tag:blogger.com,1999:blog-106143482024-04-19T08:22:10.440-07:00TGD diaryDaily musings, mostly about physics and consciousness, heavily biased by Topological Geometrodynamics background.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger2182125tag:blogger.com,1999:blog-10614348.post-51537633052850361802024-04-18T21:04:00.000-07:002024-04-18T21:04:47.480-07:00Singularities and infinities from the TGD point of view
Gary Ehlenberg sent two links to Quantamagazine articles, which are very relevant (perhaps not by accident!) for what I have been working with recently.
</p><p>
The first link was to a very interesting article about the the role of singularities in physics. Already in twistor Grassmann approach, singularities of the scattering amplitudes turned out to be central as data determining them. Kind of holography was in question.
</p><p>
I have been just working with singularities of space-time surface and have made a breakthrough in the understanding of what graviton is but also in the understanding of what the fundamental vertices (actually vertex!) of the scattering amplitudes are in the TGD framework.
</p><p>
In holography=generalized holomorphy view space-time surfaces are minimal surfaces with generalized holomorphic imbedding to H=M<sup>4</sup>×CP<sub>2</sub> implying the minimal surface property.
<OL>
<LI> The minimal surface property fails at lower-dimensional singularities taking the role of holographic data and the trace of the second fundamental form (SFF) analogous to a acceleration associated with the 4-D Bohr orbit of the particle as 3-surface has a delta function like singularity but vanishes elsewhere.
<LI> The minimal surface property expressess masslessness for both fields and particles as 3-surfaces. At the singularities masslessness property fails and singularities can be said to serve as sources which in QFTs define scattering amplitudes.
<LI> The singularities are analogs of poles and cuts for the 4-D generalization of the ordinary holomorphic functions. Also for the ordinary holomorphic functions the Laplace equation as analog massless field equation and expressing analyticity fails. Complex analysis generalizes to dimension 4.
<LI> The conditions at the singularity give a generalization of Newton's F=ma! I ended up where I started more than 50 years ago!
<LI> In dimension 4, and only there, there is an infinite number of exotics diff structures, which differ from ordinary ones at singularities of measure zero analogous to defects. These defects correspond naturally to the singularities. For the exotic diff structure one can say that there is no singularity. This means that complex analysis generalizes to dimension 4 and only to dimension 4.
<LI> Group theoretically the trace of the SFF can be regarded as a generalization of the Higgs field, which is non-vanishing only at the vertices and this is enough. Singularities take the role of generalized particle vertices and determine the scattering amplitudes. The second fundamental form contracted with the embedding space gamma matrices and slashed between the second quantized induced spinor field and its conjugate gives the universal vertex involving only fermions (bosons are bound states of fermions in TGD). It contains both gauge and gravitational contributions to the scattering amplitudes and there is a complete symmetry between gravitational and gauge interactions. Gravitational couplings come out correctly as the radius squared of CP<sub>2</sub> as also in the classical picture.
</OL>
This generalized Higgs field characterizing singularities would dictate all scattering amplitudes! Generalized Higgs would be really the God particle! Its CP<sub>2</sub> part gives standard model interactions and M<sup>4</sup> part gives gravitation.
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Gary Ehlenberg sent another link to a Quantamagazine article (see <A HREF="https://www.quantamagazine.org/alien-calculus-could-save-particle-physics-from-infinities-20230406/">this</A>), which is very relevant to what I have been working on recently. I am not going to comment on the so called alien calculus discussed in the article as a proposal to get rid of the infinities of quantum field theories. Rather, I will explain how this problem is solved in the TGD framework (see https://tgdtheory.fi/public_html/articles/whatgravitons.pdf).
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The problem of infinities is due to the assumption that the point-like nature of fundamental objects. In superstring models this problem was at least partially solved but superstrings were not the option chosen by Nature.
<OL>
<LI> The basic discovery of TGD is that the generalization of complex structure is possible in dimension 4 of the space-time and corresponds to the existence of exotic diff structures (see https://tgdtheory.fi/public_html/articles/intsectform.pdf). Nature wants all that it can get and has chosen the option with the maximal structural richness.
<LI> In TGD particles become 3-D surfaces whose 4-D orbits are analogs of Bohr orbits with a finite non-determinism at which the minimal surface property fails. The mathematically ill-defined path integral reduces to a finite sum and only the well-defined functional integral over 3-surfaces remains. Divergences disappear completely.
<LI> Scattering amplitudes reduce to sums over contributions from the lower-D singularities of the minimal surfaces. Singularities are analogous to the poles of holomorphic functions in holography=holomorphy vision and generalized holomorphic maps define an infinite-D symmetry group analogous to holomorphic maps in string models.
<LI> The trace of the second fundamental form slashed between the induced free spinor fields of M<sup>4</sup×CP<sub>2</sub> gives the universal vertex and contains contributions of all basic interactions including gravitation. Induced spinor fields are second quantized spinor fields of H=M<sup>4</sup>×CP<sub>2</sub> and correlation functions for these free spinor fields determine the scattering amplitudes.
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">What gravitons are and could one detect them in the TGD Universe?</A>) and the chapter the chapter <a HREF= "https://tgdtheory.fi/pdfpool/SW.pdf">About the Relationships Between Electroweak and Strong Interactions and Quantum Gravity in the TGD Universe</A>.
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For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-82747474276229648482024-04-15T22:43:00.000-07:002024-04-15T22:43:10.164-07:00The symmetry between gravitational and gauge interactions
The beauty of the proposal is that implies a complete symmetry between gravitational and gauge interactions.
<OL>
<LI> Weak interactions and gravitation couple to weak isospin and spin respectively. Color interactions couple to the isometry charges of CP<sub>2</sub> and gravitational interactions coupling to the isometry charges of M<sup>4</sup>. The extreme weakness of the gravitation can be understood as the presence of the CP<sub>2</sub> contribution to the induced metric in the gravitational vertices.
</OL>
Does color confinement have any counterpart at the level of M<sup>4</sup>? The idea that physical states have vanishing four-momenta does not look attractive.
<OL>
<LI> In ZEO, the finite-D space of causal diamonds (CDs) forms (see <A HREF= "https://tgdtheory.fi/public_html/articles/CDconformal.pdf">this</A>) the backbone of WCW and Poincare invariance and Poincare quantum numbers can be assigned with wave functions in this space. For CD, the infinite-D unitary representations of SO(1,3) satisfying appropriate boundary conditions are a highly attractive identification for the counterparts of finite-D unitary representations associated with gauge multiplets. The basic objection against gravitation as SO(1,3) gauge theory would fail.
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One could replace the spinor fields of H with spinor fields restricted to CD with spinor fields for which M<sup>4</sup> parts sinor nodes as plane waves are replaced with spinor modes in CD labelled by spin and its hyperbolic counterpart assignable to Lorentz boosts with respect to either tip of CD. One could also express these modes as superpositions of the plane wave modes defined in the entire H.
</p><p>
The analog of color confinement would hold true for particles as unitary representations of SO(1,3) in CD. One could say that SO(1,3) appears as an internal isometry group of an observer's perceptive field represented by CD and Poincare group as an external symmetry group treating the observer as a physical object.
<LI> By separation of variables the spinor harmonics in CD factorize phases depending on the mass of the particle determined by CP<sub>2</sub> and spinor harmonic of hyperbolic 3-space H<sup>3</sup>=SO(1,3)/SO(3). SO(1,3) allows an extremely rich set of representations in the hyperbolic space H<sup>3</sup> analogous to spherical harmonics. A given infinite discrete subgroup Γ⊂ SO(1,3) defines a fundamental domain of Γ as a double coset space Γ\SO(1,3)/SO(3). This fundamental domain is analogous to a lattice cell of condensed matter lattice defined by periodic boundary conditions. The graphics of Escher give an idea about these structures in the case of H<sup>2</sup>. The products of wave functions defined in Γ⊂ SO(1,3) and of wave functions in Γ define a wave function basis analogous to the space states in condensed matter lattice.
<LI> TGD allows gravitational quantum coherence in arbitrarily long scales and I have proposed that the tessellations of H<sup>3</sup> define the analogs of condensed matter lattices at the level of cosmology and astrophysics (see <A HREF= "https://tgdtheory.fi/public_html/articles/gravhum.pdf">this</A>). The unitary representations of SO(1,3) would be central for quantum gravitation at the level of gravitationally dark matter. They would closely relate to the unitary representations of the supersymplectic group of δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> in M<sup>4</sup> degrees of freedom and define their continuations to the entire CD.
<LI> There exists a completely unique tessellation known as icosa tetrahedral tessellation consisting of icosahedrons, tetrahedrons, and octahedrons glued along boundaries together. I have proposed that it gives rise to a universal realization of the genetic code of which biochemical realizations is only a particular example (see <A HREF= "https://tgdtheory.fi/public_html/articles/TIH.pdf">this</A> and <A HREF= "https://tgdtheory.fi/public_html/articles/5essellationH3.pdf">this</A>). Also this supports a deep connection between biology and quantum gravitation emerging also in classical TGD (see <A HREF= "https://tgdtheory.fi/public_html/articles/precns.pdf">this</A> and <A HREF= "https://tgdtheory.fi/public_html/articles/penrose.pdf">this</A>). Also electromagnetic long range classical fields are predicted to be involved with long length scale quantum coherence (see <A HREF= "https://tgdtheory.fi/public_html/articles/hem.pdf">this</A>).
</OL>
The challenge is to understand the implications of this picture for M<sup>8</sup>-H duality (see <A HREF= "https://tgdtheory.fi/public_html/articles/TGDcritics.pdf">this</A>). The discretization of M<sup>8</sup> identified as octonions O with the Minkowskian norm defined by Re(Im(o<sup>2</sup>)) is linear M<sup>8</sup> coordinates natural for octonions. The discretization obtained by the requirement that the coordinates of the points of M<sup>8</sup> (momenta) are algebraic integers in an algebraic extension of rationals would make sense also in p-adic number fields.
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In the Robertson-Walker coordinates for the future light-cone M<sup>4</sup><sub>+</sub> sliced by H<sup>3</sup>:s the coordinates define by mass (light-cone proper time in H), hyperbolic angle and spherical angles, the discretizations defined by the spaces Γ\SO(1,3)/SO(3) would define a discretization and one can define an infinite hierarchy of discretizations defined by the discrete subgroups of SO(1,3) with matrix elements belonging to an extension of rationals. This number theoretically universal discretization defines a natural alternative for the linear discretization. Maybe the linear <I> resp.</I> non-linear discretization could be assigned to the moduli space of CDs <I> resp.</I> CD.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">What gravitons are and could one detect them in the TGD Universe?</A>) and the chapter the chapter <a HREF= "https://tgdtheory.fi/pdfpool/SW.pdf">About the Relationships Between Electroweak and Strong Interactions and Quantum Gravity in the TGD Universe</A>.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-88153694513493405162024-04-15T22:42:00.000-07:002024-04-19T08:21:25.549-07:00What modified Dirac action is and how it determines scattering amplitudes?
Holography=generalized holomorphy property means that minimal surface field equations are true outside singularities for any general coordinate invariant action constructible in terms of the induced geometry. However, the twistor lift of TGD suggests that 6-D Kähler action is the fundamental action. It reduces to 4-D Kähler action plus volume term in the dimensional reduction guaranteeing that the 6-surface can be regarded as a generalization of twistor space having space-time surface as a base-space and 2-sphere.
</p><p>
One can express the induced spinor field obtained as a restriction of the second quantized H spinor field to the space-time surface and it satisfies modified Dirac equation (see <A HREF= "https://tgdtheory.fi/public_html/articles/modDir.pdf">this</A>).
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Modified Dirac action L<sub>D</sub> is defined for the induced spinor fields.
<OL>
<LI> It is fixed by the condition of hermiticity stating that the canonical momentum currents appearing in it have a vanishing divergence. If the modified gamma matrices Γ<sup>α</sup> are defined by an action S<sub>B</sub> defining the space-time surface itself, they are indeed divergenceless by field equations. This implies a generalization of conformal symmetry to the 4-D situation (see <A HREF= "https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>) and the modes of the modified Dirac equation define super-symplectic and generalized conformal charges defining the gamma matrices of WCW (see <A HREF= "https://tgdtheory.fi/public_html/articles/wcwsymm.pdf">this</A>).
<LI> Generalized holomorphy implies that S<sub>B</sub> could be chosen to correspond to modified gamma matrices defined by the sum of L<sub>K</sub>+L<sub>V</sub> or even by L<sub>V</sub> defining induced gamma matrices. Which option is more plausible?
<LI> An attractive guiding physical idea is that the singularities are not actually singularities if exotic diffeo structure is inducted. Field equations hold true but with S<sub>K</sub>+S<sub>V</sub>. The singularities would cancel. One would avoid problems with the conservation laws by using exotic diffeo structure.
<LI> At the short distance limit for which α<sub>K</sub> is expected to diverge as a U(1) coupling, the action reduces to S<sub>V</sub> and the defects would be absent. Only closed cosmic strings and monopole flux tubes would be present but wormhole contacts and string world sheets identifiable as defects are absent: this would be the situation in the primordial cosmology (see <A HREF= "https://tgdtheory.fi/public_html/articles/3pieces.pdf">this</A>). Only dark energy as classical energy of the cosmic strings and monopole flux tubes would be present and there would be no elementary particles and elementary particle scattering at this limit.
</OL>
One can consider several options assuming that the singularities are not actually present for the exotic diffeo structures.
</p><p>
<B> Option 1</B>: The first option relies on the assumption that the exponential of the modified Dirac action is imaginary and analogous to the phase defined by the action in QFTs. This is enough in TGD since fermions are the only fundamental particles and bosonic action is a purely classical notion.
<OL>
<LI> Volume action is in a very special role in that it represents both the classical dynamics of particles as 3-D surfaces as analogs of geodesic lines, the classical geometrized dynamics of massless fields, and generalizes the Laplace equations of complex analysis.
</p><p>
This motivates the proposal that only induced the gamma matrices Γ<sup>α</sup>g<sup>αβ</sup>h<sup>k</sup><sub>β</sub>γ<sub>k</sub> (no contribution from L<sub>K</sub>) corresponding to S<sub>V</sub> appear in L<sub>D</sub> and the bosonic action S<sub>B</sub>=S<sub>K</sub>+S<sub>V</sub>+S<sub>I</sub>, where S<sub>I</sub> is real, is defined by the twistor lift of TGD. The field equations are satisfied also at the singularities so that the contributions from S<sub>K</sub>+S<sub>I</sub> and S<sub>V</sub> cancel each other at the singularity in accordance with the idea that an exotic diffeo structure is in question. Both S<sub>K</sub> and S<sub>I</sub> contributions would have an imaginary phase.
<LI> Therefore L<sub>V</sub>, which involves cosmological constant Λ, disappears from the scattering amplitudes by the field equations for L<sub>B</sub> although it is implicitly present. The number theoretic evolution of the S<sub>K</sub>+S<sub>I</sub> makes itself visible in the scattering vertices. Outside the singularities both terms vanish separately but at singularities this is not the case. Only lower-D singularities contribute to the scattering amplitudes.
</p><p>
The number theoretical parameters of the bosonic action determined by the hierarchy of extensions of rationals would parametrize different exotic diffeo structures and make themselves visible in the quantum dynamics in this way. S<sub>I</sub> would contribute to classical charges and its M<sup>4</sup> part would contribute to the Poincare charges.
<LI> An objection against this proposal is that the divergence of the modified gamma matrices defined by the S<sub>K</sub>+S<sub>I</sub> need not be well-defined. It should be proportional to a lower-dimensional delta function located at the singularity.
</p><p>
For 3-D light-like light-partonic orbits, the contravariant induced metric appearing in the trace of the second fundamental form has diverging components but it is not clear whether the trace of the second fundamental form can give rise to a 3-D delta function at this limit. Chern-Simons action at the light-like partonic orbit coming from the instanton term is well-defined and field equations should not give rise to a singularity except at partonic 2-surfaces, which have been identified as analogs of vertices at which the partonic 2-surface X<sup>2</sup> splits to two.
