of wormhole contacts identifiable as boundaries of string world sheets. The fermion numbers could be also delocalized inside string world sheets inside the flux tubes or inside flux tubes. Also in condensed matter physics states localized to geometric objects of various dimensions are accepted as a basic notion (for TGD view of condensed matter see (see <A HREF="https://tgdtheory.fi/public_html/articles/TGDcondmatshort.pdf">this</A>).
</p><p>
One can identify several dichotomies, which are analogous to the lepton-quark dichotomy. There is holomorphic-symplectic dichotomy, the dichotomy between light-like partonic orbits and 3-surfaces at the boundaries of Δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub>, the dichotomy between Euclidean and Minkowskian space-time regions and the dichotomy between the 3-D holographic boundary data and interiors of the space-time surface. Could one unify all these dichotomies?
<OL>
<LI> Consider first the Minkowskian-Euclidean dichotomy. Leptons could reside inside (string world sheets of) the Minkowskian regions of space-time surface and quarks inside (the string world sheets of) the Euclidean wormhole contacts. Euclidean regions with a fixed Minkowskian region or vice versa could be regarded as two sub-WCWs.
</p><p>
The nice feature of this option is that it allows us to understand both quark/color confinement without any quark propagation and propagation of quarks in QCD. We would not see free quarks because they live inside the Euclidean regions of the space-time surface and do not propagate inside the Minkowskian regions of the space-time surface. Embedding space spinor spinor fields would however propagate in accordance in H which gives rise to quark propagators in the scattering amplitudes and conforms with the QCD picture. Notice that both quarks and leptons can appear at the partonic orbits forming the interfaces between Euclidean and Minkowskian space-time regions.
<LI> The holomorphic-symplectic dichotomy for the isometries of WCW is now well-established and one has explicit expression for the corresponding conserved charges and their fermionic counters defining gamma matrices as fermionic super charges which in anticommute to WCW metric.
</p><p>
The symplectic representations of the fermionic isometry generators associated with the light-like partonic orbits at boundaries of CD defining 3-D holomorphic data could correspond to quarks. In accordance with color confinement, quarks would not appear at Euclidean 3-surfaces at light-cone boundaries Δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub>. Classical gluon fields would define the simplest Hamiltonian fluxes and conserved quantities in the 3-D dynamics would be determined by the Chern-Simons-Kähler action with time defined by the light-like time coordinate. The Hamiltonians of S<sup>2</sup>× CP<sub>2</sub>,organized to representations of color group and of rotation group restricted to partonic 2-surface, would define the Hamiltonian fluxes.
</p><p>
The 4-D holomorphic representations in the interior of space-time surfaces and also assignable to the 3-surfaces at the boundaries of space-time surface at Δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> would correspond to leptons. Also the anticommutators of the lepton-like gamma matrices would give contributions to the metric of WCW.
<LI> Holography as a dichotomy would suggest at quantum level that in an information theoretic sense the 4-D holomorphic dynamics of leptons represents the 3-D symplectic dynamics of quarks. The possibility of a kind of holography-like relation was already discussed in (see <A HREF="https://tgdtheory.fi/public_html/articles/nuclatomplato.pdf">this</A>), where it was found that the states of nuclei could be in rather precise correspondence with the states of atomic electrons. A generalization of this holography would correspond to a kind of quark-lepton holography.
</OL>
One can argue that this general view could lead to a conflict with the possible holography-like relation between ordinary and dark quarks considered in (see <A HREF="https://tgdtheory.fi/public_html/articles/emuanomaly.pdf">this</A>) as a way to guarantee that perturbation theory converges.
<OL>
<LI> According to an intuitive argument, strong coupling strength is proportional to 1/h<sub>eff</sub> so that the increase of effective Planck constant h<sub>eff</sub> could guarantee the convergence of QFT type description expected at QFT limit of TGD. Ordinary quarks could transform in the h→ h<sub>eff</sub> transition to states, which consist of pair of quark and dark antiquark with a vanishing total color, electroweak quantum numbers and spin whereas the second dark quark with a larger value of h<sub>eff</sub> would have quantum numbers of the ordinary quark.
</p><p>
The proposal was that dark quark and antiquark reside at the Minkowskian string world sheet. This does not conform with the above proposal, which requires that all quarks are at the partonic orbits.
<LI> This problem can be solved. Many-sheeted space-time however makes it possible to imagine that the dark quark and antiquark reside at the wormhole contacts of a larger space-time sheet and form a dark meson-like object. For instance, the ordinary quark would be associated with a wormhole contact connecting the other large space-time sheet to a third smaller space-time sheet, itself part of the monopole flux tube defining the ordinary quark. This would conform with the hierarchy formed by flux tubes topologically condensed to larger flux tubes.
</OL>
<h4>Option B: Are only quarks fundamental fermions?</h4>
</p><p>
The second option stating that only quarks are fundamental particles, was motivated by the fact that only single fermion chirality seemed to be needed to construct WCW geometry. Leptons would be antibaryon-like states such that the 3 antiquarks are associated with single wormhole contact (see <A HREF="https://tgdtheory.fi/public_html/articles/leptoDelta.pdf">this</A>). Lepton itself would be a closed monopole flux tube with geometric size defined by the Compton scale.
<OL>
<LI> The first critical question is whether it makes sense to put 3 quarks to the same wormhole contact defining 2-D surface in CP<sub>2</sub> when the color degrees of freedom correspond to the "rotational" degrees of freedom in CP<sub>2</sub> but realized as spinor modes. One would have at least 2 antiquarks at the same wormhole contact. If the partonic 2-surface is homologically non-trivial geodesic sphere, the reduction of symmetry from SU(3) to U(2) subgroup with the same Cartan algebra occurs and the rotational degrees of freedom reduce to those at the partonic 2-surface. Wave functions for quarks would be wave functions for the end of the string at a partonic 2-surface having well-defined U(2) quantum numbers.
<LI> If multi-quark states at partonic 2-surfaces make sense, one can ask how to avoid the counterparts of Δ baryons with spin 3/2. Statistics constraint does not help to achieve this. Oscillator operators for color partial waves of quarks are anticommuting and there seems to be no reason excluding these states. In this sense color quantum numbers are like spin-like quantum numbers. One could of course hope that Δ-like states have a very high mass scale.
<LI> The third critical question concerns the origin of the CP breaking which would allow baryons as stable 3-quark states and only leptons as stable bound states of 3 antiquarks. Matter antimatter asymmetry would correspond to the stable condensation of antiquarks to leptons and quarks to baryons. This mechanism looks really elegant.
</OL>
</p><p>
<h3>How matter antimatter asymmetry could be generated?</h3>
</p><p>
Both options A and B for the identification of leptons must be able to explain the generation of matter-antimatter asymmetry.
<OL>
<LI> CP breaking involving M<sup>4</sup> and/or CP<sub>2</sub> Kähler forms could explain the matter antimatter asymmetry along the same lines as in the standard picture. For Option A a small asymmetry between the densities of fermions and antifermions should be generated in the early cosmology and annihilation would lead to the antisymmetry. There would be space-time regions with opposite sign of asymmetries. For Option B the densities of leptons and antileptons and baryons and antibaryons would be slightly different before the annihilation and there would be no actual asymmetry.
<LI> For both A and B option, many-sheeted space-time and the hierarchy of magnetic bodies makes it possible to imagine many different realizations for the separation of fermion and antifermion numbers. For instance, cosmic strings could contain antimatter. The ordinary matter would be generated in the decay of the energy of cosmic strings to ordinary matter. This process is the TGD counterpart of inflation and highly analogous to black hole evaporation.
</p><p>
In the simplest model, this energy would be associated with classical M<sup>4</sup> type Kähler electric fields and CP<sub>2</sub> type Kähler magnetic fields inside the cosmic string. The decay of the volume energy and the energy of the classical electroweak fields would take place by a generation of fermion-antifermion pairs via fermion 2-vertex and classical electroweak gauge potentials would appear in the vertex.
<LI> If the CP breaking induced by the classical Kähler fields makes it more probable for antifermions to remain inside the monopole flux tubes, antimatter-matter asymmetry is generated. Also the CP breaking observed in meson decays could relate to the asymmetry caused by the induced Kähler field of the meson-like monopole flux tube.
<LI> In QCD, the topological instanton term gives rise to strong CP breaking as a CP violation of the vacuum state which is not invariant under CP (so called theta parameter describes the situation, (see <A HREF="https://arxiv.org/pdf/1409.3454.pdf">this</A>).
</p><p>
In the TGD framework, the "instanton density" ∫ J∧ J for the induced Kähler field is non-vanishing and analogous to the theta therm. As a matter fact, instanton density is equal to the gluonic istanto action for the classical gluon field g<sub>A</sub>= H<sub>A</sub>J. Instanton density can be transformed to the Chern-Simons-Kähler action as a boundary term and their contribution to the action is analogous to instanton number in QCD although it need not be integer valued. The Chern-Simons-Kähler action gives a contribution to the modified Dirac action at partonic orbits giving rise to fermionic vertices.
</p><p>
The strong Kähler magnetic fields at the monopole flux tubes give rise to the analog of strong CP violation and provide a possible quantitative description for the generation of the matter-antimatter asymmetry in the decay of the energy of cosmic strings to fermion-antifermion pairs and bosons. For cosmic strings the Kähler magnetic field is extremely strong.
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/leptcp.pdf">Some comments about the identification of leptons and matter-antimatter asymmetry</A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/emuanomaly.pdf">About the TGD based views of family replication phenomenon, color confinement, identification of leptons, and matter-antimatter asymmetry</A>
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-52205001101825633972023-11-20T22:03:00.000-08:002023-11-21T22:10:30.006-08:00Objection against the idea about theoretician friendly Mother Nature
One of the key ideas behind the TGD view of dark matter is that Nature is theoretician friendly (see <A HREF="https://tgdtheory.fi/public_html/articles/emuanomaly.df">this</A>). When the coupling strength proportional to ℏ<sub>eff</sub> becomes so large that perturbation series ceases to converge, a phase transition increasing the value of h<sub>eff</sub> takes place so that the perturbation series converges.
</p><p>
One can however argue that this argument is quantum field-theoretic and does not apply in TGD since holography changes the very concept of perturbation theory. There is no path integral to worry about. Path integral is indeed such a fundamental concept that one expects it to have some approximate counterpart also in the TGD Universe. Bohr orbits are not completely deterministic: could the sum over the Bohr orbits however translate to an approximate description as a path integral at the QFT limit? The dynamics of light-like partonic orbits is indeed non-deterministic and could give rise to an analog of path integral as a finite sum.
<OL>
<LI> The dynamics implied by Chern-Simons-Kähler action assignable to the partonic 3-surface with light-one coordinate in the role of time, is very topological in that the partonic orbits is light-like 3-surface and has 2-D CP<sub>2</sub> and M<sup>4</sup> projections unless the induced M<sup>4</sup> and CP<sub>2</sub> Kähler forms sum up to zero. The light-likeness of the projection is a very loose condition and and the sum over partonic orbits as possible representation of holographic data analogous to initial values (light-likeness!) is therefore analogous to the sum over all paths appearing as a representation of Schrödinger equation in wave mechanics.
</p><p>
One would have an analog of 1-D QFT. This means that the infinities of quantum field theories are absent but for a large enough coupling strength g<sup>2</sup>/4πℏ the perturbation series fails to converge. The increase of h<sub>eff</sub> would resolve the problem. For instance, Dirac equation in atomic physics makes unphysical predictions when the value of nucler charge is larger than Z≈ 137.
<LI> I have also considered a discretized variant of this picture. The light-like orbits would consist of pieces of light-like geodesics. The points at which the direction of segment changes would correspond to points at which energy and momentum transfer between the partonic orbit and environment takes place. This kind of quantum number transfer might occur at least for the fermionic lines as boundaries of string world sheets. They could be described quantum mechanically as interactions with classical fields in the same way as the creation of fermion pairs as a fundamental vertex (see <A HREF="https://tgdtheory.fi/public_html/articles/SW.df">this</A>). The same universal 2-vertex would be in question.
<LI> What is intriguing, that the light-likeness of the projection of the CP<sub>2</sub> type extremals in M<sup>4</sup> leads to Virasoro conditions assignable to M<sup>4</sup> coordinates and this eventually led to the idea of conformal symmetries as isometries as WCW. In the case of the partonic orbits, the light-like curve would be in M<sup>4</sup>× CP<sub>2</sub> but it would not be surprising if the generalization of the Virasoro conditions would emerge also now.
</p><p>
One can write M<sup>4</sup> and CP<sub>2</sub> coordinates for the light-like curve as Fourier expansion in powers of exp(it), where t is the light-like coordinate. This gives h<sup>k</sup>= ∑ h<sup>k</sup><sub>n</sub> exp(int). If the CP<sub>2</sub> projection of the orbits of the partonic 2-surface is geodesic circle, CP<sub>2</sub> metric s<sub>kl</sub> is constant, the light-likeness condition h<sub>kl</sub>∂<sub>t</sub>h<sup>k</sup>∂l<sub>t</sub>h<sup>l</sup>=0 gives Re(h<sub>kl</sub>∑<sub>m</sub> h<sup>k</sup><sub>n-m</sub>h<sup>l</sup><sub>m</sub>=0). This does not give Virasoro conditions.
</p><p>
The condition d/dt(h<sub>kl</sub>∂<sub>t</sub>h<sup>k</sup>∂<sub>t</sub>h<sup>l</sup>=0)=0 however gives the standard Virasoro conditions stating that the normal ordered operators L<sub>n</sub>= Re(h<sub>kl</sub>∑<sub>m</sub> (n-m) h<sup>k</sup><sub>n-m</sub>h</sub><sup>l</sup><sub>m</sub>) annihilate the physical states. What is interesting is that the latter condition also allows time-like (and even space-like) geodesics.
<LI> Could massivation mean a failure of light-likeness? For piecewise light-like geodesics the light-likeness condition would be true only inside the segments. By taking Fourier transform one expects to obtain Virasoro conditions with a cutoff analogous to the momentum cutoff in condensed matter physics for crystals.
For piecewise light-like geodesics the condition would be trivially true inside the segments and therefore discretized. By taking Fourier transform one expects to obtain Virasoro conditions with a cutoff analogous to the momentum cutoff in condensed matter physics for crystals.
<LI> In TGD the Virasoro, Kac-Moody algebras and symplectic algebras are replaced by half-algebras and the gauge conditions are satisfied for conformal weights which are n-multiples of fundamentals with with n larger than some minimal value. This would dramatically reduce the effects of the non-determinism and could make the sum over all paths allowed by the light-likeness manifestly finite and reduce it to a sum with a finite number of terms. This cutoff in degrees of freedom would correspond to a genuinely physical cutoff due to the finite measurement resolution coded to the number theoretical anatomy of the space-time surfaces. This cutoff is analogous to momentum cutoff and could at the space-time picture correspond to finite minimum length for the light-like segments of the orbit of the partoic 2-surface.
</OL>
See the articles <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">About the Relationships Between Weak and Strong Interactions and Quantum Gravity in the TGD Universe</A>, <A HREF="https://tgdtheory.fi/public_html/articles/HJ.pdf">Holography and Hamilton-Jacobi Structure as 4-D generalization of 2-D complex structure</A>, and <A HREF="https://tgdtheory.fi/public_html/articles/wcwsymm.pdf">Symmetries and Geometry of the "World of Classical Worlds"</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-1267295200608098642023-11-18T23:07:00.000-08:002023-11-18T23:07:08.706-08:00The Great Narrative of theoretical physicsI have used a lot of time in pondering the Great Narrative of theoretical physics. It has two components. The stubborn belief on the idea of a continuous progress that arose during the Enlightenment: it has proven impossible to admit that huge mistakes have been made at the level of basic postulates so that progress has become illusory.
</p><p>
The second component comes from colonialism: the development of theoretical physics is seen as a series of wars of conquest. Reductionism encapsulates how conquest-war progresses. Each conquered area corresponds to a new field of physics. The community is still unable to see that the triumphal march of reductionism is a very similar illusion as colonialism was.
</p><p>
Wars of conquest have progressed in the direction of both short and long length scales. We have progressed from the planetary system to astrophysical and cosmic scales. The narrative of cosmology has started to crack more and more: there is a crisis related to the understanding of dark matter and energy and inflationary theory has been in crisis from the beginning. As a matter of fact, a state of stagnation here might be a better word than crisis since crisis means criticality and a promise for something new.
