tag:blogger.com,1999:blog-106143482022-09-27T03:04:38.569-07:00TGD diaryDaily musings, mostly about physics and consciousness, heavily biased by Topological Geometrodynamics background.Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.comBlogger1953125tag:blogger.com,1999:blog-10614348.post-64069088193928600462022-09-26T04:06:00.005-07:002022-09-26T04:55:41.660-07:00A strange behavior of hybrid matter-antimatter atoms in superfluid Helium
I received an interesting link to a popular article "ASACUSA sees surprising behaviour of hybrid matter antimatter atoms in superfluid helium" (<A HREF="https://cutt.ly/NVIzglw">this</A>), which tells of a completely unexpected discovery related to the behavior of antiproton-<sup>4</sup>He<sup>++</sup> atoms in <sup>4</sup>He superfluid. The research article by ASACUSA researchers Anna Soter et al is published in Nature (<A HREF="https://cutt.ly/LVIceiB">this</A>).
</p><p>
The formation of anti-proton-<sup>4</sup>He<sup>++</sup> hybrid atoms containing also an electron in <sup>4</sup>He was studied both above and below the critical temperature for the transition to Helium superfluid. The temperatures considered are in Kelvin range corresponding to a thermal energy of order 10<sup>-4</sup> eV.
</p><p>
Liquid Helium is much denser than Helium gas. As the temperature is reduced, a transition to liquid phase takes place and the Helium liquid gets denser with the decreasing temperature. One would expect that the perturbations of nearby atoms to the state should increase the width of both electron and antiproton spectral lines in the dense liquid phase.
</p><p>
This widening indeed occurs for the lines of electrons but something totally different occurs for the spectral lines of the antiproton. The width decreases and when the superfluidity sets on, an abrupt further narrowing of He<sup>++</sup> spectral lines takes place. The antiproton does not seem to interact with the neighboring <sup>4</sup>He atoms.
</p><p>
Researchers think that the fact that the surprising behavior is linked to the radius of the hybrid atom's electronic orbital. In contrast to the situation for many ordinary atoms, the electronic orbital radius of the hybrid atom changes very little when laser light is shone on the atom and thus does not affect the spectral lines even when the atom is immersed in superfluid helium.
</p><p>
Consider now the TGD inspired model.
<OL>
<LI> It seems that either antiprotons or the atoms of <sup>4</sup>He superfluid effectively behave like dark matter. For the electrons, the widening however takes place so that it seems that the antiproton seems to be dark. In the TGD framework, where dark particles corresponds h<sub>eff</sub>=nh<sub>0</sub> >h, h=n<sub>0</sub>h<sub>0</sub> phases of ordinary matter, the first guess is that the antiprotons are dark and reside at the magnetic flux tube like structures.
</p><p>
The dark proton would be similar to a valence electron of some rare earth atoms, which mysteriously disappear when heated (an effect known for decades, see <A HREF="https://www.nature.com/articles/s41467-017-00946-1">this</A>). Dark protons would indeed behave like a dark matter particle is expected to behave and would have no direct quantum interactions with ordinary matter. The electron of the hybrid atom would be ordinary.
<LI> Darkness might also relate to the formation mechanism of the hybrid atoms. Antiproton appears as a Rydberg orbital with a large principal quantum number N and large size proportional to N<sup>2</sup>. N>41 implies that the antiproton orbital is outside the electron orbital but this leaves the interactions with other Helium atoms. For a smaller value of N the dark proton overlaps the electronic orbital. Note that for N=1, the radius of the orbital is 10<sup>-3</sup>/8a<sub>0</sub>, a<sub>0</sub>∼ .53 × 10<sup>-10</sup> m, in the Bohr model.
<LI> The orbital radii are proportional to h<sub>eff</sub><sup>2</sup> ∝ (n/n<sub>0</sub>)<sup>2</sup> so that dark orbitals with the same energy and radius as for ordinary orbitals but effective principal quantum number (n/n<sub>0</sub>)N<sub>d</sub>=N<sub>eff</sub>, are possible. (n/n<sub>0</sub>)N<sub>d</sub>=N<sub>eff</sub> condition would give the same radius and energy for the dark orbital characterized by N<sub>d</sub> and ordinary orbital characterized by N.
</OL>
One can consider both dark-to-dark and dark-to-ordinary transitions.
<OL>
<LI> The minimal change of the effective principal quantum number N<sub>eff</sub> in dark-to-dark transitions would be n/n<sub>0</sub> and be larger than one for n>n<sub>0</sub>. There is evidence for n=n<sub>0</sub>/6 found by Randel Mills (see <AHREF="https://www.blacklightpower.com/techpapers.html">this</A>) discussed from the TGD view <A HREF="https://tgdtheory.fi/public_html/articles/Millsagain.pdf">here</A>. In this case one would have effectively fractional values of N<sub>eff</sub>. One can also consider a stronger condition, h<sub>eff</sub>/h=m , one has mN<sub>d</sub>=N. The transitions would be effectively between ordinary orbitals for which Δ N<sub>eff</sub> is a multiple of m. This could be tested if the observation of dark-to-dark transition is possible. The transformation of dark photons to ordinary photons would be needed.
<LI> Energy conserving dark-to-ordinary transitions producing an ordinary photon cannot be distinguished from ordinary transitions if the condition (n/n<sub>0</sub>)N<sub>d</sub>=N<sub>eff</sub> is satisfied.
</p><p>
The transitions (37,35)→ (38,34) and (39,35)→ (38,34) at the visible wavelengths λ =726 nm and 597 nm survive in the Helium environment. The interpretation could be that the transitions occur between dark and ordinary states such that the dark state satisfies the condition that (n/n<sub>0</sub>)N<sub>d</sub>=N<sub>eff</sub> is integer, and that an ordinary photon with λ = h/Δ E is produced. This does not pose conditions on the value of h<sub>eff</sub>/h.
</p><p>
If the condition that (n/n<sub>0</sub>)N<sub>d</sub>=N<sub>eff</sub> is an integer is dropped, effective principal quantum numbers N<sub>eff</sub> coming as multiples of n/n<sub>0</sub> are possible and the photon energy has fractional spectrum.
</OL>
If this picture makes sense, it could mean a new method to store antimatter without fear of annihilation by storing it as a dark matter in the magnetic flux tubes. They would be present in superfluids and superconductors.
</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>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-88836583820879486662022-09-25T00:54:00.003-07:002022-09-25T00:54:42.185-07:00About the TGD based notions of mass, of twistors and hyperbolic counterpart of Fermi torusThe notion of mass in the TGD framework is discussed from the perspective of M<sup>8</sup>-H duality (see <A HREF="https://tgdtheory.fi/public_html/articles/M8H1.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/M8H2.pdf">this</A>, and <A HREF="https://tgdtheory.fi/public_html/articles/twisttgd2.pdf">this</A>).
<OL>
<LI> In TGD, space-time regions are characterized by polynomials P with rational coefficients (see <A HREF="https://tgdtheory.fi/public_html/articles/X.pdf">this</A>). Galois confinement defines a universal mechanism for the formation of bound states. Momenta for virtual fermions have components, which are algebraic integers in an extension of rationals defined by a polynomial P characterizing a space-time region. For the physical many fermion states, the total momentum as the sum of fermion momenta has components, which are integers using the unit defined by the size of the causal diamond (CD) (see <A HREF="https://tgdtheory.fi/public_html/articles/zeoquestions.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/zeonew.pdf">this</A>, and <A HREF="https://tgdtheory.fi/public_html/articles/ZEOnumber.pdf">this</A>).
<LI> This defines a universal number theoretical mechanism for the formation of bound states as Galois singlets. The condition is very strong but for rational coefficients it can be satisfied since the sum of all roots is always a rational number as the coefficient of the first order term.
<LI> Galois confinement implies that the sum of the mass squared values, which are in general complex algebraic numbers in E, is also an integer. Since the mass squared values correspond to conformal weights as also in string models, one has conformal confinement: states are conformal singlets. This condition replaces the masslessness condition of gauge theories (see <A HREF="https://tgdtheory.fi/public_html/articles/padmass2022.pdf">this</A>).
</OL>
Also the TGD based notion of twistor space is considered at concrete geometric level.
<OL>
<LI> Twistor lift of TGD means that space-time surfaces X<sup>4</sup> is H=M<sup>4</sup>× CP<sub>2</sub> are replaced with 6-surfaces in the twistor space with induced twistor structure of T(H)= T(M<sup>4</sup>)× T(CP<sub>2</sub>) identified as twistor space T(X<sup>4</sup>). This proposal requires that T(H) has Kähler structure and this selects M<sup>4</sup>× CP<sub>2</sub> as a unique candidate (see <A HREF="https://tinyurl.com/pb8zpqo">this</A>) so that TGD is unique.
<LI> One ends up to a more precise understanding of the fiber of the twistor space of CP<sub>2</sub> as a space of "light-like" geodesics emanating from a given point. Also a more precise view of the induced twistor spaces for preferred extremals with varying dimensions of M<sup>4</sup> and CP<sub>2</sub> projections emerges. Also the identification of the twistor space of the space-time surface as the space of light-like geodesics itself is considered.
<LI> Twistor lift leads to a concrete proposal for the construction of scattering amplitudes. Scattering can be seen as a mere re-organization of the physical many-fermion states as Galois singlets to new Galois singlets. There are no primary gauge fields and both fermions and bosons are bound states of fundamental fermions. 4-fermion vertices are not needed so that there are no divergences.
<LI> There is however a technical problem: fermion and antifermion numbers are separately conserved in the simplest picture, in which momenta in M<sup>4</sup>⊂ M<sup>8</sup> are mapped to geodesics of M<sup>4</sup>⊂ H.The led to a proposal for the modification of M<sup>8</sup>-H duality (see <A HREF="https://tgdtheory.fi/public_html/articles/M8H1.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/M8H2.pdf">this</A>). The modification would map the 4-momenta to geodesics of X<sup>4</sup>. Since X<sup>4</sup> allows both Minkowskian and Euclidean regions, one can have geodesics, whose M<sup>4</sup> projection turns backwards in time. The emission of a boson as a fermion-antifermion pair would correspond to a fermion turning backwards in time. A more precise formulation of the modification shows that it indeed works
</OL>
The third topic of this article is the hyperbolic generalization of the Fermi torus to hyperbolic 3-manifold H<sup>3</sup>/Γ. Here H<sup>3</sup>=SO(1,3)/SO(3) identifiable the mass shell M<sup>4</sup>\subset M<sup>8</sup> or its M<sup>8</sup>-H dual in H=M<sup>4</sup>× CP<sub>2</sub>. Γ denotes an infinite subgroup of SO(1,3) acting completely discontinuously in H<sup>3</sup>. For virtual fermions also complexified mass shells are required and the question is whether the generalization of H<sup>3</sup>/Γ, defining besides hyperbolic 3-manifold also tessellation of H<sup>3</sup> analogous to a cubic lattice of E<sup>3</sup>.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/hyperbFermi.pdf">About the TGD based notions of mass, of twistors and hyperbolic counterpart of Fermi torus</A> or the chapter <A HREF="https://tgdtheory.fi/public_html/articles/fusionTGD.pdf">Trying to fuse the basic mathematical ideas of quantum TGD to a single coherent whole</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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-5126517136342674472022-09-24T21:20:00.005-07:002022-09-24T23:56:37.750-07:00Riemann zeta and the number theoretical vision of TGD
There are strong indications that Riemann zeta
(see <A HREF="https://en.wikipedia.org/wiki/Generalized_Riemann_hypothesis">this</A>)
has a deep role in physics, in particular in the physics of critical systems. TGD Universe is quantum critical. For what quantum criticaly would mean at the space-time level (see
<A HREF="https://tgdtheory.fi/public_html/articles/freezing.pdf">this</A>).
This raises the question whether also Riemann zeta could have a deep role in TGD.
</p><p>
First some background relating to the number theoretic view of TGD.
<OL>
<LI> In TGD, space-time regions are characterized by polynomials P with rational coefficients. Galois confinement defines a universal mechanism for the formation of bound states. Momenta for virtual fermions have components, which are algebraic integers in an extension of rationals defined by a polynomial P characterizing space-time region. For the physical many fermion states, the total momentum as the sum of fermion momenta has components, which are integers using the unit defined by the size of the causal diamond (CD).
</p><p>
This defines a universal number theoretical mechanism for the formation of bound states. The condition is very strong but for rational coefficients it can be satisfied since the sum of all roots is always a rational number as the coefficient of the first order term.
<LI> Galois confinement implies that the sum of the mass squared values, which are in general complex algebraic numbers in E, is also an integer. Since the mass squared values correspond to conformal weights as also in string models, one has conformal confinement: states are conformal singlets. This condition replaces the masslessness condition of gauge theories (see <A HREF="https://tgdtheory.fi/public_html/articles/padmass2022.pdf">this</A>).
</p><p>
Riemann zeta is not a polynomial but has infinite number of root. How could one end up with Riemann zeta in TGD? One can also consider the replacement of the rational polynomials with analytic functions with rational coefficients or even more general functions.
<OL>
<LI> For real analytic functions roots come as pairs but building many-fermion states for which the sum of roots would be a real integer, is very difficult and in general impossible.
<LI> Riemann zeta and the hierarchy of its generalizations to extensions of rationals (Dedekind zeta functions) is however a complete exception! If the roots are at the critical line as the generalization of Riemann hypothesis assumes, the sum of the root and its conjugate is equal to 1 and it is easy to construct many fermion states as 2N fermion states, such that they have integer value conformal weight.
</p><p>
One can wonder whether one could see Riemann zeta as an analog of a polynomial such that the roots as zeros are algebraic numbers. This is however not necessary. Could zeta and its analogies allow it to build a very large number of Galois singlets and they would form a hierarchy corresponding to extensions of rationals. Could they represent a kind of second abstraction level after rational polynomials?
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/twisttgd2.pdf">About TGD counterparts of twistor amplitudes: part II</A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/twisttgdpdf">About TGD counterparts of twistor amplitudes</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-44121222193024602412022-09-23T03:12:00.005-07:002022-09-23T03:51:30.859-07:00Invisible magnetic fields as a support for the notion of monopole flux tube
Physicists studying a system consisting of a layered structure consisting of alternate superconducting and spin liquid layers have found evidence for what they call invisible magnetic fields. The popular article is published in Scitechdaily (see <A HREF="https://cutt.ly/XVme0Xj">this</A>) and tells about research carried out by Prof. Beena Kalisky and doctoral student Eylon Persky in Bar-Ilan University. The research article is published in Nature (see <A HREF="https://cutt.ly/wVme7pu">this</A>).
</p><p>
First some basic notions.
<OL>
<LI> The notions of spin liquid and charge-spin separation are needed. Popular texts describe charge separation in a way completely incomprehensible for both layman and professional. Somehow the electron would split into two parts corresponding to its spin and charge. The non-popular definition is clear and understandable. Instead of a single electron, one considers a spin liquid as a many-electron system associated with a lattice-like structure formed by atoms. The neighboring electrons are paired. There are a very large number of possible pairings. In the ground state the spins of electrons of all pairs could be either opposite or parallel (magnetization). Pairing with a vanishing spin is favoured by Fermi statistics.
</p><p>
If the opposite spins of a single pair become parallel and this state is delocalized, one can have a propagating spin wave without moving charge. If one electron pair is removed and this hole pair is delocalized ,one obtains a moving charge +2e without any motion of spin.