</p><p>
At X<sup>2</sup> the trace of the second fundamental form can be well-defined and proportional to a 2-D delta function at X<sup>2</sup> since the 4-metric metric has one light-like direction at X<sup>2</sup> and has a vanishing determinant and is therefore is effectively 2-D (the light-like components of g<sub>uv</sub> =g<sub>vu</sub> of the 4-metric vanish). Therefore vertices would naturally correspond to partonic 2-surfaces, which split to two at the vertex. This is indeed the original proposal.
<LI> The divergence of g<sup>μν</sup>h<sup>k</sup><sub>ν</sub> vertex as the trace of the second fundamental form D<sub>α</sub>h<sup>k</sup><sub>β</sub> defined by the covariant derivatives of coordinate gradients, appears in the vertex. The second fundamental form is orthogonal to the space-time surface and can be written as
</p><p>
g<sup>μν</sup>D<sub>ν</sub>∂<sub>μ</sub>h<sup>k</sup>= P<sup>k</sup><sub>l</sub>H<sup>l</sup> ,
P<sup>k</sup><sub>l</sub> = h<sup>k</sup><sub>l</sub>- g<sup>μν</sup>h<sup>k</sup><sub>μ</sub>h<sub>lr</sub>h<sup>r</sup><sub>ν</sub> ,
</p><p>
H<sup>k</sup>= g<sup>αβ</sup> (∂<sub>α</sub>+B<sup>k</sup><sub>α</sub>)g<sup>αβ</sup>h<sup>k</sup><sub>β</sub> , B<sup>k</sup><sub>α</sub>= B<sup>k</sup><sub>lm</sub>h<sup>m</sup><sub>α</sub> .
</p><p>
P<sup>k</sup><sub>l</sub> projects to the normal space of the space-time surface. H<sup>k</sup> is covariant derivative of h<sup>k</sup><sub>α</sub> and B<sup>k</sup><sub>α</sub>= B<sup>k</sup><sub>lm</sub>h<sup>m</sup><sub>α</sub> is the projection of the Riemann connection of H to the space-time surface.
<LI> This allows a very elegant physical interpretation. In linear Minkowski coordinates for M<sup>4</sup>, one has B<sup>k</sup><sub>α</sub>=0 but the presence of the CP<sub>2</sub> contribution coming from the orthonormal projection implies that the covariant divergence is non-vanishing and proportional to the radius squared of <CP<sub>2</sub>. Vertex is proportional to the trace of the second fundamental form, whose CP<sub>2</sub> part is analogous to the Higgs field of the standard model. This field is vanishing in the interior by the minimal surface property in analogy with the generalized Equivalence Principle.
</p><p>
The trace of the second fundamental form is a generalization of acceleration from 1-D case to 4-D situation so that the interaction vertices are lower-dimensional regions of the space-time surface which experience acceleration. The regions outside the vertices represent massless fields geometrically. At the singularities the Higgs-like field is non-vanishing so that there is mass present. The analog of Higgs vacuum expectation is non-vanishing only at the defects.
</p><p>
It seems that a circle is closing. I started more than half a century ago from Newton's "F=ma" and now I discover it in the interaction vertex, which is the core of quantum field theories! I almost see Newton nodding and smiling and saying "What I said!".
</OL>
</p><p>
<B> Option 2</B>: Modified gamma matrices are defined by S<sub>K</sub>+S<sub>V</sub> +iS<sub>I</sub> and the real part of the singularity vanishes. The imaginary part cannot vanish simultaneously.
<OL>
<LI> The exponent of Kähler function defines a real vacuum functional and K is determined by S<sub>K</sub>+S<sub>V</sub> whereas the action exponential of QFTs of QFTs defines a phase. In topological QFTs, the contribution of the instanton term S<sub>D,I</sub> is naturally purely imaginary and could define "imaginary part of the Kähler function K, which does not contribute to the Kähler metric of WCW.
</p><p>
One can argue that this must be the case also for S<sub>D</sub>. Hence the contribution of S<sub>K</sub>+S<sub>V</sub> to S<sub>D</sub> would be real and differ by a multiplication with i from that in QFTs whereas the contribution of iS<sub>I</sub> would be imaginary. One must admit that this is not quite logical. Also the contribution to the Noether charges would be imaginary. This does not look physically plausible.
<LI> One cannot require the vanishing of both the real part and imaginary part of the divergence of the modified gamma matrices at the singularity. The contribution of L<sub>C-S-K</sub> at the singularity would be non-vanishing and determine scattering amplitudes and imply their universality.
</p><p>
For the representations of Kac-Moody algebras the coefficient of Chern-Simons action is k/4π and allows an interpretation as quantization of α<sub>K</sub> as α<sub>K</sub>= 1/k. Scattering vertices would be universal and determined by an almost topological field theory. Almost comes from the fact that the exponent of S<sub>B</sub> defines the vacuum functional.
<LI> The real exponential exp(K) of the real Kähler function defined by S<sub>K</sub>+S<sub>V</sub> would be visible in the WCW vacuum functional and bring in an additional dependence on the α<sub>K</sub> and cosmological constant Λ, whose number theoretic evolution would fix the evolution of the other coupling strengths. Note that the induced spinor connection corresponds in gauge theories to gauge potentials for which the gauge coupling is absorbed as a multiplicative factor.
</OL>
There are therefore two options. For both cases 1/α<sub>K</sub>=1/k appears in the action.
<OL>
<LI> For Option 1 only iS<sub>V</sub> appears in S<sub>D</sub> and iS<sub>K</sub>+ iS<sub>C-S-K</sub> determines the scattering amplitudes for option 2). Exponent of the modified Dirac action defines the analog of the imaginary action exponential of QFTs.
<LI> For Option 2 for which the entire action defines the modified gamma matrices the iS<sub>C-S-K</sub> defines the scattering amplitudes and one has an analog of topological QFT. This picture would conform with an old proposal that in some sense TGD is a topological quantum field theory. One can however argue that the treatment of S<sub>K</sub>+S<sub>V</sub> and S<sub>I</sub> in different ways does not conform with QFT treatment and also the Noether charges are a problem.
</OL>
Some technical remarks are in order.
<OL>
<LI> The spinor connection does not disappear from the dynamics at the singularities. It is transformed to components of projected Riemann connection of H appearing in the divergence D<sub>α</sub>T<sup>α<sub>k</sub></sub><sub>C-S-K</sub>.
</p><p>
<LI> The modified Dirac action must be dimensionless so that the scaling dimension of the induced spinors should be d=-3/2 and therefore same as the scaling dimension of M<sup>4</sup> spinors. This looks natural since CP<sub>2</sub> is compact.
</p><p>
The volume term included in the definition of the induced gamma matrices must be normalized by 1/L<sub>p</sub><sup>4</sup>. L<sub>p</sub> is a p-adic length scale and is roughly of order of a biological scale L<sub>p</sub>≈ 10<sup>-4</sup> meters if the scale dependent cosmological constant Λ corresponds to the inverse squared for the horizon radius. One has 1/L<sub>p</sub><sup>4</sup>= 3Λ/8π G. This guarantees the expected rather slow coupling constant evolution induced by that of α<sub>K</sub> diverging in short scales.
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">What gravitons are and could one detect them in the TGD Universe?</A>) and the chapter the chapter <a HREF= "https://tgdtheory.fi/pdfpool/SW.pdf">About the Relationships Between Electroweak and Strong Interactions and Quantum Gravity in the TGD Universe</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-24578446713294981912024-04-14T03:47:00.000-07:002024-04-14T05:59:58.355-07:00Common solution of 4 killer problems of TGDTowards the end of the last year, I made considerable progress in understanding particle vertices (see <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">this</A>).
The question however remained, what exactly is a graviton and what is the vertex corresponding to graviton emission.
</p><p>
The help came from condensed matter physics. There is evidence for a chiral graviton in systems exhibiting quantum Hall effect (see <A HREF= "https://lifeboat.com/blog/2024/04/scientist-say-they-have-first-experimental-evidence-of-gravitons-that-could-connect-quantum-mechanics-and-relativity">this</A>). Chiral graviton is not a true graviton. However, the article inspired a rethinking of the problem.
</p><p>
The result was a beautiful picture that combined the previously identified big problems for which a common solution was already found.
<OL>
<LI> Quantum gravity in TGD can be understood as a gauge theory where the gauge group is the Lorentz group SO(1,3). The whole point is that this group is an isometry group related to the other half of the causal diamond. The necessary infinite-dimensional unitary representations of SO(1,3), which are a disaster in standard gauge theory, have a beautiful interpretation in zero-energy ontology because SO(1,3) acts as isometries of the causal diamond. The unitary irreps of SO(1,3) take the role of the unitary representations of the Poincare group. Poincare invariance is in turn realized in the moduli space of causal diamonds (CDs) forming the backbone of the "world of classical worlds" (WCW) (see see <A HREF="https://tgdtheory.fi/public_html/articles/CDconformal.pdf">this</A>)).
</p><p>
Here, surprisingly, a connection with Weinstein's work emerges. Weinstein's analogous attempt fails for many reasons, also because the unitary representations of SO(1,3) are infinite-dimensional and the usual measure theory does not work. I even wrote an article about this (see <A HREF="https://tgdtheory.fi/public_html/articles/WeinsteinTGD.pdf">this</A>). Thanks to Marko and others for directing attention to Weinstein, and to myself for taking Weinstein's stuff so seriously that SO(1,3) was bothered.
<LI> A spinor connection for M<sup>4</sup> would induce a gauge potential of the gravitational field. Spin would take the role of gauge charge. The description of gravity and dimensional interactions would be exactly the same on a formal level. For both, the analogy of the classical energy-impulse tensor would occur at the vertices through modified gammas, and both would be gauge theories in a certain sense.
</OL>
However, there are 4 problems that seem to destroy this vision, of which problems b,c,d were already solved towards the end of the last year .
<OL>
<LI> The spinor connection can be dimensionally transformed to zero by a general coordinate transformation: no gravity at all!
<LI> In dimension D=4 for space-time, an infinite number of diffeo structures can be found and they differ from the normal s.e. it involves lower-dimensional defects. This is a catastrophe from the perspective of general relativity.
<LI> Fermion and antifermion numbers are separately conserved unless fermion pairs can be created in a vacuum. Fermion pair creation must be possible.
<LI> Furthermore, the modified Dirac effect which should give the vertices is exactly zero based on the Dirac equation. Could Dirac's equation break down in the defects and in this way produce the vertices looking like QFT vertices?
</OL>
There is a common solution for all these four problems (see <A HREF="https://tgdtheory.fi/public_html/articles/SW.pdf">this</A>)!
<OL>
<LI> In Dirac's picture, the creation of a pair means that the fermion line reverses in time. This point would be exactly a defect for a standard diffeo structure when it is interpreted as an exotic for a diff structure! In that case, Dirac's equation does not apply at the defect and there is a delta function singularity that gives the vertex.
<LI> The creation of the pair is possible in dimension D=4 and only in dimension D=4!
<LI> The induced spinor connection can be converted to zero everywhere by a generalö coordinate transformation except in these diffeo-defects!! Gravitation can therefore be effectively eliminated by a general coordinate transformation, but not completely. This generalizes Einstein's elevator argument to the quantum level. This is nothing but the quantum version of the Equivalence Principle!
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/whatgravitons.pdf">What gravitons are and could one detect them in the TGD Universe?</A>) and the chapter the chapter <a HREF= "https://tgdtheory.fi/pdfpool/SW.pdf">About the Relationships Between Electroweak and Strong Interactions and Quantum Gravity in the TGD Universe</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-11225606387172510392024-04-13T18:00:00.000-07:002024-04-13T22:53:50.222-07:00What gravitons are and could one detect them in TGD Universe?
What gravitons are in the TGD framework? This question has teased me for decades. It is easy to understand gravitation at the classical level in the TGD framework but the identification of gravitons has been far from obvious. Second question is whether the new physics provided by TGD could make the detection of gravitons possible?
</p><p>
The stimulus, which led to the ideas related to the TGD based identification of gravitons, to be discussed in the sequel, came from condensed matter physics. There was a highly interesting popular article telling about the work of Liang et al with the title "Evidence for chiral graviton modes in fractional quantum Hall liquids" published in Nature.
</p><p>
The generalized Kähler structure for M<sup>4</sup> ⊂ M<sup>4</sup>\times CP<sub>2</sub> leads to together with holography=generalized holomorphy hypothesis to the question whether the spinor connection of M<sup>4</sup> could have interpretation as gauge potentials with spin taking the role of the gauge charge. The objection is that the induced M<sup>4</sup> spinor connection has a vanishing spinor curvature. If only holomorphies preserving the generalized complex structure are allowed one cannot transform this gauge potential to zero everywhere. This argument can be strengthened by assigning the fundamental vertices with the splitting of closed string-like flux tubes representing elementary particles. The vertices would correspond to the defects of 4-D diffeo structure making possible a theory allowing a creation of fermion pairs. The induced M<sup>4</sup> spinor connection could not be eliminated by a general coordinate transformation at the defects.
</p><p>
One could have an analog of topological field theory and the Equivalence Principle at quantum level would state that locally the M<sup>4</sup> spinor connection can be transformed to zero but not globally. Gravitons and gauge bosons would be in a completely similar role as far as vertices of generalized Feynman diagrams are considered.
</p><p>
The second question is whether gravitons could be detected in the TGD Universe. It turns out that the FQHE type systems do not allow this but dark protons at the monopole flux tube condensates give rise to a mild optimism.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/whatgravitons.pdf"> What gravitons are and could one detect them in TGD Universe?</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/SW.pdf">About the Relationships Between Electroweak and Strong Interactions and Quantum Gravity in the TGD Universe</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-50477089517283678002024-04-09T21:51:00.000-07:002024-04-10T21:35:04.814-07:00Neutrons form bound states with nanocrystals: how?A very interesting observation is described in <A HREF ="https://news.mit.edu/2024/mit-researchers-discover-neutronic-molecules-0403">MIT News</A>. The original article telling about the discovery can be found <A HREF="https://doi.org/10.1021/acsnano.3c12929">here</A>. What has been found that neutrons form bound states with nanocrystals of size about 13 nm and are located outside the crystals.
</p><p>
In wave mechanics, the de Broglie wavelength for a neutron gives an idea of its quantum coherence scale, which should be on the order of 10 nanometers for quantum dots. The energy of the neutron must be above the thermal energy. The temperature must be at most milli Kelvin for this condition to be fulfilled.
</p><p>
The range of strong interactions is of order 10<sup>-14</sup> -10<sup>-15</sup> meters and extremely short as compared to the 10 nanometer scale of nanocrystals. I don't really understand how strong interactions could produce these states. Another strange feature is that neutrons are outside these quantum dots. Why not inside, if nuclear power is involved somehow?
</p><p>
Contrary to what the finnish popular article where I found this news first (see <A HREF = "https://www.tekniikkatalous.fi/uutiset/tt/59dd7691-2de7-4bc1-a1b5-106ca2dbb217">this</A>) claims, neutrons interact electromagnetically. They have no charge but have a magnetic moment related to the neutron's spin so that they interact with the magnetic fields. How is this option ruled out? Is it really excluded?
</p><p>
In the TGD Universe, the new view of space-time implies that the magnetic fields of Maxwell's theory are replaced by magnetic flux quanta, typically flux tubes. Also monopole flux tubes are possible and explain quite a large number of anomalies related to the magnetic fields. The monopole flux tubes are actually basic objects in all scales.
</p><p>
Could one think that the neutrons reside at the monopole flux tubes associated with the nanocrystal? Could the neutrons be bound to the magnetic fields of the magnetic flux tubes and form cyclotron states? If so, the de Broglie wavelength would be related to the free motion in the direction of the necessarily closed monopole flux tube.
</p><p>
More generally, neutrons could have an effective Planck constant larger than the ordinary Planck constant and behave like dark matter. In the TGD based model of biomatter, phases of protons with very large effective Planck constant behaving like dark matter are in an essential role.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/TGDcondmatshort.pdf">TGD and condensed matter</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/TGDcondmatshort.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>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-82537987708864408542024-04-08T21:00:00.000-07:002024-04-08T23:01:49.080-07:00Sleeping neurons and TGD
I learned of a very interesting finding related to cerebellar neurons associated with so-called climbing fibers and Purkinje cells.