</p><p>
The observations already made earlier, and especially James Webb, have now once and for all destroyed the grand cosmological narrative. The Big Bang remains, but Webb's observations call into question the concept of time at the base of cosmology (galaxies older than the universe), the assumption that coherence is only possible on short scales (correlations on cosmic scales), the assumptions about how signals propagate (or rather do not propagate) on cosmological scales, and also the existing view of the formation of astro-physical objects.
</p><p>
On the other hand, progress has been made in both directions by starting from atomic physics which was a real triumph, but molecular physics is already just phenomenology without any real theory (for example, the concept of a chemical bond is not understood on a basic level at all). In biochemistry, biocatalysis remains a complete mystery.
</p><p>
The troops marched also in the direction of nuclear physics, but it was necessary to decide that it is a completely separate area from atomic physics, even though correlations were noticed very early on. The march proceeded to electroweak interactions: this was a real success and also to hadron physics and QCD. It was agreed that hadrons have been understood even though color confinement remained a complete mystery. Standard model emerged and all that was left was the jump to the Planck length scales. The GUTs were a leap into the void producing nothing, but were accepted as a part of the great narrative, partly for reasons related to funding.
</p><p>
Finally, the super string model was built as a theory that was supposed to unify the standard model and quantum gravity. The trial was based on two theories, both of which have a huge gap. The gaps were already noticed a hundred years ago.
</p><p>
In Einstein's theory, conservation laws of the Special Relativity are lost, but perhaps because the discoverer of the gap was Emmy Noether, a woman and a Jew, this discovery was not allowed to mess with the unfolding Grand Narrative.
</p><p>
The basic paradox of quantum measurement theory was the big gap of quantum mechanics. In the spirit of pragmatism, even that was not allowed to interfere with the development of the Great Narrative so that an endless variety of interpretations were invented. So it's no wonder that the superstring theory built above these two great gaps eventually collapsed.
</p><p>
When one thinks about reductionist wars of conquest, one can't avoid comparisons to Alexander the Great's victories and the rapid collapse of the empire that followed. The Colonial Wars is another point of comparison. In between all the areas of the physics landscape agreed to be conquered, there are white areas on the map, about which nothing is actually known. The last hundred years of theoretical physics will probably be seen as the greatest intellectual self-deception in human intellectual history.
</p><p>
I remember the novel, was it the core of Darkness, which told about a similar illusion related to colonialism. It told about a commander of a British base in Africa, a drunkard who desperately tried to maintain the illusion that the situation was under control after all. In the same way the community of theoretical physicists tries to preserve its Grand Illusions. Internalized censorship takes care that new ideas challenging the basic dogmas are neither published in "prestigious" journals nor funded.
</p><p>
Can one find reasons for the recent situation? Sloppy thinking is certainly one basic reason. Colleagues must respect the rules of logic when they write computer code but when it comes to the consistency between fundamental assumptions and mathematics and empirical facts, the basic rules of logic are given up: the justification for this deadly sin of theoretician comes from "pragmatism".
</p><p>
It has been said that great narratives are dead. I do not agree with this. Great Narrative of theoretical physics is possible but it can be developed only by a continual challenging of the basic assumptions of the existing narrative. This has not been done for a century.
</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.com1tag:blogger.com,1999:blog-10614348.post-67105788446046234722023-11-18T22:00:00.000-08:002023-11-18T22:01:01.690-08:00Kundalini phenomenon from TGD point of view
There was a very interesting post by Hunter Glenn in <A HREF="https://www.facebook.com/groups/1735260376685389/">Qualia Computing Network</A> about the Kundalini phenomenon. The proposal of Glenn was that the charge separations relate somehow to the Kundalini phenomenon involving both the bliss and the dark night of the soul suggesting that (quantum) criticality is involved.
</p><p>
In bioelectromagnetism it has been known for decades that the sign of electric gradient along the longitudinal axis of the body correlates with the state of consciousness. The sign of the electric gradient changes when one falls asleep. This sign matters also at the level of brain hemispheres in horizontal direction. At the neuronal level the membrane potential changes temporarily sign during the nerve pulses. At the axonal microtubular level the sign of gradient matters and the tubule is in (quantum?) critical state in the sense that it is decaying and re-assembling all the time.
</p><p>
This suggests that the electric gradient along the spine correlates with the contents of consciousness and has a lot to do with the kundalini phenomenon. The appearance of chills in the spine could reflect the generation of electrical gradients. In my own Great Experience around 1985I experienced these chills and the subsequent "whole body consciousness" completely free from the usual "thermal noise". The attempt to understand this experience led to the development of TGD inspired theory of consciousness.
</p><p>
Charges are needed to create these gradients and the natural question is where these charges reside. Between what kind of systems the charge separations are generated?
</p><p>
Electric gradients and charge separations seem to be fundamental. In the TGD inspired quantum model of the nerve pulse, the cell membrane is regarded as a Josephson junction. Standard physics does not of course allow this: according to the Hodgkin-Huxley model the currents are ohmic currents. There is very intriguing experimental evidence in conflict with the assumption of Ohmic currents as cause of nerve pulse: they could be of course caused by it. This evidence justifies TGD inspired model of nerve pulse discussed <A HREF="https://tgdtheory.fi/public_html/articles/np2023.pdf">here</A>.
The model involves the Pollack effect as a way to generate charge separations. In presence of suitable energy feed and gel phase, water develops negatively charged regions with very high charge. 1/4:th of protons of water molecules to somewhere, "outside" the system in some sense. This generates electric gradients and all electric gradients in living matter could be created in this way by metabolic energy feed.
</p><p>
Where could the protons go? In the TGD Universe they would go to the magnetic body (MB), the TGD geometric counterpart for Maxwellian magnetic fields, and form a dark phase there. This would mean that they have non-standard and very large values of effective Planck constant so that they form a large-scale quantum coherent phase at MB: this would induce the coherence of ordinary biomatter as forced coherence. The MB in question would be a gravitational magnetic body and the value of gravitational Planck constant was proposed already by Nottale. Charge separations would reduce to those between the biological body (cell membrane, etc) and corresponding (gravitational) MB and this would allow us to understand how the electric gradients develop. Also nerve pulse would be based on the Pollack effect.
</p><p>
The spiritual aspect would come to play via the magnetic body representing higher level consciousness (an entire hierarchy of them is predicted). In Kundalini a connection to some magnetic body would be created (or lost) and could also give rise to the experience of becoming God.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/np2023.pdf">Some new aspects of the TGD inspired model of the nerve pulse</A> or the <A HREF="https://tgdtheory.fi/public_html/articles/np2023.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.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-20394626591261133752023-11-16T21:46:00.000-08:002023-11-20T23:16:15.895-08:00Symmetries and Geometry of the "World of Classical Worlds"<B>Still about the symmetries of WCW</B>
</p><p>
I have been analyzing the basic visions of TGD trying to identify weak points. WCW geometry exists only if it has maximal isometries. I have proposed that WCW could be regarded as a union of generalized symmetric spaces labelled by zero modes which do not contribute to the metric. The induced Kähler field is invariant under symplectic transformations of CP<sub>2</sub> and would therefore define zero mode degrees of freedom if one assumes that WCW metric has symplectic transformations as isometries. In particular, Kähler magnetic fluxes would define zero modes and are quantized closed 2-surfaces. The induced metric appearing in Kähler action is however not zero mode degree of freedom. If the action contains volume term, the assumption about union of symmetric spaces is not well-motivated.
</p><p>
Symplectic transformations are not the only candidates for the isometries of WCW. The basic picture about what these maximal isometries could be, is partially inspired by string models.
<OL>
<LI> A weaker proposal is that the symplectomorphisms of H define only symplectomorphisms of WCW. Extended conformal symmetries define also a candidate for isometry group. Remarkably, light-like boundary has an infinite-dimensional group of isometries which are in 1-1 correspondence with conformal symmetries of S<sup>2</sup>⊂ S<sup>2</sup>× R<sub>+</sub>= δ M<sup>4</sup><sub>+</sub>.
<LI> Extended Kac Moody symmetries induced by isometries of δ M<sup>4</sup><sub>+</sub> are also natural candidates for isometries. The motivation for the proposal comes from physical intuition deriving from string models. Note they do not include Poincare symmetries, which act naturally as isometries in the moduli space of causal diamonds (CDs) forming the "spine" of WCW.
<LI> The light-like orbits of partonic 2-surfaces might allow separate symmetry algebras. One must however notice that there is exchange of charges between interior degrees of freedom and partonic 2-surfaces. The essential point is that one can assign to these surface conserved charges when the dual light-like coordinate defines time coordinate. This picture also assumes a slicing of space-time surface by by the partonic orbits for which partonic orbits associated with wormrhole throats and boundaries of the space-time surface would be special. This slicing would correspond to Hamilton-Jacobi structure.
<LI> Fractal hierarchy of symmetry algebras with conformal weights, which are non-negative integer multiples of fundamental conformal weights, is essential and distinguishes TGD from string models. Gauge conditions are true only the isomorphic subalgebra and its commutator with the entire algebra and the maximal gauge symmetry to a dynamical symmetry with generators having conformal weights below maximal value. This view also conforms with p-adic mass calculations.
<LI> The realization of the symmetries for 3-surfaces at the boundaries of CD and for light-like orbits of partonic 2-surfaces is known. The problem is how to extend the symmetries to the interior of the space-time surface. It is natural to expect that the symmetries at partonic orbits and light-cone boundary extend to the same symmetries.
</OL>
<B>Could generalized holomorphy allow to sharpen the existing views?</B>
</p><p>
This picture is rather speculative, allows several variants, and is not proven. There is now however a rather convincing ansatz for the general form of preferred extremals. This proposal relies on the realization of holography as generalized 4-D holomorphy. Could it help to make the picture more precise?
<OL>
<LI> Explicit solution of field equations in terms of the generalized holomorphy is now known. The solution ansatz is independent of action as long it is general coordinate invariance depending only on
the induced geometric structures. Space-time surfaces would be minimal surfaces apart from lower-dimensional singular surfaces at which the field equations involve the entire action. Only the singularities, classical charges and positions of topological interaction vertices depend on the choice of the action (see <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">this</A>). Kähler action plus volume term is the choice of action forced by twistor lift making the choice of H unique.
<LI> Hamilton-Jacobi structures emerge naturally as generalized conformal structures of space-time surfaces and M<sup>4</sup> (see <A HREF="https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>). This inspires a proposal for a generalization of modular invariance and of moduli spaces as subspaces of Teichmüller spaces.
<LI> One can assign to holomorphy conserved Noether charges. The conservation reduces to the algebraic conditions satisfied for the same reason as field equations, i.e. the conservation conditions involving contractions of complex tensors of type (1,1) with tensors of type (2,0) and (0,2). The charges have the same form as Noether charges but it is not completely clear whether the action remains invariant under these transformations. This point is non-trivial since Noether theorem says that invariance of the action implies the existence of conserved charges but not vice versa. Could TGD represent a situation in which the equivalence between symmetries of action and conservation laws fails?
</p><p>
Also string models have conformal symmetries but in this case 2-D area form suffers conformal scaling. Also the fact that holomorphic ansatz is satisfied for such a large class of actions apart from singularities suggests that the action is not invariant.
<LI> The action should define Kähler function for WCW identified as the space of Bohr orbits. WCW Kähler metric is defined in terms of the second derivatives of the Kähler action of type (1,1) with respect to complex coordinates of WCW. Does the invariance of the action under holomorphies imply a trivial Kähler metric and constant Kähler function?
</p><p>
Here one must be very cautious since by holography the variations of the space-time surface are induced by those of 3-surface defining holographic data so that the entire space-time surface is modified and the action can change. The presence of singularities, analogous to poles and cuts of an analytic function and representing particles, suggests that the action represents the interactions of particles and must change. Therefore the action might not be invariant under holomorphies. The parameters characterizing the singularities should affect the value of the action just as the positions of these singularities in 2-D electrostatistics affect the Coulomb energy.
</p><p>
Generalized conformal charges and supercharges define a generalization of Super Virasoro algebra of string models. Also Kac-Moody algebras assignable to the isometries of δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> and light-like 3 surfaces generalize trivially.
<LI> An absolutely essential point is that generalized holomorphisms are <I>not</I> symmetries of Kähler function since otherwise Kähler metric involving second derivatives of type (1,1) with respect to complex coordinates of WCW is non-trivial if defined by these symmetry generators as differential operators. If Kähler function is equal to Kähler action, as it seems, Kähler action cannot be invariant under generalized holomorphies.
</p><p>
Noether's theorem states that the invariance of the action under a symmetry implies the conservation of corresponding charge but does <I>not</I> claim that the existence of conserved Noether currents implies invariance of the action. Since Noether currents are conserved now, one would have a concrete example about the situation in which the inverse of Noether's theorem does not hold true. In a string model based on area action, conformal transformations of complex string coordinates give rise to conserved Noether currents as one easily checks. The area element defined by the induced metric suffers a conformal scaling so that the action is not invariant in this case.
</OL>
<B>Challenging the existing picture of WCW geometry</B>
</p><p>
These findings make it possible to challenge and perhaps sharpen the existing speculations concerning the metric and isometries of WCW.
</p><p>
I have considered the possibility that also the symplectomorphisms of δ M<sup>4</sup>+× CP<sub>2</sub> could define WCW isometries. This actually the original proposal. One can imagine two options.
<OL>
<LI> The continuation of symplectic transformations to transformations of the space-time surface from the boundary of light-cone or from the orbits partonic 2-surfaces should give rise to conserved Noether currents but it is not at all obvious whether this is the case.
<LI> One can assign conserved charges to the time evolution of the 3-D boundary data defining the holographic data: the time coordinate for the evolution would correspond to the light-like coordinate of light-cone boundary or partonic orbit. This option I have not considered hitherto. It turns out that this option works!
</OL>
The conclusion would be that generalized holomorphies give rise to conserved charges for 4-D time evolution and symplectic transformations give rise to conserved charged for 3-D time evolution associated with the holographic data.
</p><p>
<B>About extremals of Chern-Simons-Kähler action</B>
</p><p>
Let us look first the general nature of the solutions to the extremization of Chern-Simons-Kähler action.
<OL>
<LI> The light-likeness of the partonic orbits requires Chern-Simons action, which is equivalent to the topological action J∧ J, which is total divergence and is a symplectic in variant. The field equations at the boundary cannot involve induced metric so that only induced symplectic structure remains. The 3-D holographic data at partonic orbits would extremize Cherns-Simons-Kähler action. Note that at the ends of the space-time surface about boundaries of CD one cannot pose any dynamics.
<LI> If the induced Kähler form has only the CP<sub>2</sub> part, the variation of Chern-Simons-Kähler form would give equations satisfied if the CP<sub>2</sub> projection is at most 2-dimensional and Chern-Simons action would vanish and imply that instanton number vanishes.
<LI> If the action is the sum of M<sup>4</sup> and CP<sub>2</sub> parts, the field equations in M<sup>4</sup> and CP<sub>2</sub> degrees of freedom would give the same result. If the induced Kähler form is identified as the sum of the M<sup>4</sup> and CP<sub>2</sub> parts, the equations also allow solutions for which the induced M<sup>4</sup> and CP<sub>2</sub> Kähler forms sum up to zero. This phase would involve a map identifying M<sup>4</sup> and CP<sub>2</sub> projections and force induce Kähler forms to be identical. This would force magnetic charge in M<sup>4</sup> and the question is whether the line connecting the tips of the CD makes non-trivial homology possible. The homology charges and the 2-D ends of the partonic orbit cancel each other so that partonic surfaces can have monopole charge.
</p><p>
The conditions at the partonic orbits do not pose conditions on the interior and should allow generalized holomorphy.
The following considerations show that besides homology charges as Kähler magnetic fluxes also Hamiltonian fluxes are conserved in Chern-Simons-Kähler dynamics.
</OL>
<B>Can one assign conserved charges with symplectic transformations or partonic orbits
and 3-surfaces at light-cone boundary?</B>
</p><p>
The geometric picture is that symplectic symmetries are Hamiltonian flows along the light-like partonic orbits generated by the projection A<sub>t</sub> of the Kähler gauge potential in the direction of the light-like time coordinate. The physical picture is that the partonic 2-surface is a Kähler charged particle that couples to the Hamilton H=A<sub>t</sub>. The Hamiltonians H<sub>A</sub> are conserved in this time evolution and give rise to conserved Noether currents. The corresponding conserved charge is integral over the 2-surface defined by the area form defined by the induced Kähler form.
</p><p>
Let's examine the change of the Chern-Simons-Kähler action in a deformation that corresponds, for example, to the CP<sub>2</sub> symplectic transformation generated by Hamilton H<sub>A</sub>. M<sup>4</sup> symplectic transformations can be treated in the same way:here however M<sup>4</sup> Kähler form would be involved, assumed to accompany Hamilton-Jacobi structure as a dynamically generated structure.