<LI> When a superconductor of type II is in an external magnetic field with a strength above critical value, the magnetic field penetrates to the superconductor as vortices. Inside these vortices the superconductivity is broken and electrons swirl around the magnetic field. This is how the magnetic flux quanta become visible.
</OL>
In the layered structures formed by atomic layers of spin liquid and superconductor, magnetic vortices are created spontaneously in the superconducting layers. In the Maxwellian world, magnetic fields would be created either by rotating currents or by magnetization requiring a lattice-like structure of parallel electron spins. In the recent case spontaneous magnetization should serve as a signature for the presence of these magnetic fields.
</p><p>
Surprisingly, no magnetization was observed so that one can talk of "invisible" magnetic field.
</p><p>
In the bilayered structure 4Hb-TaS<sub>2</sub>, the superconductivity is anomalous in the sense that the critical temperature is 2.7 K whereas in bulk superconductor 2H-TaS<sub>2</sub> it is .7 K. There is also a breaking of time reversal symmetry closely related t the presence of the magnetic flux quanta. The magnetic flux quanta survive above critical temperature 2.7 K up to 3.6 K and their life time is very long as compared to the electronic time scales (12 minute scale is mentioned). Therefore one can talk of magnetic memory.
</p><p>
The proposal is that a spin liquid state known as a chiral spin liquid is created and that the invisible magnetic field associated with the chiral spin liquid penetrates to the superconductor as flux quanta.
</p><p>
Could TGD explain the invisible magnetic fields?
<OL>
<LI> TGD predicts what I called monopole flux tubes, which have closed, rather than disk-like , 2-D cross sections and carry monopole flux requiring no current nor magnetization to generate it.
</p><p>
This is possible only in the TGD space-time, which corresponds to a 4-surface in 8-D space H=M<sup>4</sup>× CP<sub>2</sub>, but not in Minkowski space or in general relativistic space-time in its standard form. The reason is that the topology of the space-time surface is non-trivial in all scales.
</p><p>
The possibility of closed monopole flux tubes without magnetic monopoles, is one of the basic differences between TGD and Maxwell's theory and reflects the non-trivial homology of CP<sub>2</sub>.
<LI> Monopole flux tubes solve the mystery of why there are magnetic fields in cosmic length scales and why the Earth's magnetic field B<sub>E</sub> has not disappeared long ago by dissipation (see <A HREF="https://tgdtheory.fi/public_html/articles/Bmaintenance.pdf">this</A>)).
<LI> Electromagnetic fields at frequencies in the EEG range corresponding to cyclotron frequencies have quantal looking effects on brains of mammalians at the level of both physiology and behavior. The photon energies involved are extremely low.
</p><p>
In the TGD based quantum biology they can be understood in terms of cyclotron transitions for "dark" ions with a very large effective Planck constant h<sub>eff</sub>= nh<sub>0</sub> in a magnetic field of .2 Gauss, which is about 2/5 of the nominal value .5 Gauss of the Earth's magnetic field B<sub>D</sub>. The proposal is that B<sub>E</sub> involves a monopole flux contribution about 2B<sub>E</sub>/5 (see <A HREF="https://tgdtheory.fi/pdfpool/mec.pdf">this</A>).
</p><p>
The estimate for the invisible magnetic field was .1 Gauss so that the numbers fit nicely.
</OL>
The findings suggest that the spin liquid phase atomic layer involves the monopole flux tubes assignable to the Earth's magnetic field and orthogonal to the layer. They would not be present in the superconducting layer but would penetrate from spin liquid to the superconductor.
</p><p>
See the chapter <a HREF= "https://tgdtheory.fi/pdfpool/mec.pdf">Magnetic Sensory Canvas Hypothesis</A>.
</><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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-87066853163481516562022-09-21T03:08:00.010-07:002022-09-21T19:40:27.452-07:00Are space-time boundaries possible in the TGD Universe?
One of the key ideas of TGD from the very beginning was that the space-time surface has boundaries and we see them directly as boundaries of physical objects.
</p><p>
It however turned out that it is not at all clear whether the boundary conditions stating that no isometry currents flow out of the boundary, can be satisfied. Therefore the cautious conclusion was that perhaps the boundaries are only apparent. For instance, the space-time regions correspond to maps M<sup>4</sup> → CP<sub>2</sub>, which are many-valued and have as turning points, which have 3-D projections to M<sup>4</sup>. The boundary surfaces between regions with Minkowskian and Euclidean signatures of the induced metric seem to be unavoidable, at least those assignable to deformations of CP<sub>2</sub> type extremals assignable to wormhole contacts.
</p><p>
There are good reasons to expect that the possible boundaries are light-like and possibly also satisfy the det(g<sub>4</sub>)=0 condition and I have considered the boundary conditions but have not been able to make definite conclusions about how they could be realized.
<OL>
<LI> The action principle defining space-times as 4-surfaces in H=M<sup>4</sup>× CP<sub>2</sub> as preferred extremals contains a 4-D volume term and the Kähler action plus possible boundary term if boundaries are possible at all. This action would give rise to a boundary term representing a normal flow of isometry currents through the boundary. These currents should vanish.
<LI> There could also be a 3-D boundary part in the action but if the boundary is light-like, it cannot depend on the induced metric. The Chern-Simons term for the Kähler action is the natural choice. Twistor lift suggests that it is present also in M<sup>4</sup> degrees of freedom. Topological field theories utilizing Chern-Simons type actions are standard in condensed matter physics, in particular in the description of anyonic systems, so that the proposal is not so radical as one might think. One might even argue that in anyonic systems, the fundamental dynamics of the space-time surface is not masked by the information loss caused by the approximations leading to the field theory limit of TGD.
</p><p>
Boundary conditions would state that the normal components of the isometry currents are equal to the divergences of Chern-Simons currents and in this way guarantee conservation laws. In CP<sub>2</sub> degrees of freedom the conditions would be for color currents and in M<sup>4</sup> degrees of freedom for 4-momentum currents.
<LI> This picture would conform with the general view of TGD. In zero energy ontology (ZEO) (see <A HREF="https://tgdtheory.fi/public_html/articles/zeoquestions.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/zeonew.pdf">this</A>) phase transitions would be induced by macroscopic quantum jumps at the level of the magnetic body (MB) of the system. In ZEO, they would have as geometric correlates classical deterministic time evolutions of space-time surface leading from the initial to the final state (see <A HREF = "https://tgdtheory.fi/public_html/articles/Bohrdead.pdf">this</A>). The findings of Minev et al provide (see <A HREF="https://arxiv.org/abs/1803.00545">this</A>) lend support for this picture.
</OL>
<B>Light-like 3-surfaces from det(g<sub>4</sub>)=0 condition</B>
</p><p>
How the light-like 3- surfaces could be realized?
<OL>
<LI> A very general condition considered already earlier is the condition det(g<sub>4</sub>)=0 at the light-like 4-surface. This condition means that the tangent space of X<sup>4</sup> becomes metrically 3-D and the tangent space of X<sup>3</sup> becomes metrically 2-D. In the local light-like coordinates, (u,v,W,Wbar) g<sub>>uv</sub>= g<sub>vu</sub>) would vanish (g<sub>uu</sub> and g<sub>vv</sub> vanish by definition.
</p><p>
Could det(g<sub>4</sub>)=0 and det(g<sub>3</sub>)=0 condition implied by it allow a universal solution of the boundary conditions? Could the vanishing of these dimensional quantities be enough for the extended conformal invariance?
<LI> 3-surfaces with det(g<sub>4</sub>)=0 could represent boundaries between space-time regions with Minkowskian and Euclidean signatures or genuine boundaries of Minkowskian regions.
</p><p>
A highly attractive option is that what we identify the boundaries of physical objects are indeed genuine space-time boundaries so that we would directly see the space-time topology. This was the original vision. Later I became cautious with this interpretation since it seemed difficult to realize, or rather to understand, the boundary conditions.
</p><p>
The proposal that the outer boundaries of different phases and even molecules make sense and correspond to 3-D membrane like entities (see <A HREF="https://tgdtheory.fi/public_html/articles/minimal.pdf">this</A>) served as a partial inspiration for this article but this proposal is not equivalent with the proposal that light-like boundaries defining genuine space-time boundaries can carry isometry charges and fermions.
<LI> How does this relate to M<sup>8</sup>-H duality (see <A HREF="https://tgdtheory.fi/public_html/articles/M8H1.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/M8H1.pdf">this</A>)? At the level of rational polynomials P determined 4-surfaces at the level of M<sup>8</sup> as their "roots" and the roots are mass shells. The points of M<sup>4</sup> have interpretation as momenta and would have values, which are algebraic integers in the extension of rationals defined by P.
</p><p>
Nothing prevents from posing the additional condition that the region of H<sup>3</sup>⊂ M<sup>4</sup>⊂ M<sup>8</sup> is finite and has a boundary. For instance, fundamental regions of tessellations defining hyperbolic manifolds (one of them appears in the model of the genetic code (see <A HREF="https://tgdtheory.fi/public_html/articles/TIH.pdf">this</A>) could be considered. M<sup>8</sup>-H duality would give rise to holography associating to these 3-surfaces space-time surfaces in H as minimal surfaces with singularities as 4-D analogies to soap films with frames.
</p><p>
The generalization of the Fermi torus and its boundary (usually called Fermi sphere) as the counterpart of unit cell for a condensed matter cubic lattice to a fundamental region of a tessellation of hyperbolic space H<sup>3</sup> acting is discussed is discussed in <A HREF="https://tgdtheory.fi/public_html/articles/twisttgd2.pdf">this</A>. The number of tessellations is infinite and the properties of the hyperbolic manifolds of the "unit cells" are fascinating. For instance, their volumes define topological invariants and hyperbolic volumes for knot complements serve as knot invariants.
</OL>
<B>Can one allow macroscopic Euclidean space-time regions</B>
</p><p>
Euclidean space-time regions are not allowed in General Relativity. Can one allow them in TGD?
<OL>
<LI> CP<sub>2</sub> type extremals with a Euclidean induced metric and serving as correlates of elementary particles are basic pieces of TGD vision. The quantum numbers of fundamental fermions would reside at the light-like orbit of 2-D wormhole throat forming a boundary between Minkowskian space-time sheet and Euclidean wormhole contact- parton as I have called it. More precisely, fermionic quantum numbers would flow at the 1-D ends of 2-D string world sheets connecting the orbits of partonic 2-surfaces. The signature of the 4-metric would change at it.
<LI> It is difficult to invent any mathematical reason for excluding even macroscopic surfaces with Euclidean signature or even deformations of CP<sub>2</sub> type extremals with a macroscopic size. The simplest deformation of Minkowski space is to a flat Euclidean space as a warping of the canonical embedding M<sup>4</sup>⊂ M<sup>4</sup>× S<sup>1</sup> changing its signature.
<LI> I have wondered whether space-time sheets with an Euclidean signature could give rise to black-hole like entities. One possibility is that the TGD variants of blackhole-like objects have a space-time sheet which has, besides the counterpart of the ordinary horizon, an additional inner horizon at which the signature changes to the Euclidean one. This could take place already at Schwarzschild radius if g<sub>rr</sub> component of the metric does not change its sign.
</OL>
<B>But are the normal components of isometry currents finite?</B>
</p><p>
Whether this scenario works depends on whether the normal components for the isometry currents are finite.
<OL>
<LI> det(g<sub>4</sub>)=0 condition gives boundaries of Euclidean and Minkowskian regions as 3-D light-like minimal surfaces. There would be no scales in accordance with generalized conformal invariance. g<sub>uv</sub> in light-cone coordinates for M<sup>2</sup> vanishes and implies the vanishing of det(g<sub>4</sub>) and light-likeness of the 3-surface.
</p><p>
What is important is that the formation of these regions would be unavoidable and they would be stable against perturbations.
<LI> g<sup>uv</sup>|det(g<sub>4</sub>)|<sup>1/2</sup> is finite if det(g<sub>4</sub>)=0 condition is satisfied, otherwise it diverges. The terms g<sup>ui</sup>∂<sub>i</sub>h<sup>k</sup> |det(g<sub>4</sub>)|<sup>1/2</sup> must be finite. g<sup>ui</sup>= cof(g<sub>iu</sub>)/det(g<sub>4</sub>) is finite since g<sub>uv</sub>g<sub>vu</sub> in the cofactor cancels it from the determinant in the expression of g<sup>ui</sup>. The presence of |det(g<sub>4</sub>)|<sup>1/2</sup>|<sup>1/2</sup> implies that the these contributions to the boundary conditions vanish. Therefore only the condition boundary condition for g<sup>uv</sup> remains.
<LI> If also Kähler action is present, the conditions are modified by replacing T<sup>uk</sup>= g<sup>uα</sup>∂<sub>α</sub>h<sup>k</sup>|det(g<sub>4</sub>)|<sup>1/2</sup> with a more general expression containing also the contribution of Kähler action. I have discussed the details of the variational problem in <A HREF="https://tgdtheory.fi/pdfpool/prext.pdf">this</A>.
</p><p>
The Kähler contribution involves the analogy of Maxwell's energy momentum tensor, which comes from the variation of the induced metric and involves sum of terms proportional to J<sub>α μ</sub>J<sub>μ</sub><sup>beta</sub> and g<sup>αβ</sub>J<sup>μν</sub>J<sub>μν</sub>.
</p><p>
In the first term, the dangerous index raisings by g<sup>uv</sup> appear 3 times. The most dangerous term is given by J<sup>uv</sup>J<sub>v</sub><sup>v</sup>|det(g<sub>4></sub>|<sup>1/2</sup>= g<sup>uμ</sup>g<sup>vν</sup>J<sub>αβ</sub> g<sup>vu</sup>J<sub>vu</sub>|det(g<sub>4></sub>|<sup>1/2</sup>. The divergent part is g<sup>uv</sup>g<sup>vu</sup>J<sub>uv</sub> g<sup>vu</sup>J<sub>vu</sub>|det(g<sub>4></sub>|<sup>1/2</sup>. The diverging g<sup>uv</sup> appears 3 times and J<sub>uv</sub>=0 condition eliminates two of these. g<sup>vu</sup>|det(g<sub>4></sub>|<sup>1/2</sup> is finite by |det(g<sub>4></sub>|=0 condition. J<sub>uv</sub>=0 guarantees also the finiteness of the most dangerous part in g<sup>αβ</sup>J<sup>μν</sup>J<sub>μν</sub> |det(g<sub>4></sub>|<sup>1/2</sup>.
</p><p>
There is also an additional term coming from the variation of the induced Kähler form. This to the normal component of the isometry current is proportional to the quantity J<sup>nα</sup>J<sup>k</sup><sub>l</sub>∂<sub>β</sub>h<sup>l</sup>|det(g<sub>4></sub>|<sup>1/2</sup>. Also now, the most singular term in J<sup>uβ</sup>= g<sup>uμ</sup>g<sup>βν</sup>J<sub>μν</sub> corresponds to J<sup>uv</sup> giving g<sup>uv</sup>g<sup>vu</sub>J<sup>uv</sup>|det(g<sub>4></sub>|<sup>1/2</sup>. This term is finite by J<sub>uv</sub>=0 condition.
</p><p>
Therefore the boundary conditions are well-defined but only because det(g<sub>4</sub>)=0 condition is assumed.