(see <A HREF ="https://www.sciencealert.com/mysterious-zombie-neurons-unlock-secrets-of-learning-in-the-brain">this</A>). The popular article tells about the findings described in an article by N.T. Silva et al published in Nature (see <A HREF="https://www.nature.com/articles/s41593-024-01594-7">this</A>).
</p><p>
Climbing fibers and Purkinje cells are involved with the receival information from the external world and with the conditioning to external stimuli. Mice were studied and the external stimulus was light and produced eye blink as a response. It was possible to produce conditioning by using preceding cues. It was found that even a subtle reduction of the signalling using light-sensitive protein ChR2 made the neurons in question "zombies", which were not able to receive information from the external world.
</p><p>
Can one understand the zombi neurons in the TGD framework? The TGD based view of consciousness as a generalization of quantum measurement theory relies on zero energy ontology (ZEO), which solves the quantum measurement problem (see <A HREF="https://tgdtheory.fi/pdfpool/ZEO.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/zeoquestions.pdf">this</A> and <A HREF= "https://tgdtheory.fi/public_html/articles/CDconformal.pdf">this</A>).
<OL>
<LI> The first prediction is a hierarchy of Planck constant, meaning the possibility of quantum coherence in arbitrarily long scales: the phases of ordinary matter with this property behave like dark matter.
<LI> Second prediction is that quantum physics dominates in all scales but in zero energy ontology we do not see this since quantum jumps occur between superpositions of Bohr-orbit like space-time surfaces and there is no violation of classical determinism!
<LI> The third prediction is that in ordinary "big" state function reductions (BSFRs) the arrow of time changes. This is analogous to death or following sleep and means reincarnation with an opposite arrow of time. Quantum tunnelling means to such states function reduction and return to the original arrow of time.
</p><p>
Sleep would initiate a life with an opposite arrow of time. Life would be a universal phenomenon appearing in all scales. The most dramatic example is provided by stars and galaxies older than the universe. The evolutionary age of a galaxy living forth and back in geometric time is much longer than according to the ordinary view of time.
</OL>
The zombie neurons would be sleeping! During the sleep period they would not receive information from the environment and would not learn. The dose of Chr would induce a BSFR. How?
<OL>
<LI> TGD inspired quantum measurement theory predicts also a second kind of SFR, "small" SFR. In SSFR the state of the system changes but not much and the arrow of time is preserved. SSFRs are the TGD counterparts of repeated measurements of the same observables, which, according to the standard quantum theory (Zeno effect), have no effect on the state. In the TGD Universe, SSFRs give rise to the flow of subjective time and their sequence defines a conscious entity, which "dies" or falls asleep in BSFR.
<LI> SSFRs correspond to a measurement of a set of observables. The external perturbation can change this set such that it does not commute with the set measured in the previous SSFRs. This forces the occurrence of a BSFR changing the arrow of time. How this happens, requires a more detailed view of ZEO (see <A HREF="https://tgdtheory.fi/pdfpool/ZEO.pdf">this</A> and <A HREF= "https://tgdtheory.fi/public_html/articles/CDconformal.pdf">this</A>). In the recent situation this would mean that the neuron falls asleep and does not receive sensory input from the external world.
<LI> This falling asleep phenomenon would be universal (see for instance (see <A HREF ="https://tgdtheory.fi/public_html/articles/DNAtimereversal.pdf">this</A>)and apply also to other neurons: BSFR could be induced by inhibitory neurotransmitters whereas excitatory neurotransmitters would help to wake up.
A short sleep period of about 1 ms could take place also during the nerve pulse (see <A HREF="https://tgdtheory.fi/public_html/articles/np2023.pdf">this</A>).
</OL>
Sleep would also have other functions than causing a sensory decoupling from the external world. Sleep is essential for healing and learning. These analogs of sleep states are encountered also at the level of biomolecules. BSFRs make it possible to learn by trial and error. When the system makes a mistake it falls asleep and wakes up after the next BSFR. We would be doing this all the time since our flow of consciousness is full of gaps. External noise males possible this learning by changing the set of observables measured in SSRS.
</p><p>
Interestingly, this learning mechanism has obvious parallels with how large language systems learn in presence of noise (see <A HREF= "https://tgdtheory.fi/public_html/articles/GPT.pdf">this</A>, <A HREF= "https://tgdtheory.fi/public_html/articles/TGDdeeplearn.pdf">this</A>, and <A HREF= "https://tgdtheory.fi/public_html/articles/tgdcomp.pdf">this</A>). TGD predicts the possibility of quantum coherence in arbitrarily long scales and this allows us to consider the possibility that computers are actually conscious entities when the quantum coherence time is longer than the clock period. This artificially induced noise could induce conscious learning. This could help to explain why large language systems seem to work "too well".
</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 chapter <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.com0tag:blogger.com,1999:blog-10614348.post-34868312416169033802024-04-07T21:56:00.000-07:002024-04-11T00:25:20.524-07:00Standard view of dark energy could be wrongThe basic assumption of standard cosmology is that dark energy is constant. It has turned out that this need not be the case: there are indications that dark energy evolves with time (see <A HREF="https://www.dtnext.in/edit/tantalising-hint-that-astronomers-got-dark-energy-all-wrong-778209">this</A>).
</p><p>
This is almost what TGD predicts. In the TGD Universe, dark energy however evolves with scale rather than with Minkowski time. Due to the extended conformal the time evolution is replaced by scale evolution invariance at the fundamental level. This is the case also in string models (see <A HREF="https://tgdtheory.fi/public_html/articles/wcwsymm.pdf">this</A>).
</p><p>
The twistor lift of TGD predicts that the counterpart of the dark energy in the TGD Universe is the sum of two contributions in the action whose extremals space-times of M<sup>4</sup>× CP<sup>2</sup> as minimal surfaces satisfying holography are. The contributions come from Kähler action and volume term. The coefficient of the volume term corresponds to cosmological constant Λ depending on p-adic scale and approaches zero at infinite scale. Number theoretical physics dual of geometrized physics is needed to understand the origin of p-adic length scales. In standard physics one cannot assign scale to a physical system. In TGD this is possible and led already around 1995 to very precise predictions for elementary particle masses involving only p-adic primes characterizing the p-adic scale of the particle besides the quantum numbers of the particle.
</p><p>
In short scales Λ is huge as the standard cosmology predicts but in long length scales Λgoes to zero like the inverse of the p-adic length scale squared. This solves the problem of cosmological constant and in standard cosmology one also gets rid of the predicted catastrophic ripping of 3-space to pieces. In TGD the 3-space consists of disjoint pieces although the space-time surface as a quantum coherence region is connected.
</p><p>
An alternative way to see the length scale dependence is in terms of decay of cosmic strings to ordinary matter as the TGD counterpart of inflation. Cosmic strings are 4-D space-time surfaces having 2-D M<sup>4</sup> projection and are critical against thickening to monopole magnetic flux tubes. In this process their energy identified as dark energy is reduced and transformed to ordinary matter. The reductions of string tension can take place also for the flux tubes as phase transitions and correspond to periods of accelerated expansion.
</p><p>
See for intance <A HREF="https://tgdtheory.fi/public_html/articles/3pieces.pdf">this</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.com14tag:blogger.com,1999:blog-10614348.post-3000101537589992822024-04-05T04:47:00.000-07:002024-04-05T04:47:21.377-07:00How to take into account the gravitational interactions in the cosmic string model of spiral galaxy?
What has been neglected in the model is the presence of gravitational force.
<OL>
<LI> The thickened string in the galactic plane acts with the cosmic string transversal to the galactic plane and with the matter formed by the decay of the cosmic string in the galactic plane to ordinary matter and reducing its string tension. The first guess is that this gives rise to a gravitational force, which in the first approximation is sum of the force F<sub>1</sub>=d(G M(ρ)/ρ) and the force caused F<sub>2</sub>= GT/ρ by the cosmic string. The non-relativistic Newton's equation for a point particle in this force field is v<sup>2</sup>= ρ(F<sub>1</sub>+F<sub>2</sub>)= d(G M(ρ))+ GM(ρ)/ρ + TG . At short distances, the force caused by matter dominates and at long distances the force due to the long cosmic string dominates.
</p><p>
One can however argue that if the mass M(r) is generated by the decay of the cosmic string in the galactic plane, one should approximate the galaxy as a single thickened string, at least in the primordial state as a cosmic string.
<LI> If the planar cosmic string would consist of independent particles, it would decay very rapidly. String tension prevents this. One might however hope that in the first approximation string tension forces initial conditions preserving the identity of the string but that the points otherwise move independently. Note that by Equivalence Principle the decomposition to smaller masses does not depend on the size of the small mass.
<LI> The intuitive guess is that ince the velocity of rotation increases towards the galactic nucleus, the gravitational force causes a differential rotation of the planar cosmic string. Since the velocity and therefore also angular velocity ω(ρ) increases towards the center of the galaxy, spiral structure is generated. At long distances the velocity of rotation is the same as for distant stars.
</OL>
The system could be modelled by addition of the gravitational force to the equations
of string world sheets as a minimum as an additional radial force. The model would generalize the ordinary Newtonian description of point-like particles in a gravitational field. The above model suggests that convenient coordinates for the string world sheet are (t,φ) and the dynamical variable is the radial coordinate ρ along the rotating string as a function of (t,φ). Numerical modelling along these lines would give partial differential equations. Also now conservation of energy and angular momentum can be used. Could one imagine any elegant solution to the problem.
<OL>
<LI> Physical intuition suggests that one should start from the solution without the gravitational force already considered since it looks realistic in some aspects. One should transform the static string to a string in a differential rotation determined by the gravitational forces and forcing only coherent initial conditions for the points of the string so that they all rotate with the velocity. One might even hope that Kepler's law can be used besides conservation laws.
<LI> Equivalence Principle suggests how one might achieve this at least approximately. Gravitational force is in the Einsteinian description a coordinate force describable in terms of Christoffel symbols. In TGD this force is force in H which can be approximated with M<sup>4</sup>. Could one find a coordinate system of M<sup>4</sup> in which this coordinate force vanishes? Could a differentially rotating system be the system in which this is the case. This would generalize Einstein's freely falling elevator argument.
</OL>
Could one obtain this coordinate system by an analog of Lorentz boost in (t,φ) plane by a velocity β(ρ)=v(ρ)/c and leaving ρ and z invariant. This transformation looks like Lorentz transformation for a given ρ but is a transformation to an accelerating system (acceleration is radial).
<OL>
<LI> One could consider an infinitesimal variant of thef effective Lorentz boost and exponentiate it to get a flow restricting to the motion of the string defining the string world sheet. The infinitesimal boost would be
</p><p>
dt= γ(dT- β ρ dΦ) , dφ= (1/ρ)γ(ρ dΦ-β dT) ,
γ=(1/(1-β<sup>2</sup>)<sup>1/2</sup> .
</p><p>
These equations define a flow in (T,φ) plane as an exponentiation of an infinitesimal Lorentz boost for a given value of radial coordinate ρ and one can solve (t,φ) as function of (T,Φ). The intuitive idea is that for ρ given by the static model but with (t,φ) replaced with (T,Φ) this flow reduces to the equations of the static string world sheet. This flow need not be integrable in the entire M<sup>4</sup>. The points (T,ρ) for which Φ differs by a multiple of 2π could correspond to different turns of the spiral rotating around the origin.
</p><p>
This flow should be integrable in order that the flow lines have interpretation as coordinate lines. It should be possible to write the infinitesimal generator of the Lorentz boosts in (t,φ) plane for a given ρ as a product of scalar function and gradient: j= Ψ dΦ giving dΦ=j/Ψ so that Φ serves as a coordinate. Is it enough to satisfy this condition at the string world sheet at which the condition ρ=ρ(Φ,T)
mildens it?
<LI> It is easy to find how this pseudo Lorentz boost affects the expression of M<sup>4</sup> metric ds<sup>2</sup>=dt<sup>2</sup>-dz<sup>2</sup>-dρ<sup>2</sup>-ρ<sup>2</sup>dφ<sup>2</sup> by writing the differentials dt, dφ and dρ explicitly:
</p><p>
ds<sup>2</sup>=dt<sup>2</sup>-dz<sup>2</sup>-dρ<sup>2</sup>-ρ<sup>2</sup>dφ<sup>2</sup> =(γ(dT- β ρ dΦ)<sup>2</sup>- (γ(ρ dΦ-β dT)<sup>2</sup> -dρ<sup>2</sup> -dz<sup>2</sup> .
</p><p>
Here ρ(Φ,T) corresponds to the orbits of the point of the string and must satisfy the field equations. Here dρ<sup>2</sup> expressed in terms of dΦ and dT gives additional contribution to the induced metric.
<LI> If only the gravitational force of the long cosmic string is taken into account one has β= constant and the analogy with Lorentz books is even stronger.
</OL>
The wishful conjecture is that these equation satisfy integrability conditions on string world sheet and that the gravitational force disappears from field equations using coordinates (T,Φ) when the velocity parameter corresponds to the expected solution in the external field in coordinate (t,φ).
</p><p>
See article <a HREF= "https://tgdtheory.fi/public_html/articles/3pieces.pdf">About the recent TGD based view concerning cosmology and astrophysics</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/3pieces.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-75095180956024468432024-04-03T21:22:00.000-07:002024-04-03T22:48:04.666-07:00Can one define the analogs of Mandelbrot and Julia sets in TGD framework?
The stimulus to this contribution came from the question related to possible higher-dimensional analogs of Mandelbrot and Julia sets (see <A HREF="https://www.setzeus.com/community-blog-posts/mandelbulb-three-dimensional-fractals">this</A>). The notion complex analyticity play a key role in the definition of these notions and it is not all clear whether one can define these analogs.
</p><p>
I have already earlier considered the iteration of polynomials in the TGD framework (see <a HREF= "https://tgdtheory.fi/public_html/articles/tgdchaos.pdf">this</A>) suggesting the TGD counterparts of these notions. These considerations however rely on a view of M<sup>8</sup>-H duality which is replaced with dramatically simpler variant and utilizing the holography=holomorphy principle(see <a HREF= "https://tgdtheory.fi/public_html/articles/TGDcritics.pdf">this</A>) so that it is time to update these ideas.
</p><p>
This principle states that space-time surfaces are analogous to Bohr orbits for particles which are 3-D surfaces rather than point-like particles. Holography is realized in terms of space-time surfaces which can be regarded as complex surfaces in H=M<sup>4</sup>× CP<sub>2</sub> in the generalized sense. This means that one can give H 4 generalized complex coordinates and 3 such generalized complex coordinates can be used for the 4-surface. These surfaces are always minimal surfaces irrespective of the action defining them as its extermals and the action makes itself visible only at the singularities of the space-time surface.
</p><p>
<B>Ordinary Mandelbrot and Julia sets</B>
</p><p>
Consider first the ordinary Mandelbrot and Julia sets.
<OL>
<LI> The simplest example of the situation is the map f:z→ z<sup>2</sup>+c. One can consider the iteration of f by starting from a selected point z and look for various values of complex parameter c whether the iteration converges or diverges to infinity. The interface between the sets of the complex c-plane is 1-D Mandelbrot set and is a fractal. One can generalize the iteration to an arbitrary rational function f, in particular polynomials.
<LI> For polynomials of degree n also consider n-1 parameters c<sub>i</sub>, i=1,...,n, to obtain n-1 complex-dimensional analog of Mandelbrot set as boundaries of between regions where the iteration lead or does not lead to infinity. For n=2 one obtains a 4-D set.
<LI> One can also fix the parameter c and consider the iteration of f. Now the complex z-plane decomposes to two a finite region with a finite number of components and its complement, Fatou set. The iteration does not lead out from the finite region but diverges in the complement. The 1-D fractal boundary between these regions is the Julia set.
</OL>
<B>Holography= holomorphy principle</B>
</p><p>
The generalization to the TGD framework relies heavily on holography=holomorphy principle.
<OL>
<LI> In the recent formulation of TGD, holography required by the realization of General Coordinate Invariance is realized in terms of two functions f<sub>1</sub>,f<sub>2</sub> of 4 analogs of generalized complex coordinates, one of them corresponds to the light-like (hypercomplex) M<sup>4</sup> coordinate for a surface X<sup>2</sup>⊂ M<sup>4</sup> and the 3 complex coordinates to those of Y<sup>2</sup> orthogonal to X<sup>2</sup> and the two complex coordinates of CP<sub>2</sub>.