</p><p>
<OL>
</p><p>
<LI> Instanton density for the induced Kähler form reduces to a total divergence and gives Chern-Simons-Kähler action, which is TGD analog of topological action. This action should change in infinitesimal symplectic transformations by a total divergence, which should vanish for extremals and give rise to a conserved current. The integral of the divergence gives a vanishing charge difference between the ends of the partonic orbit. If the symplectic transformations define symmetries, it should be possible to assign to each Hamiltonian H<sub>A</sub> a conserved charge. The corresponding quantal charge would be associated with the modified Dirac action.
</p><p>
<LI> The conserved charge would be an integral over X<sup>2</sup>. The surface element is not given by the metric but by the symplectic structure, so that it is preserved in symplectic transformations. The 2-surface of the time evolution should correspond to the Hamiltonian time transformation generated by the projection A<sub>α</sub>=A<sub>k</sub> ∂<sub>α</sub>s<sup>k</sup> of the Kähler gauge potential A<sub>k</sub> to the direction of light-like time coordinate x<sup>α</sub>== t.
</p><p>
<LI> The effect of the generator j<sub>A</sub><sup>k</sup>= J<sup>kl</sup>∂<sub>l</sub>H<sub>A</sub> on the Kähler potential A<sub>l</sub> is given by j<sup>k</sup><sub>A</sub>∂<sub>k</sub>A<sub>l</sub>. This can be written as ∂<sub>k</sub>A<sub>l</sub>=J<sub>kl</sub> + ∂<sub>l</sub>A<sub>k</sub>. The first term gives the desired total divergence ∂<sub>α</sub> (ε<sup>αβγ</sup>J<sub>βγ</sub> H<sub>A</sub>).
</p><p>
The second term is proportional to the term ∂<sub>α</sub>H<sub>A</sub>- {A<sub>α</sub>,H}. Suppose that the induced Kähler form is transversal to the light-like time coordinate t, i.e. the induced Kähler form does not have components of form J<sub>tμ</sub>. In this kind of situation the only possible choice for α corresponds to the time coordinate t. In this situation one can perform the replacement ∂<sub>α</sub>H<sub>A</sub>-{A<sub>α</sub>,H}→ dH<sub>A</sub>/dt-{A<sub>t</sub>,H}. This corresponds to a Hamiltonian time evolution generated by the projection A<sub>t</sub> acting as a Hamiltonian. If this is really a Hamiltonian time evolution, one has dH<sub>A</sub>/dt-{A,H}=0. Because the Poisson bracket represents a commutator, the Hamiltonian time evolution equation is analogous to the vanishing of a covariant derivative of H<sub>A</sub> along light-like curves: ∂<sub>t</sub>H<sub>A</sub> +[A,H<sub>A</sub>]= 0. The physical interpretation is that the partonic surface develops like a particle with a Kähler charge. As a consequence the change of the action reduces to a total divergence.
</p><p>
An explicit expression for the conserved current J<sub>A</sub><sup>α</sup>=H<sub>A</sub> ε<sup>αβγ</sup>J<sub>βγ</sub> can be derived from the vanishing of the total divergence. Symplectic transformations on X<sup>2</sup> generate an infinite-dimensional symplectic algebra. The charge is given by the Hamiltonian flux Q<sub>A</sub> =∫ H<sub>A</sub> J<sub>αβ</sub>dx<sup>α</sup>∧dx<sup>β</sup>.
<LI> If the projection of the partonic path CP<sub>2</sub> or M<sup>4</sup> is 2-D, then the light-like geodesic line corresponds to the path of the parton surface. If A<sub>l</sub> can be chosen parallel to the surface, its projection in the direction of time disappears and one has A<sub>t</sub>=0. In the more general case, X<sup>2</sup> could, for example, rotate in CP<sub>2</sub>. In this case A<sub>t</sub> is nonvanishing. If J is transversal (no Kähler electric field), charge conservation is obtained.
</OL>
Do the above observations apply at the boundary of the light-cone?
<OL>
<LI> Now the 3-surface is space-like and Chern-Simons-Kähler action makes sense. It is not necessary but emerges from the "instanton density" for the Kähler form. The symplectic transformations of δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> are the symmetries. The most time evolution associated with the radial light-like coordinate would be from the tip of the light-cone boundary to the boundary of CD. Conserved charges as homological invariants defining symplectic algebra would be associated with the 2-D slices of 3-surfaces. For closed 3-surfaces the total charges from the sheets of 3-space as covering of δ M<sup>4</sup><sub>+</sub> must sum up to zero.
<LI> Interestingly, the original proposal for the isometries of WCW was that the Hamiltonian fluxes assignable to M<sup>4</sup> and CP<sub>2</sub> degrees of freedom at light-like boundary act define the charges associated with the WCW isometries as symplectic transformations so that a strong form of holography would have been be realized and space-time surface would have been effectively 2-dimensional. The recent view is that these symmetries pose conditions only on the 3-D holographic data. The holographic charges would correspond to additional isometries of WCW and would be well-defined for the 3-surfaces at the light-cone boundary.
</OL>
To sum up, one can imagine many options but the following picture is perhaps the simplest one and is supported
by physical intuition and mathematical facts. The isometry algebra ofδ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> consists of generalized conformal and KM algebras at 3-surfaces in δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> and symplectic algebras at the light cone boundary and 3-D light-like partonic orbits. The latter symmetries give constraints on the 3-D holographic data. It is still unclear whether one can assign generalized conformal and Kac-Moody charges to Chern-Simons-K\"ahler action. The isomorphic subalgebras labelled by a positive integer and their commutators with the entire algebra would annihilate the physical states.
</p><p>
<B>The TGD counterparts of the gauge conditions of string models</B>
</p><p>
The string model picture forces to ask whether the symplectic algebras and the generalized conformal and Kac-Moody algebras could act as gauge symmetries.
<OL>
<LI> In string model picture conformal invariance would suggest that the generators of the generalized conformal and KM symmetries act as gauge transformations annihilate the physical states. In the TGD framework, this does not however make sense physically. This also suggests that the components of the metric defined by supergenerators of generalized conformal and Kac Moody transformations vanish. If so, the symplectomorphisms δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> localized with respect to the light-like radial coordinate acting as isometries would be needed. The half-algebras of both symplectic and conformal generators are labelled by a non-negative integer defining an analog of conformal weight so there is a fractal hierarchy of isomorphic subalgebras in both cases.
<LI> TGD forces to ask whether only subalgebras of both conformal and Kac-Moody half algebras, isomorphic to the full algebras, act as gauge algebras. This applies also to the symplectic case. Here it is essential that only the half algebra with non-negative multiples of the fundamental conformal weights is allowed. For the subalgebra annihilating the states the conformal weights would be fixed integer multiples of those for the full algebra. The gauge property would be true for all algebras involved. The remaining symmetries would be genuine dynamical symmetries of the reduced WCW and this would reflect the number theoretically realized finite measurement resolution. The reduction of degrees of freedom would also be analogous to the basic property of hyperfinite factors assumed to play a key role in thee definition of finite measurement resolution.
<LI> For strong holography, the orbits of partonic 2-surfaces and boundaries of the spacetime surface at δ M<sup>4</sup><sub>+</sub> would be dual in the information theoretic sense. Either would be enough to determine the space-time surface.
</OL>
See the articles <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">About the Relationships Between Weak and Strong Interactions and Quantum Gravity in the TGD Universe</A>, <A HREF="https://tgdtheory.fi/public_html/articles/HJ.pdf">Holography and Hamilton-Jacobi Structure as 4-D generalization of 2-D complex structure</A>, <A HREF="https://tgdtheory.fi/public_html/articles/wcwsymm.pdf">Symmetries and Geometry of the "World of Classical Worlds"</A> and the chapter <A HREF="https://tgdtheory.fi/pdfpool/wcwnew.pdf">Recent View about K\"ahler Geometry and Spin Structure of "World of Classical Worlds"</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-33791616374445008792023-11-14T05:24:00.000-08:002023-11-16T07:17:34.956-08:00Still about the symmetries of WCW
I have been analyzing the basic visions of TGD trying to identify weak points. WCW geometry exists only if it has maximal isometries. I have proposed that WCW could be regarded as a union of generalized symmetric spaces labelled by zero modes which do not contribute to the metric. The induced Kähler field is invariant under symplectic transformations of CP<sub>2</sub> and would therefore define zero mode degrees of freedom if one assumes that WCW metric has symplectic transformations as isometries. In particular, Kähler magnetic fluxes would define zero modes and are quantized closed 2-surfaces. The induced metric appearing in Kähler action is however not zero mode degree of freedom. If the action contains volume term, the assumption about union of symmetric spaces is not well-motivated.
</p><p>
Symplectic transformations are not the only candidates for the isometries of WCW. The basic picture about what these maximal isometries could be, is partially inspired by string models.
<OL>
<LI> A weaker proposal is that the symplectomorphisms of H define only symplectomorphisms of WCW. Extended conformal symmetries define also a candidate for isometry group. Remarkably, light-like boundary has an infinite-dimensional group of isometries which are in 1-1 correspondence with conformal symmetries of S<sup>2</sup>⊂ S<sup>2</sup>× R<sub>+</sub>= δ M<sup>4</sup><sub>+</sub>.
<LI> Extended Kac Moody symmetries induced by isometries of δ M<sup>4</sup><sub>+</sub> are also natural candidates for isometries. The motivation for the proposal comes from physical intuition deriving from string models. Note they do not include Poincare symmetries, which act naturally as isometries in the moduli space of causal diamonds (CDs) forming the "spine" of WCW.
<LI> The light-like orbits of partonic 2-surfaces might allow separate symmetry algebras. One must however notice that there is exchange of charges between interior degrees of freedom and partonic 2-surfaces. The essential point is that one can assign to these surface conserved charges when the dual light-like coordinate defines time coordinate. This picture also assumes a slicing of space-time surface by by the partonic orbits for which partonic orbits associated with wormrhole throats and boundaries of the space-time surface would be special. This slicing would correspond to Hamilton-Jacobi structure.
<LI> Fractal hierarchy of symmetry algebras with conformal weights, which are non-negative integer multiples of fundamental conformal weights, is essential and distinguishes TGD from string models. Gauge conditions are true only the isomorphic subalgebra and its commutator with the entire algebra and the maximal gauge symmetry to a dynamical symmetry with generators having conformal weights below maximal value. This view also conforms with p-adic mass calculations.
<LI> The realization of the symmetries for 3-surfaces at the boundaries of CD and for light-like orbits of partonic 2-surfaces is known. The problem is how to extend the symmetries to the interior of the space-time surface. It is natural to expect that the symmetries at partonic orbits and light-cone boundary extend to the same symmetries.
</OL>
<B>Could generalized holomorphy allow to sharpen the existing views?</B>
</p><p>
This picture is rather speculative, allows several variants, and is not proven. There is now however a rather convincing ansatz for the general form of preferred extremals. This proposal relies on the realization of holography as generalized 4-D holomorphy. Could it help to make the picture more precise?
<OL>
<LI> Explicit solution of field equations in terms of the generalized holomorphy is now known. The solution ansatz is independent of action as long it is general coordinate invariance depending only on
the induced geometric structures. Space-time surfaces would be minimal surfaces apart from lower-dimensional singular surfaces at which the field equations involve the entire action. Only the singularities, classical charges and positions of topological interaction vertices depend on the choice of the action (see <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">this</A>). Kähler action plus volume term is the choice of action forced by twistor lift making the choice of H unique.
<LI> Hamilton-Jacobi structures emerge naturally as generalized conformal structures of space-time surfaces and M<sup>4</sup> (see <A HREF="https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>). This inspires a proposal for a generalization of modular invariance and of moduli spaces as subspaces of Teichmüller spaces.
<LI> One can assign to holomorphy conserved Noether charges. The conservation reduces to the algebraic conditions satisfied for the same reason as field equations, i.e. the conservation conditions involving contractions of complex tensors of type (1,1) with tensors of type (2,0) and (0,2). The charges have the same form as Noether charges but it is not completely clear whether the action remains invariant under these transformations. This point is non-trivial since Noether theorem says that invariance of the action implies the existence of conserved charges but not vice versa. Could TGD represent a situation in which the equivalence between symmetries of action and conservation laws fails?
</p><p>
Also string models have conformal symmetries but in this case 2-D area form suffers conformal scaling. Also the fact that holomorphic ansatz is satisfied for such a large class of actions apart from singularities suggests that the action is not invariant.
<LI> The action should define Kähler function for WCW identified as the space of Bohr orbits. WCW Kähler metric is defined in terms of the second derivatives of the Kähler action of type (1,1) with respect to complex coordinates of WCW. Does the invariance of the action under holomorphies imply a trivial Kähler metric and constant Kähler function?
</p><p>
Here one must be very cautious since by holography the variations of the space-time surface are induced by those of 3-surface defining holographic data so that the entire space-time surface is modified and the action can change. The presence of singularities, analogous to poles and cuts of an analytic function and representing particles, suggests that the action represents the interactions of particles and must change. Therefore the action might not be invariant under holomorphies. The parameters characterizing the singularities should affect the value of the action just as the positions of these singularities in 2-D electrostatistics affect the Coulomb energy.
</p><p>
Generalized conformal charges and supercharges define a generalization of Super Virasoro algebra of string models. Also Kac-Moody algebras assignable to the isometries of δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> and light-like 3 surfaces generalize trivially.
<LI> An absolutely essential point is that generalized holomorphisms are <I>not</I> symmetries of Kähler function since otherwise Kähler metric involving second derivatives of type (1,1) with respect to complex coordinates of WCW is non-trivial if defined by these symmetry generators as differential operators. If Kähler function is equal to Kähler action, as it seems, Kähler action cannot be invariant under generalized holomorphies.
</p><p>
Noether's theorem states that the invariance of the action under a symmetry implies the conservation of corresponding charge but does <I>not</I> claim that the existence of conserved Noether currents implies invariance of the action. Since Noether currents are conserved now, one would have a concrete example about the situation in which the inverse of Noether's theorem does not hold true. In a string model based on area action, conformal transformations of complex string coordinates give rise to conserved Noether currents as one easily checks. The area element defined by the induced metric suffers a conformal scaling so that the action is not invariant in this case.
</OL>
<B>Challenging the existing picture of WCW geometry</B>
</p><p>
These findings make it possible to challenge and perhaps sharpen the existing speculations concerning the metric and isometries of WCW.
</p><p>
I have considered the possibility that also the symplectomorphisms of δ M<sup>4</sup>+× CP<sub>2</sub> could define WCW isometries. This actually the original proposal. One can imagine two options.
<OL>
<LI> The continuation of symplectic transformations to transformations of the space-time surface from the boundary of light-cone or from the orbits partonic 2-surfaces should give rise to conserved Noether currents but it is not at all obvious whether this is the case.
<LI> One can assign conserved charges to the time evolution of the 3-D boundary data defining the holographic data: the time coordinate for the evolution would correspond to the light-like coordinate of light-cone boundary or partonic orbit. This option I have not considered hitherto. It turns out that this option works!
</OL>
The conclusion would be that generalized holomorphies give rise to conserved charges for 4-D time evolution and symplectic transformations give rise to conserved charged for 3-D time evolution associated with the holographic data.
</p><p>
<B>About extremals of Chern-Simons-Kähler action</B>
</p><p>
Let us look first the general nature of the solutions to the extremization of Chern-Simons-Kähler action.
<OL>
<LI> The light-likeness of the partonic orbits requires Chern-Simons action, which is equivalent to the topological action J∧ J, which is total divergence and is a symplectic in variant. The field equations at the boundary cannot involve induced metric so that only induced symplectic structure remains. The 3-D holographic data at partonic orbits would extremize Cherns-Simons-Kähler action. Note that at the ends of the space-time surface about boundaries of CD one cannot pose any dynamics.
<LI> If the induced Kähler form has only the CP<sub>2</sub> part, the variation of Chern-Simons-Kähler form would give equations satisfied if the CP<sub>2</sub> projection is at most 2-dimensional and Chern-Simons action would vanish and imply that instanton number vanishes.