<LI> Twistor lift strongly suggests that the assignment of the analogy of Kähler action also to M<sup>4</sup> and also this would contribute. All terms are finite if det(g<sub>4</sub>)=0 condition is satisfied.
<LI> The isometry currents in the normal direction must be equal to the divergences of the corresponding currents assignable to the Chern-Simons action at the boundary so that the flow of isometry charges to the boundary would go to the Chern-Simons isometry charges at the boundary.
</p><p>
If the Chern-Simons term is absent, one expects that the boundary condition reduces to ∂<sub>v</sub>h<sup>k</sup>=0. This would make X<sup>3</sup> 2-dimensional so that Chern-Simons term is necessary. Note that light-likeness does not force the M<sup>4</sup> projection to be light-like so that the expansion of X<sup>2</sup> need not take with light-velocity. If CP<sub>2</sub> complex coordinates are holomorphic functions of W depending also on U=v as a parameter, extended conformal invariance is obtained.
</OL>
This picture resonates with an old guiding vision about TGD as an almost topological quantum field theory (QFT) (see <A HREF="https://tgdtheory.fi/pdfpool/WhyTGD.pdf">this</A>), which I have even regarded as a third strand in the 3-braid formed by the basic ideas of TGD based on geometry-number theory-topology trinity.
<OL>
<LI> Kähler Chern-Simons form, also identifiable as a boundary term to which the instanton density of Kähler form reduces, defines an analog of topological QFT.
<LI> In the recent case the metric is however present via boundary conditions and in the dynamics in the interior of the space-time surface. However, the preferred extremal property essential for geometry-number theory duality transforms geometric invariants to topological invariants. Minimal surface property means that the dynamics of volume and Kähler action decouple outside the singularities, where minimal surface property fails. Coupling constants are present in the dynamics only at these lower-D singularities defining the analogs of frames of a 4-D soap film.
</p><p>
Singularities also include string worlds sheets and partonic 2-surfaces. Partonic two-surfaces play the role of topological vertices and string world sheets couple partonic 2-orbits to a network. It is indeed known that the volume of a minimal surface can be regarded as a homological invariant.
<LI> If the 3-surfaces assignable to the mass shells H<sup>3</sup> define unit cells of hyperbolic tessellations and therefore hyperbolic manifolds, they also define topological invariants. Whether also string world sheets could define topological invariants is an interesting question.
</OL>
<B>det(g<sub>4</sub>)=0 condition as a realization of quantum criticality</B>
</p><p>
Quantum criticality is the basic dynamical principle of quantum TGD. What led to its discovery was the question "How to make TGD unique?". TGD has a single coupling constant, Kähler couplings strength, which is analogous to a critical temperature. The idea was obvious: require quantum criticality. This predicts a spectrum of critical values for the Kähler coupling strength. Quantum criticality would make the TGD Universe maximally complex. Concerning living matter, quantum critical dynamics is ideal since it makes the system maximally sensitive and maximallt reactive.
</p><p>
Concerning the realization of quantum criticality, it became gradually clear that the conformal invariance accompanying 2-D criticality, must be generalized. This led to the proposal that super symplectic symmetries, extended isometries and conformal symmetries of the metrically 2-D boundary of lightcone of M<sup>4</sup>, and the extension of the Kac-Moody symmetries associated with the light-like boundaries of deformed CP<sub>2</sub> type extremals should act as symmetries of TGD extending the conformal symmetries of 2-D conformal symmetries. These huge infinite-D symmetries are also required by the existence of the Kähler geometry of WCW (see <A HREF="https://tgdtheory.fi/public_html/articles/TGD2021.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/fusionTGD.pdf">this</A>).
</p><p>
However, the question whether light-like boundaries of 3-surfaces with scale larger than CP<sub>2</sub> are possible, remained an open question. On the basis of preceding arguments, the answer seems to be affirmative and one can ask for the implications.
<OL>
<LI> At M<sup>8</sup> level, the concrete realization of holography would involve two ingredients. The intersections of the space-time surface with the mass shells H<sup>3</sup> with mass squared value determined as the roots of polynomials P and the tlight-like 3-surfaces as det(g<sub>4</sub>)=0 surfaces as boundaries (genuine or between Minkowskian and Euclidean regions) associated by M<sup>8</sup>-H duality to 4-surface of M<sup>8</sup> having associative normal space, which contains commutative 2-D subspace at each point. This would make possible both holography and M<sup>8</sup>-H duality.
</p><p>
Note that the identification of the algebraic geometric characteristics of the counterpart of det(g<sub>4</sub>)=0 surface at the level of H remains still open.
</p><p>
Since holography determines the dynamics in the interior of the space-time surface from the boundary conditions, the classical dynamics can be said to be critical also in the interior.
<LI> Quantum criticality means ability to self-organize. Number theoretical evolution allows us to identify evolution as an increase of the algebraic complexity. The increase of the degree n of polynomial P serves as a measure for this. n=h<sub>eff</sub>/h<sub>0</sub> also serves as a measure for the scale of quantum coherence, and dark matter as phases of matter would be characterized by the value of n.
<LI> The 3-D boundaries would be places where quantum criticality prevails.
Therefore they would be ideal seats for the development of life. The proposal that the phase boundaries between water and ice serve as seats for the evolution of prebiotic life, is discussed from the point of TGD based view of quantum gravitation involving huge value of gravitational Planck constant ℏ<sub>eff</sub>= ℏ<sub>gr</sub>= GMm/v <sub>0</sub> making possible quantum coherence in astrophysical scales (see <A HREF="https://tgdtheory.fi/public_html/articles/penrose.pdf">this</A>). Density fluctuations would play an essential role, and this would mean that the volume enclosed by the 2-D M<sup>4</sup> projection of the space-time boundary would fluctuate. Note that these fluctuations are possible also at the level of the field body and magnetic body.
<LI> It has been said that boundaries, where the nervous system is located, distinguishes living systems from inanimate ones. One might even say that holography based on det(g<sub>4</sub>)=0 condition realizes nervous systems in a universal manner.
<LI> I have considered several variants for the holography in the TGD framework, in particular strong form of holography (SH). SH would mean that either the light-like 3-surfaces or the 3-surfaces at the ends of the causal diamond (CD) determine the space-time surface so that the 2-D intersections of the 3-D ends of the space-time surface with its light-like boundaries would determine the physics.
</OL>
This condition is perhaps too strong but a fascinating, weaker, possibility is that the internal consistency requires that the intersections of the 3-surface with the mass shells H<sup>3</sup> are identifiable as fundamental domains for the coset spaces SO(1,3)/Γ defining tessellations of H<sup>3</sup> and hyperbolic manifolds. This would conform nicely with the TGD inspired model of genetic code (see <A HREF="https://tgdtheory.fi/public_html/articles/TIH.pdf">this</A>).
</OL>
See the article <A HREF= "https://tgdtheory.fi/public_html/articles/freezing.pdf">TGD inspired model for freezing in nano scales</A> or the <A HREF= "https://tgdtheory.fi/pdfpool/freezing.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com1tag:blogger.com,1999:blog-10614348.post-15821459919980173192022-09-20T05:14:00.000-07:002022-09-20T05:14:01.429-07:00Some comments of the notion of mass
In the sequel some comments related to the notion of mass.
</p><p>
<B>M<sup>8</sup>-H duality and tachyonic momenta</B>
</p><p>
Tachyonic momenta are mapped to space-like geodesics in H or possibly to the geodesics of X<sup>4</sup> (see <A HREF ="https://tgdtheory.fi/public_html/articles/M8H1.pdf">this</A>, <A HREF ="https://tgdtheory.fi/public_html/articles/M8H2.pdf">this</A> and <A HREF ="https://tgdtheory.fi/public_html/articles/TGD2021.pdf">this</A>). This description could allow to describe pair creation as turning of fermion backwards in time (see <A HREF ="https://tgdtheory.fi/public_html/articles/twisttgd2.pdf">this</A>). Tachyonic momenta correspond to points of de Sitter space and are therefore outside CD and would go outside the space-time surface, which is inside CD. Could one avoid this?
<OL>
<LI> Since the points of the twistor spaces T(M<sup>4</sup>) and T(CP<sub>2</sub>) are in 1-1 correspondence, one can use either T(M<sup>4</sup>) or T(CP<sub>2</sub>) so that the projection to M<sup>4</sup> or CP<sub>2</sub> would serve as the base space of T(X<sup>4</sup>). One could use CP<sub>2</sub> coordinates or M<sup>4</sup> coordinates as space-time coordinates if the dimension of the projection is 4 to either of these spaces. In the generic case, both dimensions are 4 but one must be very cautious with genericity arguments which fail at the level of M<sup>8</sup>.
<LI> There are exceptional situations in which genericity fails at the level of H. String-like objects of the form X<sup>2</sup>× Y<sup>2</sup> ⊂ M<sup>4</sup>⊂ CP<sub>2</sub> is one example of this. In this case, X<sup>6</sup> would not define 1-1 correspondence between T(M<sup>4</sup>) or T(CP<sub>2</sub>).
</p><p>
Could one use partial projections to M<sup>2</sup> and S<sup>2</sup> in this case? Could T(X<sup>4</sup>) be divided locally into a Cartesian product of 3-D M<sup>4</sup> part projecting to M<sup>2</sup> ⊂ M<sup>4</sup> and of 3-D CP<sub>2</sub> part projected to Y<sup>2</sup>⊂ CP<sub>2</sub>.
<LI> One can also consider the possibility of defining the twistor space T(M<sup>2</sup>× S<sup>2</sup>). Its fiber at a given point would consist of light-like geodesics of M<sup>2</sup>× S<sup>2</sup>. The fiber consists of direction vectors of light-like geodesics. S<sup>2</sup> projection would correspond to a geodesic circle S<sup>1</sup>⊂ S<sup>2</sup> going through a given point of S<sup>2</sup> and its points are parametrized by azimuthal angle Φ. Hyperbolic tangent tanh(η) with range [-1,1] would characterize the direction of a time like geodesic in M<sup>2</sup>. At the limit of η → +/- ∞ the S<sup>2</sup> contribution to the S<sup>2</sup> tangent vector to length squared of the tangent vector vanishes so that all angles in the range (0,2\pi) correspond to the same point. Therefore the fiber space has a topology of S<sup>2</sup>.
</p><p>
There are also other special situations such as M<sup>1</sup>× S<sup>3</sup>, M<sup>3</sup> × S<sup>1</sup> for which one must introduce specific twistor space and which can be treated in the same way.
</OL>
During the writing of this article I realized that the twistor space of H defined geometrically as a bundle, which has as H as base space and fiber as the space of light-like geodesic starting from a given point of H need not be equal to T(M<sup>4</sup>)× T(CP<sub>2</sub>), where T(CP<sub>2</sub>) is identified as SU(3)/U(1)× U(1) characterizing the choices of color quantization axes.
<OL>
<LI> The definition of T(CP<sub>2</sub>) as the space of light-like geodesics from a given point of CP<sub>2</sub> is not possible. One could also define the fiber space of T(CP<sub>2</sub>) geometrically as the space of geodesics emating from origin at r=0 in the Eguchi-Hanson coordinates (see <A HREF ="https://tgdtheory.fi/pdfpool/append.pdf">this</A>) and connecting it to the homologically non-trivial geodesic sphere S<sup>2</sup><sub>G</sub> r=∞. This relation is symmetric.
</p><p>
In fact, all geodesics from r=0 end up to S<sup>2</sup>. This is due to the compactness and symmetries of CP<sub>2</sub>. In the same way, the geodesics from the North Pole of S<sup>2</sup> end up to the South Pole. If only the endpoint of the geodesic of CP<sub>2</sub> matters, one can always regard it as a point S<sup>2</sup><sub>G</sub>.
</p><p>
The two homologically non-trivial geodesic spheres associated with distinct points of CP<sub>2</sub> always intersect at a single point, which means that their twistor fibers contain a common geodesic line of this kind. Also the twistor spheres of T(M<sup>4</sup>) associated with distinct points of M<sup>4</sup> with a light-like distance intersect at a common point identifiable as a light-like geodesic connecting them.
<LI> Geometrically, a light-like geodesic of H is defined by a 3-D momentum vector in M<sup>4</sup> and 3-D color momentum along CP<sub>2</sub> geodesic. The scale of the 8-D tangent vector does not matter and the 8-D light-likeness condition holds true. This leaves 4 parameters so that T(H) identified in this way is 12-dimensional.
</p><p>
The M<sup>4</sup> momenta correspond to a mass shell H<sup>3</sup>. Only the momentum direction matters so that also in the M<sup>4</sup> sector the fiber reduces to S<sup>2</sup> . If this argument is correct, the space of light-like geodesics at point of H has the topology of S<sup>2</sup>× S<sup>2</sup> and T(H) would reduce to T(M<sup>4</sup>)× T(CP<sub>2</sub>) as indeed looks natural.
</OL>
<B>Conformal confinement at the level of H</B>
</p><p>
The proposal of <A HREF ="https://tgdtheory.fi/public_html/articles/padmass2022.pdf">this</A>, inspired by p-adic thermodynamics, is that all states are massless in the sense that the sum of mass squared values vanishes. Conformal weight, as essentially mass squared value, is naturally additive and conformal confinement as a realization of conformal invariance would mean that the sum of mass squared values vanishes. Since complex mass squared values with a negative real part are allowed as roots of polynomials, the condition is highly non-trivial.
</p><p>
M<sup>8</sup>-H duality (see <A HREF ="https://tgdtheory.fi/public_html/articles/M8H1.pdf">this</A> and <A HREF ="https://tgdtheory.fi/public_html/articles/M8H2.pdf">this</A>) would make it natural to assign tachyonic masses with CP<sub>2</sub> type extremals and with the Euclidean regions of the space-time surface. Time-like masses would be assigned with time-like space-time regions. It was <A HREF ="https://tgdtheory.fi/public_html/articles/freezing.pdf">found</A> that, contrary to the beliefs held hitherto, it is possible to satisfy boundary conditions for the action action consisting of the Kähler action, volume term and Chern-Simons term, at boundaries (genuine or between Minkowskian and Euclidean space-time regions) if they are light-like surfaces satisfying also det{g<sub>4</sub>}=0. Masslessness, at least in the classical sense, would be naturally associated with light-like boundaries (genuine or between Minkowskian and Euclidean regions).
</p><p>
<B>About the analogs of Fermi torus and Fermi surface in H<sup>3</sup></B>
</p><p>
Fermi torus (cube with opposite faces identified) emerges as a coset space of E<sup>3</sup>/T<sup>3</sup>, which defines a lattice in the group E<sup>3</sup>. Here T<sup>3</sup> is a discrete translation group T<sup>3</sup> corresponding to periodic boundary conditions in a lattice.
</p><p>
In a realistic situation, Fermi torus is replaced with a much more complex object having Fermi surface as boundary with non-trivial topology. Could one find an elegant description of the situation?
</p><p>
<I> 1. Hyperbolic manifolds as analogies for Fermi torus?</I>
</p><p>
The hyperbolic manifold assignable to a tessellation of H<sup>3</sup> defines a natural relativistic generalization of Fermi torus and Fermi surface as its boundary. To understand why this is the case, consider first the notion of cognitive representation.