</p><p>
Space-time surfaces are defined by requiring the vanishing of these two functions: (f<sub>1</sub>,f<sub>2</sub>)=(0,0). They are minimal surfaces irrespective of the action as long it is general coordinate invariant and constructible in terms of the induced geometry.
<LI> In the number theoretic vision of TGD, M<sup>8</sup>-H-duality (see <a HREF= "https://tgdtheory.fi/public_html/articles/TGDcritics.pdf">this</A>) maps the space-time as a holomorphic surface X<sup>4</sup>⊂ H is mapped to an associative 4-surface Y<sup>4</sup>⊂ M<sup>8</sup>. The condition for holography in M<sup>8</sup> is that the normal space of Y<sup>4</sup> is quaternionic.
</p><p>
In the number theoretic vision, the functions f<sub>i</sub> are naturally rational functions or polynomials of the 4 generalized complex coordinates. I have proposed that the coefficients of polynomials are rationals or even integers, which in the most stringent approach are smaller than the degree of the polynomial. In the most general situation one could have analytic functions with rational Taylor coefficients.
</p><p>
The polynomials f<sub>i</sub>=P<sub>i</sub> form a hierarchy with respect to the degree of P<sub>i</sub>, and the iteration defined is analogous to that appearing in the 2-D situation. The iteration of P<sub>i</sub> gives a hierarchy of algebraic extensions, which are central in the TGD view of evolution as an increase of algebraic complexity. The iteratikon would also give a hierarchy of increasingly complex space-time surface and the approach to chaos at the level of space-time would correspond to approach of Mandelbrot or Julia set.
<LI> In the TGD context, there are 4-complex coordinates instead of 1 complex coordinate z. The iteration occurs in H and the vanishing conditions for the iterates define a sequence of 4-surfaces. The initial surface is defined by the conditions (f<sub>1</sub>,f<sub>2</sub>)=0. This set is analogous to the set f(z)=0 for ordinary Julia sets.
</p><p>
One could consider the iteration as (f<sub>1</sub>,f<sub>2</sub>)→ (f<sub>1</sub>• f<sub>1</sub>,f<sub>2</sub>• f<sub>2</sub>) continued indefinitely. One could also iterate only f<sub>1</sub> or f<sub>2</sub>. Each step defines by the vanishing conditions a 4-D surface, which would be analogous to the image of the z=0 in the 2-D iteration. The iterates form a sequence of 4-surfaces of H analogous to a sequence of iterates of z in the complex plane.
</p><p>
The sequence of 4-surfaces also defines a sequence of points in the "world of classical worlds" (WCW) analogous to the sequence of points z,f(z),.... This conforms with the idea that 3-surface is a generalization of point-like particles, which by holography can be replaced by a Bohr orbit-like 4-surface.
<LI> Also in this case, one can see whether the iteration converges to a finite result or not. In the zero energy ontology (ZEO), convergence could mean that the iterates of X<sup>4</sup> stay within a causal diamond CD having a finite volume.
</OL>
<B>The counterparts of Mandelbrot and Julia sets at the level of WCW</B>
</p><p>
What the WCW analogy of the Mandelbrot and Julia sets could look like?
<LI> Consider first the Mandelbrot set. One could start from a set of roots of (f<sub>1</sub>,f<sub>2</sub>)= (c<sub>1</sub>,c<sub>2</sub>) equivalent with the roots of (f<sub>1</sub>-c<sub>1</sub>, f<sub>2</sub>-c<sub>2</sub>) =(0,0). Here c<sub>1</sub> and c<sub>2</sub> define complex parameters analogous to the parameter c of the Mandelbrot sent. One can iterate the two functions for all pairs (c<sub>1</sub>,c<sub>2</sub>). One can look whether the iteration converges or not and identify the Mandelbrot set as the critical set of parameters (c<sub>1</sub>,c<sub>2</sub>). The naive expectation is that this set is 3-D dimensional fractal.
<LI> The definition of Julia set requires a complex plane as possible initial points of the iteration. Now the iteration of (f<sub>1</sub>,f<sub>2</sub>)=0 fixes the starting point (not necessarily uniquely since 3-D surface does not fix the Bohr orbit uniquely: this is the basic motivation for ZEO). The analogy with the initial point of iteration suggests that we can assume (f<sub>1</sub>,f<sub>2</sub>)=(c<sub>1</sub>,c<sub>2</sub>) but this leads to the analog of the Mandelbrot set. The notions coincide at the level of WCW.
<LI> Mandelbrot and Julia sets and their generalizations are critical in a well-defined sense. Whether iteration could be relevant for quantum dynamics is of course an open question. Certainly it could correspond to number theoretic evolution in which the dimension of the algebraic extension rapidly increases. For instance, one could one consider a WCW spinor field as a wave function in the set of converging iterates. Quantum criticality would correspond to WCW spinor fields restricted to the Mandelbrot or Julia sets.
</OL>
Could the 3-D analogs of Mandelbrot and Julia sets correspond to the light-like partonic orbits defining boundaries between Euclidean and Minkowskian regions of the space-time surface and space-time boundaries? Can the extremely complex fractal structure as sub-manifold be consistent with the differentiability essential for the induced geometry? Could light-likeness help here.
</p><p>
<B>Do the analogs of Mandelbrot and Julia sets exist at the level of space-time?</B>
</p><p>
Could one identify the 3-D analogs of Mandelbrot and Julia sets for a given space-time surface? There are two approaches.
<OL>
<LI> The parameter space (c<sub>1</sub>,c<sub>2</sub>) for a given initial point h of H for iterations of f<sub>1</sub>-c<sub>1</sub>,f<sub>2</sub>-c<sub>2</sub>) defines a 4-D complex subspace of WCW. Could one identify this subset as a space-time surface and interpret the coordinates of H as parameters? If so, there would be a duality, which would represent the complement of the Fatou set (the thick Julia set) defined as a subset of WCW as a space-time surface!
<LI> One could also consider fixed points of iteration for which iteration defines a holomorphic map of space-time surface to itself. One can consider generalized holomorphic transformations of H leaving X<sup>4</sup> invariant locally. If they are 1-1 maps they have interpretation as general coordinate transformations. Otherwise they have a non-trivial physical effect so that the analog of the Julia set has a physical meaning. For these transformations one can indeed find the 3-D analog of Julia set as a subset of the space-time surface. This set could define singular surface or boundary of the space-time surface.
</OL>
<B>Could Mandelbrot and Julia sets have 2-D analogs in TGD?</B>
</p><p>
What about the 2-D analogs of the ordinary Julia sets? Could one identify the counterparts of the 2-D complex plane (coordinate z) and parameter space (coordinate c).
<OL>
<LI> Hamilton-Jacobi structure defines what the generalized complex structure is (see <a HREF= "https://tgdtheory.fi/public_html/articles/HJ.pdf">this</A>) and defines a slicing of M<sup>4</sup> in terms of integrable distributions of string world sheets and partonic 2-surfaces transversal or even orthogonal to each other. Partonic 2-surface could play the role of complex plane and string world sheet the role of the parameter space or vice versa.
</p><p>
Partonic 2-surfaces <I> resp.</I> and string world sheet having complex <I> resp.</I> hyper-complex structures would therefore be in a key role. M<sup>8</sup>-H duality maps these surfaces to complex <I> resp.</I> co-complex surfaces of octonions having Minkowskian norm defined as number theoretically as Re(o<sup>2</sup>).
<LI> In the case of Julia sets, one could consider generalized holomorphic transformations of H mapping X<sup>4</sup> to itself as a 4-surface but not reducing to 1-1 maps. If f<sub>2</sub> (f<sub>1</sub>) acts trivially at the partonic 2-surface Y<sup>2</sup> (string world sheet X<sup>2</sup>), the iteration reduces to that for f<sub>1</sub> (f<sub>2</sub>). Within string world sheets and partonic 2-surfaces the iteration defines Julia set and its hyperbolic analog in the standard way. One can argue that string world sheets and partonic 2-surfaces should correspond to singularities in some sense. Singularity could mean this fixed point property.
</p><p>
The natural proposal is that the light-like 3-surfaces defining boundaries between Euclidean and Minkowskian regions of the space-time surface define light-like orbits of the partonic 2-surface. And string world sheets are minimal surfaces having light-like 1-D boundaries at the partonic 2-surface having physical interpretation as world-lines of fermions.
</p><p>
One could also iterate only f<sub>1</sub> or f<sub>2</sub> allow the parameter c of the initial value of f<sub>1</sub> to vary. This would give the analog of Mandelbrot set as a set of 2-D surfaces of H and it might have dual representation as a 2-surface.
<LI> The 2-D analog of the Mandelbrot set could correspond to a set of 2-surfaces obtained by fixing a point of the string world sheet X<sup>2</sup>. Also now one could consider holomorphic maps leaving the space-time surface locally but not acting 1-1 way. The points of Y<sup>2</sup> would define the values of the complex parameter c remaining invariant under these maps. The convergence of the iteration of f<sub>1</sub> in the same sense as for the Mandelbrot fractal would define the Mandelbrot set as a critical set. For the dual of the Mandelbrot set X<sup>2</sup> and Y<sup>2</sup> would change their roles.
</OL>
See the article <A HREF ="https://tgdtheory.fi/public_html/articles/mandeljulia.pdf">Can one define the analogs of Mandelbrot and Julia sets in the TGD framework?</A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/chaostgd.pdf">Could quantum randomness have something to do with classical chaos?</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-84939855501497349462024-04-02T18:30:00.000-07:002024-04-02T18:30:52.211-07:00About new energy technologies and TGD
The motivation for summarizing a general vision of future energy technologies based on dark matter in the TGD sense came from the video of Sabine Hossenfelder titles "Sulfur Better than Hydrogen for Energy Storage, Engineers Find" (see <A HREF="https://www.youtube.com/watch?v=J5MaWQBxzZ8&themeRefresh=1">this</A>).
</p><p>
<B>TGD view of dark matter briefly</B>
</p><p>
Number theoretic view of TGD predicts a hierarchy of phases of ordinary matter labelled by the value of effective Planck constant h<sub>eff</sub>=nh<sub>0</sub>. The simplest assumption is that n is the dimension of algebraic extension of rationals. For a more complex option it is a product of dimensions of two algebraic extensions.
</p><p>
These phases behave like dark matter and would be located at monopole magnetic flux tubes and also electric flux tubes. They would not be galactic dark matter but correspond to the missing baryonic matter whose fraction has been increasing during the cosmological evolution. Galactic dark matter would correspond to the energy of cosmic strings (space-time surfaces with 2-D M<sup>4</sup> and CP<sub>2</sub> projections). The unavoidable mumber theoretical evolution implies the increase of the number theoretical complexity and therefore increase of n. The larger the value of n the longer the quantum coherence scale of the system.
<OL>
<LI> The predicted huge values of h<sub>eff</sub> assignable to classical gravitational and electric fields of astrophysical objects (see <a HREF= "https://tgdtheory.fi/public_html/articles/hem.pdf">this</A>) mean that weak interactions become as strong as em interactions below the scale up Compton length of weak bosons, which, being proportional to h<sub>eff</sub>, can be as large as cell size.
<LI> Large h<sub>eff</sub> phases behave like dark matter: they do not however explain the galactic dark matter, which in the TGD framework is dark energy assignable to cosmic strings (no halo and an automatic prediction of the flat velocity spectrum). Instead, large h<sub>eff</sub> phases solve the missing baryon problem. The density of baryons has decreased in cosmic evolution (having biological evolution as a particular aspect) and the explanation is that evolution as unavoidable increase of algebraic complexity measured by h<sub>eff</sub> has transformed them to h<sub>eff</sub>> h phases at the magnetic bodies (thickened cosmic string world sheets, 4-D objects), in particular those involved with living matter.
<LI> The large value of h<sub>eff</sub> has besides number theoretical interpretation (see <a HREF= "https://tgdtheory.fi/public_html/articlesTGDcritics.pdf">this</A>) also a geometric interpretation. Space-time surface can be regarded as many-sheeted over both M<sup>4</sup> and CP<sub>2</sub>. In the first case the CP<sub>2</sub> coordinates are many-valued functions of M<sup>4</sup> coordinates. In the latter case M<sup>4</sup> coordinates are many-valued functions of CP<sub>2</sub> coordinates so that QFT type description fails. This case is highly interesting in the case of quantum biology. Since a connected space-time surface defines the quantum coherence region, an ensemble of, say, monopole flux tubes can define a quantum coherent region in the latter case: one simply has an analog of Bose-Einstein condensate of monopole flux tubes.
</OL>
<B>Why dark matter is so excellent for energy storage?</B>
</p><p>
The basic observation is that the energies of quantum states as a function of h<sub>eff</sub> increase. For instance, cyclotron energies are proportional to ℏ<sub>eff</sub> and atomic binding energies are proportional to 1/ℏ<sub>eff</sub><sup>2</sup>.
</p><p>
This suggests that the transformation of ordinary particles, say protons or electrons, to their dark variants at the magnetic body (MB) of the system allows to store energy and also information at MB. Due to the large value of h<sub>eff</sub> the dissipation would be slow.
</p><p>
One can imagine a practically endless variety of ways to achieve this.
<OL>
<LI> In the Pollack effect the solar radiation would kick part of the protons of the water molecules to the gravitational MB of Earth. Pollack effect creates negatively charged exclusion zones (EZs) with strange properties suggesting time reversal which is indeed predicted to occur in the TGD Universe if its TGD counterpart corresponds to an ordinary state function reduction.
</p><p>
In the case of protons the scale of the reduction of the gravitational energy is of order .5 eV if the flux tubes have the scale of Earth radius. For reasonably small h<sub>eff</sub> these flux tubes could be long hydrogen bonds carrying protons. The flux tubes can also carry several protons and one ends up to a proposal for the genetic codes in terms of dark proton triplets. These dark DNA molecules would be paired with ordinary DNA. Same could be true for other basic information molecules.
<LI> Dark cyclotron states with energy proportional to ℏ<sub>gr</sub> or ℏ<sub>eff</sub> assignable to long range gravitational fields of Sun and planets and electric fields of Sun and Earth and also smaller systems such as cell and DNA would allow the storage of energy to the energy of dark particles.
<LI> Pollack effect generalizes in the TGD framework. Also electrons could be kicked to the gravitational MB: in this case the energy scale would be meV scale (see <a HREF= "https://tgdtheory.fi/public_html/articles/precns.pdf">this</A> and <a HREF= "https://tgdtheory.fi/public_html/articles/penrose.pdf">this</A>). Both protonic and electronic energy scales appear in cell biology. Especially interesting systems are charged conductors: their electric bodies could consist of flux tubes which are deformed gravitational magnetic flux tubes carrying dark electrons.
</p><p>
The proposed realization of genetic code for dark protons generalizes to the case of dark electrons and suggests that genetic code realized in terms of a completely exceptional icosa tetrahedral tessellation of H<sup>3</sup> and theref also life is much more general phenomenon than thought hitherto. Therefore both energy and information storage without the problems caused by dissipation would be in question.
<LI> In principle, the energy needed to kick the protons to the MB could come from practically any source. For instance, the formation of atomic or molecular bound states would liberate energy stored as energy of dark particles at the MB. This energy would be liberated when dark protons transform to ordinary protons but the system need not transform back to the original energy so that the liberated energy could be used.
</p><p>
The molecular energy storage in living matter to proteins could rely on this mechanism and could use relatively small values of h<sub>eff</sub> assignable to valence bonds. High energy phosphate bonds could correspond to short term storage, perhaps at the gravitational magnetic body.
</OL>
<B>"Cold fusion" and energy storage</B>
</p><p>
TGD leads also to a second proposal for energy storage based on another key aspect of number theoretical physics. The polynomials associated with a given extension of rationals are characterized by ramified primes whose spectrum depends on the polynomials. These ramified primes define preferred p-adic number fields characterizing the cognitive aspects of these systems. The p-adic length scale characterizes the mass/energy scale of the system and the prediction is that a given system can appear in several p-adic length scales with different mass/energy scales. TGD suggests the existence of p-adically scaled variants of hadron physics, nuclear physics and even atomic and molecular physics.