<LI> If the action is the sum of M<sup>4</sup> and CP<sub>2</sub> parts, the field equations in M<sup>4</sup> and CP<sub>2</sub> degrees of freedom would give the same result. If the induced Kähler form is identified as the sum of the M<sup>4</sup> and CP<sub>2</sub> parts, the equations also allow solutions for which the induced M<sup>4</sup> and CP<sub>2</sub> Kähler forms sum up to zero. This phase would involve a map identifying M<sup>4</sup> and CP<sub>2</sub> projections and force induce Kähler forms to be identical. This would force magnetic charge in M<sup>4</sup> and the question is whether the line connecting the tips of the CD makes non-trivial homology possible. The homology charges and the 2-D ends of the partonic orbit cancel each other so that partonic surfaces can have monopole charge.
</p><p>
The conditions at the partonic orbits do not pose conditions on the interior and should allow generalized holomorphy.
The following considerations show that besides homology charges as Kähler magnetic fluxes also Hamiltonian fluxes are conserved in Chern-Simons-Kähler dynamics.
</OL>
<B>Can one assign conserved charges with symplectic transformations or partonic orbits
and 3-surfaces at light-cone boundary?</B>
</p><p>
The geometric picture is that symplectic symmetries are Hamiltonian flows along the light-like partonic orbits generated by the projection A<sub>t</sub> of the Kähler gauge potential in the direction of the light-like time coordinate. The physical picture is that the partonic 2-surface is a Kähler charged particle that couples to the Hamilton H=A<sub>t</sub>. The Hamiltonians H<sub>A</sub> are conserved in this time evolution and give rise to conserved Noether currents. The corresponding conserved charge is integral over the 2-surface defined by the area form defined by the induced Kähler form.
</p><p>
Let's examine the change of the Chern-Simons-Kähler action in a deformation that corresponds, for example, to the CP<sub>2</sub> symplectic transformation generated by Hamilton H<sub>A</sub>. M<sup>4</sup> symplectic transformations can be treated in the same way:here however M<sup>4</sup> Kähler form would be involved, assumed to accompany Hamilton-Jacobi structure as a dynamically generated structure.
</p><p>
<OL>
</p><p>
<LI> Instanton density for the induced Kähler form reduces to a total divergence and gives Chern-Simons-Kähler action, which is TGD analog of topological action. This action should change in infinitesimal symplectic transformations by a total divergence, which should vanish for extremals and give rise to a conserved current. The integral of the divergence gives a vanishing charge difference between the ends of the partonic orbit. If the symplectic transformations define symmetries, it should be possible to assign to each Hamiltonian H<sub>A</sub> a conserved charge. The corresponding quantal charge would be associated with the modified Dirac action.
</p><p>
<LI> The conserved charge would be an integral over X<sup>2</sup>. The surface element is not given by the metric but by the symplectic structure, so that it is preserved in symplectic transformations. The 2-surface of the time evolution should correspond to the Hamiltonian time transformation generated by the projection A<sub>α</sub>=A<sub>k</sub> ∂<sub>α</sub>s<sup>k</sup> of the Kähler gauge potential A<sub>k</sub> to the direction of light-like time coordinate x<sup>α</sub>== t.
</p><p>
<LI> The effect of the generator j<sub>A</sub><sup>k</sup>= J<sup>kl</sup>∂<sub>l</sub>H<sub>A</sub> on the Kähler potential A<sub>l</sub> is given by j<sup>k</sup><sub>A</sub>∂<sub>k</sub>A<sub>l</sub>. This can be written as ∂<sub>k</sub>A<sub>l</sub>=J<sub>kl</sub> + ∂<sub>l</sub>A<sub>k</sub>. The first term gives the desired total divergence ∂<sub>α</sub> (ε<sup>αβγ</sup>J<sub>βγ</sub> H<sub>A</sub>).
</p><p>
The second term is proportional to the term ∂<sub>α</sub>H<sub>A</sub>- {A<sub>α</sub>,H}. Suppose that the induced Kähler form is transversal to the light-like time coordinate t, i.e. the induced Kähler form does not have components of form J<sub>tμ</sub>. In this kind of situation the only possible choice for α corresponds to the time coordinate t. In this situation one can perform the replacement ∂<sub>α</sub>H<sub>A</sub>-{A<sub>α</sub>,H}→ dH<sub>A</sub>/dt-{A<sub>t</sub>,H}. This corresponds to a Hamiltonian time evolution generated by the projection A<sub>t</sub> acting as a Hamiltonian. If this is really a Hamiltonian time evolution, one has dH<sub>A</sub>/dt-{A,H}=0. Because the Poisson bracket represents a commutator, the Hamiltonian time evolution equation is analogous to the vanishing of a covariant derivative of H<sub>A</sub> along light-like curves: ∂<sub>t</sub>H<sub>A</sub> +[A,H<sub>A</sub>]= 0. The physical interpretation is that the partonic surface develops like a particle with a Kähler charge. As a consequence the change of the action reduces to a total divergence.
</p><p>
An explicit expression for the conserved current J<sub>A</sub><sup>α</sup>=H<sub>A</sub> ε<sup>αβγ</sup>J<sub>βγ</sub> can be derived from the vanishing of the total divergence. Symplectic transformations on X<sup>2</sup> generate an infinite-dimensional symplectic algebra. The charge is given by the Hamiltonian flux Q<sub>A</sub> =∫ H<sub>A</sub> J<sub>αβ</sub>dx<sup>α</sup>∧dx<sup>β</sup>.
<LI> If the projection of the partonic path CP<sub>2</sub> or M<sup>4</sup> is 2-D, then the light-like geodesic line corresponds to the path of the parton surface. If A<sub>l</sub> can be chosen parallel to the surface, its projection in the direction of time disappears and one has A<sub>t</sub>=0. In the more general case, X<sup>2</sup> could, for example, rotate in CP<sub>2</sub>. In this case A<sub>t</sub> is nonvanishing. If J is transversal (no Kähler electric field), charge conservation is obtained.
</OL>
Do the above observations apply at the boundary of the light-cone?
<OL>
<LI> Now the 3-surface is space-like and Chern-Simons-Kähler action makes sense. It is not necessary but emerges from the "instanton density" for the Kähler form. The symplectic transformations of δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> are the symmetries. The most time evolution associated with the radial light-like coordinate would be from the tip of the light-cone boundary to the boundary of CD. Conserved charges as homological invariants defining symplectic algebra would be associated with the 2-D slices of 3-surfaces. For closed 3-surfaces the total charges from the sheets of 3-space as covering of δ M<sup>4</sup><sub>+</sub> must sum up to zero.
<LI> Interestingly, the original proposal for the isometries of WCW was that the Hamiltonian fluxes assignable to M<sup>4</sup> and CP<sub>2</sub> degrees of freedom at light-like boundary act define the charges associated with the WCW isometries as symplectic transformations so that a strong form of holography would have been be realized and space-time surface would have been effectively 2-dimensional. The recent view is that these symmetries pose conditions only on the 3-D holographic data. The holographic charges would correspond to additional isometries of WCW and would be well-defined for the 3-surfaces at the light-cone boundary.
</OL>
To sum up, one can imagine many options but the following picture is perhaps the simplest one and is supported
by physical intuition and mathematical facts. The isometry algebra ofδ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> consists of generalized conformal and KM algebras at 3-surfaces in δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> and symplectic algebras at the light cone boundary and 3-D light-like partonic orbits. The latter symmetries give constraints on the 3-D holographic data. It is still unclear whether one can assign generalized conformal and Kac-Moody charges to Chern-Simons-K\"ahler action. The isomorphic subalgebras labelled by a positive integer and their commutators with the entire algebra would annihilate the physical states.
</p><p>
<B>The TGD counterparts of the gauge conditions of string models</B>
</p><p>
The string model picture forces to ask whether the symplectic algebras and the generalized conformal and Kac-Moody algebras could act as gauge symmetries.
<OL>
<LI> In string model picture conformal invariance would suggest that the generators of the generalized conformal and KM symmetries act as gauge transformations annihilate the physical states. In the TGD framework, this does not however make sense physically. This also suggests that the components of the metric defined by supergenerators of generalized conformal and Kac Moody transformations vanish. If so, the symplectomorphisms δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> localized with respect to the light-like radial coordinate acting as isometries would be needed. The half-algebras of both symplectic and conformal generators are labelled by a non-negative integer defining an analog of conformal weight so there is a fractal hierarchy of isomorphic subalgebras in both cases.
<LI> TGD forces to ask whether only subalgebras of both conformal and Kac-Moody half algebras, isomorphic to the full algebras, act as gauge algebras. This applies also to the symplectic case. Here it is essential that only the half algebra with non-negative multiples of the fundamental conformal weights is allowed. For the subalgebra annihilating the states the conformal weights would be fixed integer multiples of those for the full algebra. The gauge property would be true for all algebras involved. The remaining symmetries would be genuine dynamical symmetries of the reduced WCW and this would reflect the number theoretically realized finite measurement resolution. The reduction of degrees of freedom would also be analogous to the basic property of hyperfinite factors assumed to play a key role in thee definition of finite measurement resolution.
<LI> For strong holography, the orbits of partonic 2-surfaces and boundaries of the spacetime surface at δ M<sup>4</sup><sub>+</sub> would be dual in the information theoretic sense. Either would be enough to determine the space-time surface.
</OL>
See the articles <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">About the Relationships Between Weak and Strong Interactions and Quantum Gravity in the TGD Universe</A> and <A HREF="https://tgdtheory.fi/public_html/articles/HJ.pdf">Holography and Hamilton-Jacobi Structure as 4-D generalization of 2-D complex structure</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-70173269547047553872023-11-13T23:01:00.000-08:002023-11-13T23:01:09.293-08:004-D generalization of holomorphies and Kac-Moody symmetries as isometries of the "world of classical worlds"?
Quite recently, I learned that the generalized holomorphies of space-time surfaces define non-trivial conserved charges. Also a generalization of Super-Kac-Moody charges associated with certain embedding space isometries emerges. This suggests a very close connection with string models and provides a possibility to provide answers to the longstanding questions relating to the identification of the isometry group of the "world of classical worlds" (WCW). Generalized holomorphy not only solves explicitly the equations of motion but, as found quite recently, also gives corresponding conserved Noether currents and charges.
<OL>
<LI> Generalized holomorphy algebra generalizes the Super-Virasoro algebra and the Super-Kac-Moody algebra related to the conformal invariance of the string model. The corresponding Noether charges are conserved. Modified Dirac action allows to construct the supercharges having interpretation as WCW gamma matrices.
This suggests an answer to a longstanding question related to the isometries of the "world of the classical worlds" (WCW).
<LI> Either the generalized holomorphies or the symplectic symmetries of H=M<sup>4</sup>× CP<sub>2</sub> or both together define WCW isometries and corresponding super algebra. It would seem that symplectic symmetries induced from H are <I>not</I> necessarily needed and might actually correspond to symplectic symmetries of WCW. This would give a close similarity with the string model, except that one has <I> half-algebra</I> for which conformal weights are proportional to non-negative integers and gauge conditions only apply to an isomorphic subalgebra. These are labeled by positive integers and one obtains a hierarchy.
<LI> By their light-likeness, the light cone boundary and orbits of partonic 2-surfaces allow an infinite-dimensional isometry group. This is possible only in dimension four. Its transformations are generalized conformal transformations of 2-sphere (partonic 2-surface) depending on light-like radial coordinate such that the radial scaling compensates for the usual conformal scaling of the metric. The WCW isometries would thus correspond to the isometries of the parton orbit and of the boundary of the light cone! These two representations could provide alternative representations for the charges if the strong form of holography holds true and would realize a strong form of holography. Perhaps these realizations deserve to be called inertial and gravitational charges.
</p><p>
Can these transformations leave the action invariant? For the light-cone boundary, this looks obvious if the light-cone is sliced by a surface parallel to the light-cone boundary. Note however that the tip of this surface might produce problems. A slicing defined by the Hamilton-Jacobi structure would be naturally associated with partonic orbits.
<LI> What about Poincare symmetries? They would act on the center of mass coordinates of causal diamonds (CDs) as found already earlier (see <A HREF="https://tgdtheory.fi/public_html/articles/CDconformal.pdf">this</A>). CDs form the "spine" of WCW, which can be regarded as fiber space with fiber for a given CD containing as a fiber the space-time surfaces inside it.
</OL>
The super-symmetric counterparts of holomorphic charges for the modified Dirac action and bilinear in fermionic oscillator operators associated with the second quantization of free spinor fields in H, define gamma matrices of WCW. Their anticommutators define the Kähler metric of WCW. There is no need to calculate either the action defining the classical Kähler action defining the Kähler function or its derivatives with respect to WCW complex coordinates and their conjugates. What is important is that this makes it possible to speak about WCW metric also for number theoretical discretization of WCW with space-time surfaces replaced with their number theoretic discretizations.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">About the Relationships Between Weak and Strong Interactions and Quantum Gravity in the TGD Universe</A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/nuclatomplato.pdf">About Platonization of Nuclear String Model and of Model of Atoms</A> or .
</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-74789346519206095982023-11-13T22:15:00.000-08:002023-11-13T22:57:19.735-08:00About the proposal of Phil Gibbs that energy is conserved in General Relativity
I have been analyzing the basic visions of TGD trying to identify weak points. Symmetries are central in TGD. The basic motivation for TGD was the loss of Poincare invariance in GRT and in the following I will analyze the claim of Phil Gibbs that one obtains energy conservation in GRT.
</p><p>
The following considerations are inspired by discussions with Marko Manninen and related to whether in general relativity it could be possible to define conserved quantities associated with at least some general coordinate transformations as proposed by Phil Gibbs (see <A HREF="https://www.researchgate.net/publication/277044387_Energy_Is_Conserved_in_the_Classical_Theory_of_General_Relativity">this</A>). This is certainly in conflict with the general idea that the choice of coordinates cannot have any physical effect and personally I am skeptic. I however decided to analyze the proposal in detail and found that it relates to a possible generalization of the notion of Newtonian gravitational flux, which gives the gravitational mass of the system.
<OL>
<LI> Gibbs' proposal for Noether charges associated with general coordinate transformations says nothing detailed about charges and the straightforward application of the basic formula gives vanishing charges since these currents turn out to be proportional to T-G which vanishes by Einstein's equations. However, the action includes a term containing second derivatives of the metric. Could this give an anomalous contribution to the Noether charge?
<LI> In electrodynamics and gauge theories, charges are obtained in connection with gauge transformations that become constant at a distance. The gauge charge density is a total divergence and gauge charge can be expressed as an electric flux across a very large sphere. On the other hand, in Newton's theory, the gravitational flux far enough from the system gives its mass. Could mass correspond to a time translation as a symmetry? Could the transformation of the charge into total divergence generalize to other general coordinate transformations?
<LI> Einstein action (curvature scalar) contains terms proportional to the second order partial derivatives of the metric: these terms come from the part of the curvature scalar linear in Riemann connection, which serves as analogs of non-abelian gauge potentials. However, this does not give third derivatives to the equations of motion. The reason is that the second derivatives occur linearly. If the square of the curvature tensor would define the action as an analog of Yang-Mills action, the situation would be different. This term is analogous to a dissipative and might relate to the general features of GRT dynamics (blackholes as asymptotic states).
</p><p>
Is the divergence term taken into account automatically in the straightforward Noetherian guess for the conserved currents? Or could the charges associated with the general coordinate transformations emerge as analogs of electric charge as a flux integral over a very large sphere. This would certainly contradict the fact that general coordinate transformations do nothing to the system, so that they cannot relate physically non-equivalent configurations.
<LI> The deduction of field equations involves transformation of the terms containing derivatives for the variation of the metric so that only terms involving only the variation of the metric remains besides total divergences, which must vanish for symmetries leaving the action invariant. This gives an explicit formula for the conserved Noether currents. In the case of the curvature scalar, the first term in the conserved current comes from the variation of the first derivatives of the metric. The second term comes from the variation of the second derivatives of the metric tensor and an explicit expression can be deduced for it. This gives a total divergence. Is this term automatically included in the term proportional to T-G? This seems very likely.
</OL>
Just for curiosity, let us consider the possibility that the total divergence term is not included in T-G and must be included as an additional term.
<OL>
<LI> As a total divergence this term can be transformed into a surface integral and is proportional to the vector field generating the transformation. This term could give a non-vanishing contribution as an integral over the boundary at infinity which can be regarded as an infinitely large sphere. If the space-time is asymptotically Minkowskian, the counterparts of 4-momentum, angular momentum and also charges associated with Poincare transformation are obtained. Also the charges associated with arbitrary general coordinate transformations are obtained but these are not in general conserved.