<OL>
<LI> Momenta for the cognitive representations (see <A HREF ="https://tgdtheory.fi/public_html/articles/fusionTGD.pdf">this</A>)define a unique discretization of 4-surface in M<sup>4</sup> and, by M<sup>8</sup>-H duality, for the space-time surfaces in H and are realized at mass shells H<sup>3</sup>⊂ M<sup>4</sup>⊂ M<sup>8</sup> defined as roots of polynomials P. Momentum components are assumed to be algebraic integers in the extension of rationals defined by P and are in general complex.
</p><p>
If the Minkowskian norm instead of its continuation to a Hermitian norm is used, the mass squared is in general complex. One could also use Hermitian inner product but Minkowskian complex bilinear form is the only number-theoretically acceptable possibility. Tachyonicity would mean in this case that the real part of mass squared, invariant under SO(1,3) and even its complexification SO<sub>c</sub>(1,3), is negative.
<LI> The active points of the cognitive representation contain fermion. Complexification of H<sup>3</sup> occurs if one allows algebraic integers. Galois confinement(see <A HREF ="https://tgdtheory.fi/public_html/articles/fusionTGD.pdf">this</A> and <A HREF ="https://tgdtheory.fi/public_html/articles/McKayGal.pdf">this</A>) states that physical states correspond to points of H<sup>3</sup> with integer valued momentum components in the scale defined by CD.
</p><p>
Cognitive representations are in general finite inside regions of 4-surface of M<sup>8</sup> but at H<sup>3</sup> they explode and involve all algebraic numbers consistent with H<sup>3</sup> and belonging to the extension of rationals defined by P. If the components of momenta are algebraic integers, Galois confinement allows only states with momenta with integer components favored by periodic boundary conditions.
</OL>
Could hyperbolic manifolds as coset spaces SO(1,3)/Γ, where Γ is an infinite discrete subgroup SO(1,3), which acts completely discontinuously from left or right, replace the Fermi torus? Discrete translations in E<sup>3</sup> would thus be replaced with an infinite discrete subgroup Γ. For a given P, the matrix coefficients for the elements of the matrix belonging to Γ would belong to an extension of rationals defined by P.
<OL>
<LI> The division of SO(1,3) by a discrete subgroup Γ gives rise to a hyperbolic manifold with a finite volume. Hyperbolic space is an infinite covering of the hyperbolic manifold as a fundamental region of tessellation. There is an infinite number of the counterparts of Fermi torus (see <A HREF ="https://tgdtheory.fi/public_html/articles/TIH.pdf">this</A>). The invariance respect to Γ would define the counterpart for the periodic boundary conditions.
</p><p>
Note that one can start from SO(1,3)/Γ and divide by SO(3) since Γ and SO(3) act from right and left and therefore commute so that hyperbolic manifold is SO(3)\setminus SO(1,3)/Γ.
<LI> There is a deep connection between the topology and geometry of the Fermi manifold as a hyperbolic manifold. Hyperbolic volume is a topological invariant, which would become a basic concept of relativistic topological physics (see <A HREF="https://cutt.ly/RVsdNl3">this</A>).
</p><p>
The hyperbolic volume of the knot complement serves as a knot invariant for knots in S<sup>3</sup>. Could this have physical interpretation in the TGD framework, where knots and links, assignable to flux tubes and strings at the level of H, are central. Could one regard the effective hyperbolic manifold in H<sup>3</sup> as a representation of a knot complement in S<sup>3</sup>?
</p><p>
Could these fundamental regions be physically preferred 3-surfaces at H<sup>3</sup> determining the holography and M<sup>8</sup>-H duality in terms of associativity (see <A HREF ="https://tgdtheory.fi/public_html/articles/M8H1.pdf">this</A> and <A HREF ="https://tgdtheory.fi/public_html/articles/M8H2.pdf">this</A>). Boundary conditions at the boundary of the unit cell of the tessellation should give rise to effective identifications just as in the case of Fermi torus obtained from the cube in this way.
</OL>
<I> 2. De Sitter manifolds as tachyonic analogs of Fermi torus
do not exist</I>
</p><p>
Can one define the analogy of Fermi torus for the real 4-momenta having negative, tachyonic mass squared? Mass shells with negative mass squared correspond to De-Sitter space SO(1,3)/SO(1,2) having a Minkowskian signature. It does not have analogies of the tessellations of H<sup>3</sup> defined by discrete subgroups of SO(1,3).
</p><p>
The reason is that there are no closed de-Sitter manifolds of finite size since no infinite group of isometries acts discontinuously on de Sitter space: therefore these is no group replacing the Γ in H<sup>3</sup>/Γ (see <A HREF="https://cutt.ly/XVsdLwY">this</A>).
</p><p>
<I> 3. Do complexified hyperbolic manifolds as analogs of Fermi torus exist?</I>
</p><p>
The momenta for virtual fermions defined by the roots defining mass squared values can also be complex. Tachyon property and complexity of mass squared values are not of course not the same thing.
<OL>
<LI> Complexification of H<sup>3</sup> would be involved and it is not clear what this could mean. For instance, does the notion of complexified hyperbolic manifold with complex mass squared make sense.
<LI> SO(1,3) and its infinite discrete groups Γ act in the complexification. Do they also act discontinuously? p<sup>2</sup> remains invariant if SO(1,3) acts in the same way on the real and imaginary parts of the momentum leaves invariant both imaginary and complex mass squared as well as the inner product between the real and imaginary parts of the momenta. So that the orbit is 5-dimensional. Same is true for the infinite discrete subgroup Γ so that the construction of the coset space could make sense. If Γ remains the same, the additional 2 dimensions can make the volume of the coset space infinite. Indeed, the constancy of p<sub>1</sub>• p<sub>2</sub> eliminates one of the two infinitely large dimensions and leaves one.
</p><p>
Could one allow a complexification of SO(1,3), SO(3) and SO(1,3)<sub>c</sub>/SO(3)<sub>c</sub>? Complexified SO(1,3) and corresponding subgroups Γ satisfy OO<sup>T</sup>=1. Γ<sub>c</sub> would be much larger and contain the real Γ as a subgroup. Could this give rise to a complexified hyperbolic manifold H<sup>3</sup><sub>c</sub> with a finite volume?
<LI> A good guess is that the real part of the complexified bilinear form p• p determines what tachyonicity means. Since it is given by Re(p)<sup>2</sup>-Im(p)<sup>2</sup> and is invariant under SO<sub>c</sub>(1,3) as also Re(p)• Im(p), one can define the notions of time-likeness, light-likeness, and space-likeness using the sign of Re(p)<sup>2</sup>-Im(p<sup>2</sup>) as a criterion. Note that Re(p)<sup>2</sup> and Im(p)<sup>2</sup> are separately invariant under SO(1,3).
</p><p>
The physicist's naive guess is that the complexified analogs of infinite discrete and discontinuous groups and complexified hyperbolic manifolds as analogs of Fermi torus exist for Re(P<sup>2</sup>)-Im(p<sup>2</sup>)>0 but not for Re(P<sup>2</sup>)-Im(p<sup>2</sup>)<0 so that complexified dS manifolds do not exist.
<LI> The bilinear form in H<sup>3</sup><sub>c</sub> would be complex valued and would not define a real valued Riemannian metric. As a manifold, complexified hyperbolic manifold is the same as the complex hyperbolic manifold with a hermitian metric (see <A HREF="https://cutt.ly/qVsdS7Y">this</A>) and <A HREF="https://cutt.ly/kVsd3Q2">this</A>) but has different symmetries. The symmetry group of the complexified bilinear form of H<sup>3</sup><sub>c</sub> is SO<sub>c</sub>(1,3) and the symmetry group of the Hermitian metric is U(1,3) containing SO(1,3) as a real subgroup. The infinite discrete subgroups Γ for U(1,3) contain those for SO(1,3). Since one has complex mass squared, one cannot replace the bilinear form with hermitian one. The complex H<sup>3</sup> is not a constant curvature space with curvature -1 whereas H<sup>3</sup><sub>c</sub> could be such in a complexified sense.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/padmass2022.pdf">Some objections against p-adic thermodynamics and their resolution</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/twisttgd.pdf">About TGD counterparts of twistor amplitudes</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-25190927249539091182022-09-14T04:02:00.007-07:002022-09-18T01:48:19.214-07:00TGD inspired model for freezing in nano scalesFreezing is a phase transition, which challenges the existing view of condensed matter in nanoscales. In the TGD framework, quantum coherence is possible in all scales and gravitational quantum coherence should characterize hydrodynamics in astrophysical and even shorter scales. The hydrodynamics at the surface of the planet such as Earth the mass of the planet and even that of the Sun should characterize gravitational Planck constant h<sub>gr</sub> assignable to gravitational flux tubes mediating gravitational interactions. In this framework, quantum criticality involving h<sub>eff</sub>=nh<sub>0</sub>>h phases of ordinary matter located at the magnetic body (MB) and possibly controlling ordinary matter, could be behind the criticality of also ordinary phase transitions.
</p><p>
In this article, a model inspired by the finding that the water-air boundary involves an ice-like layer. The proposal is that also at criticality for the freezing a similar layer exists and makes possible fluctuations of the size and shape of the ice blob. At criticality the change of the Gibbs free energy for water would be opposite that for ice and the Gibbs free energy liberated in the formation of ice layer would transform to the energy of surface tension at water-ice layer.
</p><p>
This leads to a geometric model for the freezing phase transition involving only the surface energy proportional to the area of the water-ice boundary and the constraint term fixing the volume of water. The partial differential equations for the boundary surface are derived and discussed.
</p><p>
If Δ P=0 at the critical for the two phases at the boundary layer, the boundary consists of portions, which are minimal surfaces analogous to soap films and conformal invariance characterizing 2-D critical systems is obtained. For Δ P≠ 0, conformal invariance is lost and analogs of soap bubbles are obtained.
</p><p>
In the TGD framework, the generalization of the model to describe freezing as a dynamical time evolution of the solid-liquid boundary is suggestive. An interesting question is whether this boundary could be a light-like 3-surface in H=M<sup>4</sup>× CP<sub>2</sub> and thus have a vanishing 3-volume. A huge extension of ordinary conformal symmetries would emerge.
</p><p>
See the article <A HREF= "https://tgdtheory.fi/public_html/articles/freezing.pdf">TGD inspired model for freezing in nano scales</A> or the <A HREF= "https://tgdtheory.fi/pdfpool/freezing.pdf">chapter</A> with the same title.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-74923625059227162322022-09-08T01:52:00.002-07:002022-09-09T23:14:43.473-07:00Strange glass spheres in the Moon
\subsubsection{Strange glass spheres in the Moon}
According to the Eurekalert article (see <A HREF="https://cutt.ly/3CWde6M">this</A>), translucent glass globules have been found on the Moon in a study led by Dr. Zhiyong Xiao (Planetary Environmental and Astrobiological Research Laboratory, School of Atmospheric Sciences, Sun Yat-sen University), who is a core scientific team member of the first in-situ lunar mission to the Moon, Chang'E-4.
<OL>
<LI> The team examined images taken by the panorama camera onboard the Yutu-2 rover, and discovered several translucent spherical and dumbbell-shaped glassy globules (see the images of the <A HREF="https://cutt.ly/3CWde6M">article</A>). Perching on the surface regolith, the globules are transparent to translucent, and they exhibit a light brownish color. Such centimeter-sized translucent glass globules are not found on the Moon before and their presence was unexpected.
<LI> This kind of glassy globules were found also by Apollo astronauts and their size was also below 1 cm but they were mostly opaque and clast rich, which means that the glass crystals are accompanied by some other material . The sizes of tektites found at the surface of Earth, believed to be produced in terrestrial impact events, are opaque and have sizes ranging from micrometers (microtektites) to a few centimeters. They are believed to be produced in impact events creating craters.
</OL>
There is an alternative theory explaining the formation of craters in planets and Moons related to the notion of the Electric Universe (see <A HREF="http://tinyurl.com/y3bsgevu">this</A>). Electric Universe in its extreme nothing-but-version claims that electromagnetism determines everything even in astrophysical scales and that one can forget gravitation, whereas the standard view is that gravitation determines everything.
</p><p>
In the TGD framework, both gravitation and the analog of electromagnetism are key players in astrophysics. In particular, the Kähler magnetic flux tubes carrying monopole flux are predicted to be key players in all scales from biology to the formation of galaxies and stars. This explains anomalies such as the existence of magnetic fields in cosmic scales and also the stability of the Earth's magnetic field.
<OL>
<LI> The craters, and also glass spheres, could be due to strong electric currents flowing between planets rather than due to the collisions of meteors and meteorites. Lightning strikes could cause these strong currents. Volcanic lightning is indeed known to cause the formation of glass spheres (see <A HREF="https://cutt.ly/wCWsKSM">this</A>). I have discussed both the standard view and the lightning theory for the formation of craters from the TGD point of view (see <A HREF= "https://tgdtheory.fi/public_html/articles/elecricuniverse.pdf">this</A>).
<LI> If the electric currents arrive orthogonally to the surface of the planet, this theory explains various anomalies such as the fact that craters are disk-like. For collisions of meteors one would expect all elliptic shapes depending on the arrival angle. This theory could also explain the glass balls.
<LI> In the TGD framework, these currents could consist of very high energy dark matter particles (dark in the TGD sense, and thus having ℏ<sub>eff</sub>=ℏ<sub>gr</sub>= GMm/β<sub>0</sub> >>ℏ, β<sub>0</sub>=v_0/c ≤ 1) arriving along monopole flux tubes of Kähler magnetic field to the surface and liberating energy as they transform to ordinary particles. This would generate a high temperature, which would melt the quartz and produce the glass spheres and dumb-bell like objects. The large value of h<sub>eff</sub> at flux tubes implies a very low rate of dissipation, which would explain the association of relativistic electrons and gamma rays with lightnings. In the atmosphere, they would rapidly lose their energy.
<LI> The gravitational Compton length associated with particles of mass m is given by Λ<sub>gr</sub>= ℏ<sub>gr</sub>/m= GM/β<sub>0</sub>= r<sub>s</sub>/2β<sub>0</sub> and does not depend on the mass of dark particle (Equivalence Principle). If M is the Earth's mass M<sub>E</sub>, one has Λ<sub>gr</sub>>.45 cm. Intriguingly, this is the size scale of the glass spheres found on the Moon and of tektonites found on the Earth.
</p><p>
Moon mass is 1.2 percent of M<sub>E</sub> so that the size scale would be above 45 μm, the size scale of a cell, for the gravitational flux tubes assignable to the Moon. The size scale of one centimeter would suggest that the monopole flux tubes of the Earth's magnetic field extends at least to the Moon, whose distance from Earth is about 30 Earth radii.
</p><p>
Interestingly, the size scale of snowflakes is also this and the explanation could be based one gravitational quantum coherence predicted to be possible in arbitrarily long scales (see <A HREF ="https://tgdtheory.fi/public_html/articles/penrose.pdf">this</A>).
</OL>
The same mechanism could explain the reported and published finding of glass spheres around crop circles available <A HREF="https://www.bltresearch.com/published.html">here</A>. I have discussed crop circles from the TGD point of view (see <A HREF="https://tgdtheory.fi/pdfpool/crop1.pdf">this</A> and <A HREF="https://tgdtheory.fi/pdfpool/crop2.pdf">this</A>).
<OL>
<LI> The high temperature explains boiling, which has occurred for the crops (like for a tomato in a microwave oven) would make possiböle the formation of crop circle. Meteoric iron has been found in the glass balls and could have arrived along magnetic flux tubes and originate from a meteorite arriving in the atmosphere.