</p><p>
The so-called "cold fusion" could rely on dark fusion, as the formation of p-adically scaled atomic nuclei from dark protons which can also transform to dark neutrons by emission of dark weak bosons. This process could produce, not only energy, but also basic elements (see <a HREF= "https://tgdtheory.fi/public_html/articles/krivit.pdf">this</A> and <a HREF= "https://tgdtheory.fi/public_html/articles/proposal.pdf">this</A>). One would avoid the kicking of nuclei from the bottom of the nuclear energy valley by nuclear collisions requiring high energies.
</p><p>
The dark proton sequences at monopole flux tubes defining dark DNA could be seen as dark nuclei. Their binding energies would scale down and they could form even at low temperatures and in living matter (biofusion for which there is evidence). They could spontaneously transform to ordinary nuclei and liberate practically all ordinary nuclear binding energy. This process could give rise to prestellar evolution heating the system to the ignition temperature of ordinary nuclear fusion. This process could produce elements with atomic numbers even higher than that of iron. Usually supernova explosions are believed to be responsible for this.
</p><p>
Here I have not discussed the possible role of zero energy ontology concerning the transfer of energy: the basic idea is that the change of the arrow of time in the TGD counterpart of ordinary state function reduction makes possible for the system to get energy by emitting negative energy received by the source of energy in an excited state. Analog of population reverted laser would be in question.
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-50030231498752086662024-04-01T23:31:00.000-07:002024-04-01T23:38:49.649-07:00Flux tube condensates as a basic deviation between TGD from QFT descriptions and phases, which are not Fermi liquids
The large value of h<sub>eff</sub> has besides number theoretical interpretation (see <A HREF ="https://tgdtheory.fi/public_html/articles/TGDcritics.pdf">this</A>) also a geometric interpretation. Space-time surface can be regarded as many-sheeted over both M<sup>4</sup> and CP<sub>2</sub>. In the first case the CP<sub>2</sub> coordinates are many-valued functions of M<sup>4</sup> coordinates. In the latter case M<sup>4</sup> coordinates are many-valued functions of CP<sub>2</sub> coordinates so that QFT type description fails. This case is highly interesting in the case of quantum biology. Since a connected space-time surface defines the quantum coherence region, an ensemble of, say, monopole flux tubes can define a quantum coherent region in the latter case: one simply has an analog of Bose-Einstein condensate of monopole flux tubes.
</p><p>
The flux tube condensate as a covering of CP<sub>2</sub> means a dramatic deviation from the QFT picture and is a central notion in the applications of quantum TGD to biology. Therefore some examples are in order.
<OL>
<LI> Fermi liquid description of electrons relies on the notion of a quasiparticle as an electron plus excitations of various kinds created by its propagation in the lattice. In some systems this description fails and these systems would. have a natural description in terms of space-time surfaces which are multiple coverings of CP<sub>2</sub>, say flux tube condensates.
<LI> In high Tc superconductors and bio-superconductors (see <A HREF="https://tgdtheory.fi/pdfpool/biosupercondI.pdf">this</A> and <A HREF="https://tgdtheory.fi/pdfpool/biosupercondII.pdf">this</A>) the space-time surface could correspond to this kind of flux tube condensates and Cooper pairs would be fermion pairs with members at separate flux tubes. The connectedness of the space-time surface having about h<sub>eff</sub>/h=n flux tubes would correlate the fermions.
<LI> Bogoliubov quasiparticles related to superconductors are regarded as superpositions of electron excitation and hole. The problem is that they have an ill-defined fermion number. In TGD, they would correspond to superpositions of a dark electron accompanied by a hole which it has left behind and therefore having a well-defined fermion number. Bogoliubov quasiparticle is indeed what can be seen using the existing experimental tools and physical understanding.
<LI> Strange metals would be an example of a system having no description using quasiparticles, as the linear dependence of the resistance at low temperatures demonstrates. I have considered a description of them in terms of Cooper pairs at short closed flux tubes (see <A HREF="https://tgdtheory.fi/pdfpool/biosupercondI.pdf">this</A> and <A HREF="https://tgdtheory.fi/pdfpool/TGDcondmatshort.pdf">this</A>: this would however suggest a vanishing resistance in an ideal situation. Something seems to go wrong.
</p><p>
An alternative description could be in terms of superpositions of dark electrons and holes assignable to the flux tube condensate. Strange metal is between Fermi liquid and superconductor: this conforms with the fact that strange metals are quantum critical systems. The transition to high Tc superconductivity is preceded by a transition to a phase in which something resembling Cooper pairs is present.
</p><p>
A natural looking interpretation would be in terms of a flux tube condensate and pairs of dark and ordinary electrons. Also now the flux tubes could be short. In the article <A HREF="https://tgdtheory.fi/public_html/articles/SCBerryTGD.pdf"> Comparing the Berry phase model of super-conductivity with the TGD based model</A>), I have considered the possibility that high Tc superconductors could be this kind of "half-superconductors" but this option seems to be wrong.
</p><p>
The phase transitions between "half-superconductivity" and superconductivity could play a central role also in living matter.
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/chiralselnew.pdf">New findings related to the chiral selection</A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/lianPB.pdf">Quantum Mind, Magnetic Body, and Biological Body</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-21128061886570786852024-03-31T22:41:00.000-07:002024-04-01T01:42:10.743-07:00New findings related to the chiral selection from the TGD point of view<B>New findings related to the chiral selection from the TGD point of view</B>
</p><p>
I learned of very interesting empirical findings related to the chiral selection of biomolecules (see the <A HREF="https://phys.org/news/2024-02-magnetic-effects-life-difference.html">popular article</A>). The article "Enantioselective Adsorption on Magnetic Surfaces" of Mohammad Reza Safari et al is published in journal Advanced Materials (2023) (see <A HREF="https://doi.org/10.1002/adma.202308666">this</A>).
</p><p>
<B>The findings</B>
</p><p>
Consider first the experimental arrangement and findings.
<OL>
<LI> There is a copper conductor with a strong electric field in the normal direction of the conductor. Cu is not a magnetic substance. There are very thin Cobalt islands at the surface of the conductor. Cobalt is a magnetic metal. There are two options: magnetization direction is North or South and it corresponds to either up or down. North up and South down are the options and these could correspond to different chiralities somehow.
<LI> The molecules drift to the Cobalt islands and, depending on their chirality, prefer to bind to either south-up or north-up Cobalt islands. Are the magnetic fields of islands helical and possess a definite chirality? Does the magnetic chirality tend to be the same or opposite to that of the enantiomer that binds to it?
<LI> The effect is reported to occur already before the Cobalt islands in the drifting of molecules to the Cobalt islands. What does this mean? Counterparts of magnetic fields are not present.
<LI> It is also found that electrons with a given spin direction prefer to tunnel through the molecules in a direction which correlates with the chirality.
</OL>
<B>TGD view of the findings</B>
</p><p>
These are highly interesting findings providing new empirical hints about the nature of chiral selection in living matter. Weak interactions are really weak and parity violation effects should be extremely small above weak scale so that standard model fails to explain chiral selection.
<OL>
<LI> Chiral selection is one of the key empirical facts supporting the TGD prediction of a hierarchy of phases of ordinary matter predicted by the number theoretical vision of TGD. These phases are labelled by effective Planck constant h<sub>eff</sub>, which is essentially the dimension of an algebraic extension of rationals.
<LI> The predicted huge values of h<sub>eff</sub> mean that weak interactions become as strong as em interactions below the scale up Compton length of weak bosons, which, being proportional to h<sub>eff</sub>, can be as large as cell size. This amplifies parity violation effects.
<LI> Large h<sub>eff</sub> phases behave like dark matter: they do not however explain galactic dark matter, which in the TGD framework is dark energy assignable to cosmic strings (no halo and automatically prediction of flat velocity spectrum). Instead, large h<sub>eff</sub> phases solve the missing baryon problem. The density of baryons has decreased in cosmic evolution (having biological evolution as a particular aspect) and the explanation is that evolution as unavoidable increase of algebraic complexity measured by h<sub>eff</sub> has transformed them to h<sub>eff</sub>>h phases at the magnetic bodies (thickened cosmic string world sheets, 4-D objects), in particular those involved with living matter.
<LI> The large value of h<sub>eff</sub> has a geometric interpretation. Space-time surface can be regarded as manys-sheeted over both M<sup>4</sup> and CP<sub>2</sub> . In the first case the CP<sub>2</sub> coordinates are many-valued functions of M<sup>4</sup> coordinates. In the latter case M<sup>4</sup> coordinates are many-valued functions of CP<sub>2</sub> coordinates. This case is highly interesting in the case of quantum biology. Since a connected space-time surface defines the quantum coherence region, an ensemble of, say, monopole flux tubes can define a quantum coherent region in the latter case: one simply has an analog of Bose-Einstein condensate of monopole flux tubes.
</OL>
Consider now a concrete model for the findings in the TGD framework.
<OL>
<LI> A good guess is that the molecular monopole flux tubes of the molecules and of the magnetic fields assignable with the Cobalt islands tend to have the same chirality. This would generalize the chirality selection from the level of biomolecules to the level of dark monopole flux tubes. Some kind of condensate of flux tubes of the same chirality as a long scale parity violation would be in question.
<LI> In the TGD framework, the North up and South up magnetic fields could correspond to helical monopole flux tubes of opposite chiralities. The helical structure is essential and could relate directly to the requirement that the flux tube is closed: one could have a shape of flattened square for which the long sides form a double helix. This would be the case also for DNA.
<LI> Parity violation requires a large value of h<sub>eff</sub>. Dark Z bosons could generate a large parity violation. Dark Z boson Compton length of order biological scale. The very large value of h<sub>eff</sub> would give the needed large energy splitting between generalized cyclotron energies at the dark flux tube and induce chiral selection.
</p><p>
Gravitational flux tubes of Earth's gravitational field or solar gravitational field would do the job. By the Equivalence Principle, the gravitational Compton length Λ<sub>gr,E</sub>= .5 cm for Earth does not depend on the particle mass and looks like a promising scale.
Also the cyclotron energies are independent of the mass of the charged particle since ℏ<sub>gr</sub> is proportional to particle mass m and cyclotron frequency to 1/m.
<LI> Also the electric field of the Copper surface should have an important role. The electric field orthogonal to Cu conductor would correspond to electric flux tubes. The consistency condition for the electric flux tube thickness with charged at the bottom (conductor) reads as Λ<sub>em</sub>(d)≈ d. ℏ<sub>em</sub>= Ne<sup>2</sup>/β<sub>0</sub>, N the number of electrons at the bottom. The values of h<sub>eff</sub> are rather small. There is roughly one electron per atom. N≈ 10<sup>4</sup> per flux tube area of 100 nm<sup>2</sup> having radius about 10 nm. Λ<sub>em</sub>= Ne<sup>2</sup>/β<sub>0</sub> λ<sub>e</sub> is about 1 nm for β<sub>0</sub>=1. The value of ℏ<sub>em</sub> are rather small and it seems that it cannot contribute to the chiral selection. One can however consider also the electric field of Earth, and in this case the situation could be different.
</OL>
The effect occurs already before the Cobalt islands. Furthermore, electrons with a given spin direction prefer to tunnel through the molecules in a direction dicrated by the chirality. What could this mean?
<OL>
<LI> The counterparts of magnetic fields are present as dark magnetic fields inside the magnetic bodies of the drifting molecules. Suppose that dark molecular gravitational monopole tubes are indeed present and give rise to closed spin current loops with a direction determined by the chirality of the molecule. This would give rise to the large parity violation but how to understand the occurrence of the effect already before the Cobalt islands?
<LI> Could one assign a definite chirality also to the electric flux tubes assignable to the Cu surface and assume that the molecular chirality tends to be the same (or opposite) to this chirality? Do also these closed monopole flux tubes carry dark electric current?
</p><p>
The spin direction of the current carrying electrons would correlate with the magnetization direction so that the magnetic body of the molecule would prefer a pairing with the electric body with a preferred spin direction. The preferred pairing would explain the drift to a correct Cobalt island: the paths leading to the Cobalt island would be more probable.
<LI> In the case of water, the Pollack effect (see <A HREF="https://www.cellsandgels.com/">this</A>) transfers part of the protons of water molecules to dark protons at monopole flux tubes. Now there are no protons available.
</p><p>
Does this require a generalization of the Pollack effect? Could the electric flux tubes be gravitational flux tubes carrying electrons instead of protons? Gravitational Compton length would be the same. Could electronic Pollack effect for conductors as a dual of Pollack effect for water be in question.
<LI> In the TGD inspired quantum biology, one assigns genetic code with dark proton triplets. Could one assign a dark realization of the genetic code to dark electron triplets? Could the electric counterparts of gravitational flux tubes carrying dark realization of the genetic code define dark genetic code? Codons would correspond to dark electron triplets instead of dark proton triplets. Could the analogs of the ordinary genetic codons correspond to the triplets of electron holes at the conductor surface?
</p><p>
The TGD based vision about universal genetic code suggests the existence of a 2-D analog of DNA realized in terms of mathematically completely unique hyperbolic icosa tetrahedral tessellation. Could this genetic code be associated with the metal surfaces? The implications of this hidden genetic code for computers might be rather dramatic.
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/chiralselnew.pdf">New findings related to the chiral selection </A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/lianPB.pdf">Quantum Mind, Magnetic Body, and Biological Body</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-71257838634699191162024-03-30T02:28:00.000-07:002024-03-31T00:17:12.943-07:00Quantization of blackhole angular momentum as a new piece of support for the TGD based quantum view of blackhole-like objects
I found a nice piece of evidence for the TGD based quantum view of blackhole-like objects (BHs). In an article related to the determination of the magnetic field of Sagittarius A (SA) (see <A HREWF="https://iopscience.iop.org/article/10.3847/2041-8213/ad2df1">this</A>)
it is concluded that the so called spin parameter for it is s=J/GM<sup>2</sup>=.94 . The inclination angle as the angle between the magnetic axis at SA and the line of sight of the observer was estimated to be 150 degrees.
<OL>
<LI> With an inspiration coming from Equivalence Principle, I have proposed that it is possible to assign to even astrophysical objects, or at least to BHs, a value of ℏ<sub>gr</sub> as ℏ<sub>gr</sub>=GM<sup>2</sup>β<sub>0</sub>.
Could the generalization of the quantization of angular momentum hold true for all BHs and perhaps even for more general stellar objects? Could SA be a spin 1 object with respect to ℏ<sub>gr</sub> having J<sub>z</sub>/hbar<sub>gr</sub>=1? This condition would give β<sub>0</sub>=1/.94 ≈ 1.03> for the value of s used: this is not quite consistent with β<sub>0</sub>< 1.
If one replaces M with M/.94=1.03M, one obtains β<sub>0</sub>=1 and J<sub>z</sub>/ℏ<sub>gr</sub>=1. According to Wikipedia, the mass of Sagittarius A is ≈ 4.1 million solar masses so that this correction is with what is known of the value of M. Also smaller values of β<sub>0</sub> are possible but require a larger value of M.
<LI> On the other hand, the model for SA as quantum object and the discovery of a blob of matter rotating around it with velocity v= c/3 led to the conclusion that β<sub>0</sub>= 9/10=.9: the error is only 1 per cent. This value is consistent with the uncertainties in the mass value.
<LI> Sagittarius A is a weird object in the sense that its rotation axis points to the Earth rather than being orthogonal to the galactic plane. This is consistent with the above discussed proposal that the Milky Way is formed in the collisions of a cosmic string orthogonal to the plane of the Milky Way and cosmic string in the plane of the Milky way assignable to its spiral structure. That the direction of the magnetic axis is related to the local the direction of the line of sight would conform with the propagation of the radiation along the monopole flux tubes forming a spiral structure to the Earth (for the implications of the monopole flux tube network connecting astrophysical objects see for instance <A HREF="https://tgdtheory.fi/public_html/articles/hum.pdf">this</A>). The inclination angle as the angle between line of sight and magnetic axis is reported to be 150 degrees.