<LI> The explicit form for the conserved current associated with infinitesimal general coordinate transformation generated by the vector field j<sup>μ</sup> is
</p><p>
J<sup>μ</sup>(j)= L<sup>αβμ</sup> Dg<sub>αβ</sub>
+ L<sup>αβμν</sup> ∂<sub>ν</sub>Dg<sub>αβ</sub>
</p><p>
=L<sup>αβμ</sup>Dg<sub>αβ</sub>
+∂<sub>ν</sub>L<sup>αβμ</sup> Dg<sub>αβ</sub>
- ∂<sub>ν</sub>[L<sup>αβμ</sup>Dg<sub>αβ</sub>],
</p><p>
where one has
</p><p>
L<sup>αβμ</sup>= ∂ L/∂(∂<sub>μ</sub> g<sub>αβ</sub>),<BR>
L<sup>αβμν</sup>= ∂ L/∂(∂<sub>μν</sub>g<sub>αβ</sub>), <BR>
Dg<sub>αβ</sub>=j<sup>ρ</sup>∂<sub>ρ</sub> g<sub>αβ</sub> .
</p><p>
The third term at the second line is a total divergence and this contribution, call it Q<sub>3</sub>(j) to the expression for the charge as a 3-D integral of the μ=t component of the current can be transformed to a surface integral.
</p><p>
Q<sub>3</sub>(j)= -∫<sub>S<sup>2</sup></sub>[∂ L/∂(∂<sub>tr</sub> ∂<sub>ρ</sub> g<sub>αβ</sub>)] ∂<sub>ρ</sub> g<sub>αβ</sub>j<sup>ρ</sup>]dS .
<LI> In the stationary case, the g<sub>tt</sub> component of the metric includes the gravitational potential and its radial derivative gives a 1/r<sup>2</sup> term whose flux over the spherical surface is non-vanishing and gives the same result as gravitational flux in Newton's theory. Therefore there is a 1/r<sup>2</sup> term in the curvature tensor, which is analogous to the electric field. This interpretation requires that the space is asymptotically Minkowski space, so it is possible to talk about Poincare symmetry as an asymptotic symmetry. Constant time shift corresponds to mass.
<LI> The flux contribution to the charge must be linear in Christoffel symbols and involve the indices t and r. A good guess is that the charge is proportional to
</p><p>
Q<sub>3</sub>(j)= ∫<sub>S<sup>2</sup></sub> C(t,rρ) j<sup>ρ</sup>dS .
</p><p>
where C(t,rρ) denotes Christoffel symbol. For Schwarzschild metric this gives Newtonian gravitational flux for time translation j<sup>ρ</sup>=δ<sup>ρ,t</sup>.
<LI> One must pose additional conditions guaranteeing that these charges do not flow radially out of the infinite sphere. This becomes a condition that the second derivatives of the metric with respect to the radial coordinate r approach zero faster than 1/r<sup>2</sup>. This holds true very generally. Note however that the flux associated with arbitrary j need not be conserved. Consider as an example generalized coordinate transformations which approach trivial transformations in the future and non-trivial transformations in the past.
<LI> Year or two ago there was a lot of talk about an infinite number of charges that can be connected in this way as asymptotic charges to conformal transformations of an infinitely large sphere. These charges could be a special case of pseudo charges described above.
</OL>
To conclude, there are two options. Personally I am convinced that the T-G option is the right one. For the T-G=0 option, the total charges related to general coordinate transformations are therefore zero. One could however say that the total Noether charges are always zero but that they can be divided into interior and flux parts according to holography and cancel out each other. Flux part would correspond to what is called gravitational charge. In this sense the charges related to general coordinate transformations or at least Poincare transformations can be assigned with the system via holography as flux integrals. This could perhaps be interpreted within the framework of holography. These fluxes would characterize the asymptotic behavior giving in turn information about the dynamics in the interior.
</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-32481116323024859942023-11-09T07:06:00.001-08:002023-11-09T07:10:18.712-08:00The age of the Universe is twice the usual estimate for the age suggests James Webb: what does this mean?
James Webb telescope has reported stars and galaxies older than the Universe. This finding is new but cannot be put under the rug anymore. It has been proposed (see <A HREF="https://www.youtube.com/watch?v=n6E6ch3DS8g">this</A> that the age of the Universe is about 26.7 billion years and rather precisely twice the standard age about 13.2 billion years.
</p><p>
In TGD the time arrow changes in ordinary "big" state function reductions (BSFRs) which can take place in arbitrarily long time scales. This means that the system lives forth and back in time. One must distinguish between ordinary age and developmental age.
</p><p>
Remarkably, the total evolutionary time spent per given ordinary time interval is roughly twice(!) this time interval! This view explains stars and galaxies older than the Universe and might also explain why the researchers have concluded that the age of the universe is twice the standard age.
</p><p>
The most dramatic implications relate to living systems. BSFR means death and reincarnation with a reversed arrow of time. Similar doublings might occur in biology: for instance, the developmental age of the genome could be twice the age deduced from, say fossiles.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/JWagain.pdf">TGD view of the paradoxical findings of the James Webb telescope</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-18649041523450161812023-11-08T02:40:00.003-08:002023-11-08T03:21:30.032-08:00Questions related to the generalized holomorphies and fundamental vertices according to TGD
We had very inspiring discussions with Marko Manninen at a birthday meal with wine. During the trip back home some questions and ideas emerged. Could the 4-D generalization of holomorphy realizing holography allow an infinite hierarchy of conserved charges generalizing the Super Virasoro algebra. Could the only particle vertex in TGD correspond to a creation of fermion-antifermion pair: in this 2-vertex fermion state and fermionic line, partonic orbit, or Bohr orbit turns back in time.? Can one identify the graviton emission vertex?
</p><p>
<B>4-D generalization of the holomorphy allows conserved charges associated with the generalized holomorphies</B>
</p><p>
Does the 4-D analogy of holomorphy as a realization of holography give rise to conserved quantities? Now the symmetries would not be isometries, nor some other symmetries of the action, but dynamic symmetries satisfied only by the Bohr orbits. A little calculation that one can do in your head shows that one obtains conserved currents: the reason is the same as in the case of field equations. The divergence of the Noether current is a contraction of tensors with no common index pairs for the generalization of complex coordinates.
</p><p>
Unlike those associated with the general coordinate invariance, these conserved quantities do not vanish. They correspond to the 4-D generalization of conformal transformations and give rise to a generalization of the Virasoro algebra and also of Super Virasoro algebra realized in terms of the modified Dirac action for the induced spinor fields obtained from the free second quantized spinor fields of H.
</p><p>
In the string model, these conformal charges are assumed to annihilate the physical states. In TGD, I have proposed that only a subalgebra that is isomorphic to the whole algebra, having conformal weights which are integer multiples of the entire algebra, does this. In TGD framework, the conformal weights are necessarily non-negative and ZEO allows this. One obtains a whole hierarchy of subalgebras and a sub-hierarchy of algebras for which conformal symmetry as gauge symmetry is "broken" to dynamical Lie symmetries for physical states having conformal weight below some maximum value. These hierarchies could correspond to the hierarchies of algebraic extensions for rationals defined by composite polynomials.
</p><p>
<B>Are fermionic 2-vertices all that is needed in TGD?</B>
</p><p>
In quantum field theories, already the interaction vertex for 3 particles leads to divergences. In a typical 3-vertex, fermion emits a boson or boson decays to a fermion-antifermion pair. In TGD, the situation changes.
<OL>
<LI> Fermions are the only fundamental particles in TGD. Since fundamental bosons are missing, there is no vertex representing emission of a fundamental boson emission from fermion or a vertex producing fermion antifermion pair from a fundamental boson. In TGD, bosons as elementary particles (distinguished from fundamental bosons) are fermion-antifermion pairs, and the emission of elementary bosons is possible. However, the problem is that the total fermion and antifermion numbers are separately conserved. Unless it is possible to create fermion pairs from classical fields!
<LI> In the standard theory fermion-antifermion pairs can be indeed created in classical gauge fields. This creation is an experimental fact but it is thought that this description is only a convenient approximation. In TGD however, the classical fields associated with the Bohr orbits of 3-surfaces are an exact part of quantum theory. Could this description be accurate in TGD? In the classical induced fields associated with particles, pairs could arise. Approximation would become exact in TGD.
</OL>
A 2-vertex for creation of fermion-antifermion pair (or corresponding boson) is needed. In this vertex, the fermion turns must turn backwards in time.
<OL>
<LI> I managed to identify the fermionic 2-vertex was specified towards the end of this year as I realized the connection to the problem of general relativity, which arises from the existence of GRT space-times for which the 4-D diffeo structure is non-standard. There are a lot of these. For an exotic diffeo structure, the standard diffeo structure can be said to have point-like defects analogous to lattice defects.
<LI> Remarkably, this problem is encountered only in the space-time dimension 4 (see <a HREF= "https://tgdtheory.fi/public_html/articles/masterformula.pdf">this</A>)! Physical intuition suggests that it must be possible to turn this problem from a disaster to victory. In TGD, this is what actually happens: these point-like diffeo-defects can be identified as interaction vertices, the fermion turns back in the direction of time. Pair creation would be possible only in space-time dimension 4!
</p><p>
A generalization of the classical fermion pair creation vertex has the same general form as in QFT. As a special case the pair can correspond to a boson as a fermion-antifermion bound state. This vertex also has geometric variants in different dimensions. A fermion line, string world sheet, the orbit of a partonic 2-surface and also the Bohr orbit of 3 surface can turn backwards in time and the fermion states associated with the induced spinor fields do the same.
</OL>
This inspires two questions.
<OL>
<LI> Is the creation of a pair actually the only vertex or is it possible to have a geometric 3-vertex and is it really needed? At the fermion level only the 2-vertex described above is not possible, but for the topological reactions of surfaces one could think of 3-vertices and in the earlier picture I thought these are needed. They do not seem to be necessary however.
</p><p>
If so, the theory would be extremely simple compared to quantum field theories. There dangerous genuine 3-vertices would be absent and diffeo defects defining 2 vertices, which give all that is needed! At the geometric level, monopole fluxes would replicate and break and join. Intriguingly, this is what would happen at the magnetic bodies of DNA and induce similar reactions at the level of DNA molecules! Maybe biology has been doing its best to tell us what the fundamental particle dynamics is!
<LI> Since only the induced electroweak gauge potentials couple to fermions, the question arises whether color and strong interactions are obtained. How is it possible to have strong interactions without parity violation when basic vertices involve weak parity violation? I have already discussed this question (see <a HREF= "https://tgdtheory.fi/public_html/articles/SW.pdf">this</A>).
</OL>
<B>Vertex for graviton emission</B>
</p><p>
There is still one crucially important question left. Is it possible and what would happen in it? Can one obtain a vertex, where the analog for a contraction T<sup>αβ</sup>δ g<sub>αβ</sub> of energy-momentum tensor with the deviation of the metric from the Minkowski metric appears?
<OL>
<LI> In TGD all elementary particles, also gravitons, are identified as closed 2-sheeted monopole flux tubes with two wormhole contacts at its "ends" and opposite wormhole throats carrying fermions and antifermions (see <a HREF= "https://tgdtheory.fi/public_html/articles/nuclatomplato.pdf">this</A> and <a HREF= "https://tgdtheory.fi/public_html/articles/SW.pdf">this</A>). For gravitation one has 1 fermion or antifermion for each wormhole throat.
</p><p>
The graviton emission vertex should correspond to a splitting of flux tubes. Mopole flux tubes with fermion-antifermion pairs assignable to both wormhole contacts should appear. The fermion and antifermion should reside at the opposite throats of each wormhole contact. This should happen in the splitting of a monopole flux tube and second monopole flux tube would correspond to graviton. That two bosonic vertices are involved with the emission, brings to mind the proposal that gravitation is in some sense a square of gauge theory.
<LI> The vertex is the same as for gauge boson emission and for a creation of a fermion-antifermion pair. The definition of the modified gamma matrices as Γ<sup>α</sup>= T<sup>α</sup><sub>k</sub>Γ<sup>k</sup> appearing in the modified Dirac action (see <A HREF= "https://tgdtheory.fi/pdfpool/cspin.pdf">this</A>), involving the modified Dirac operator Γ<sup>μ</sup>D<sub>μ</sub> makes it possible to identify the gravitational part of the vertex. Here the quantities T<sup>α</sup><sub>k</sub>=∂ L/∂(∂<sub>α</sub>h<sup>k</sup>) are canonical momentum currents associated with the action defining the space-time surface and also the analog of the energy-momentum tensor.
</p><p>
Modified gamma matrices are required by hermiticity forcing the vanishing of the divergence of the vector Γ<sup>α</sup> giving classical field equations for space-time surfaces. This implies a supersymmetry between the dynamics of fermions and 3-surfaces. The gravitational interaction would correspond to the deviation of the induced metric from the induced metric defined by induced CP<sub>2</sub> metric. CP<sub>2</sub> radius must correspond to Planck length l<sub>P</sub>. This requires that the CP<sub>2</sub> as R≈ 10<sup>4</sup>l<sub>P</sub> must correspond to h= nh<sub>0</sub>, n≈ 10<sup>7</sup> as found already earlier.
<LI> The cosmological term in GRT has coefficient 1/8π GΛ== 1/R<sup>4</sup> so that the modified gamma matrices would contain a term proportional to 1/R<sup>4</sup> plus a term coming from the Kähler action. In the TGD framework (see <A HREF= "https://tgdtheory.fi/public_html/articles/twistquestions.pdf">this</A> and <A HREF= "https://tgdtheory.fi/public_html/articles/twistorTGD.pdf">this</A>) cosmological constant Λ depends on the p-adic length scale, which is assumed to correspond to a ramified prime for an extension of rationals associated with the polynomial P determining to high degree the space-time surface and approaches to zero in cosmic scales. The cosmological value corresponds to R≈ 10<sup>-4</sup> meters, i.e. cell length scale and a scale near neutrino Compton length.
</p><p>
In the general coordinate invariant formalism, one does not assign dimension to the coordinates or to covariant derivative D<sub>α</sub>. Metric has dimension 2. The scale dimension of T<sup>α</sup><sub>k</sub>g<sup>1/2</sup> is the same dimension of Lg<sup>1/2</sup> and thus vanishes. Γ<sup>α</sup> has scale dimension -1. The modified Dirac action must be dimensionless so that the induced spinors must have scale dimension 1/2.
<LI> The cosmological constant as the coefficient of the action depends on the p-adic length scale unlike. This term contributes to the string tension of string-like objects an additional term, which among other things can explain hadronic string tension. This term is visible also in the interaction vertices. The Kähler part of the bosonic action terms comes from the deviation of the induced metric from the flat metric and should give the usual gravitational interactions with matter.
<LI> Holomorphy hypothesis allows any general coordinate invariant action constructible in terms of the induced geometry. Although preferred extremals are always minimal surfaces, the properties of the action are visible via classical conservation laws, via the field equation at singular 3-surfaces involving the entire action, and via the vertices.
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">About the Relationships Between Weak and Strong Interactions and Quantum Gravity in the TGD Universe</A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/nuclatomplato.pdf">About Platonization of Nuclear String Model and of Model of Atoms</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-72948805222083370382023-11-06T05:37:00.015-08:002023-11-25T22:17:37.630-08:00Gravitational hum and the precise form of M8-H duality
The precise form of M<sup>8</sup>-H duality (see <A HREF= "https://tgdtheory.fi/public_html/articles/M8H1.pdf">this</A>, <A HREF= "https://tgdtheory.fi/public_html/articles/M8H2.pdf">this</A>, and <A HREF= "https://tgdtheory.fi/public_html/articles/M8Hagain.pdf">this</A>) has remained open since one consider several variants for the duality in M<sup>4</sup>⊂ M<sup>8</sup>=M<sup>4</sup>× E<sup>4</sup> degrees of freedom mapped to M<sup>4</sup>⊂ M<sup>4</sup>× CP<sub>2</sub> degrees of freedom.
</p><p>
The model for gravitational hum involves diffraction in the tessellation of H<sup>3</sup> formed by stars or rather, by their magnetic bodies (see <A HREF= "https://tgdtheory.fi/public_html/articles/gravhum.pdf">this</A>). Reciprocal lattice is closely related to diffraction and equals to the lattice only in the case of cubic lattice. This is expected to be true also for tessellations and suggests that M<sip>8</sup>-H duality mapping momentum 4-surfaces of M<sup>8</sup> to space-time surfaces of H maps the tessellation of H<sup>3</sup>⊂ M<sup>4</sup>⊂ M<sup>8</sup> to a reciprocal tessellation of H<sup>3</sup>⊂ M<sup>4</sup>⊂ H.
</p><p>
The first problem is that the momenta at the M<sup>8</sup> side are complex unlike the space-time points at the H side. The basic condition comes from the Uncertainty Principle in semiclassical form but does not complettessellationely fix the duality.