<LI> In TGD, the magnetic bodies (MBs) consisting of momopole flux tubes and sheets with a very large value of h<sub>eff</sub> equal to h<sub>gr</sub> would be intelligent entities controlling various biosystems.
Quite generally, h<sub>eff</sub> would serve as a measure of algebraic complexity and the level of intelligence in TGD based view of consciousness and cognition based on number theory (see <A HREF ="https://tgdtheory.fi/pdfpool/adelephysics.pdf">this</A>).
</p><p>
Even crop fields would have MB. The charged meteoric iron could have ended up in the monopole flux tubes of the MB of the crop field, accelerated in the electric field parallel to flux tubes to very high energies , and ended up to the surface of Earth and made the presence of MB manifest as a crop circle. An alternative idea is that the crop circles are purposefully manufactured by a higher intelligence using this mechanism.
</p><p>
Crop circles could be analogous to neural representations but in crop fields instead of brains. The large value of h<sub>gr</sub> for flux tubes is the same as for living matter in general and could explain why crop fields can have aspects, which bring to mind the brain. The conscious intelligence would however reside at the level of the magnetic body.
</p><p>
These flux tubes would connect astrophysical objects, even galactic blackhole-like objects to distant stars and make the Universe a kind of neural network.
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/electricuniverse.pdf">Comparing Electric Universe hypothesis and TGD</A> or the <A HREF="https://tgdtheory.fi/pdfpool/electricuniverse.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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-8184734046097982482022-09-07T22:29:00.000-07:002022-09-07T22:29:00.834-07:00M8-H duality at the level of "world of classical worlds"
The "world of classical worlds" (WCW) emerges in the geometric view of quantum TGD. M<sup>8</sup>-H duality should lso work for WCW. What is the number theoretic counterpart of WCW? What is the geometric counterpart of the discretization characteristic to the number theoretic approach? </p><p> In the number theoretic vision in which WCW is discretized by replacing space-time surfaces with their number theoretical discretizations determined by the points of X<sup>4</sup>⊂ M<sup>8</sup> having the octonionic coordinates of M<sup>8</sup> in an extension of rationals and therefore making sense in all p-adic number fields? How could an effective discretization of the real WCW at the geometric H level, making computations easy in contrast to all expectations, take place?
<OL>
<LI> The key observation is that any functional or path integral with integrand defined as exponent of action, can be <I> formally</I> calculated as an analog of Gaussian integral over the extrema of the action exponential exp(S). The configuration space of fields would be effectively discretized. Unfortunately, this holds true only for the so called integrable quantum field theories and there are very few of them and they have huge symmetries. But could this happen for WCW integration thanks to the maximal symmetries of the WCW metric?
<LI> For the Kähler function K, its maxima (or maybe extrema) would define a natural effective discretization of the sector of WCW corresponding to a given polynomial P defining an extension of rationals. </p><p> The discretization of the WCW defined by polynomials P defining the space-time surfaces should be equivalent with the number theoretical discretization induced by the number theoretical discretization of the corresponding space-time surfaces. Various p-adic physics and corresponding discretizations should emerge naturally from the real physics in WCW.
<LI> The physical interpretation is clear. The TGD Universe is analogous to the spin glass phase (see <A HREF ="https://tgdtheory.fi/public_html/articles/sg.pdf">this</A>). The discretized WCW corresponds to the energy landscape of spin glass having an ultrametric topology. Ultrametric topology of WCW means that discretized WCW decomposes to p-adic sectors labelled by polynomials P. The ramified primes of P label various p-adic topologies associated with P.
</OL>
See the article <A HREF ="https://tgdtheory.fi/public_html/articles/fusionTGD.pdf">Trying to fuse the basic mathematical ideas of quantum TGD to a single coherent whole</A> or the <A HREF ="https://tgdtheory.fi/pdfpool/fusionTGD.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> <A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-11746147786764440862022-08-30T01:03:00.002-07:002022-08-30T01:03:48.371-07:00Trying to fuse the basic mathematical ideas of quantum TGD to a single coherent wholeThe theoretical framework behind TGD involves several different strands and the goal is to unify them to a single coherent whole. TGD involves number theoretic and geometric visions about physics and M<sup>8</sup>-H duality, analogous to Langlands duality, is proposed to unify them. Also quantum classical correspondence (QCC) is a central aspect of TGD. One should understand both the M<sup>8</sup>-H duality and QCC at the level of detail.
</p><p>
The following mathematical notions are expected to be of relevance for this goal.
<OL>
<LI> Von Neumann algebras, call them M, in particular hyperfinite factors of type II<sub>1</sub> (HFFs), are in a central role. A both the geometric and number theoretic side, QCC could mathematically correspond to the relationship between M and its commutant M'.
</p><p>
For instance, symplectic transformations leave induced Kähler form invariant and various fluxes of Kähler form are symplectic invariants and correspond to classical physics commuting with quantum physics coded by the super symplectic algebra (SSA). On the number theoretic side, the Galois invariants assignable to the polynomials determining space-time surfaces are analogous classical invariants.
<LI> The generalization of ordinary arithmetics to quantum arithmetics obtained by replacing + and × with ⊕ and ⊗ allows us to replace the notions of finite and p-adic number fields with their quantum variants. The same applies to various algebras.
<LI> Number theoretic vision leads to adelic physics involving a fusion of various p-adic physics and real physics and to hierarchies of extensions of rationals involving hierarchies of Galois groups involving inclusions of normal subgroups. The notion of adele can be generalized by replacing various p-adic number fields with the p-adic representations of various algebras.
<LI> The physical interpretation of the notion of infinite prime has remained elusive although a formal interpretation in terms of a repeated quantization of a supersymmetric arithmetic QFT is highly suggestive. One can also generalize infinite primes to their quantum variants. The proposal is that the hierarchy of infinite primes generalizes the notion of adele.
</OL>
The formulation of physics as Kähler geometry of the "world of classical worlds" (WCW) involves of 3 kinds of algebras A; supersymplectic isometries SSA acting on δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub>; affine algebras Aff acting on light-like partonic orbits; and isometries of light-cone boundary δ M<sup>4</sup><sub>+</sub>, allowing hierarchies of subalgebras A<sub>n</sub>.
</p><p>
The braided Galois group algebras at the number theory side and algebras {A<sub>n</sub>} at the geometric side define excellent candidates for inclusion hierarchies of HFFs. M<sup>8</sup>-H duality suggests that n corresponds to the degree nof the polynomial P defining space-time surface and that the n roots of P correspond to n braid strands at H side. Braided Galois group would act in A<sub>n</sub> and hierarchies of Galois groups would induce hierarchies of inclusions of HFFs. The ramified primes of P would correspond to physically preferred p-adic primes in the adelic structure formed by p-adic variants of A<sub>n</sub> with + and × replaced with ⊕ and ⊗.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/fusionTGD.pdf">Trying to fuse the basic mathematical ideas of quantum TGD to a single coherent whole</A> or the <A HREF= "https://tgdtheory.fi/pdfpool/fusionTGD.pdf">chapter</A> with the same title.
</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com3tag:blogger.com,1999:blog-10614348.post-48968691784293166962022-08-22T00:35:00.002-07:002022-08-24T04:31:12.174-07:00TGD view of Krebs cycle
This article was inspired by the YouTube video (see <A HREF="
https://cutt.ly/7XTY1Cc">this</A>) in which biologist Nick Lane talked of Krebs cycle, also known as citric acid cycle. The title of the video was "How the Krebs cycle powers life and death?".
</p><p>
Krebs cycle is central in the metabolism of animal cells, liberating metabolic energy from glucose and leading to the emergence of the basic building blocks of fundamental biomolecules. Lane talks also of the reverse Krebs cycle appearing in photosynthesis. Lane proposes a vision of how life could have evolved from in-organic chemistry in thermal vents. Lane emphasizes the importance of charge separation at the level of the cell and even at the level of Earth.
</p><p>
The objections against Lane's view give a good motivation for developing a TGD based view about Krebs cycle. This view is based on some basic ideas of TGD inspired quantum biology. In particular the zero energy ontology (ZEO) in which Krebs cycle and its reversal could be seen as time reversal of each other at the control level; the quantum gravitational view of metabolism and evolution of life; the TGD inspired view about how Pollack effect induces charge separations leading also to a view of genetic code, which at fundamental level would be realized in terms of both dark proton and dark photon triplets; and the TGD proposal for what happened in Cambrian explosion in which oxygenated oceans and highly developed multicellulars emerged apparently out of nowhere.
</p><p>
The discussion leads to a more precise view of metabolism before the Cambrian explosion, according to which the dark photons generated by the Earth's core would have provided the photons for photosynthesis in underground oceans and led to their oxygenation.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/krebs.pdf">Krebs cycle from TGD point of view</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/precns.pdf">Quantum gravitation and quantum biology in TGD Universe</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-26147644187790139202022-08-17T01:50:00.006-07:002022-08-17T05:44:05.049-07:00Some TGD inspired questions and thoughts about hyperfinite factors of type II1I have had a very interesting discussion with Baba Ilya Iyo Azza about von Neumann algebras. I have a background of physicists and have suffered a lot of frustration in trying to understand hyperfinite factors of type II<sub>1</sub> (HFFs) by trying to read mathematicians' articles.
</p><p>
I cannot understand without a physical interpretation and associations to my own big vision TGD. Yesterday I again stared at the basic definitions, ideas and concepts trying to build a physical interpretation. I try to summarize what I possibly understood.
<OL>
<LI> One starts from the algebra of bounded operators in Hilbert space B(H). von Neumann algebra is a subalgebra of B(H). Already here an analog of inclusion is involved (see <a HREF= "https://cutt.ly/3XkPO2s">this</A>). There are also inclusions between von Neumann algebras.
</p><p>
What could the inclusion of von Neumann algebra to B(H) as subalgebra mean physically?
<LI> In the TGD framework, I can find several analogies. Space-time is a 4-surface in H=M<sup>4</sup>× CP<sub>2</sub>: analog of inclusion reducing degrees of freedom. Space-time is not only an extremal of an action, but also satisfies holography so that this 4-surface is almost uniquely defined by a 3-surface. I talk about preferred extremals (PEs).
</p><p>
Clearly, there is an analogy with von Neumann algebras, in particular HFFs with extremely nice mathematical properties, as a subalgebra of B(H) and quantum classical correspondence suggests that this analogy is not accidental.
</OL>
The notion of the commutant M' of M is essential. Also M' defines HFF.What could be its physical interpretation?
<OL>
<LI> In TGD, one has indeed an excellent candidate for the commutant. Supersymplectic symmetry algebra (SSA) of δ M<sup>4</sup><sub>+</sub>× CP<sub>2</sub> (δ M<sup>4</sup><sub>+</sub> denotes the boundary of a future directed light-cone) is proposed to act as isometries of the "world of classical worlds" (WCW) consisting of space-time surfaces as PEs (very, very roughly).
</p><p>
Symplectic symmetries are generated by Hamiltonians, which are products of Hamiltonians associated with δ M<sup>4</sup><sub>+</sub> (metrically sphere S<sup>2</sup>) and CP<sub>2</sub>. Symplectic symmetries are conjectured to act as isometries of WCW and gamma matrices of WCW extend symplectic symmetries to super-symplectic ones.
</p><p>
Hamiltonians and their super-counterparts generate the super-symplectic algebra (SSA) and quantum states are created by using them. SSA is a candidate for HFF. Call it M. What about M ?
</p><p>
<LI> The symplectic symmetries leave invariant the induced Kähler forms of CP<sub>2</sub> and contact form of δ M<sup>4</sup><sub>+</sub> (assignable to the analog of Kähler structure in M<sup>4</sup>).
<LI> The wave functions in WCW depending of magnetic fluxes defined by these Kähler forms over 2-surfaces are physically observables which commute SSA and with M. These fluxes are in a central role in the classical view about TGD and define what might perhaps be regarded as a dual description necessary to interpret quantum measurements.
</p><p>
Could M' correspond or at least include the WCW wave functions (actually the scalar parts multiplying WCW spinor fields with WCW spinor for given 4-surface a fermionic Fock state) depending on these fluxes only? I have previously talked of these degrees of freedom as zero modes commuting with quantum degrees of freedom and of quantum classical correspondence.
<LI> Note that there are also number theoretic degrees of freedom, which naturally appear from the number theoretic M<sup>8</sup> description mapped to H-description: Galois groups and their representations, etc...
</OL>
There are further algebraic notions involved. The article of John Baez (see <A HREF="https://cutt.ly/VXlQyqD">this</A>) describes these notions nicely.
<OL>
<LI> The condition M'' = M is a defining algebraic condition for von Neumann algebras. What does this mean? Or what could its failure mean? Could M'' be larger than M? It would seem that this condition is achieved by replacing M with M''.
</p><p>
M''=M codes algebraically the notion of weak continuity, which is motivated by the idea that functions of operators obtained by replacing classical observable by its quantum counterpart are also observables. This requires the notion of continuity. Every sequence of operators must approach an operator belonging to the von Neumann algebra and this can be required in a weak sense, that is for matrix elements of the operators.
<LI> There is also the notion of hermitian conjugation defined by an antiunitary operator J: a<sup>†</sup>= JAJ. This operator is absolutely essential in quantum theory and in the TGD framework it is geometrized in terms of the Kä form of WCW. The idea is that entire quantum theory, rather than only gravitation or gravitation and gauge interactions should be geometrized. Left multiplication by JaJ corresponds to right multiplication by a.
<LI> The notion of factor as a building brick of more complex structures is also central and analogous to the notion of simple group or prime. It corresponds to a von Neumann algebra, which is simple in the sense that it has a trivial center consisting of multiples of unit operators. The algebra is direct sum or integral over different factors.
<LI> A highly non-intuitive and non-trivial axiom relating to HFFs is that the trace of the unit operator equals to 1. The intuitive idea is that the density matrix for an infinite-D system identified as a unit operator gives as its trace total probability equal to one. These factors emerge naturally for free fermions. For factors of type I associated with three bosons, the trace equals n in the n-D case and ∞ in the infinite-D case.
</p><p>
The factors of type I<sub>∞</sub> are tensor products of factors of type I and HFFs and could describe free bosons and fermions.
</p><p>
In quantum field theory (QFT), factors of type III appear and in this case the notion of trace becomes useless. These factors are pathological and in QFT they lead to divergence difficulties. The physical reason is the idea about point-like particles, leading in scattering amplitudes to powers of delta functions having no mathematical meaning. In the TGD framework, the generalization of a point-like particle to 3-surface saves from these difficulties and leads to factors of type I and HFFs.
</p><p>
Measurement resolution implies unique number theoretical discretization and further simplifies the situation in the TGD framework. In particular, "hyperfinite" expresses the fact that the approximation of a factor with its finite-D cutoff is an excellent approximation.
</OL>
One cannot avoid philosophical considerations related to the interpretations of quantum measurement theory. The standard interpretations are known to lead to problems in the case of HFFs.
<OL>
<LI> An important aspect related to the probabilistic interpretation is that physical states are characterized by a density matrix so that quantum theory reduces to probability theory, which would become in some sense non-commutative for von Neumann algebras.
</p><p>
The problem is that no pure normal states as counterparts of quantum states do not exist for HFFs. Furthermore, the phenomenon of interference central in quantum theory does not have a direct description. One can of course argue that in practice the system studied is entangled with the environment and that this forces the description in terms of a density matrix even when pure states are realized at the fundamental level.