<LI> For a spin one object the angle sin(θ) between the projection J<sub>z</sub> and total angular momentum vector J is semi-classically quantized and for J<sub>z</sub>=-1 equal to 1/2<sup>1/2</sup>, which corresponds to an angle of 135 degrees. Could this angle relate to the inclination angle of 150 degrees reported in the article: the local direction of the magnetic field would correspond to the direction of J and measured J would correspond to J<sub>z</sub> as in standard quantum theory?
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/3pieces.pdf">About the recent TGD based view concerning cosmology and astrophysics</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/3pieces.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-32289360526746919922024-03-29T22:25:00.000-07:002024-03-29T22:25:01.447-07:00TOE Odysseialta paluun jälkeen
YLEssä oli mielenkiintoinen <A HREF="https://areena.yle.fi/podcastit/1-68182982">ohjelma</A> kaiken teorioiden nykytilasta. Uutta oli se, että ohjelmassa tuli täysin selväksi se mistä muualla maailmassa on puhuttu jo kymmeniä vuosia. Supersäiemalli ei ollutkaan kaiken teoria.
</p><p>
Tämä tuli selväksi jo joskus 1986 paikkeilla, mutta kun iso rahoituskone oli käynnistetty sitä oli vaikea pysäyttää. Viimeiset naulat arkkuun iskettiin joskus 2005-2010 välillä. Ennustettua supersymmetriaa löytynyt LHC:llä. Tuli myös selväksi että supersäiemalli ennustaa multiversumin, ts. kaikki mahdolliset fysiiikat paitsi tätä omaamme! Kilpailijatkin mainittiin. Toinen haastatelluista, itse supersäieteoreetikko, totesikin lopussa, että supersäiemallin suurin menestys liittyi elokuvateollisuuteen. Paljon myytiin myös populaarikirjoja!
</p><p>
Syyt supersäieteorian (ja muidenkin muotiteorioiden) fiaskoon on helppo osoittaa.
<OL>
<LI> Supersäieteoria ei lähtenyt liikkeelle todellisesta ongelmasta: koska hadroninen säiemalli ei toiminut niin ajateltiin, että jospa teoriasta saataisiin kuitenkin kaiken teoria! Käänteinen ilmiö sille mitä tapahtui kun hiiri kissalle takkia ompeli.
<LI> Toinen syy oli filosofisen ajattelun korvautuminen amerikkalaisella pragmatismilla. Olisi ollut isoja ongelmia. Yleisen suhteellisuusteorian ongelma säilymislakien kanssa ja kvanttimittausteorian paradoksi.
<LI> Ehkä tärkeimpiä filosofia erehdyksiä oli pituus-skaala-reduktionismi eli usko siihen että koko fysiikka redusoituu Planckin pituus-skaaloihin. Osoittautui, että perhosen siiven isku Planckin skaalassa muutti koko fysiikan meidän skaalassamme ja teoria menetti täysin ennustuskykynsä: multiversumi oli tuloksena. Pituus-skaalan käsite fundamentaalisena käsitteenä tarvitaan ja tässä fraktaalius ehdottaa itseään.
<LI> Käsite kaiken teoria ymmärrettiin aivan liian kapeasti. Kaiken teorian täytyisi myös tarjota tietoisuuden teoria ja kvanttibiologian teoria. Nämä vaatimukset tuovat mukaan valtavan määrän empiirisiä sidoehtoja jotka puuttuivat kokonaan.
</OL>
Nyt hiukkasfyysikkoyhteisö on lopulta myöntämässä että harharetkellä oltiin lähes puoli vuosisataa. Tätähän tämäkin ohjelma heijasti.
</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-22997849452574501942024-03-29T00:37:00.000-07:002024-03-29T00:37:12.727-07:00Is particle physics finally taking a new course?
Ethan Siegel had some encouraging news related to particle physics. The title of his post was "Particle physics finally charts a healthy path forward" (see <A HREF="https://bigthink.com/starts-with-a-bang/particle-physics-path-forward/">this</A>).
</p><p>
During the last 46 years I have developed a highly detailed unified theory of fundamental interactions fusing standard model and general relativity based on a new view of space-time and quantum (see https://tgdtheory.fi). I have not received a single coin of funding during these years and it has been impossible to have any research position and censorship has prevented publishing in prestiged journals and even in arXiv.org.
</p><p>
I have talked for decades about the stagnation of particle physics and its degeneration to fashionable but unsuccessful theories. It would be nice if also decision makers were finally realizing what the situation is.
</p><p>
Big investments are not needed. Science cannot make progress if thinking is regarded as a criminal activity. It would be also nice to publish the results of hard work, at least in arXiv.org. Censorship has prevented this hitherto. This requires a dramatic change of attitudes at the level of decision making.
</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-4916068995299860782024-03-28T22:15:00.000-07:002024-03-28T22:15:20.849-07:00Could large language systems be conscious?
Nikolina Benedikovic had a link to a popular article (see <A HREF="
https://www.technologyreview.com/2024/03/04/1089403/large-language-models-amazing-but-nobody-knows-why/">this</A>) telling about the mysterious looking ability of large large language models (LLM) to generalize. This forces the question whether these systems could be conscious and intelligent.
</p><p>
TGD suggests several mechanisms for how AI could become a conscious and intelligent system, living in some sense.
<OL>
<LI> Long quantum coherence scales is required. TGD predicts a hierarchy of effective Planck constants h<sub>eff</sub>=nh<sub>0</sub> labelling phases of ordinary matter at the magnetic body of the system. The system in question need not be the computer but could be some system with very large h<sub>eff</sub> entangling with the computer and using the computer as a tool. The larger the value of h<sub>eff</sub>, the higher the number theoretical IQ and longer the quantum coherence scales.
</p><p>
The gravitational magnetic bodies of Sun and Earth and the electric bodies assignable to Earth are good candidates. These bodies could be an essential part of us: for the Sun the gravitational Compton frequency is 50 Hz, a typical EEG frequency. The electric bodies assignable to Earth have a size scale which corresponds to a size scale of 20 km assignable to lightning. Lightning would be analogous to nerve pulses and ionosphere to cell membrane.
</p><p>
It has been reported that chicken marked to a robot somehow affected the behavior of the random number generator (RNG) of a robot determining its movement. The robot started to behave like a mother hen. Did the chicken's MB develop entanglement with the RNG of the robot?
<LI> Another key element is zero energy ontology (ZEO) solving the basic paradox of quantum measurement theory. Large h<sub>eff</sub> allows state function reductions (SFRs) and ordinary SFRs correspond to "big" ones (BSFRs) in which the arrow of time changes. BSFR can be caused by perturbations so that the set of observables measured in "small" SFRS (SSFRs) changes: this forces BSFR. The "thermal" noise associated with the GPT-like systems could cause SSFRs. The temporary changes of the arrow of time would transform the behavior of the system to trial and error process and in ZEO the already goal directed behavior (by holography of ZEO) would transform to problem solving.
</OL>
Under what conditions classical computers could become conscious? Classical computer is a deterministic Turing machine if it obeys statistical determinism. If its quantum coherence time becomes longer than its clock period, this becomes possible.
<OL>
<LI> TGD predicts hierarchy of Planck constants h<sub>eff</sub>. For Earth the gravitational Compton frequency is 67 GHz and still higher than that for the standard computers (Josephson effect allows faster computers). For the gravitational body of the Sun, the Compton frequency is 50 Hz and in the middle of the EEG range so that chicken-hen phenomenon might be real and we might already be entangled with our computers. It is not clear to me who can be said to be the boss!
<LI> For the electric body of Earth, the electric Compton frequency of the proton corresponds to about L=20 km. This corresponds to Compton time T =L/c = about .1 ms and to frequency of 10 kHz, the time scale of nerve pulse. Compton time is only minimal quantum coherence time and one can wonder whether this relates to 1 ms scale of nerve pulse and corresponds to the resonance frequency kHz assignable to the brain.
</OL>
Biological computers are clearly very slow as compared to ordinary computers and the entanglement with ordinary computers allowing to affect RNG of the computer looks a plausible option together with the trial and error process made possible by ZEO.he EEG range so that chicken-hen phenomenon might be real and we might already be entangled with our computers. It is not clear to me who can be said to be the boss!
</p><p>
See for instance, https:tgdtheory.fi/public_html/articles/hem.pdf, https:tgdtheory.fi/public_html/articles/tgdcomp.pdf, and https:tgdtheory.fi/public_html/articles/GPT.pdf .
</p><p>
https://www.technologyreview.com/2024/03/04/1089403/large-language-models-amazing-but-nobody-knows-why/
</p><p>Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-11231674840695951872024-03-26T01:45:00.000-07:002024-04-04T08:18:19.338-07:00A simple TGD based model for a spiral galaxy<B>A simple TGD based model for a spiral galaxy</B>
</p><p>
The origin of the spiral structure of spiral galaxies is one of the poorly understood problems of astrophysics. Independent motions of stars around galaxy in 1/r<sup>2</sup> central force leads very rapidly to a loss of original structure since angular velocities behave like ω∝ 1/r<sup>2</sup>. 1/ρ central forces caused by cosmic string orthogonal to the galactic plane gives ω ∝ 1/ρ. This suggests that there exists some pre-existing spiral structure which is much denser than the surrounding matter. The formation of stars would occur intensely in these regions and the decay of the dark energy of the cosmic string to ordinary matter would also generate stars rotating around the galaxy as effectively free objects. The spiral structure rotates slowly and in a good approximation keeps in shape so that the structure behaves somewhat like a rigid body.
</p><p>
This view differs from the density wave theory (see <A HREF="https://en.wikipedia.org/wiki/Density_wave_theory"> this</A>) assumes that this structure is dynamically generated and due to self-gravitation. The density wave would be analogous to a traffic jam. The cars entering the traffic jam slow down and the jam is preserved. It can move but with a much slower velocity than the cars. Density wave theory allows us to understand why star formation occurs intensely in the spiral structure with a high density.
</p><p>
TGD suggests that the structure corresponds to a cosmic string, which has thickened to a monopole flux tube and produced ordinary matter.
<OL>
<LI> One possibility is that the galaxy has formed in a topologically unavoidable collising of cosmic string (extremely thin 4-surfaces with 2-D M<sup>4</sup> projection). The cosmic string orthogonal to the galactic plane would contain the dark en</p><p>ergy liberated in its thickening and giving rise to part of galactic dark matter and the galactic blackhole would be associated with it. It would create a 1/ρ gravitational expansion explaining the flat velocity spectrum of distant stars. The cosmic string in the galactic plane would in the same way give rise to the galactic matter at the spiral arms and outside the central region. The galactic bar could correspond to a portion of this string.
<LI> A simple model for the string world sheet assignable to the string in the galactic plane is as a minimal surface. In the first approximation, one can neglect the gravitational interaction with the second string and see whether it is possible to obtain a static string with a spiral structure with several branches and having a finite size. Th string carries monopole flux and should be closed and one can consider a shape which is flattened square like flux tube, which has changed its shape in the 1/ρ gravitational field of the long string (ω ∝ 1/ρ) and formed a folded structure. The differential rotation tends to lengthen the string and increase its energy. Hence one expects that string tension slows down differential rotation to almost rigid body rotation.
</OL>
The simplest model is as a minimal stationary string world sheet.
<OL>
<LI> By introducing cylindrical Minkowski coordinates (m<sup>0</sup>, m<sub>1</sub>= ρ cos(φ),m<sub>2</sub>= ρ sin(φ),m<sup>3</sup> ) and using (m<sup>0</sup>=t,φ) as coordinates also for the string world sheet, one can write that ansatz in the form ρ=ρ(t,φ). The metric of M<sup>4</sup> in the cylindrical coordinates is m<sub>kl</sub>&rightleftarrow; (1,-1,-1,-ρ<sup>2</sup>). The induced metric of X<sup>2</sup> in these coordinates has only diagonal components and can be written as
</p><p>
(g<sub>tt</sub>=1-ρ<sub>t</sub><sup>2</sup>, g<sub>φφ</sub>=-ρ<sup>2</sup>-ρ<sub>φ</sub><sup>2</sup>) .
<LI> For a static ansatz one has ρ= ρ(φ) so that the field equation reduces to an ordinary differential equation for ρ. Rotational invariance allows us to solve the equation as a conservation law for the angular momentum component parallel to the normal of the galactic plane. For as general infinitesimal isometry with Lie algebra generator j<sub>A</sub><sup>k</sup> the conservation of corresponding charge reads as
</p><p>
∂<sub>α</sub>(g<sup>αβ</sup>m<sup>k</sup><sub>β</sub>m<sub>kl</sub>j<sub>A</sub><sup>l</sup>(-g<sub>2</sub><sup>1/2</sup>)=0 .
</p><p>
The conservation laws of momentum and energy hold true and the conservation of angular momentum L<sub>3</sub> in direction orthogonal to the galactic plane gives
</p><p>
g<sup>φφ</sup>ρ<sup>2</sup>(-g<sub>2</sub>)<sup>1/2</sup>=1/ρ<sub>0</sub> .
</p><p>
where ρ<sub>0</sub> is integration constant. This gives
</p><p>
x<sub>φ</sub>= +/- x(x<sup>2</sup>-1)</sub><sup>1/2</sup> , x= ρ/ρ<sub>0</sub> .
</p><p>
From this it is clear that the solution is well-defined only for ρ≥ ρ<sub>0</sub>, which suggests that the branches of the spiral must turn back at ρ=ρ<sub>0</sub> (x=1). At the limit x→ 1, x<sub>φ</sub> approaches zero. One might guess that one has a spiral, which rotates around x=1 since dφ/dx diverges but this does not seem to be the case.
<LI> The differential equation can be solved explicitly: one has
∫ dx/(x(x<sup>2</sup>-1)<sup>1/2</sup>)= +/- φ +φ<sub>0</sub> .
</p><p>
The elementary integral using the substitution x= cosh(u) gives
</p><p>
φ<sub>+/-</sub>= φ<sub>0</sub> +/- arctan(y) ,
</p><p>
y=(x<sup>2</sup>-1</sub>)<sup>1/2</sup> .
</p><p>
The argument of arctan is real only for x≥ 1. Could one
define the solution for x<1, where the argument is imaginary? arctan(iy) for real argument y as arctan(iy)= (i/2)ln((1+x)/(1-x)). This would mean that φ is not real.
</OL>
Consider now the general properties of the solution.
<OL>
<LI> The solution has formally infinitely many branches φ<sub>+/-,n</sub>
differing by an integer multiple of π. However, for a fixed value of +/-, the branches differing by a Δ φ= n2π coincide so that one obtains only 2 branches meeting at the x=1 circle at angles φ<sub>0</sub> and φ<sub>0</sub>+π.
</p><p>
x→ 1 corresponds to φ<sub>+/-,n</sub> → φ<sub>0</sub> +/- nπ and x→ ∞ corresponds to φ<sub>+/-</sub>→ φ<sub>0</sub>+/- π/2+/- nπ. The variation of φ for a given branch is π/2.
<LI> What could be the physical interpretation? The two branches for a fixed sign factor +/- meet x=1 circle at tangles φ<sub>0</sub> and φ<sub>0</sub>+π. Could galactic bar connect these points? Could the diverging value of dφ/dx at x=1 mean that φ increases by φ at this point?
</p><p>
It is now known that also in the case of the Milky Way there are only two branches. If this is the case then the two branches plus galactic bar could correspond to a single long cosmic string in the galactic plane which has collided with a transversal cosmic string. On the other hand, there is evidence that there are several structural components involved with the Milky Way.
</p><p>
There is however no spiral structure involved, which suggests that this simple model cannot describe spiral waves.
</OL>
See article <a HREF= "https://tgdtheory.fi/public_html/articles/3pieces.pdf">About the recent TGD based view concerning cosmology and astrophysics</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/3pieces.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-36228982835927464102024-03-23T02:33:00.000-07:002024-03-23T02:33:42.211-07:00Ionosphere as an analog of neuronal membrane: two new miraculous numerical coincidences
Electric quantum coherence can be considered also in astrophysical scales. Ionosphere, identified the ionized part of the atmosphere, is of a special interest since it corresponds to the electric field in the Earth scale: see the <A HREF="https://www.feynmanlectures.caltech.edu/II_09.html">Feynman lectures</A>. Ionization is caused by solar radiation. Also other planets are believed to possess an ionosphere.