<OL>
<LI> If the momenta are real, the simplest option is that the mass shell is mapped to a time shell a=h<sub>eff</sub>/m, where a is light-cone proper time. For physical states the momenta are real by Galois confinement and have integer components when the momentum scale is defined by causal diamond (CD). For virtual fermions, the momenta are assumed to be algebraic integers and can be complex. The question is whether one should apply M<sup>8</sup>-H a duality only too the real momenta of physical states or also the virtual momenta.
<LI> For virtual momenta the M<sup>8</sup>-H duality must be consistent with that for real momenta and the simplest option is that one projects the real part of the virtual momentum and applies M<sup>8</sup>-H duality to it. The square m<sub>R</sub><sup>2</sup> for the real part Re(p) of momentum however varies for the points on the complex mass shell since only the real part Re(m<sup>2</sup>) of mass squared is constant at the complex mass shell. If 3-momenta are real, one has (Re(p))<sup>2</sup>= Re(p<sub>0</sub>)<sup>2</sup> -p<sub>3</sub><sup>2</sup>=m<sub>R</sub><sup>2</sup> and is not constant and in general larger than Re(p<sup>2</sup>)=Re(p<sub>0</sub>)<sup>2</sup>-Im(p<sub>0</sub>)<sup>2</sup> -p<sub>3</sub><sup>2</sup>=Re(m<sup>2</sup>). Should one use m<sub>R</sub><sup>2</sup> or Re(m<sup>2</sup>) in M<sup>8</sup>-H duality?
</p><p>
Re(m<sup>2</sup>) is constant at M<sup>8</sup> side in accordance with the definition of mass shell. The value of a<sup>2</sup>= h<sub>eff</sub><sup>2</sup>(m<sub>R</sub><sup>2</sup>)/Re(m<sup>2</sup>)<sup>2</sup> at H side varies and has a width defined by the variation of Im(p<sub>0</sub>) at the points of the mass shell. m<sub>R</sub><sup>2</sup> is not constant at the M<sup>8</sup> side. This might relate to the fact that particle masses have a width and would relate Im(p<sub>0</sub> to a physical observable. The time shell is given by a<sup>2</sup>= h<sub>eff</sub><sup>2</sup>/m<sub>R</sub><sup>2</sup> and is genuine H<sup>3</sup>.
</OL>
The model for the gravitational hum (see <A HREF= "https://tgdtheory.fi/public_html/articles/gravhum.pdf">this</A>) provides another problem, which can serve as an additional guideline.
<OL>
<LI> The model was based on gravitational diffraction in the tessellation defined by a discrete subgroup of SL(2,C). This tessellation is a hyperbolic analog of a lattice in E<sup>3</sup> with a discrete translation group replaced with a discrete subgroup Γ of the Lorentz group or its covering SL(2,C). The matrix elements of the matrices in Γ should belong to the extension of rationals defined by the polynomial P defining the space-time surface by M<sup>8</sup>-H duality.
<LI> For ordinary lattices, the reciprocal lattice assigns to a spatial lattice a momentum space lattice, which automatically satisfies the constraint from the Uncertainty Principle. Could the notion of the reciprocal lattice generalize to H<sup>3</sup>? What is needed are 3 basis vectors (at least) characterizing the position of a fundamental region and having components that must belong to the algebraic extension of rationals considered. The application of Γ would then produce the entire lattice. In this case a linear superposition of lattice vectors is not possible.
<LI> The (at least) 3 basic 3-vectors p<sub>3,i</sub> need not be orthogonal or have the same length. They should have components, which are algebraic integers in the extension of rationals defined by P. M<sup>4</sup>⊃ H<sup>3</sup> is a subspace of complexified quaternions with the space-like part of momentum vector, which is imaginary with respect to commuting imaginary unit i to transform the algebraic scalar product (no conjugation with respect to i). The ordinary cross product appearing in the definition of the reciprocal lattice appears in the quaternionic product. This suggests that the (at least) 3 reciprocal vectors p<sub>3,i</sub> as M<sup>4</sup> projections of four-momentum vectors are proportional to the cross products of the basis vectors apart from a normalization factor determined by the condition that the light-cone proper time is proportional to the inverse of mass. One would have x<sub>3</sub><sup>i</sup>∝ ε<sup>ijk</sup>p<sub>3,j</sub>× p<sub>3,k</sub>.
</p><p>
Physical intuition suggests that the components of spatial momentum are real for the basis vectors p<sub>3,i</sub> so that only the energy has imaginary part. For their discrete Lorentz books by Γ this cannot be the case in M<sup>8</sup><sub>c</sub>.
<LI> Mass shell condition p<sub>i</sub><sup>2</sup>= M<sup>2</sup> must be replaced with x<sup>2</sup><sub>i</sub>= h<sub>eff</sub>/M<sup>2</sup>. The precise identification of M<sup>2</sup> will be considered below. The image of the real part of the energy p<sub>0,i</sub> is the time coordinate t<sup>0</sup><sub>i</sub>= h<sub>eff</sub>Re(p<sub>0,i</sub>)/M<sup>2</sup>. For the naive option considered earlier, the time shell condition is satisfied if the dual position vectors x<sub>3</sub><sup>i</sup> are of form x<sub>3</sub><sup>i</sup> =h<sub>eff</sub> [(p<sup>2</sup><sub>i</sub>)<sup>1/2</sup>/M<sup>2</sup>]e<sup>i</sup>, where e<sup>i</sup> is a unit vector in the direction of p<sub>i</sub>. This option is correct if the momenta p<sub>i</sub> are orthogonal since in this case the reciprocal unit vectors and vectors co-insider. In the general case, one must replace the unit vector e<sup>i</sup> with the unit vector associated with the vector X<sup>i</sup>= ε<sup>ijk</sup>p<sub>3,j</sub> p<sub>3,j</sub> given by e<sup>i</sup>=X<sup>i</sup>/((X<sup>i</sup>)<sup>2</sup>)<sup>1/2</sup> so that the formula for x<sup>3</sup><sub>i</sub> remains otherwise the same.
<LI> The conditions have a similar form independently of whether one takes the mass squared parameter M<sup>2</sup> to be M<sup>2</sup>=Re(m<sup>2</sup>) or M<sup>2</sup>=m<sub>R</sub><sup>2</sup>. The time components of the momentum vectors p<sub>i</sub> associated with p<sub>3,i</sub>, which are assumed to be real, are determined by the mass shell condition Re(p<sub>0,i</sub>)<sup>2</sup>-Im(p<sub>0,i</sub>)<sup>2</sup>- Re(p<sub>i</sub><sup>2</sup>) =Re(m<sup>2</sup>). Spatial coordinates in M<sup>4</sup> must obey similar formula, which implies the length of the image vector is r= h<sub>eff</sub>×p<sub>3,i</sub>/M<sup>2</sup> so that time shell condition t<sup>2</sup>-r<sup>2</sup>= h<sub>eff</sub><sup>2</sup>/M<sup>2</sup> conforms with the Uncertainty Principle.
<LI> Which option is correct: M<sup>2</sup>=Re(m<sup>2</sup>) or M<sup>2</sup>=m<sub>R</sub><sup>2</sup>? For the first option the discretized real mass shell m<sub>R</sub><sup>2</sup> is deformed and might be essential for having a non-trivial number theoretical holography implying by M<sup>8</sup>-H duality a non-trivial holography at H side. One can however defend the second option by non-trivial holography at H side.
</OL>
Note that the proposed definition of M<sup>8</sup>-H duality is indirect in that it is applied only to the
(at least) 3 basic vectors and the action of Γ gives the tessellation in H<sup>3</sup>⊂ H. One can also apply the entire Lorentz group to these vectors to obtain the time shell.
</p><p>
The proposed construction assumed that the basis of 3 vectors is essential for the definition of tessellation and that it is possible to assign a set of reciprocal vectors to it in the proposed way involving cross product, which is essentially 3-D notion and relates to quaternions. Is this really the case for all tessellations of H<sup>3</sup>?
<OL>
<LI> In Euclidian 3-space E<sup>3</sup> only cubic lattice defines a regular tessellation and for the reciprocal lattices is well-defined. In this case, the linear combinations of 3 basic vectors define the lattice. Note that Platonic solids have duals but this duality has nothing to do with the reciprocal lattice.
<LI> In hyperbolic 3-space H<sup>3</sup> one can have cubic tessellation, 2 icosahedral tessellations, and dodecahedral tessellation as regular tessellations. There is also icosa tetrahedral tessellation involving both tetrahedra, octahedra and icosahedra (see <A HREF="https://tgdtheory.fi/public_html/articles/tessellationH3.pdf">this</A>). Linear combinations of the basic vectors do not exist now. If 3 basic vectors of the tessellation are known, it would be their orbit under the discrete group Γ which defines the tessellation. If Γ is transitive, a single point in principle defines the tessellation as the orbit of Γ.
<LI> One can assign to tessellations of H<sup>3</sup> what might be called a fundamental tetrahedron as a 4-simplex, which is not a regular tetrahedron in the general case. Could the loci of its vertices with respect to a selected vertex define the fundamental tetrahedron? For a cube in E<sup>3</sup> this tetrahedron would correspond to a tetrahedron defined by the 3 nearest vertices of a selected vertex of the cube. At least in E<sup>3</sup> one can select the vertex by requiring that the distances of the neighbouring vertices from the selected vertex are minimal. In this case, the remaining 3 vertices form an orbit under Z<sup>3</sup> .
<LI> Could one reduce the situation from H<sup>3</sup> to E<sup>3</sup> by considering the 3 basic vectors for the projection of the fundamental tetrahedron from H<sup>3</sup> to t=constant hyperplane E<sup>3</sup>?The 3 basic vectors would be from the selected vertex defining the origin to neighboring vertices: note that here the submanifold property H<sup>3</sup>⊂ M<sup>4</sup> is essential.
</p><p>
Could one assign to this triplet a reciprocal in the same way as in the Euclidian case using the cross product induced by the quaternion structure? The notion of dual basis is also behind the bra-ket formalism of quantum mechanics and is based on the notion of vector space and its dual? The following considerations rely on this optimistic assumption.
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/gravhum.pdf">The TGD view of the recently discovered gravitational hum as gravitational diffraction</A>, the articles <A HREF="https://tgdtheory.fi/public_html/articles/magnbubble1.pdf">Magnetic Bubbles in TGD Universe: Part I</A> and <A HREF="https://tgdtheory.fi/public_html/articles/magnbubble2.pdf">Magnetic Bubbles in TGD Universe: Part II</A> or the chapter<A HREF="https://tgdtheory.fi/pdfpool/qastro.pdf"> Quantum 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-15023024320445735252023-11-03T22:47:00.006-07:002023-11-03T23:29:13.194-07:00Pollack effect and evaporation without heating
It has been found
(see <A HREF="https://www.iflscience.com/the-photomolecular-effect-it-appears-light-can-evaporate-water-without-any-heat-71378">this</A>) that irradiation by visible light can evaporate water without any heat, this is called photomolecular effect.
</p><p>
What comes first in mind for a habitant of the TGD Universe is that the photomolecular effect reduces to Pollack effect in which light in visible and infrared wavelength range induces a formation of negatively charged regions, exclusion zones (EZs) containing fourth phase of water, as Pollack calls them. These regions have very strange properties suggesting time reversal: for instance, they clean themselves from impurities which suggests diffusion with a reversed arrow of time at the magnetic body of EZ. EZs are layered structures with effective stoichiometry H<sub>1.5</sub>O. Pollack talks of EZs fourth phase of water and the ordered water at the surfaces of say biomolecules like DNA and folded proteins could consist of this kind of phase.
</p><p>
TGD proposes a model of Pollack effect based on the TGD view of dark matter. Part of protons would go to the magnetic body of water and form dark proton sequences. Pollack effect has become one of the key mechanisms of the TGD inspired quantum biology and would appear in metabolism (ATP), biocatalysis, and nerve pulse generation: see https://tgdtheory.fi/public_html/articles/np2023.pdf .
</p><p>
Quite recently it has been learned that the water-air boundary has a thin cover, which consists of a phase analogous to ice (see <A HREF="https://cutt.ly/DCVWM6C">this</A>). A reasonable hypothesis is that this phase consists of the fourth phase of water and is responsible for the surface tension of the bulk water. I have developed a TGD based model for the anomalies related to freezing in nanoscales explaining also this phenomenon (see <A HREF="https://tgdtheory.fi/public_html/articles/freezing.pdf">this</A>).
</p><p>
How could the Pollack effect induce evaporation without heat? Evaporation occurs at criticality. In TGD it could be accompanied by quantum criticality meaning the presence of dark matter at the magnetic body of the water, in particular dark protons generated in the Pollack effect. At quantum criticality the bulk water is unstable against the formation of water droplets surrounded by layers of fourth phase. The surface area of droplets plus bulk water is larger than that of bulk. More of the fourth phase of water must be created and this requires energy. The irradiation would provide this energy by the Pollack effect.
</p><p>
See the article <A HREF= "https://tgdtheory.fi/public_html/articles/freezing.pdf">TGD inspired model for freezing in nano scales</A> or the <A HREF= "https://tgdtheory.fi/pdfpool/freezing.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-19938633139730936742023-11-02T21:23:00.001-07:002023-11-02T21:23:48.015-07:00 About the Relationship Between Strong and Weak Interactions in the TGD Universe
In the TGD view, classical electroweak interactions are basically local and only classical electroweak gauge potentials appear in the TGD analogs of fundamental interaction vertices describing splitting and reconnection of monopole flux tubes, which describe also strong interactions at the particle level. The basic problem is to understand how strong interactions can be parity conserving while the classical electroweak dynamics violates parity conservation.
</p><p>
The proposed model, argued to overcome this problem, involves several topological elements.
<OL>
<LI> The topological explanation of the family replication phenomenon in terms of the genus of partonic 2-surface carrying fermion lines as boundaries of string world sheets.
<LI> The view of holography as a 4-D analog of holomorphy reducing to 2-D holomorphy for partonic 2-surfaces. This predicts two kinds of partonic 2-surfaces as complex 2-surfaces in CP<sub>2</sub> with a spherical topology. Tor the homologically non-trivial geodesic sphere induced weak fields vanish (no parity violation classically) and for the second complex sphere they do not. A natural working hypothesis is that these two spheres explain the difference between strong and weak interactions.
<LI> The homology (Kähler magnetic) charge h of the partonic 2-surface correlates with the genus of the partonic 2-surface. For complex partonic 2-surfaces in CP<sub>2</sub>, the genus is given g=(h-1)(h-2)/2-s, where s is the number of singularities. Only the genera g=(h-1)(h-2)/2 are free of singularities. For g=0, this includes h=1 and h=2. Already for g=2 there would be singularity. It is however possible to overcome this problem since partonic 2-surfaces can be deformed to M<sup>4</sup> degrees of freedom and one can add handles in this way. A rather detailed picture of partonic 2-surfaces and monopole flux tubes emerges.
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">About the Relationship Between Strong and Weak Interactions in the TGD Universe</A> and the chapter <A HREF="https://tgdtheory.fi/pdfpool/nuclatomplato.pdf">About Platonization of Nuclear String Model and of Model of Atoms</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-76316499779240160222023-11-02T00:40:00.000-07:002023-11-02T00:40:02.917-07:00About the difference between electroweak and strong interactions assuming generalized holomorphy
It is interesting to find what the holography as a generalization to 4-D holomorphy hypothesis predicts when combined with the proposed explanation of the family replication phenomenon and the proposal for how parity violation is avoided in strong interactions despite the fact that only electroweak induced fields appear in the fundamental vertices for the creation of various particles identified as closed 2-sheeted monopole flux tubes. This includes mesons and gluons. The following considerations force a rather detailed picture about partonic 2-surfaces.
<OL>
<LI> Monopole flux tubes can be regarded as M<sup>4</sup> deformations of cosmic strings representable as Cartesian products of string world sheet X<sup>2</sup>⊂ M<sup>4</sup> and 2-surface Y<sup>2</sup>⊂ CP<sub>2</sub>. Partonic 2-surfaces would appear as "ends" of 2-sheeted monopole flux tubes. If the holomorphic realization of holography makes sense, the space-time surfaces are complex algebraic surfaces. In the simplest situation the 2-D cross section of a cosmic string is a complex surface of CP<sub>2</sub>. A more general option is as a complex algebraic curve in E<sup>2</sup>× CP<sub>2</sub>.