<LI> TGD strongly suggests the generalization of the state as density matrix to a "complex square root" of density matrix proportional to exponent of a real valued Kähler function of WCW identified as Kähler action for the space-time region as a preferred extremal and a phase factor defined by the analog of of action exponential. The quantum state would be proportional to an exponent of Kähler function of WCW identified as Kähler action for space-time surface as a preferred extrema.
<LI> There are also problems with the interpretations of quantum theory, which actually strongly suggest that something is badly wrong with the standard ontology.
</p><p>
This requires a generalization of quantum measurement theory (see <a HREF= "https://tgdtheory.fi/public_html/articles/zeoquestions.pdf">this</A> and <a HREF= "https://tgdtheory.fi/pdfpool/ZEO.pdf">this</A>) based on zero energy ontology (ZEO) and Negentropy Maximization Principle (NMP) \cite{allb/nmpc}. The key motivation is that ZEO is implied by an almost exact holography forced by general coordinate invariance for space-times as 4-surface. That holography and, as a consequence, classical determinism are not quite exact, has important implications for the understanding of the space-time correlates of cognition and intentionality in the TGD framework.
</p><p>
In the TGD framework, the basic postulate is that quantum measurement as a reduction of entanglement can in principle occur for any entangled system pair.
</OL>
Consider now the standard construction leading to a hierarchy of HFFs and their inclusions.
<OL>
<LI> One starts from an inclusion M⊂ N of HFFs. I will later consider what these algebras could be in the TGD framework.
<LI> One introduces the spaces L<sup>2</sup>(M) <I> resp.</I> L<sup>2</sup>(N) of square integrable functions in M <I> resp.</I> N.
</p><p>
From the physics point of view, bringing in L<sup>2</sup> is something extremely non-trivial. Space is replaced with wave functions in space: this corresponds to what is done in wave mechanics, that is quantization! One quantizes in M, particles as points of M are replaced by wave functions in M, one might say.
<LI> At the next step one introduces the projection operator e as a projection from L<sup>2</sup>(N) to L<sup>2</sup>(M): this is like projecting wave functions in N to wave functions in M. I wish I could really understand the physical meaning of this. The induction procedure for second quantized spinor fields in H to the space-time surface by restriction is completely analogous to this procedure.
</p><p>
After that one generates a HFF as an algebra generated by e and L<sup>2</sup>(N): call it < L<sup>2</sup>(N), e>. One has now 3 HFFs and their inclusions: M<sub>0</sub>== M, M<sub>1</sub>== N, and < L<sup>2</sup>(N), e>== M<sub>2</sub>.
</p><p>
An interesting question is whether this process could generalize to the level of induced spinor fields?
<LI> Even this is not enough! One constructs L<sup>2</sup>(M<sub>2</sub>)== M<sub>3</sub> including M<sub>2</sub>. One can continue this indefinitely. Physically this means a repeated quantization.
</p><p>
One could ask whether one could build a hierarchy M<sub>0</sub>, L<sup>2</sup>(M<sub>0</sub>),..., L<sup>2</sup>(L<sup>2</sup>...(M<sub>0</sub>))..): why is this not done?
</p><p>
The hierarchy of projectors e<sub>i</sub> to M<sub>i</sub> defines what is called Temperley-Lieb algebra involving quantum phase q=exp(iπ/n) as a parameter. This algebra resembles that of S<sub>∞</sub> but differs from it in that one has projectors instead of group elements. For the braid group e<sub>i</sub><sup>2</sup>=1 is replaced with a sum of terms proportional to e<sub>i</sub> and unit matrix: mixture of projector and permutation is in question.
<LI> There is a fascinating connection in TGD and theory of consciousness. The construction of what I call infinite primes (see <a HREF= "https://tgdtheory.fi/pdfpool/visionc.pdf">this</A>) is structurally like repeated second quantization of a supersymmetric arithmetic quantum field theory involving fermions and bosons labelled by the primes of a given level I conjectured that it corresponds physically to quantum theory in the manysheeted space-time.
</p><p>
Also an interpretation in terms of a hierarchy of statements about statements about .... bringing in mind hierarchy of logics comes to mind. Cognition involves generation of reflective levels and this could have the quantization in the proposed sense as a quantum physical correlate.
</OL>
Connes tensor product is natural for modules having algebra as coefficients. For instance, matrix multiplication has an interpretation as Connes tensor product reduct tensor product of matrices to a matrix product. The number of degrees of freedom is reduced.
<OL>
<LI> Inclusion of Galois group algebra of extension to its extension could define Connes tensor product. Composite polynomial instead of product of polynomials: this would describe interaction physically: the degree of composite is product of degrees of factors and the same holds true for the product of polynomials. This rule for the dimensions holds also for the tensor product. Composite structure implies correlations and formation of bound states so that the number of degrees of freedom is reduced.
<LI> Also the inclusion SSA<sub>n+1</sub> to SSA<sub>n</sub> should define Connes tensor product. Note that the inclusions are in different directions. Could it be that these two inclusion sequences correspond to the sequences assignable to M and M'?
</p><p>
What about the already mentioned "classical" degrees of freedom associated with the fluxes of the induced Kähler form? Should one include the additional degrees of freedom to M' or are they dual to the number theoretic degrees of freedom assignable to Galois groups. How does the M<sup>8</sup>-H duality, relating number theoretic and geometric descriptions in analogy with Langlands duality, relate to this?
</OL>
I do not have an intuitive grasp about category theory. In any case, one would have a so-called 2-category (see <a HREF= "https://cutt.ly/3XkPO2s">this</A>). M and N correspond to 0-morphisms (objects). One can multiply L<sup>2</sup>(M) and L<sup>2</sup>(N) by M or N. The bimodules <sub>M</sub>L<sup>2</sup>(M)<sub>M</sub>, <sub>N</sub>L<sup>2</sup>(N)<sub>N</sub> correspond to 1-morphisms which are units whereas the bimodules <sub>M</sub>M<sub>N</sub>, and <sub>N</sub>M<sub>M</sub> correspond to generating 1-morphisms mapping M into N. Bimodule map corresponds to 2-morphisms. Connes tensor product defines a tensor functor.
</p><p>
Extended ADE Dynkin diagrams for ADE Lie groups, which correspond to finite subgroups of SU(2) by McKay correspondence, characterize inclusions of HFFs. For a subset of ADE groups not containing E<sub>7</sub> and D<sub>2n+1</sub>, there are inclusions, which correspond to Dynkin diagrams of finite subgroups of the quantum group SU(2)<sub>q</sub>. What is interesting that E<sub>6</sub> (tetrahedron) and E<sub>8</sub> (icosahedron/dodecahedron) appear in the TGD based model of bioharmony and genetic code but not E<sub>7</sub> (see <a HREF= "https://tgdtheory.fi/public_html/articles/TIH.pdf">this</A>).
<OL>
<LI> Why finite subgroups of SU(2) (or SU(2)<sub>q</sub>) should appear as characterizers of the inclusions in the tunnel hierarchies with the same value of the quantum dimension M<sub>n+1</sub>:M<sub>n</sub> of quantum algebra.
</p><p>
In the TGD interpretation M<sub>n+1</sub> reduces to a tensor product of M<sub>n</sub> and quantum group, when M<sub>n</sub> represents reduced measurement resolution and quantum group the added degrees of freedom. Quantum groups would represent the reduced degrees of freedom. This has a number theoretical counterpart in terms of finite measurement resolution obtained when an extension....of rationals is reduced to a smaller extension. The braided relative Galois group would represent the new degrees of freedom.
<LI> The identification of HFF as tensor product of GL(2,c) or GL(n,C) and the identification as analog of McKay graph for the irreps of a closed subgroup defines an invariant characterizing the fusion rules involved with the reduction of the tensor product is involved but I do not really understand this. What comes to mind is that all the essential features of tensor products of HFFs reduce to tensor products of finite subgroups of SU(2) or of SU(2)<sub>q</sub>.
<LI> In the TGD framework, SU(2) could correspond to a covering group of quaternionic automorphisms and number theoretic discretization (cognitive representations) would naturally lead to discrete and finite subgroups of SU(2).
</OL>
What could HFFs correspond to in TGD?
<OL>
<LI> Braid group B(G) of group (say Galois group as subgroup of S<sub>n</sub>) and its group algebra would correspond to B(G) and L<sup>2</sup>(B(G)).
<LI> Braided Galois group and its group algebra could correspond to B(G) and L<sup>2</sup>(B(G)). Composite polynomials define hierarchies of Galois groups such that the included Galois group is a normal subgroup. This kind of hierarchy could define an increasing sequence of inclusions of braided Galois groups.
<LI> Elements of SSA are labelled by non-negative integers. One can construct a hierarchy of subalgebras SSA<sub>n</sub> , such that elements with large conformal weight annihilate the physical state and also their commutators with SSA<sub>n</sub> do this. SSA<sub>n+1</sub> is included by SSA<sub>n</sub> and one has a kind of reversed sequence of inclusions.
<LI> Braided Galois groups and a hierarchy of SSA<sub>n</sub> could correspond to commuting algebras M and M'.
<LI> Question: Does the standard construction bring in something totally new to these hierarchies or is the resulting structure equivalent with that given by the standard construction?
</OL>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-86834637584284375742022-08-14T21:33:00.006-07:002022-08-14T22:30:31.521-07:00Do the inclusion hierarchies of extensions of rationals correspond to inclusion hierarchies of hyperfinite factors?
I have enjoyed discussions with Baba Ilya Iyo Azza about von Neumann algebras. Hyperfinite factors of type II<sub>1</sub> (HFF) (see <A HREF="https://cutt.ly/lXp6MDB">this</A>) are the most interesting von Neumann algebras from the TGD point of view. One of the conjectures motivated by TGD based physics, is that the inclusion sequences of extensions of rationals defined by compositions of polynomials define inclusion sequences of hyperfinite factors. It seems that this conjecture might hold true!
</p><p>
Already von Neumann demonstrated that group algebras of groups G satisfying certain additional constraints give rise to von Neumann algebras. For finite
groups they correspond to factors of type I in finite-D Hilbert spaces.
</p><p>
The group G must have an infinite number of elements and satisfy some additional conditions to give a HFF. First of all, all its conjugacy classes must have an infinite number of elements. Secondly, G must be amenable. This condition is not anymore algebraic. Braid groups define HFFs.
</p><p>
To see what is involved, let us start from the group algebra of a finite group G. It gives a finite-D Hilbert space, factor of type I.
<OL>
<LI> Consider next the braid groups B<sub>n</sub>, which are coverings of S<sub>n</sub>. One can check from Wikipedia that the relations for the braid group B<sub>n</sub> are obtained as a covering group of S<sub>n</sub> by giving up the condition that the permutations sigma<sub>i</sub> of nearby elements e<sub>i</sub>,e<sub>i+1</sub> are idempotent. Could the corresponding braid group algebra define HFF?
</p><p>
It is. The number of conjugacy classes g<sub>n</sub> σ<sub>i</sub>g<sub>n</sub><sup>-1</sup>, g<sub>n</sub> == σ <sub>n+1</sub> is infinite. If one poses the additional condition e<sub>i</sub><sup>2</sup>= U× 1, U a root of unity, the number is finite. Amenability is too technical a property for me but from Wikipedia one learns that all group algebras, also those of the braid group, are hyperfinite factors of type II<sub>1</sub> (HFFs).
<LI> Any finite group is a subgroup G of some S<sub>n</sub>. Could one obtain the braid group of G and corresponding group algebra as a sub-algebra of group algebra of B<sub>n</sub>, which is HFF. This looks plausible.
<LI> Could the inclusion for HFFs correspond to an inclusion for braid variants of corresponding finite group algebras? Or should some additional conditions be satisfied? What the conditions could be?
</OL>
Here the number theoretic view of TGD comes to rescue.
<OL>
<LI> In the TGD framework, I am primarily interested in Galois groups, which are finite groups. The vision/conjecture is that the inclusion hierarchies of extensions of rationals correspond to the inclusion hierarchies for hyperfinite factors. The hierarchies of extensions of rationals defined by the hierarchies of composite polynomials P<sub>n</sub> ˆ ...ˆ P<sub>1</sub> have Galois groups which define a hierarchy of relative Galois groups such that the Galois group G<sub>k</sub> is a normal subgroup of G<sub>k+1</sub>. One can say that the Galois group G is a semidirect product of the relative Galois groups.
<LI> One can decompose any finite subgroup to a maximal number of normal subgroups, which are simple and therefore do not have a further decomposition. They are primes in the category of groups.
<LI> Could the prime HFFs correspond to the braid group algebras of simple finite groups acting as Galois groups? Therefore prime groups would map to prime HFFs and the inclusion hierarchies of Galois groups induced by composite polynomials would define inclusion hierarchies of HFFs just as speculated.
</p><p>
One would have a deep connection between number theory and HFFs. This would also give a rather precise mathematical formulation of the number theoretic vision.
</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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com1tag:blogger.com,1999:blog-10614348.post-31082895897165300702022-08-12T23:04:00.002-07:002022-08-12T23:04:22.971-07:00Does the phenomenon of super oscillation challenge energy conservation?
The QuantaMagazine popular article
"Puzzling Quantum Scenario Appears Not to Conserve Energy" (see <A HREF="https://cutt.ly/QXylTIr">this</A>) told about puzzling observations the quantum physicists Sandu Popescu, Yakir Aharonov and Daniel Rohrlich made 1990 (see <A HREF="https://cutt.ly/3XylIY5">this</A>). These findings challenge energy conservation at the level of quantum theory.
</p><p>
The experiment of authors starts from the purely mathematical observation that a function can behave faster than any of the Fourier components in its Fourier transform when restricted to a volume smaller than the domain of Fourier transform. This is rather obvious since representing the restricted function as a Fourier transform in the smaller domain one obtains faster Fourier components. This phenomenon is called super oscillation.
</p><p>
Does this phenomenon have a quantum counterpart? The naive replacement of Fourier coefficients with oscillation operators for photons need not make sense. If one makes the standard assumption that classical states correspond to coherent states, also super-oscillations should correspond to a coherent state.
</p><p>
Coherent states are eigenstates of the annihilation operator and proportional to exponential exp(α a<sup>†</sup>)|0>, where "0" refers to the ground state an a<sup>†</sup> to creation operator. These states contain N-photon states with an arbitrarily large photon number. For some number of photons the probability is maximum.
</p><p>
This raises several questions.
<OL>
<LI> Coherent states are not eigen-states of energy: can one really accept this? This kind of situation is encountered also in the model of superconductivity assuming coherent state of Cooper pairs having an ill-defined fermion number.
<LI> Could the super oscillation correspond to the presence of N-photon states with a large number of photons? Could the state of n parallel photons behave like a Bose-Einstein condensate having N-fold total energy in standard physics or its modification, such as TGD?
</OL>
Authors tested experimentally whether the super-oscillation has a quantum counterpart. In an ideal situation one would have a single photon inside an effectively 1-D box. One opens the box for time T and inserts a mirror inside the box to the region where super oscillation takes place and the photon looks like a short wavelength photon. The mirror reflects the photon with some probability out of the box. If T is long one expects that the procedure does not affect the photon appreciably. What was observed were photons with the energy of a super photon rather than energy of any of its low energy components.