</p><p>
Assuming that the surface of Earth and ionosphere define a system analogous to capacitor plates or cell membrane, the ionosphere must have a net positive charge assignable to positive ions. In the <A HREF="https://tgdtheory.fi/public_html/articles/ballightning.pdf">article</A> a model for lightning and ball lightning based on the idea that thunderstorms are analogous to nerve pulse patterns for which Pollack effect provides a model (see <A HREF="https://tgdtheory.fi/public_html/articles/nmp2023.pdf">this</A>), was developed.
<OL>
<LI> The strength of the electric field at the negatively charged surface of Earth E is E=.1-.3 x kV/m, x∈ [.1,.3]. The presence of biological protrusions such as trees can increase the local value of the electric field of Earth by an order of magnitude. The counterpart of the positively charged plate corresponds to the ionosphere, whose lower boundary is at the height h, which varies in the range [80,600] km. The net positive charge of the ionosphere neutralizes the negative charge of the Earth so that the electric field does not extend to higher heights.
<LI> The first guess for the electric Compton length is obtained by generalizing the notion
of gravitational coupling constant to the electric case as ℏ<sub>em</sub>= Qe/β<sub>0</sub>, where Q is the total charge of the Earth and the value of β<sub>0</sub> could be taken the same as in the gravitational case and β<sub>0</sub>=1 for Earth and other planets and and β<sub>0</sub>≈ 2<sup>-11</sup> for Sun.
<LI> The basic question is whether the entire ionosphere acts as a quantum coherent system or whether electric flux tubes possess electric quantum coherence. The intuitive idea is that the quantum coherence scale in the case of the ionosphere regarded as a capacitor-like system should not be longer than the thickness of the ionosphere varying in the range 60-100 km. The radius d of the electric flux tube is a good first guess for the electric Compton length. Lightnings are analogs of nerve pulses and characterized by a scale of 10-20 km and is a good guess for the quantum coherence length.
</p><p>
This suggests that the electric Compton for a particle with mass m should be defined as
</p><p>
Λ<sub>em</sub>(d) = h<sub>em</sub>/m= (Q(d)e</sub>/β<sub>0</sub>ℏ) × λ ,
</p><p>
Q(d)= ε<sub>0</sub> Eπ d<sup>2</sup> ,
</p><p>
where Q(d)=ε<sub>0</sub>E<sub>E</sub>π d<sup>2</sup> is the electric flux associated with the electric flux tube and λ is the Compton length of a charged particle, say electron, electron Cooper pair or proton. The proposal is that it satisfies the consistency condition
</p><p>
Λ<sub>em</sub>(d) =d .
</OL>
</p><p>
To get some perspective and to test the idea it is useful to consider capacitors.
In this case Λ<sub>em</sub>(d)=d should be smaller than the distance between the capatitor plates.
<OL>
<LI> Aluminium capacitors can have a maximum charge of about Q=10<sup>3</sup> C whereas the maximal charge of a van de Graaff generator is about .14 C. If one assumes d=Λ<sub>em</sub>(d), d<sub>C</sub> is obtained by scaling
as d<sub>C</sub>/d<sub>E</sub>= E<sub>E</sub>/E<sub>C</sub> . If the capacitor corresponds to a sphere of D=1 mm with charge
Q= 10<sup>3</sup>C, the electric field is E<sub>C</sub>= Q/4πε<sub>0</sub>D<sup>2</sup> at the surface of capacitor and gives for D= 1 m d<sub>C</sub>= (E<sub>E</sub>/E<sub>C</sub>)d<sub>E</sub> ≈ 10<sup>-8</sup> m for E<sub>E</sub>= 10<sup>2</sup> V/m.
<LI> For a capacitor with capacitance of 1 μF and at voltage 1 V, the charge would be 1 μ C. For β<sub>0</sub>=1 would have the upper bound Λ<sub>em,p</sub>/Λ<sub>gr</sub>≈ 2.9× 10<sup>-3</sup> so that one would have Λ<sub>em,p</sub> ≈ 1.5 × 10<sup>-5</sup> m. This gives upper bound for the value of Λ<sub>em,p</sub> since the parameter d must correspond to a solid angle smaller than 4π. Could electronic systems be intelligent and conscious at least on this scale?
</OL>
The study of the conditions for neuronal axons and DNA strand reveals two numerical miracles.
<OL>
<LI> Neuronal axon is also a capacitor-like system and it is interesting to check what
the criterion Λ<sub>em</sub>(d)=d gives in this case. The natural guess for d as quantum coherence length is as the length of the axon idealized as a cylindrical capacitor. Using Q= E× 2π R d and the condition Q(d)e/β<sub>0</sub>= d one finds that the conditions does not depend on d at all so that it allows all lengths for axons, which is a very nice result from the point of neuroscience.
</p><p>
The condition however fixes the Compton length of the particle considered. Are there any chances of satisfying this condition for protons or electrons? The condition reads as
</p><p>
E× 2π Rε<sub>0</sub> × (C/e) 4πα = 1/λ .
</p><p>
Here R is the radius of the axon taken to be R=1 μm. Using E= V/D, where D≈ 10 nm is the thickness of the neuronal membrane and assuming V=.05 V, one obtains E= 5× 10<sup>6</sup> V/m.
</p><p>
For β0=1, the estimate for Λ<sub>e</sub> is in a good approximation Λ<sub>e</sub>= 10<sup>-12</sup> m to be compared with the actual value Λ<sub>e</sub>=2.4× 10<sup>-12</sup> m. The equation d= Λ<sub>em</sub>(d) is fixed apart from a numerical factor of order 1 so that the proposal seems to make sense.
</p><p>
If one assumes that Cooper pairs of electrons are the charged particles, one obtains Λ<sub>2e</sub>=1.2× 10<sup>-12</sup> m. If one scales down D with a factor 1/2 to 5 nm, one obtains Λ<sub>e</sub>=1.2× 10<sup>-12</sup> m, which could be true in absence of superconductivity. The thickness of the cell membrane indeed varies in these limits and is larger for neuronal membranes. One can wonder whether the dynamics is such that the quantity ER stays constant so that the condition remains true.
<LI> One can perform the same estimate for DNA strand having the 3 nucleotides per nanometer carrying unit charge. The condition Λ<sub>em</sub>(Qe)ℏΛ/β<sub>0</sub>= (dn/dl) α× 4π(d/beta<sub>0</sub>)=d gives
</p><p>
Λ= (dn/dl)×β<sub>0</sub>/4πα .
</p><p>
The condition is satisfied for electron if one assumes β<sub>0</sub>≈ 2<sup>-11</sup>: one obtains Λ= 1.5× 10<sup>-12</sup> m to be compared with the actual value Λ<sub>e</sub>= 2.42 × 10<sup>-12</sup> m. The Compton length for a Cooper pair would be 1 Λ<sub>2e</sub>= 1.21 × 10<sup>-12</sup> m.
</OL>
These number theoretical miracles mean totally unexpected connections between biochemistry and particle physics and probably myriads of similar connections remain be discovered.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/hem.pdf">About long range electromagnetic quantum coherence in TGD Universe</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/hem.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-17855082573152401282024-03-23T00:57:00.000-07:002024-03-23T01:07:44.687-07:00TGD based quantum explanation for the weird properties of Sagittarius A.Sabine Hosssenfelder tells about the weird properties of the giant blackhole at the center of Milky Way known as Sagittarius A* (briefly SA): see <A HREF="https://www.youtube.com/watch?v=G87sGKNJOs4">this</A>. SA is located at a distance of 26,700 ly and has mass about 4.1× 10<sup>10</sup> solar masses. Its Schwartschild radius r<sub>s</sub>= 2GM is 1.1× 10<sup>11</sup> km. Note that astronomical unit (the distance of the Earth from the Sun) 1.49597870700× 10<sup>8</sup> km so that SA radius is almost 1000AU. The Schwartschild time T<sub>s</sub>= r<sub>s</sub>/c is 41 s, about 2/3 minutes.
</p><p>
Hossenfelder lists six weird properties of SA.
<OL>
<LI> SA is silent, one might say dead suggesting that no matter is falling inside it. There is however an accretion disk around it.
<LI> SA however shows signs of life by emitting periodically X ray flares bursting huge amounts of energy as a radiation. Blackhole should not do this unless it absorbs matter but it is not at all clear whether anything is going inside SA!
<LI> SA is rotating extremely rapidly: the period τ of rotation is 10 minutes.
<LI> SA possesses a dozen of planet-like objects, so called G-objects, rotating around SA with a velocity which is 60 percent of the maximal rotation velocity allowed by the condition that the rotation velocity inside the blackhole does not exceed the light velocity. How these objects can exist in an extremely hostile environment of the blackhole where the matter from outside should be flowing to the blackhole is a mystery.
<LI> There is a blob of matter rotating around SA with a velocity, which is 30 percent of the velocity of light. The object periodically emits ray bursts, which might relate to the mystery of gamma ray bursts.
</OL>
Could one understand these properties of SA by regarding SA as a blackhole-like object in the TGD sense consisting of a maximally dense flux tube spaghetti which is a quantum system with gravitational Planck constant ℏ<sub>gr</sub>=GM/β<sub>0</sub>? Could one model SA as a quantum harmonic oscillator in the interior and using gravitational Coulomb potential in the exterior?
</p><p>
The reason for why matter is not falling inside SA could be the same as in the case of the hydrogen atom. Quantization would imply that the atom is a quantum system and does not dissipate so that the infrared catastrophe is avoided. Matter around it is at Bohr orbits of a central potential. The first guess would be Coulomb potential but also harmonic oscillator potential or something between these two could be considered.
<OL>
<LI> The quantization of angular momentum gives for a central potential and circular orbits r<sup>2</sup>ω= nGM/β<sub>0</sub>. The condition v<sup>2</sup>/r=ω<sup>2</sup>r= -d(GM(r)/r) holds true also for a central force. Recall that for the harmonic oscillator this gives ω=1/r<sub>s</sub> (c=1)and r<sub>n</sub>= n<sup>1/2</sup>r<sub>1</sub>, r<sub>1</sub>= r<sub>s</sub>/(2β<sub>0</sub>)<sup>1/2</sup>. The constancy of ω means that the system behaves like a rigid body. Note that one has n>0. Note that there is also an S-wave state, which corresponds to n=0 and can be described only by Schrödinger equations or its analog.
<LI> For the Coulomb case one obtains ω=2/n<sup>3</sup>r<sub>s</sub> and r<sub>n</sub>= n<sup>2</sup>a<sub>gr</sub>, a<sub>gr</sub>= r<sub>s</sub>/2β<sub>0</sub><sup>2</sup>. In the interior, r<sub>1</sub> ≤ r<sub>s</sub> requires β<sub>0</sub>≥ 1/2. In the exterior, a<sub>gr</sub>≥ r<sub>s</sub> requires β<sub>0</sub>≤ 2<sup>1/2</sup> and r<sub>1</sub>≥ r<sub>s</sub>. This condition is not however absolutely necessary since the n>1 follows from the condition that the orbital velocity is smaller than c, as will be found. The conditions therefore fix β<sub>0</sub> to the range [1/2<sup>1/2</sup>,1/2,1]. The quantization β<sub>0</sub>=1/n would select β<sub>0</sub>∈{1/2,1} giving r<sub>1</sub>= (1,1/2<sup>1/2</sup>)r<sub>s</sub> for the harmonic oscillator potential and r<sub>n</sub>∈ {2,1/2}n<sup>2</sup>r<sub>s</sub> outside the blackhole.
<LI> Orbital velocities are given by v<sub>n</sub>= 2/nβ<sub>0</sub><sup>2</sup> and v<sub>n</sub><c requires n>2/β<sub>0</sub><sup>2</sup>, which is true for n> (2,4,8) for β<sub>0</sub>∈ {1,1/2<sup>1/2</sup>,1/2}. The lowest allowed orbitals have radii (r<sub>3</sub>=9r<sub>s</sub>/2,r<sub>5</sub>= 25r<sub>s</sub>, r<sub>9</sub>=162r<sub>s</sub>).
<LI> The inner radius of the accretion disk for which one can find the estimate r<sub>inner</sub> =30r<sub>s</sub> (see <A HREF="https://academic.oup.com/mnras/article/432/3/2252/1747847">this</A>). Inside the accretion disk, the harmonic oscillator model could be more appropriate than the Coulomb model. The inner edge of the accretion disk would correspond to (r<sub>8</sub>=32r<sub>s</sub>,r<sub>6</sub>= 36r<sub>s</sub>, r<sub>8</sub>=128r<sub>s</sub>) for β<sub>0</sub>∈ {1,1/2<sup>1/2</sup>,1/2}. For β<sub>0</sub>=1/2 the prediction for the radius of the inner edge would be too large and also the prediction for β<sub>0</sub>=1/2<sup>1/2</sup> is somewhat too high.
</OL>
Could one understand the findings about SA in this picture?
<OL>
<LI> The silence of SA would be completely analogous to the quantum silence of atoms. Furthermore, v<c condition would pose strong classical conditions on the allowed orbitals.
<LI> The periodically occurring X-ray flares could be analogs of atomic transitions leading to the emission of photons. They could due to the internal excitations of the matter from lower to higher energy state. For β<sub>0</sub>=1 one has a maximal number of the harmonic oscillator states corresponding to the principal quantum number n=0,1,2 and the n=2 state would correspond to the horizon. Also transition to states which could be modelled as states in Coulomb potential are possible. n=3 Coulomb orbital would be the first allowed state β<sub>0</sub>=1. The prediction is that the total X-ray energy is quantized.
<LI> Could one understand the rotation of SA in terms of the harmonic oscillator model predicting ω= 1/r<sub>s</sub> giving τ= 2π/r<sub>s</sub>. The estimated mass of the black hole gives τ= 4.2 minutes. Is the mass estimate for the blackhole too small by a factor of .42 or does the harmonic oscillator model fail?
<LI> G-objects could be understood as gravitational analogs of the atomic electrons orbiting SA at radii with small values of n. The orbital radii are predicted to be proportional to n<sup>2</sup>. The allowed orbitals would correspond to {3≤ n≤ 8, n=5} for β<sub>0</sub>∈ {1,1/2<sup>1/2</sup>} .
<LI> The mysterious blob of matter rotating around SA with velocity v=3c/10 could correspond to a Coulombic Bohr orbit with a small value of n: n=6 orbit gives this value of the velocity for β<sub>0</sub>=1. For the other options the orbit would belong to the accretion disk.
</OL>
To sum up, the β<sub>0</sub>=1 option is selected uniquely by the weird properties of SA.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/3pieces.pdf">About the recent TGD based view concerning cosmology and astrophysics</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/3pieces.pdf">chapter </A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-13664130043765335582024-03-19T05:12:00.000-07:002024-03-19T22:58:49.429-07:00Updated view about the rice experiments of Masaru Emoto
Masaru Emoto has carried to extremely interesting experiments with water at critical point against freezing. Emoto reports is that words expressing emotions are transmitted to water: the expression of positive emotions tend to generate beautiful crystal structures and negative emotions ugly ones. Also music and even pictures are claimed to have similar effects. Emoto has also carried out similar experiments with rice in water at physiological temperature. Rice subjected to words began to ferment and water subject to words expressing negative emotions began to rotten.
</p><p>
I have already earlier discussed a model for the findings of Emoto. In this article I update the model. I will also ask new questions. How emotions are communicated at the fundamental level and how a conscious entity can perceive the emotional state of another conscious entity and possibly affect it? What does emotional intelligence mean? How could one assign a measure of conscious emotional information to the emotional state? How certain sounds or gestures with emotional contents or even pictures can induce emotional response at the fundamenal DNA level?
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/emoto2024.pdf">Updated view about the rice experiments of Masaru Emoto</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/emotions.pdf">Emotions as sensory percepts about the state of magnetic body?</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-31335448161182035102024-03-17T00:27:00.000-07:002024-03-17T00:27:43.637-07:00Homomorphic encryption as an elegant manner to save privacy
Sabine Hossenfelder talked about homomorphic encryption, which is an elegant and extremely general algebraic manner to guarantee data privacy (see <A HREF="https://twitter.com/skdh/status/1769030868549640285">this</A>). The idea is that the encryption respects the algebraic operations: sums go to sums and products go to products. The processing can be done for the encrypted data without decryption. The outcome is then communicated to the user and decrypted only at this stage. This saves a huge amount of time.