<LI> Riemann-Roch theorem (see <A HREF="https://en.wikipedia.org/wiki/Riemann Roch_theorem">this</A>) allows to define geometric genus (see <A HREF="https://en.wikipedia.org/wiki/Genus_(mathematics)">this</A>) of a complex algebraic curve in CP<sub>2</sub> as
</p><p>
g= (d-1)(d-2)/2-s ,
</p><p>
where s is the number of singularities, which are cones and as a special case cusps (infinitely sharp cones). According to the Wikipedia article, this formula generalizes to algebraic surfaces in higher than 2-D complex manifolds, or at least projective space.
</p><p>
From this one can conclude for the (d-1)(d-2)/2 ≥ g for partonic 2-surfaces as complex surfaces in CP<sub>2</sub>, there are always singularities. For s=0, g=0 allows d=0 and d=1. For s=0, g=1 allows d=3 related to elliptic functions. Already for g=2 one has s≥ 1. The genera g=(d-1)(d-2)/2 are special in that they also allow s=0.
<LI> It is known (see <A HREF="https://en.wikipedia.org/wiki/Genus_(mathematics)">this</A>) that for s=0 the topological genus, algebraic genus and arithmetic genus are identical. This might be relevant for the definition of genus for the p-adic counterparts of partonic 2-surfaces, where the topological genus does not make sense. This could make g ∈ {0,1, (d-1)(d-2)2} cognitively special.
It would seem that p-adic variants of g=2 partonic 2-surfaces do not make sense unless one can eliminate the singularities by a deformation of Y<sup>2</sup> to a complex 2-surface in E<sup>2</sup>× Y<sup>2</sup>. One should also be able to represent g>0 surfaces as surfaces in E<sup>2</sup>× CP<sub>2</sub>, where CP<sub>1</sub> corresponds to either d=1 of d=2.
</OL>
<B>Generalized holomorphy, difference between strong and weak interactions, and family replication phenomenon</B>
</p><p>
It is instructive to consider the CP<sub>2</sub> option and its generalization in more detail from the perspective of weak and strong interactions and family replication phenomenon.
<OL>
<LI> g=0 option is the most natural one for cosmic strings and allows polynomials of degree d=1 and d=2. d=1 would correspond to the homologically non-trivial geodesic sphere of CP<sub>2</sub> and d=2 a more complex surface. For the homologically non-trivial sphere only the Kähler form would contribute to the vertex related to the splitting of the cosmic string. This could explain why the generation of hadronic and gluonic monopole strings does not lead to a parity violation.
</p><p>
For d=2 and g=0 induced electroweak fields are non-vanishing and parity violations are predicted. Could photons and gluons correspond to cosmic strings with cross section as d=1 surface of CP<sub>2</sub>? Could parity violating weak bosons relate to cosmic strings with a d=2 spherical cross section so that the difference between strong and weak interactions would reduce to algebraic geometry?
<LI> The genus g=1 could be also realized for cosmic strings with d=3 to which elliptic functions. In this case, the induced weak fields would be present for the CP<sub>2</sub> option. This does not conform with the idea that parity breaking effects do not depend on the genus (generation of fermion).
</p><p>
Could the deformations of partonic 2-surfaces in M<sup>4</sup> degrees of freedom come in rescue? For partons as complex 2-surfaces in E<sup>2</sup>× S<sup>2</sup> ⊂ E<sup>2</sup>× CP<sub>2</sub>, S<sup>2</sup> homologically non-trivial geodesic sphere, no charged weak fields would be present. If this picture is correct the deformations in E<sup>2</sup> degrees of freedom would distinguish between fermion families but the difference should be subtle. I do not know whether the formula for algebraic surfaces in projective spaces still holds true.
<LI> Genus g=2 partonic 2-surface in CP<sub>2</sub> would have at least one singular point. Is this physically acceptable? Is it possible to avoid the singularity for the Y<sup>2</sup> ⊂ E<sup>2</sup>× S<sup>2</sup> ⊂ E<sup>2</sup>× CP<sub>2</sub> option? Blowing up of the singularities by removing a small disk of S<sup>2</sup> around the singularity and gluing back a disk of E<sup>2</sup>× S<sup>2</sup> is what comes to mind. Blowup, in particular a blowup at a given point of complex manifold, such as a cone singularity of complex surface, is described in the Wikipedia article (see <A HREF="https://en.wikipedia.org/wiki/Blowing_up">this</A>).
</p><p>
Topologically this means construction of a connected sum with the projective space CP<sub>1</sub> by removing a small disk around the singularity. The realization of this operation would now occur in E<sup>2</sup>× Y<sup>2</sup>. If the genus g= d(d-1)/2-s is preserved in the blowup so that one would obtain non-singular representatives also in g=2 case. Obviously the formula for the genus would not hold anymore.
<LI> Since all quark genera g ≤ 2 appear in strong interactions, which do not violate parity, one should have a way of constructing g>0 surfaces from the homologically non-trivial sphere CP<sub>1</sub>⊂ CP<sub>2</sub> with n=1 complex surface in E<sup>2</sup>⊂ CP<sub>1</sub>. Addition of handles should be the way. These surfaces would be associated with quarks, gluons and mesons, which all would correspond to 2-sheeted monopole fluxe tubes.
</p><p>
This operation should be possible also for the d=2 complex sphere carrying induced weak gauge fields. The predicted higher families of weak bosons as analogs of mesons could be obtained from d=2 monopole flux tubes. The existence of strong and weak interactions would reflect the existence of d=1 and d=2 complex spheres of CP<sub>2</sub>. In particular, one obtains non-singular g=2 fermions. Also leptons could correspond to d=2 spheres.
</OL>
<B>About the relationship between Kähler magnetic charge and genus</B>
</p><p>
What can one say about the homological (Kähler magnetic) charge of a partonic 2-surface with a given genus. At least homological charges +/- 1 and +/- 2 should be realized for the partonic 2-surfaces. For about 4 decades ago, my friend Lasse Holmström, who is a mathematician, gave me as a gift a Bulletin of American Mathematical Society containing articles about 4-D topology and also about topology of CP<sub>2</sub>. At page 124 there were interesting results related to the realization of homologically non-trivial 2-surfaces in CP<sub>2</sub>, in particular there were conditions on the minimal genus of these surfaces.
</p><p>
The basic result was that a surface with homology charge h can be realized as a surface with genus g=(h-1)(h-2)/2 and there are no known realizations with a smaller genus. For d=h, this sequence would correspond to the sequence g= (d-1)(d-2)/2 for complex surfaces without singularities. This correlation between genus and homology charge troubled me since in the TGD framework h∈{+/- 1,+/- 2} should be possible for all genera. The addition of handles to d=1,2 complex spheres of CP<sub>1</sub>⊂ CP<sub>1</sub>⊂ E<sup>2</sup> would solve the problem. An interesting question is whether the sequence 0,1,6,10,15,... of homologically special genera could have a physical interpretation and perhaps predict a hierarchy of analogs of strong and weak interactions.
</p><p>
<B>About the number of complex deformations of a given partonic 2-surface</B>
</p><p>
It is interesting to ask about how many deformations a given partonic 2-surface represents as a complex surface in E<sup>2</sup>× CP<sub>1</sub>, where CP<sub>1</sub> corresponds to the surface of CP<sub>2</sub> with d∈{1,2}. For the deformations of CP<sub>1</sub> with d=1,2, one can express E<sup>2</sup> complex coordinate as a meromorphic function of CP<sub>1</sub> complex coordinate. More generally, one can consider the partonic 2-surface in E<sup>2</sup>× S<sup>2</sup> as a surface with given genus g and consider the complex deformations of this surface. The dimension of the space of these deformations is of obvious physical interest if generalized holomorphy is accepted.
</p><p>
In the case of a pole, the E<sup>2</sup> point would go to infinity so that poles are not allowed. If the notion of Hamilton-Jacobi structure (see <A HREF="https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>) makes sense, one can slice M<sup>4</sup> also using closed partonic 2-surfaces with complex coordinates so that meromorphic functions with poles are allowed. In TGD, rational functions with rational coefficients of corresponding polynomials are favoured.
</p><p>
These functions can be characterized by so-called principal divisors expressible as formal superpositions D=∑ ν<sub>k</sub>P<sub>k</sub>. Here P<sub>k</sub> are the singular points (zeros for ν<sub>k</sub>>0 and poles for ν<sub>k</sub><0). One can assign also to complex one-forms divisors: this kind of divisor is known as canonical divisor and is unique apart from addition of principal divisor, which corresponds to a multiplication of the 1-form with a meromorphic function. The degree of the divisor can be defined as deg(D)= ∑ ν<sub>k</sub>.
</p><p>
Riemann-Roch theorem applies also to algebraic surfaces such as complex surfaces in E<sup>2</sup>× CP<sub>1</sub>, and allows to get grasp about the numbers of the surfaces obtained as deformations of CP<sub>1</sub> with a given divisor D for a surface with a given genus g. These numbers correspond to the dimensions of the linear spaces of rational functions, whose poles are not worse than the coefficients of D, where P<sub>k</sub> are the singular points (zeros for n<sub>k</sub>>0 and poles for n<sub>k</sub><0). The Riemann-Roch formula reads as
</p><p>
l(D)-l(K-D)=deg(D)-g+1 .
</p><p>
Here l(D) is the dimension of the space of meromorphic functions h for which all the coefficients of (h)+D are non-negative (no poles). The term -l(K-D) is a correction term present only for low degrees deg(D) defining the analog of polynomial degree characterizing the winding number of h. Because l(K-D) is a dimension of vector space, it cannot be negative and vanishes for large enough degrees. For large values of deg(D) the formula reads therefore as l(D)=deg(D)-g+1.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/nuclatomplato.pdf">About Platonization of Nuclear String Model and of Model of Atoms</A> or the <A HREF="https://tgdtheory.fi/pdfpool/nuclatomplato.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-45560130711111168712023-10-30T06:00:00.005-07:002023-10-30T06:00:32.252-07:00How could strong interactions emerge at the level of scattering amplitudes?
The above considerations are dangerous in that the intuitive QFT based thinking based is applied in TGD context where all interactions reduced to the dynamics of 3-surfaces and fields are geometrized by reducing them to the induced geometry at the level of space-time surface. Quantum field theory limit is obtained as an approximation and the applications of its notions at the fundamental level might be dangerous. In any case, it seems that only electroweak gauge potentials appear in the fermionic vertices and this might be a problem.
<OL>
<LI> By holography perturbation series is not needed in TGD. Scattering amplitudes are sums of amplitudes associated with Bohr orbits, which are not completely deterministic: there is no path integral. Whether path integral could be an approximate approximation for this sum under some conditions is an interesting question.
<LI> It is best to start from a concrete problem. Is pair creation possible in TGD? The problem is that fermion and antifermion numbers are separately conserved for the most obvious proposals for scattering amplitudes. This essentially due to the fact that gauge bosons correspond to fermion-antifermion pairs. Intuitively, fermion pair creation means that fermion turns backwards in time. If one considers fermions in classical background fields this turning back corresponds to a 2-particle vertex. Could pair creation in classical fields be a fundamental process rather than a mere approximation in the TGD framework. This would conform with the vision that classical physics is an exact part of quantum physics.
</p><p>
The turning back in time means a sharp corner of the fermion line, which is light-like elsewhere. M<sup>4</sup> time coordinate has a discontinuous derivative with respect to the internal time coordinate of the line. I have propoeed (see <A HREF="https://tgdtheory.fi/public_html/articles/intsectform.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/masterformula.pdf">this</A>) that this kind of singularities are associated with vertices involving pair creation and that they correspond to local defects making the differentiable structure of X<sup>4</sup> exotic. The basic problem of GRT would become a victory in the TGD framework and also mean that pair creation is possible only in 4-D space-time.
</OL>
One can imagine two kinds of turning backs in time.
<OL>
<LI> The turning back in time could occur for a 3-D surface such as monopole flux tube and induce the same process the string world sheets associated with the flux tubes and for the ends of the string world sheets as fermion lines ending at the 3-D light-like orbits of partonic 2-surfaces.
<LI> In the fusion of two 2-sheeted monopole flux tubes along their "ends" identifiable as partonic 2-surfaces wormhole contacts, the ends would fuse instantaneously (this process is analogous to "join along boundaries". The time reversal of this process would correspond to the splitting of the monopole flux tube inducing a turning back in time for a partonic 2-surface and for fermionic lines as boundaries of string world sheets at the partonic 2-surface.
</p><p>
This would be analogous to a creation of a fermion pair in a classical induced gauge field, which is electroweak. The same would occur for the partonic 2-surfaces as opposite wormhole throats and for the string world sheets having light-like boundaries at the orbits of partonic 2-suraces.
<LI> The light-like orbit of a partonic 2-surface contains fermionic lines as light-like boundaries of string world sheets. A good guess is that the singularity is a cusp catastrophe so that the surface turns back in time in exactly the opposite direction. One would have an infinitely sharp knife edge.
</OL>
What one can say about the scattering amplitudes on the basis of this picture? Can one obtain the analog for the 2-vertex describing a creation of a fermion pair in a classical external field?
<OL>
<LI> The action for a geometric object of a given dimension defines modified gamma matrices in terms of canonical momentum currents as Γ<sup>α</sup>= T<sup>αk</sup>Γ<sub>k</sub>, T<sup>α</sup><sub>k</sub>= ∂ L/∂(∂<sub>α</sub> h<sup>k</sup>). By hermiticity, the covariant divergence D<sub>α</sub>Γ<sup>α</sup> of the vector defined by modified gamma matrices must vanish. This is true if the field equations are satisfied. This implies supersymmetry between fermionic and bosonic degrees of freedom.
</p><p>
For space-time surfaces, the action is Kähler action plus volume term. For the 3-D light-partonic orbits one has Chern-Simons-Kähler action. For string world sheets one has area action plus the analog of Kähler magnetic flux. For the light-boundaries of string world sheets defining fermion lines one has the integral ∫ A<sub>μ</sub>dx<sup>μ</sup>. The induced spinors are restrictions of the second quantized spinors fields of H=M<sup>4</sup>× CP<sub>2</sub> and the argument is that the modified Dirac equation holds true everywhere, except possibly at the turning points.
</p><p>
<LI> Consider now the interaction part of the action defining the fermionic vertices. The basic problem is that the entire modified Dirac action density is present and vanishes if the modified Dirac equation holds true everywhere. In perturbative QFT, one separates the interaction term from the action and obtains essentially Ψbar</sub>Γ<sup>α</sup> D<sub>α</sub>Ψ. This is not possible now.
</p><p>
The key observation is that the modified Dirac equation could fail at the turning points! QFT vertices would have purely geometric interpretation. The gamma matrices appearing in the modified Dirac action would be continuous but at the singularity the derivative ∂<sub>μ</sub>Ψ= ∂<sub>μ</sub>m<sup>k</sup> ∂<sub>k</sub>Ψ of the induced free second quantized spinor field of H would become discontinuous. For a Fourier mode with momentum p<sup>k</sup>, one obtains
</p><p>
∂<sub>μ</sub>Ψ<sub>p</sub>= p<sub>k</sub>∂<sub>μ</sub> m<sup>k</sup>Ψ<sub>p</sub> == p<sub>μ</sub>Ψ<sub>p</sub>.
</p><p>
This derivative changes sign in the blade singularity. At the singularity one can define this derivative as an average and this leaves from the action Ψbar Γ<sup>α</sup> D<sub>α</sub>Ψ only the term ΨbarΓ<sup>α</sup> A<sub>α</sub>Ψ. This is just the interaction part of the action!
<LI> This argument can be applied to singularities of various dimensions. For D=3, the action contains the modified gamma matrices for the Kähler action plus volume term. For D=2, Chern-Simons-Kähler action defines the modified gamma matrices. For string world sheets the action could be induced from area action plus Kähler magnetic flux. For fermion lines from the 1-D action for fermion in induced gauge potential so that standard QFT result would be obtained in this case.
</OL>
How does this picture relate to perturbative QFT?
<OL>
<LI> The first thing to notice is that in the TGD framework gauge couplings do not appear at all in the interaction vertices. The induced gauge potentials do not correspond to A but to gA. The couplings emerge only at the level of scattering amplitudes when one goes to the QFT limit. Only the Kähler coupling strength and cosmological constant appear in the action.
<LI> The basic implication is that only the electroweak gauge potentials appear in the vertices. This conforms with the dangerous looking intuition that also strong interactions can be described in terms of electroweak vertices but this is of course a potential killer prediction. One should be able to show that the presence of WCW degrees of freedom taken into account minimally in terms of fermionic color partial waves in CP<sub>2</sub> predicts strong interactions and predicts the value of α<sub>s</sub>. Note that the restriction of spinor harmonics of CP<sub>2</sub> to a homologically non-trivial geodesic sphere gives U(2) partial waves with the same quantum numbers as SU(3) color partial waves have.