</p><p>
In the experiment described in the popular article, red light would correspond to photons with energy around 2 eV and gamma rays to photons with energies around MeV, a million times higher energy. The first guess of standard quantum theorists would be that the energies of mirrored photons are the same as for the photons in the box. Second guess would be that, if the coherent state corresponds to the super oscillation as a classical state, then the measured high energy photons could correspond to or result from collinear n-photon states present in the coherent state.
</p><p>
In the TGD framework zero energy ontology (ZEO) provides a solution to the problem related to the conservation of energy. In ZEO, quantum states are replaced by zero energy states as pairs of states assignable to the boundaries of causal diamond (intersection of light-cones with opposite time directions) with opposite total quantum numbers. By Uncertainty Principle this is true for Poincare charges only at an infinite volume limit for the causal diamond but this has no practical consequences. The members of the pair are analogs of initial and final states of a particle reaction. In ZEO, it is possible to have a superposition of pairs for which the energy of the state at either boundary varies. In particular, coherent states have a representation which does not lead to problems with conservation laws.
</p><p>
What about the measurement outcome? The only explanation for the finding that I can invent in TGD is based on the hierarchy phases of ordinary matter labelled by effective Planck constants and behaving like a hierarchy of dark matter predicted by the number theoretical vision of TGD.
<OL>
<LI> Dark photons with h<sub>eff</sub>= nh<sub>0</sub> > h can be formed from ordinary photons with h<sub>eff</sub>= h. The energy would be by a factor h<sub>eff</sub>/h larger than for an ordinary photon with the same wavelength. Note that dark photons play a key role in the TGD based view of living matter.
</p><p>
TGD also predicts dark N-photons as analogs of Bose-Einstein condensates. They are predicted by number theoretic TGD and there is empirical evidence for them (see <a HREF= "https://tgdtheory.fi/public_html/articles/fluteteleport.pdf">this</A>). This would require a new kind of interaction and number theoretical view about TGD predicts this kind of interaction based on the notion Galois confinement giving rise to N-photons as Galois confined bound states of virtual photons with energies give by algebraic integers for an extension of rationals defined by a polynomial defining the space-time region considered.
</p><p>
I have proposed an analogous energy conserving transformation of dark photon or dark N-photon to ordinary photon as an explanation for the mysterious production of bio-photons in biomatter. The original model for dark photons is discussed <a HREF= "https://tgdtheory.fi/pdfpool/biohotonslian.pdf">here</A>. Now the value of h<sub>eff</sub> could be much larger: as large as h<sub>eff</sub> ≈ 10<sup>14</sup>: in this case the wavelength would be of order Earth size scale.
<LI> What comes to mind is that an N-photon state present in the coherent state can transform to a single photon state with N-fold energy. In the standard model this is not possible. On the other hand, in the experiments, discussed from the TGD point of view in <a HREF= "https://tgdtheory.fi/public_html/articles/fluteteleport.pdf">here</A>, it is found that N-photon states behaving like a single particle are produced. Could the N-photon states present in a coherent state be Galois confined bound states or could they transform to such states with some probability?
</p><p>
In the recent case, the dark photons would have the same wavelength as red photons in the box but energy would be a million times higher. Could a dark photon or N-photon with Nh<sub>eff</sub>/h ≈ 10<sup>6</sup> be reflected from the mirror and transform to an ordinary photon with gamma ray energy.
</p><p>
One must notice that the real experiment must use many-photon states N-photons might be also formed from N separate photons.
</OL>
To sum up, new physics would be involved. ZEO is needed to clarify the issues related to energy conservation and the number theoretic physics predicting dark matter hierarchy is needed to explain the observation of high energy photons.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/TGDcondmatshort.pdf">TGD and condensed matter</A> of 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>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-49768814788707259942022-08-10T22:17:00.006-07:002022-08-10T22:20:09.951-07:00Chemical bonds as flux tube links and realization of dark codons using only dark protons
In the proposed model of dark DNA, one must assume that the dark codon is formed by a triplet of dark nucleons (proton and neutron). In the TGD framework one could justify the presence of neutrons by the large value of Planck constant increasing the weak scale to at least atomic length scale so that weak bosons would behave like massless particles in atomic scales at the MB. Therefore the dark protons could transform to dark neutrons easily. Neutron would be connected to either neighbor by a meson-like flux tube bond which is positively charged so that each codon would have a charge of 3 units neutralized by an opposite charge of 3 phosphates.
</p><p>
The introduction of neutrons brings in an additional bit. Therefore one could use only dark protons, if one could bring in this additional bit in some way. An obvious candidate would be the direction of a monopole magnetic flux assignable to the letter of the codon as a closed flux tube with respect to reference direction defined by the DNA sequence. If the letters of codon are closed linked flux tubes containing dark protons forming dark DNA as a chain, this kind of option might work. Consider first the topology of the monopole flux tubes.
<OL>
<LI> Magnetic monopole flux tubes correspond to closed 3-surfaces in the TGD framework. They are closed because the boundary conditions do not allow boundaries with a monopole charge nor boundaries at all. In dimension 3, these flux tubes can become knotted and closed flux tubes can get linked.
<LI> If one has a braiding of N flux tubes, one can connect the ends of the N flux tubes. There are many manners to connect the ends, and one obtains at most N linked closed flux tubes, which are knots. The simplest option is that the ends of each braid strand are connected so that one has N linked flux tubes. This corresponds to the "upper" ends as a trivial permutation of the "lower" ends.
<LI> Any permutation in the permutation group S<sub>N</sub> is possible. A given permutation can be expressed as a product of permutations such that each permutation leaves invariant a subset. Permutations are therefore characterized by a partition of N objects to subsets such that the given set consist of N<sub>i</sub> objects with ∑ N<sub>i</sub>=N and that these sets do not decompose to smaller subsets. The allowed permutations for N<sub>i</sub> objects correspond to elements of the cyclic group Z<sub>N<sub>i</sub></sub>. These cyclic permutations give rise to a single closed tube when the ends of the braid ends and permuted braid ends are connected. The number of closed flux tubes is therefore the number of summands in ∑ N<sub>i</sub>=N.
These permutations are obtained by reconnections from the permutation corresponding to N closed loops so that there are two levels: the level of braiding and the level of reconnections behind the stages not visible in the properties of the braiding.
</OL>
Linking is a metaphor for bonding. One speaks of the chain of generations, of a weak link in the chain, etc.
<OL>
<LI> Chemical bonds are classified into ionic bonds, valence bonds involving delocalization of electrons, and hydrogen bonds involving delocalization of protons. Chemical bonds are not well-understood in the framework of standard chemistry. TGD suggests that they involve space-time topology: monopole flux tube pairs would be associated with the bonds and the splitting of the bond would correspond to a reconnection splitting the pair to two U-shaped flux tubes. Flux tubes and connecting molecules as nodes are proposed to form a network.
<LI> I have not considered in detail how the U-shaped flux tubes are associated with the nodes. Bonding=linking metaphor encourages a crazy question. The members of the flux tube pairs, which are proposed to connect molecules, which serve as nodes of a network . These flux tubes must close and could be linked with shorter closed flux tubes assignable to molecules.
<LI> Could this linking bind the molecules and atoms to a single topological structure. If so, both chemistry and topological quantum computation (TQC) in the TGD framework would involve linking, braiding, and reconnections as new topological elements. Biomatter at molecular level would consist of chains of closed flux tubes which can be also stretched and give rise to braids.
</p><p>
Note that 2 U-shaped flux tubes can reconnect and this transition can lead to a pair of flux tubes or to a linked pair of U-shaped flux tubes so that 3 different states are possible.
<LI> I have proposed that the pairing of molecules by a pair of monopole flux tubes serves as a correlate for entanglement. If dark protons are associated with closed flux tubes, they must entangle. Could also the linking of the U-shaped flux tubes give rise to entanglement? Stable linking correlates the positions of the flux tubes but this need not mean entanglement since wave function can be a product of wave functions in cm coordinates and relative coordinates.
</OL>
Linking as an additional topological element inspires some quantum chemical and -biological speculations.
<OL>
<LI> Could the presence of valence-/hydrogen bonds involve a closed flux tube at which the electron (pair)/proton is delocalized and that this flux tube is linked with another such flux tube. This picture is consistent with the proposed role of quantum gravitation in metabolism (see <a HREF= "https://tgdtheory.fi/public_html/articles/penrose.pdf">this</A>) and generation of the predecessor of the nervous system (see <a HREF= "https://tgdtheory.fi/public_html/articles/precns.pdf">this</A>) based on ver,y long variants of hydrogen bonds characterized by gravitational Planck constant. In this view, living matter would be an extremely highly organized structure whereas in the standard chemistry organism would be a soup of biomolecules.
<LI> What comes to mind as an example, is the secondary structure of proteins (see <A HREF="https://cutt.ly/sZ5rRiQ">this</A>) involving α- helices, β-strands and β-sheets. Tertiary structure refers to 3-D structure created by a single protein molecule. It can have several domains. There are also quaternary structures formed by several polypeptide chains. Proteins consist of relatively few substructures known as domains, motives and folds. Could these structures involve braided and linked flux tube structures with dynamical reconnections?
</OL>
Consider now a possible model of dark DNA involving only dark protons.
<OL>
<LI> One can imagine that dark protons are associated with closed flux tubes acting as hydrogen bonds, such that 3 closed flux tubes as letters are linked to form a dark codon. The dark codons could in turn be linked to form genes as sequences of codons. The direction of the magnetic flux can be opposite or parallel to that of the chain so that each closed flux tube represents a bit of topological information. The chains of links would define sequences of bits and even qubits. Could this define the predecessor of the genetic code for which letter represents a single bit?
<LI> If one has only dark protons, one obtains only 32 dark codons. An additional bit is required to get 64 codons. Could the direction of the closed flux tube in the chain provide the missing bit?
</OL>
It is known that the genetic code has a slightly broken symmetry with respect to the last letter of the codon. For almost all RNA codons U and C resp. A and G define code for the same amino-acid. An attractive interpretation of the symmetry is that this symmetry is that U-C pair and A-G pair correspond to the bits defined by magnetic flux so that the sign of magnetic flux would not matter much at the level of proteins. For this interpretation, the additional bit would not mean much at the level of proteins.
</p><p>
This need not be the case at the level of dark codons. In (see <a HREF= "https://tgdtheory.fi/public_html/articles/fluteteleport.pdf">this</A>) it was found that the earlier 1-1 correspondence between dark codons and ordinary genetic codons is unnecessarily strict and a modification of the earlier picture of the relation between dark and chemical genetic code and of the function of dark genetic code was considered.
<OL>
<LI> Dark DNA (DDNA) strand is dynamical and has the ordinary DNA strand associated with it and dark gene state can be in resonant interaction with ordinary gene only when it corresponds to the ordinary gene. This applies also to DRNA, DtRNA and DAA (AA is for amino acids).
</p><p>
This would allow DDNA, DRNA, DtRNA and DAA to perform all kinds of information processing such as TQC by applying dark-dark resonance in quantum communications. The control of fundamental biomolecules by their dark counterparts by energy resonance would be only one particular function.
<LI> Most importantly, flux tubes magnetization direction could define qubit. If the additional qubit corresponds to nucleon isospin, it is not clear whether this is the case. One can also allow superpositions of the dark genes representing 6-qubit units. A generalization of quantum computation so that it would use 6-qubits units instead of a single qubit as a unit, is highly suggestive.
<LI> Genetic code code could be also interpreted as an error code in which dark proteins correspond to logical 6-qubits and the DNA codons coding for the protein correspond to the physical qubits associated with the logical qubit.
<LI> The teleportation mechanism discussed in (see <a HREF= "https://tgdtheory.fi/public_html/articles/penrose.pdf">this</A>) could make possible remote replication and remote transcription of DNA by sending the information about the ordinary DNA strand to the corresponding dark DNA strand by energy resonance. After that, the information would be teleported to a DNA strand in a ferromagnetic ground state at the receiver. After this, ordinary replication or transcription, which would also use the resonance mechanism, would take place.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/darkcode.pdf">The Realization of Genetic Code in Terms of Dark Nucleon and Dark Photon Triplets</A> or the <a HREF= "https://tgdtheory.fi/pdfpool/darkcode.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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-50848332575665325502022-08-09T02:44:00.005-07:002022-08-09T23:48:51.571-07:00Ultradiffuse galaxies as a problem of cold dark matter and MOND scenarios
The existence of ultradiffuse galaxies for which the velocity of distant rotating stars is extremely low (see <A HREF="https://www.science-astronomy.com/2022/08/in-wild-twist-physicists-have-revived.html">this</A>), means difficulties for the cold dark matter scenario since in some cases there seems to be no dark matter at all, and in some cases there seems to be only dark matter. These objects has been proposed as a support for MOND, but also MOND has grave difficulties with them.
</p><p>
The problem in the case of galaxy AGC 114905 is(see <A HREF="https://earthsky.org/space/dark-matter-missing-from-galaxy-agc-114905/">this</A>) is dcussed in a popular article "In a Wild Twist, Physicists Have Revived an Alternative Theory of Gravity" published in Science-Astronomy (<A HREF="https://cutt.ly/UZ9zBMh">this</A>). This galaxy is of the same size as Milky Way and seems to have very small amount of dark matter, if any.
</p><p>
Mancera Pina et al (see <A HREF="https://doi.org/10.1093/mnras/stab3491">this</A>)argue that both cold dark matter scenario and MOND fail to explain the anomalously low value of the rotation velocity of distant stars. The proposal of Banik et al (see <A HREF="https://doi.org/10.1093/mnras/stac1073">this</A>) is that the inclination between the galactic disc and skyplane is overestimated, which leads to a too small estimate for the estimate for the rotation velocity so that MOND could be saved.
</p><p>
In the TGD framework (see <A HREF="https://tgdtheory.fi/public_html/articles/meco.pdf">this</A>,
<A HREF="https://tgdtheory.fi/public_html/articles/galaxystars.pdf">this</A>, and
<A HREF="https://tgdtheory.fi/public_html/articles/galjets.pdf">this</A>), the rotation velocity is proportional to the square root of the product GT, where T is the string tension of a long magnetic flux tube formed from a cosmic string carrying dark energy and possibly also matter. In the ordinary situation, the flux tube would be considerably thickened only in a tangle associated with the galaxy as part of volume- and magnetic energies would have decayed to ordinary matter, in analogy with the decay of inflaton field. </p><p>
If the flux tube itself has a very long thickened portion such that ordinary matter has left this region by free helical motion along the string or by gravitational attraction of some other object, the string tension T is small and very small velocity is possible. Ordinary bound state of matter is not necessary since the gravitational force of the flux tubes binds the stars. This might explain why the galaxy can be ultradiffuse.
</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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-54504420207139590732022-08-09T01:06:00.004-07:002022-08-09T01:06:36.982-07:00Is pair creation really understood in the twistorial picture?
Twistorialization leads to a beautiful picture about scattering amplitudes at the level of M<sup>8</sup> (see <a HREF= "https://tgdtheory.fi/pdfpool/twistgd.pdf">this</A>). In the simplest picture, scattering would be just a re-organization of Galois singlets to new Galois singlets. Fundamental fermions would move as free particles.