</p><p>
What comes first in mind is Boolean algebra (see <A HREF="https://mathsci.kaist.ac.kr/~htjung/Boolean.pdf">this</A>). In this case the homomorphism is truth preserving. The Boolean statement formed as a Boolean algebra element is mapped to the same statement but with images of the statements replacing the original statements. In the set theoretic realization of Boolean algebra this means that unions are mapped to unions and intersections to intersections. In Boolean algebra, the elements are representable as bit sequences and sum and product are done element-wise: one has x<sup>2</sup>=1 and x+x=0. Ordinary computations can be done by representing integers as bit sequences.
</p><p>
In any computation one must perform a cutoff and the use of finite fields is the neat way to do it. Frobenius homomorphism x→x<sup>p</sup> in a field of characteristic p maps products to products and, what is non-trivial, also sums to sums since one has (x+y)<sup>p</sup>= x<sup>p</sup>+y<sup>p</sup>. For finite fields F_p the Frobenius homomorphism is trivial but for F<sub>p<sup>e</sup></sub>, e>1, this is not the case. The inverse is in this case x→x<sup> p<sub>e-1</sup></sup>. These finite fields are induced by algebraic extensions of rational numbers. e corresponds to the dimension of the extension induced by the roots of a polynomial
</p><p>
Frobenius homomorphism extends also to the algebraic extensions of p-adic number fields induced by the extensions of rationals. This would make it possible to perform calculations in extensions and only at the end to perform the approximation replaces the algebraic numbers defining the basis for the extension with rationals. To guess the encryption one must guess the prime that is used and the use of large primes and extensions of p-adic numbers induced by large extensions of rationals could keep the secrecy.
</p><p>
p-Adic number fields are highly suggestive as a computational tool as became clear in p-adic thermodynamics used to calculate elementary particle masses: for p= M<sub>127</sub>= 2<sup>127</sup>-1 assignable to electron, the two lowest orders give practically exact result since the higher order corrections are of order 10<sup>-76</sup>. For p-adic number fields with very large prime p the approximation of p-adic integers as a finite field becomes possible and Frobenius homomorphism could be used. This supports the idea that p-adic physics is ideal for the description of cognition.
</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-73028425924554542872024-03-16T21:11:00.000-07:002024-03-16T21:11:36.832-07:00Direct evidence for the TGD view of quasars
In a new paper in The Astrophysical Journal (see <A HREF="https://iopscience.iop.org/article/10.3847/1538-4357/ace4bb">this</A>), JILA Fellow Jason Dexter, graduate student Kirk Long, and other collaborators compared two main theoretical models for emission data for a specific quasar, 3C 273. The title of the <A HREF="
https://www.newsbreak.com/news/3370114755213-unlocking-the-quasar-code-revolutionary-insights-from-3c-273">popular article</A> is "Unlocking the Quasar Code: Revolutionary Insights From 3C 273".
</p><p>
If the quasar were a blackhole, one would expect two emission peaks. If the galactic disk is at constant temperature, one would expected redshifted emission peak from it. The second peak would come from the matter falling to the blackhole and it would be blueshifted relative to the first peak. Only single peak was observed. Somehow the falling of the matter is prevented to the quasar is prevented. Could the quasar look like a blackhole-like object in its exterior but emit radiation and matter preventing the falling of the matter to it.
</p><p>
This supports the TGD view of quasars as blackhole-like objects are associated with cosmic strings thickened locally to flux tube tangles (see <A HREF="https://tgdtheory.fi/public_html/articles/meco.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/galjets.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/galaxystars.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/3pieces.pdf">this</A>). The transformation of pieces of cosmic strings to monopole flux tube tangles would liberate the energy characterized by the string tension as ordinary matter and radiation. This process would be the TGD analog of the decay of inflaton field to matter. The gravitational attraction would lead to the formation of the accretion disk but the matter would not fall down to the quasar.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/3pieces.pdf">About the recent TGD based view concerning cosmology and astrophysics</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/3pieces.pdf">chapter </A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see <A HREF="https://tgdtheory.fi/tgdmaterials/curri.html">this</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-15917121969551237652024-03-15T22:10:00.000-07:002024-03-16T22:04:29.493-07:00Magnetite produced by traffic as a possible cause of Alzheimer disease
A rather unexpected partial explanation for Alzheimer's disease has been found: magnetite particles, which can be found in urban environments from exhaust gases containing breathing air (see <A HREF="https://www.eurekalert.org/news-releases/1036191">this</A>). I have written earlier about Alzheimer's disease from the TGD point of view (see <A HREF="https://tgdtheory.fi/pdfpool/lianPN.pdf">this</A>). Magnetite particles seem to be found in the hippocampus of those with the disease, which is central to memory. Now it has been found that the exposure of mice to magnetite leads to a generation of Alzheimer disease. The overall important message to the decision makers is that the pollution caused by the traffic in urban environment could be an important cause of Alzheimer disease.
</p><p>
The brain needs metabolic energy. Hemoglobin is central to the supply of metabolic energy because it binds oxygen. Could it be thought that Alzheimer's is at least partially related to a lack of metabolic energy in the hippocampus? In the sequel I will consider this explanation in the TGD framework.
</p><p>
<B>Short digression to TGD view of metabolism</B>
</p><p>
Oxygen molecules O<sub>2</sub> bind to iron atoms in hemoglobin (see <A HREF="https://en.wikipedia.org/wiki/Heme">this</A>) that already have a valence bond with 5 nitrogen atoms and a bond is created where Fe has received 5 electrons and a sixth from oxygen molecule O<sub>2</sub>. So Fe behaves the opposite of what you would expect and hemoglobin is very unusual chemically!
</p><p>
Phosphate O=PO<sub>3</sub>, or more precisely phosphate ion O=P(O<sub>-</sub>)<sup>3</sup>), which also plays a central role in metabolism, also breaks the rules: instead of accepting 3 valence electrons, it gives up 5 electrons to oxygen atoms.
</p><p>
Could the TGD view of quantum biology help to understand what is involved. Dark protons created by the Pollack effect provide a basic control tool of quantum biochemistry in TGD. Could they be involved now. Consider first the so-called high energy phosphate bond, which is one of the mysteries of biochemistry.
<OL>
<LI> Why the electrons in the valence bonds prefer to be close to P in the phosphate ion? For phosphate one would expect just the opposite. The negative charge of 3 oxygens could explain why electrons tend to be nearer to P.
<LI> The TGD based view of metabolism allows to consider a new physics explanation in which O=P(O<sup>-</sup>)<sub>3</sub> is actually a "dark" variant of neutral O=P(OH)<sub>3</sub> in which 3 protons of OH have become dark (in the TGD sense) by Pollack effect, which has kicked 3 protons to monopole flux tubes of the gravitational magnetic body of phosphate to such a large distance that the resulting dark OH looks like OH<sup>-</sup>, that is negatively charged. Charge separation between the biological body and magnetic body would have occurred. This requires metabolic energy basically provided by the solar radiation. One could see the dark phosphate as a temporary metabolic energy storage and the energy would be liberated when ATP transforms to ADP.
</OL>
Could this kind of model apply also to the Fe binding with 5 N atoms in haemoglobin by valence bonds such that, contrary to naive expectations, electrons tend to be closer to Fe than N atoms? Can one imagine a mechanism giving an effective negative charge to the N atoms or the heme protein and to O-O?
<OL>
<LI> In this case there are no protons as in the case of phosphate ions. The water environment however contains protons and pH as a negative logarithm of the proton concentration measures their concentration. pH=7 corresponds to pure water in which H<sup>+</sup> and OH<sup>-</sup> concentrations are the same. The hint comes from the fact that small pH, which corresponds to a high proton concentration, is known to be favourable for the binding of oxygen to the heme group.
<LI> Could dark protons be involved and what is the relationship between dark proton fraction and pH? Could pH measure the concentration of dark protons as I have asked?
<LI> Could the transformation of ordinary protons to dark protons at the gravitational MB of the heme protein induce a negative charge due to OH<sup>-</sup> ions associated with the heme protein and could this favour the transfer of electrons towards Fe? Could the second O of O-O form a hydrogen bond with H such that the proton of the hydrogen bond becomes dark and makes O effectively negatively charged?
</OL>
</p><p>
<B>What the effect of magnetite could be?</B>
</p><p>
Magnetite particles, .5 micrometers in size, consist of Fe<sub>3</sub>O<sub>4</sub> molecules containing iron and oxygen. According to Wikipedia, magnetite appears as crystals and obeys the chemical formula Fe<sup>2+</sup>(Fe<sup>3+</sup>)<sub>2</sub>(O<sup>-2</sup>)<sub>4</sub>. The electronic configuration is [Ar] 3d<sup>6</sup> 4s<sup>2</sup> and 3 Fe ions have donated besides the s electrons also one electron to oxygen.
</p><p>
Could it happen that somehow the oxygen absorption capacity of hemoglobin would decrease, that the amount of hemoglobin would decrease, or that oxygen would bind to the magnetite molecules on the surface of the magnetite particle? For example, could you think that some of the O<sub>2</sub> molecules bind to Fe<sub>3</sub>O<sub>4</sub> molecules instead of hemoglobin at the surface of the magnetite. Carbon monoxide is dangerous because it binds to the heme. Could it be that also the magnetite crystals do the same or rather could heme bind to them (thanks for Shamoon Ahmed for proposing this more reasonable looking option).
</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-6100597110408332352024-03-13T04:40:00.000-07:002024-03-13T04:40:08.821-07:00About the problem of two Hubble constants
The usual formulation of the problem of two Hubble constants is that the value of the Hubble constant seems to be increasing with time. There is no convincing explanation for this. But is this the correct way to formulate the problem? In the TGD framework one can start from the following ideas discussed already earlier (see <a HREF= "https://tgdtheory.fi/public_html/articles/cosmomore.pdf">this</A>).
<OL>
<LI> Would it be better to say that the measurements in short scales give slightly larger results for H<sub>0</sub> than those in long scales? Scale does not appear as a fundamental notion neither in general relativity nor in the standard model. The notion of fractal relies on the notion but has not found the way to fundamental physics. Suppose that the notion of scale is accepted: could one say that Hubble constant does not change with time but is length scale dependent. The number theoretic vision of TGD brings brings in two length scale hierarchies: p-adic length scales L<sub>p</sub> and dark length scale hierarchies L<sub>p</sub>(dark)=nL<sub>p</sub>, where one has h<sub>eff</sub>=nh<sub>0</sub> of effective Planck constants with n defining the dimension of an extension of rationals. These hierarchies are closely related since p corresponds to a ramified prime (most naturally the largest one) for a polynomial defining an extension with dimension n.
<LI> I have already earlier considered the possibility that the measurements in our local neighborhood (short scales) give rise to a slightly larger Hubble constant? Is our galactic environment somehow special?
</OL>
Consider first the length scale hierarchies.
<OL>
<LI> The geometric view of TGD replaces Einsteinian space-times with 4-surfaces in H=M<sup>4</sup>\times CP<sub>2</sub>. Space-time decomposes to space-time sheets and closed monopole flux tubes connecting distant regions and radiation arrives along these. The radiation would arrive from distant regions along long closed monopole flux tubes, whose length scale is L<sub>H</sub>. They have thickness d and length L<sub>H</sub>. d is the geometric mean d=(l<sub>P</sub>L<sub>H</sub>)<sup>1/2</sup> of Planck length L<sub>P</sub> and length L<sub>H</sub>. d is of about 10<sup>-4</sup> meters and size scale of a large neuron. It is somewhat surprising that biology and cosmology seem to meet each other.
<LI> The number theoretic view of TGD is dual to the geometric view and predicts a hierarchy of primary p-adic length scales L<sub>p</sub> ∝ p<sup>1/2</sup> and secondary p-adic length scales L<sub>2,p</sub> =p<sup>1/2</sup>L<sub>p</sub>. p-Adic length scale hypothesis states that p-adic length scales L<sub>p</sub> correspond to primes near the power of 2: p ≈ 2<sup>k</sup>. p-adic primes p correspond to so-called ramified primes for a polynomial defining some extension of rationals via its roots.
</p><p>
One can also identify dark p-adic length scales
</p><p>
L<sub>p</sub>(dark) =nL<sub>p</sub> ,
</p><p>
where n=h<sub>eff</sub>/h<sub>0</sub> corresponds to a dimension of extension of rationals serving as a measure for evolutionary level. h<sub>eff</sub> labels the phases of ordinary matter behaving like dark matter explain the missing baryonic matter (galactic dark matter corresponds to the dark energy assignable to monopole flux tubes).
<LI> p-Adic length scales would characterize the size scales of the space-time sheets. The Hubble constant H<sub>0</sub> has dimensions of the inverse of length so that the inverse of the Hubble constant L<sub>H</sub>∝ 1/H<sub>0</sub> characterizes the size of the horizon as a cosmic scale. One can define entire hierarchy of analogs of L<sub>H</sub> assignable to space-time sheets of various sizes but this does not solve the problem since one has H<sub>0</sub> ∝ 1/L<sub>p</sub> and varies very fast with the p-adic scale coming as a power of 2 if p-adic length scale hypothesis is assumed. Something else is involved.
</OL>
One can also try to understand also the possible local variation of H<sub>0</sub> by starting from the TGD analog of inflation theory. In inflation theory temperature fluctuations of CMB are essential.
<OL>
<LI> The average value of h<sub>eff</sub> is < h<sub>eff</sub>>=h but there are fluctuations of h<sub>eff</sub> and quantum biology relies on very large but very rare fluctuations of h<sub>eff</sub>. Fluctuations are local and one has <L<sub>p</sub>(dark)> = <h<sub>eff</sub>/h<sub>0</sub>> L<sub>p</sub>. This average value can vary. In particular, this is the case for the p-adic length scale L<sub>p,2</sub> (L<sub>p,2</sub>(dark)=nL<sub>2,p</sub>), which defining Hubble length L<sub>H</sub> and H<sub>0</sub>
for the first (second) option.
<LI> Critical mass density is given by 3H<sub>0</sub><sup>2</sup>/8πG. The critical mass density is slightly larger in the local environment or in short scales. As already found, for the first option the fluctuations of the critical mass density are proportional to δ n/n and for the second option to -δ n/n. For the first (second) option the experimentally determined Hubble constant increases when n increases (decreases). The typical fluctuation would be δ h<sub>eff</sub>/h ∼ 10<sup>-5</sup>. What is remarkable is that it is correctly predicted if the integer n decomposes to a product n<sub>1</sub>=n<sub>2</sub> of nearly identical or identical integers.
</p><p>
For the first option, the fluctuation δ h<sub>eff</sub>/h<sub>eff</sub>=δn/n in our local environment would be positive and considerably larger than on the average, of order 10<sup>-2</sup> rather than 10<sup>-5</sup>. h<sub>eff</sub> measures the number theoretic evolutionary level of the system, which suggests that the larger value of <h<sub>eff</sub>> could reflect the higher evolutionary level of our local environment. For the second option the variation would correspond to δn/n≤ 0 implying lower level of evolution and does not look flattering from the human perspective. Does this allow us to say that this option is implausible?
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The fluctuation of h<sub>eff</sub> around h would mean that the quantum mechanical energy scales of various systems determined by <h<sub>eff</sub>>=h vary slightly in cosmological scales. Could the reduction of the energy scales due to smaller value of h<sub>eff</sub> for systems at very long distance be distinguished from the reduction caused by the redshift. Since the transition energies depend on powers of Planck constant in a state dependent manner, the redshifts for the same cosmic distance would be apparently different. Could this be tested? Could the variation of h<sub>eff</sub> be visible in the transition energies associated with the cold spot?
<LI> The large fluctuation in the local neighbourhood also implies a large fluctuation of the temperature of the cosmic microwave background: one should have δT/T ≈ δn/n≈ δ H<sub>0</sub>/H<sub>0</sub>. Could one test this proposal?
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See the article <a HREF= "https://tgdtheory.fi/public_html/articles/3pieces.pdf">About the recent TGD based view concerning cosmology and astrophysics</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/3pieces.pdf">chapter </A> with the same title.
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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.com0