<LI> TGD approach differs dramatically from the perturbative QFT. Since 1/α<sub>s</sub> appears in the vertex, the increase of h<sub>eff</sub> in the vertex increases it: just the opposite occurs in the perturbative QFT! This seems to be in conflict with QFT intuition suggesting a perturbation series in α<sub>s</sub> ∝ 1/ℏ<sub>eff</sub>. The explanation is that 1/α<sub>K</sub> appears as a coupling parameter instead of α<sub>s</sub>.
</p><p>
This reminds of the electric-magnetic duality between perturbative and non-perturbative phases of gauge theories, where magnetic coupling strength is proportional to the inverse of the electric coupling strength. The description in terms of monopole flux tubes is therefore analogous to the description in terms of magnetic monopoles in the QFT framework. In TGD, it is the only natural description at the fundamental level. The decrease of α<sub>K</sub> by increase of h<sub>eff</sub> would indeed correspond to the QFT type description reduction of α<sub>s</sub>.
</p><p>
Could the description based on Maxwellian non-monopole flux tubes correspond to the usual perturbative phase without magnetic monopoles? In the Maxwellian phase there is huge vacuum degeneracy due to the presence of vacuum extremals with a vanishing Kähler form at the limit of vanishing volume action. Could this degeneracy allow path integral as a practical approximation at QFT limit.
<LI> h<sub>eff</sub>/h<sub>0</sub> = n is proposed to correspond to the dimension of algebraic extension of rationals associated with the space-time surface and serve as a measure for algebraic complexity. The increase of algebraic complexity of the space-time region defining the strong interaction volume would also make interactions strong. In TGD, the fundamental coupling strength would be α<sub>K</sub> and the increase of α<sub>K</sub> for ordinary value of h would force the increase of h. This should happen below the electroweak scale or at least the confinement scales and make perturbation theory describing strong interactions possible. This description would involve monopole flux tubes and their reconnections.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/nuclatomplato.pdf">About Platonization of Nuclear String Model and of Model of Atoms</A> or the <A HREF="https://tgdtheory.fi/pdfpool/nuclatomplato.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-53157089819772849232023-10-25T01:06:00.004-07:002023-10-25T01:06:47.841-07:00About the identification of the Schrödinger galaxy
The latest mystery related created by the observations of James Webb (see <A HREF="
https://www.cnet.com/science/space/james-webb-space-telescopes-latest-puzzle-is-schrodingers-galaxy-candidate/">this</A> and <A HREF="https://arxiv.org/pdf/2208.02794.pdf">this</A>).
</p><p>
It has been found that the determination of the redshift 1+ z = a<sub>now</sub>/a<sub>emit</sub> gives two possible space-time positions for the Schrödinger galaxy CEERS-1749 a<sub>now</sub> <I> resp.</I> a<sub>emit</sub> corresponds to the scale factor for the recent cosmology <I> resp.</I> cosmology when the radiation was emitted. Note that for not too large distances the recession velocity β satisfies the Hubble law β= HD. The nickname "Schrödinger galaxy" comes from the impression that the same galaxy could have existed in two different times in the same direction.
</p><p>
Accordingly, CHEERs allows two alternative identifications: either as an exceptionally luminous galaxy with z≈ 17 or as a galaxy with exceptionally low luminosity with z≈ 5. Both these identifications challenge the standard view about galaxy formation based on Λ CDM cosmology.
<OL>
<LI> The first interpretation is that CHEERS is very luminous, much more luminous than the standard cosmology would suggest, and has the redshift z≈ 17, which corresponds to light with the age of 13.6 billion years. The Universe was at the moment of emission t<sub>emit</sub>=220 million years old.
</p><p>
In the TGD framework, the puzzlingly high luminosity might be understood in terms of a cosmic web of monopole flux tubes guiding the radiation along the flux tubes. This would also make it possible to understand other similar galaxies with a high value of z but would not explain their very long evolutionary ages and sizes. Here the zero energy ontology (ZEO) of TGD could come in rescue (see <a HREF= "https://tgdtheory.fi/public_html/articles/JWagain.pdf">this</A>, <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> Another analysis suggest that the environment of the CHEERS contains galaxies with redshift z≈ 5. The mundane explanation would be that CHEERS is an exceptionally dusty/quenched galaxy with the redshift z≈ 5 for which light would be 12.5 billion years old.
</p><p>
Could TGD explain the exceptionally low luminosity of z≈ 5 galaxy? Zero energy ontology (ZEO) and the TGD view of dark matter and energy predict that also galaxies should make "big" state function reductions (BSFRs) in astrophysical scales. In BSFRs the arrow of time changes so that the galaxy would become invisible since the classical signals from it would propagate to the geometric past. This might explain the passive periods of galaxies quite generally and the existence of galaxies older than the Universe. Could the z≈ 5 galaxy be in this passive phase with a reversed arrow of time so that the radiation from it would be exceptionally weak.
</OL>
TGD seems to be consistent with both explanations. To make the situation even more confusing, one can ask whether two distinct galaxies at the same light of sight could be involved. This kind of assumption seems to be unnecessary but one can try to defend this question in the TGD framework.
<OL>
<LI> In the TGD framework space-times are 4-surfaces in M<sup>4</sup>× CP<sub>2</sub>. A good approximation is as an Einsteinian 4-surface, which by definition has a 4-D M<sup>4</sup> projection. The scale factor a corresponds to the light-cone proper time assignable to the causal diamond CD with which the space-time surface is associated. a is a very convenient coordinate since it has a simple geometrical interpretation at the level of embedding space M<sup>4</sup>× CP<sub>2</sub>. The cosmic time t assignable to the space-time surface is expressible as t(a).
<LI> Astrophysical objects, in particular galaxies, can form comoving tessellations (lattice-like structures) of the hyperbolic space H<sup>3</sup>, which corresponds to a=constant, and thus t(a) constant surfaces. The tessellation of H<sup>3</sup> is expanding with cosmic time a and the values of the hyperbolic angle η and spatial direction angles for the points of the tessellation do not depend on the value of a. The direction angles and hyperbolic angle for the points of the tessellation are quantized in analogy with the angles characterizing the points of a Platonic solid and this gives rise to a quantized redshift.
</p><p>
A tessellation for stars making possible gravitational diffraction and therefore channelling and amplification of gravitational radiation in discrete directions, could explain the recently observed gravitational hum (see <a HREF= "https://tgdtheory.fi/public_html/articles/gravhum.pdf">this</A>).
</p><p>
These tessellations could also explain the mysterious God's fingers, discovered by Halton Arp, as sequences of identical look stars or galaxies of hyperbolic tessellations along the line of sight (see <a HREF= "https://tgdtheory.fi/public_html/articles/minimal.pdf">this</A> and <a HREF= "https://tgdtheory.fi/pdfpool/cosmo.pdf">this</A>. Maybe something similar is involved now.
</OL>
This raises two questions.
<OL>
<LI> Could two similar galaxies at the same line of sight be behind Schrödinger galaxy and correspond to the points of scaled versions of the tessellation of H<sup>3</sup> having therefore different values of a and hyperbolic angle η? The spatial directions characterized by direction angle would be the same. Could one think that the tessellation consists of similar galaxies in the same way as lattices in condensed matter physics? The proposed explanation for the recently observed gravitational hum indeed assumes tessellation form by stars and most stars are very similar to our Sun (see <a HREF= "https://tgdtheory.fi/public_html/articles/gravhum.pdf">this</A>).
</p><p>
The obvious question is whether also the neighbours of the z≈ 5 galaxy belong to the scaled up tessellation. The scaling factor between these two tessellations would be a<sub>5</sub>/a<sub>17</sub>= 17/5. Could it be that the resolution does allow to distinguish the neighbors of the z≈ 17 galaxy from each other so that they would be seen as a single galaxy with an exceptionally high luminosity? Or could it be that the z≈ 5 galaxy is in a passive phase with a reversed arrow of time and does not create any detectable signal so that the signal is due to z≈ 17 galaxy.
</p><p>
<LI> Could one even think that the values of hyperbolic angles are the same for the two galaxies in which case the z≈ 5 galaxy could correspond to z≈ 17 galaxy but in the passive phase with an opposite arrow of time? The ages of most galaxies are between 10 and 13.6 billion years so that this option deserves to be excluded. Could the hyperbolic tessellation explain why two similar galaxies could exist at the same line of sight in a 4-dimensional sense?
</p><p>
This option is attractive but is actually easy to exclude. The light arriving from the galaxies propagates along light-like geodesics. Suppose that a light-like geodesic connects the observer to the z≈ 17 galaxy. The position of the z≈ 5 galaxy would be obtained by scaling the H<sup>3</sup> of the older galaxy by the ratio a(young)/a(old). Geometrically it is rather obvious that the geodesic connecting it to the observer cannot be lightlike but becomes space-like. If one approximates space-time with M<sup>4</sup> this is completely obvious.
</p><p>
For more detailed analysis, see the article <a HREF= "https://tgdtheory.fi/public_html/articles/JWagain.pdf">TGD view of the paradoxical findings of the James Webb telescope</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/galjets.pdf">TGD View of the Engine Powering Jets from Active Galactic Nuclei</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>.
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-42192342222401573662023-10-23T23:46:00.004-07:002023-10-24T00:04:50.276-07:00Pollack effect as a universal energy transfer mechanism?
The proposal of the recent article <a HREF= "https://tgdtheory.fi/public_html/articles/np2023.pdf">Some New Aspects of the TGD Inspired Model of the Nerve Pulse</A> is that nerve pulse generation relies on the flip-flop mechanism using the energy liberated in the reversal of Pollack effect at one side of cell membrane to induce Pollack effect at the opposite side. The liberate energy would be channelled along the pair of monopole flux tubes emerging by re-connection from two U-shaped monopole flux tubes. The flip-flop mechanism is highly analogous to a seesaw in which the gravitational binding energy at the first end of the seesaw is reduced and transforms to kinetic energy reducing gravitational binding energy at the second end of the seesaw.
</p><p>
All biochemical processes involve a transfer of metabolic energy. Could the flip-flop mechanism serve as a universal mechanism of energy transfer accompanying biochemical processes?
</p><p>
The first example is TGD based view of biocatalysis according to which a phase transition reduces the value of h<sub>eff</sub> and thus the length for the monopole flux tube pair connecting the reactants liberates energy, which kicks the reactants over the potential energy wall and in this way increases dramatically the rate of the reaction. Also now, the liberated energy could propagate as dark photons along the flux tube pair raise the system above the reaction wall or at least reduce its height.
</p><p>
Also the ADP→ ADP process could involve the Pollack effect and its reversal. In this process 3 protons are believed to flow through the cell membrane and liberate energy given to the ADP so that the process ADP+P<sub>i</sub> → ATP takes place. This system has been compared to an energy plant. This raises heretic questions. Does the flow of ordinary protons through the mitochondrial membrane really occur? Could the charge separation be also now between the cell interior and its magnetic body?
<OL>
<LI> The protons believed to flow through the mitochondrial membrane would be in the initial situation gravitationally dark and generated by Pollack effect for which the energy would be provided as energy liberated by biomolecules in a process which could be a time reversal for its storage in photosynthesis.
<LI> The reverse Pollack effect inside the mitochondrial membrane could transform the dark protons to ordinary protons and liberate energy, which is carried through the membrane as dark photons to the opposite side. This would allow the high energy phosphate bond of ATP to form in the reaction ADP+P<sub>i</sub> → ATP. According to the TGD proposal (see <a HREF= "https://tgdtheory.fi/public_html/articles/penrose.pdf">this</A> and <a HREF= "https://tgdtheory.fi/public_html/articles/precns.pdf">this</A>), the liberated energy could be used to kick the proton to the gravitational monopole flux tube, which would have length of order Earth size scale so that gravitational potential energy would of the same order of magnitude as the metabolic energy quantum with a nominal value .5 eV. This dark proton would be the energy carrier in the mysterious high phosphate energy bond, which does not quite fit the framework of biochemistry.
<LI> ATP would donate the phosphate ion P<sup>-</sup> for the target molecule, which would utilize this temporarily stored metabolic energy as the dark proton transforms to an ordinary one. Depending on the lifetime of the dark proton, this could occur as the target molecule receives P or later. In any case, this should involve the transformation P<sup>-</sup>→ P<sub>i</sub>. This could correspond to the transformation of the gravitationally dark proton to ordinary proton so that the charge separation giving rise to P<sup>-</sup> would be between P<sub>i</sub> and its magnetic body.
</OL>
In the chemical storage of the metabolic energy in photosynthesis, ATP provides the energy for the biomolecule storing the energy. This process should be accompanied by the transformation of P<sup>-</sup> to P<sub>i</sub>. It is instructive to consider two options that come immediately into mind.
</p><p>
<B> Option I</B>: The realistic looking option is that the energy is stored as the energy of an ordinary chemical bond.
<OL>
<LI> Hydrogen bond, which can form between a proton and other electronegative atoms such as O or N, is a natural candidate. Hydrogen bond indeed has an energy, which is of the order of metabolic energy quantum .5 eV. The simplest option is that the metabolic energy provided by the gravitational flux tube of ATP is liberated and used to generate a hydrogen bond of the protein. The dark gravitational flux tube loop would be nothing but a very long hydrogen bond.
<LI> For negatively charged molecules, the proton of a hydrogen bond could be gravitationally dark. For dark positively charged ions, some valence electrons could be gravitationally dark. In the electronic case the reduction of the gravitational binding energy would be roughly by a factor m<sub>e</sub>/m<sub>p</sub>∼ 2<sup>-11</sup> smaller and this leads to a proposal of electronic metabolic energy quantum (see <a HREF= "https://tgdtheory.fi/public_html/articles/penrose.pdf">this</A> and <a HREF= "https://tgdtheory.fi/public_html/articles/precns.pdf">this</A> and <a HREF= "https://tgdtheory.fi/public_html/articles/henegg.pdf">this</A>) for which there is some empirical support from the work of Adamatsky (see <A HREF="https://arxiv.org/pdf/2112.09907.pdf">this</A>.
</OL>
<B> Option II</B>: The less realistic looking option is that the molecule stores the metabolic energy permanently as a gravitationally dark proton. The motivation for its detailed consideration is that it provides insights to the Pollack effect.
<OL>
<LI> The dark proton associated with P<sup>-</sup> should become a dark proton associated with the molecule. In this case the length of hydrogen bond would become very long, increasing the ability to store metabolic energy.
</p><p>
The hydrogen bonded structure would be effectively negatively charged but this is just what happens in the EZ in Pollack effect! This supports the view that the Pollack effect for water basically involves the lengthening of the hydrogen bonds to U-shaped gravitational monopole flux tubes.
<LI> The Pollack effect requires a metabolic energy feed since the value of h<sub>gr</sub> tends to decrease spontaneously. This suggests that the dark gravitational hydrogen bonds are not long-lived enough for the purpose of long term metabolic energy storage. Rather, they would naturally serve as a temporary metabolic energy storage needed in the transfer of metabolic energy. The temporary storage of the metabolic energy to ATP would be a quantum variant of the seesaw.
<LI> The first naive guess for the scale of the life-time of the gravitationally dark proton would be given as a gravitational Compton time determined by the gravitational Compton length Λ<sub>gr</sub>= GM/β<sub>0</sub> =r<sub>S</sub>(M)/2β<sub>0</sub>. For the Earth with r<sub>S</sub>∼ 1 cm, one has T<sub>gr</sub>=1.5 × 10<sup>-11</sup> s corresponding to the energy .6 meV for the ordinary Planck constant and perhaps related to the miniature membrane potentials. For the Moon with mass M<sub>M</sub>=.01M<sub>E</sub>, this time is about T<sub>gr</sub>∼ 1.5× 10<sup>-13</sup> ns. For the ordinary Planck constant, this time corresponds to energy of .07 eV and is not far from the energy assignable to the membrane potential. For the Sun, one would gravitational Compton length is one half of the Earth's radius, which gives T<sub>gr</sub>= .02 s, which corresponds to 50 Hz EEG frequency.
</p><p>
Note that the rotation frequency for the ATP synthase analogous to a power plant is around 300 Hz which is the cyclotron frequency of the proton in the
endogenous magnetic field .2 Gauss interpreted in TGD as the strength of the monopole fluz part of the Earth's magnetic field.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/np2023.pdf"> Some New Aspects of the TGD Inspired Model of the Nerve Pulse</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/np2023.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.com0