</p><p>
The components of the 4-momentum of virtual fundamental fermion with mass m would be algebraic integers and therefore complex. The real projection of 4-momentum would be mapped by M<sup>8</sup>-H duality to a geodesic of M<sup>4</sup> starting from either vertex of the causal diamond (CD) . Uncertainty Principle at classical level requires inversion so that one has a= ℏ<sub>eff</sub>/m, where ab denotes light-cone proper time assignable to either half-cone of CD and m is the mass assignable to the point of the mass shell H<sup>3</sup>⊂ M<sup>4</sup>⊂ M<sup>8</sup>.
</p><p>
The geodesic would intersect the a=ℏ<sub>eff</sub>/m 3-surface and also other mass shells and the opposite light-cone boundaries of CDs involved. The mass shells and CDs containing them would have a common center but Uncertainty Principle at quantum level requires that for each CD and its contents there is an analog of plane wave in CD cm degrees of freedom.
</p><p>
One can however criticize this framework. Does it really allow us to understand pair creation at the level of the space-time surfaces X<sup>4</sup>⊂ H?
<OL>
<LI> All elementary particles consist of fundamental fermions in the proposed picture. Conservation of fermion number allows pair creation occurring for instance in the emission of a boson as fermion-antifermion pair in f→ f+b vertex.
<LI> The problem is that if only non-space-like geodesics of H are allowed, both fermion and antifermion numbers are conserved separately so that pair creation does not look possible. Pair creation is both the central idea and source of divergence problems in QFTs.
<LI> One can identify also a second problem: what are the anticommutation relations for the fermionic oscillator operators labelled by tachyonic and complex valued momenta? Is it possible to analytically continue the anticommutators to complexified M<sup>4</sup>⊂ H and M<sup>4</sup>⊂ M<sup>8</sup>? Only the first problem will be considered in the following.
</OL>
Is it possible to understand pair creation in the proposed picture based on twistor scattering amplitudes or should one somehow bring the bff 3-vertex or actually ff fbar fbar vertex to the theory at the level of quark lines? This vertex leads to a non-renormalizable theory and is out of consideration.
</p><p>
One can first try to identify the key ingredients of the possible solution of the problem.
<OL>
<LI> Crossing symmetry is fundamental in QFTs and also in TGD. For non-trivial scattering amplitudes, crossing moves particles between initial and final states. How should one define the crossing at the space-time level in the TGD framework? What could the transfer of the end of a geodesic line at the boundary of CDs to the opposite boundary mean geometrically?
<LI> At the level of H, particles have CP<sub>2</sub> type extremals - wormhole contacts - as building bricks. They have an Euclidean signature (of the induced metric) and connect two space-time sheets with a Minkowskian signature.
</p><p>
The opposite throats of the wormhole contacts correspond to the boundaries between Euclidean and Minkowskian regions and their orbits are light-like. Their light-like boundaries, orbits of partonic 2-surfaces, are assumed to carry fundamental fermions. Partonic orbits allow light-like geodesics as possible representation of massless fundamental fermions.
</p><p>
Elementary particles consist of at least two wormhole contacts. This is necessary because the wormhole contacts behave like Kähler magnetic charges and one must have closed magnetic field lines. At both space-time sheets, the particle could look like a monopole pair.
<LI> The generalization of the particle concept allows a geometric realization of vertices. At a given space-time sheet a diagram involving a topological 3-vertex would correspond to 3 light-like partonic orbits meeting at the partonic 2-surface located in the interior of X<sup>4</sup>. Could the topological 3-vertex be enough to avoid the introduction of the 4-fermion vertex?
</OL>
Could one modify the definition of the particle line as a geodesic of H to a geodesic of the space-time surface X<sup>4</sup> so that the classical interactions at the space-time surface would make it possible to describe pair creation without introducing a 4-fermion vertex? Could the creation of a fermion pair mean that a virtual fundamental fermion moving along a space-like geodesics of a wormhole throat turns backwards in time at the partonic 3-vertex. If this is the case, it would correspond to a tachyon. Indeed, in M<sup>8</sup> picture tachyons are building bricks of physical particles identified as Galois singlets.
<OL>
<LI> If fundamental fermion lines are geodesics at the light-like partonic orbits, they can be light-like but are space-like if there is motion in transversal degrees of freedom.
<LI> Consider a geodesic carrying a fundamental fermion, starting from a partonic 2-surface at either light-like boundary of CD. As a free fermion, it would propagate to the opposite boundary of CD along the wormhole throat.
</p><p>
What happens if the fermion goes through a topological 3-vertex? Could it turn backwards in time at the vertex by transforming first to a space-like geodesic inside the wormhole contact leading to the opposite throat and return back to the original boundary of CD? It could return along the opposite throat or the throat of a second wormhole contact emerging from the 3-vertex. Could this kind of process be regarded as a bifurcation so that it would correspond to a classical non-determinism as a correlate of quantum non-determinism?
<LI> It is not clear whether one can assign a conserved space-like M<sup>4</sup> momentum to the geodesics at the partonic orbits. It is not possible to assign to the partonic 2-orbit a 3-momentum, which would be well-defined in the Noether sense but the component of momentum in the light-like direction would be well-defined and non-vanishing.
</p><p>
By Lorentz invariance, the definition of conserved mass squared as an eigenvalue of d'Alembertian could be possible. For light-like 3-surfaces the d'Alembertian reduces to the d'Alembertian for the Euclidean partonic 2-surface having only non-positive eigenvalues. If this process is possible and conserves M<sup>4</sup> mass squared, the geodesic must be space-like and therefore tachyonic.
</p><p>
The non-conservation of M<sup>4</sup> momentum at single particle level (but not classically at n-particle level) would be due to the interaction with the classical fields.
<LI> In the M<sup>8</sup> picture, tachyons are unavoidable since there is no reason why the roots of the polynomials with integer coefficients could not correspond to negative and even complex mass squared values. Could the tachyonic real parts of mass squared values at M<sup>8</sup> level, correspond to tachyonic geodesics along wormhole throats possibly returning backwards along the another wormhole throat?
</OL>
How does this picture relate to p-adic thermodynamics (see <a HREF= "https://tgdtheory.fi/public_html/articles/padmass2022.pdf">this</A>) as a description of particle massivation?
<OL>
<LI> The description of massivation in terms of p-adic thermodynamics suggests that at the fundamental level massive particles involve non-observable tachyonic contribution to the mass squared assignable to the wormhole contact, which cancels the non-tachyonic contribution.
</p><p>
All articles, and for the most general option all quantum states could be massless in this sense, and the massivation would be due the restriction of the consideration to the non-tachyonic part of the mass squared assignable to the Minkowskian regions of X<sup>4</sup>.
<LI> p-Adic thermodynamics would describe the tachyonic part of the state as "environment" in terms of the density matrix dictated to a high degree by conformal invariance, which this description would break. A generalization of the blackhole entropy applying to any system emerges and the interpretation for the fact that blackhole entropy is proportional to mass squared. Also gauge bosons and Higgs as fermion-antifermion pairs would involve the tachyonic contribution and would be massless in the fundamental description.
<LI> This could solve a possible and old problem related to massless spin 1 bosons. If they consist of a collinear fermion and antifermion, which are massless, they have a vanishing helicity and would be scalars, because the fermion and antifermion with parallel momenta have opposite helicities. If the fermion and antifermion are antiparallel, the boson has correct helicity but is massive.
</p><p>
Massivation could solve the problem and p-adic thermodynamics indeed predicts that even photons have a very small thermal mass. Massless gauge bosons (and particles in general) would be possible in the sense that the positive mass squared is compensated by equally small tachyonic contribution.
<LI> It should be noted however that the roots of the polynomials in M<sup>8</sup> can also correspond to energies of massless states. This phase would be analogous to the Higgs=0 phase. In this phase, Galois symmetries would not be broken: for the massive phase Galois group permutes different mass shells (and different a=constant hyperboloids) and one must restrict Galois symmetries to the isotropy group of a given root. In the massless phase, Galois symmetries permute different massless momenta and no symmetry breaking takes place.
</OL>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/twisttgd1.pdf">About TGD counterparts of twistor amplitudes: part II</A> or the chapter <A HREF="https://tgdtheory.fi/pdfpool/twisttgd.pdf">About TGD counterparts of twistor amplitudes</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-91679824561690209472022-08-08T00:30:00.002-07:002022-08-08T04:18:00.302-07:00Universe as a dodecahedron?: two decades later
I encountered a link to a popular article in Physics World with the title "Is the Universe a dodecahedron" (see <A HREF="https://physicsworld.com/a/is-the-universe-a-dodecahedron/">this</A>) telling about the proposal of Luminet et al that the Universe has a geometry of dodecahedron. I have commented on this finding almost 20 years ago (see <a HREF= "https://tgdtheory.fi/pdfpool/cosmo.pdf">this</A>). A lot has happened during these two decades and it is interesting to take a fresh TGD inspired view.
</p><p>
In the TGD framework, one can imagine two starting points concerning the explanation of the findings.
<OL>
<LI> Could there be a connection with the redshift quantization along some lines ("God's fingers"") proposed by Halton Arp (see <A HREF="https://en.wikipedia.org/wiki/Halton_Arp">this</A>) and Fang-Sato. I have considered several explanations for the quantization. In TGD cosmic=time constant surface corresponds to hyperbolic 3-space H<sup>3</sup> of Minkowski space in TGD. H<sup>3</sup> allows an infinite number of tessellations (lattice-like structures).
</p><p>
I have proposed an explanation for the redshift quantization in terms of tessellations of H<sup>3</sup>. The magnetic bodies (MBs) of astrophysical objects and even objects themselves could tend to locate at the unit cells of the tessellation.
<LI> Icosa-tetrahedral tessellation (lattice-like structure in hyperbolic space H<sup>3</sup>) plays a key role in the TGD model of genetic code (see <A HREF ="https://tgdtheory.fi/public_html/articles/TIH.pdf">this</A>) suggested to be universal. Lattice-like structures make possible diffraction if the incoming light has a wavelength, which is of the same order as the size of the unit cell.
</OL>
In the sequel I will consider only the latter option.
<OL>
<LI> In X ray diffraction, the diffraction pattern reflects the structure of the dual lattice: the same should be true now. Only the symmetries of the unit cell are reflected in diffraction. If CMB is diffracted in the tessellation, the diffraction pattern reflects the symmetries of the dual of the tessellation and does not depend on the value of the effective Planck constant h<sub>eff</sub>. Large values of Planck constant make possible large crystal-like structures realized as part of the magnetic body having large enough size, now realized at the magnetic body (MB).
<LI> Icosatetrahedral tessellation plays a key role in the TGD inspired model of the genetic code. Dodecahedron is the dual of icosahedron and tetrahedron is self-dual! [Note however that also the octahedron is involved with the unit cell although "icosa-tetrahedral" does not reflect its presence. Cube is the dual of the octahedron.]
</p><p>
So: could the gravitational diffraction of CMB on a local crystal having the structure of icosa-tetrahedral tessellation create the illusion that the Universe is a dodecahedron?
</OL>
Could the possible dark part of the CMB radiation diffract in local tessellations assigned with the local MBs?
<OL>
<LI> In diffraction, the wavelength of diffracted radiation must correspond to the size of the unit cell of the lattice-like structure involved. The maximum wavelength of CMB intensity as function of wavelength corresponds to a wavelength of about .5 cm. Can one imagine a tessellation with the unit cell of size about .5 cm?
<LI> The gravitational Planck constant ℏ<sub>gr</sub> =GMm/β<sub>0</sub>, where M is large mass and m a small mass, say proton mass (see <A HREF ="https://tgdtheory.fi/pdfpool/astro.pdf">this</A>, <A HREF ="https://tgdtheory.fi/public_html/articles/vzero.pdf">this</A>, <A HREF ="https://tgdtheory.fi/public_html/articles/mseeg.pdf">this</A>, <A HREF ="https://tgdtheory.fi/public_html/articles/penrose.pdf">this</A> and <A HREF ="https://tgdtheory.fi/public_html/articles/precns.pdf">this</A>). Both masses are assignable to the monopole flux tubes mediating gravitational interaction. β<sub>0</sub>=v<sub>0</sub>/c is velocity parameter and near to unity in the case of Earth.
<LI> The size scale of the unit cell of the dark gravitational crystal would be naturally given by Λ<sub>gr</sub> = ℏ<sub>gr</sub>/m= GM/β<sub>0</sub> and would be depend on M only and would be rather large and depend on the local large mass M, say that of Earth. Λ<sub>gr</sub> does not depend on m (Equivalence Principle).
<LI> For Earth, the size scale of the unit cell would be of the order of Λ<sub>gr</sub>= GM<sub>E</sub>/β<sub>0</sub> ≈ .45 cm, where β<sub>0</sub>= 0=v<sub>0</sub>/c ≈ 1 is near unity from the experimental inputs emerging from quantum hydrodynamics (see <A HREF ="https://tgdtheory.fi/public_html/articles/TGDhydro.pdf">this</A>) and quantum model of EEG (see <A HREF ="https://tgdtheory.fi/public_html/articles/mseeg.pdf">this</A>) and quantum gravitational model for metabolism (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>). Λ<sub>gr</sub> could define the size of the unit cell of the icosa-tetrahedral tessellation. Note that Earth's Schwartschild radius r<sub>S</sub>=2GM≈ .9 cm.
</p><p>
Encouragingly, the wavelength of CMB intensity as a function of wavelength around .5 cm to be compared with Λ<sub>gr</sub> ≈ .45 cm! Quantum gravitational diffraction might take place for dark CMB and give rise to the diffraction peaks!
<LI> Diffraction pattern would reflect astroscopic quantum coherence, and the findings of Luminet et al could have an explanation in terms of the geometry of local gravitational MB rather than the geometry of the Universe! Diffraction could also explain the strange deviations of CMB correlation functions from predictions for large values of the angular distance. It might be also possible to understand the finding that CMB seems to depend on the features of the local environment of Earth, which is in a sharp conflict with the cosmological principle. According to Wikipedia article (see <A HREF ="https://cutt.ly/YZXJ7ao">this</A>), even in the COBE map, it was observed that the quadrupole (l=2, spherical harmonic) has a low amplitude compared to the predictions of the Big Bang. In particular, the quadrupole and octupole (l=3) modes appear to have an unexplained alignment with each other and with both the ecliptic plane and equinoxes.
<LI> Could the CMB photon transform to a gravitationally dark photon in the diffraction? This would be a reversal for the transformation of dark photons to ordinary photons interpreted as biophotons. Also in quantum biology the transformation of ordinary photons to dark ones takes place. If so the wave length for a given CMB photon would be scaled up by the factor ℏ<sub>gr</sub>/ℏ =(GM<sub>E</sub>m/β<sub>0</sub>)/ℏ ≈ 3.5× 10<sup>12</sup> for proton. This gives Λ=1.75 × 10<sup>7</sup> km, to be compared with the radius of Earth about 6.4× 10<sup>6</sup> km.
</OL>
See the chapter <a HREF= "https://tgdtheory.fi/pdfpool/cosmo.pdf">TGD and cosmology</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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A></p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-20501350582040184772022-08-04T21:31:00.005-07:002022-08-08T03:39:47.141-07:00Antipodal duality and TGD
The so called antipodal duality has received considerable attention. The calculations of Dixon et al based on the earlier calculations of Goncharow et al suggests a new kind of duality relating color and electroweak interactions. The calculations lead to an explicit formula for the loop contributions to the 6-gluon scattering amplitude in <I>N</I>=4 SUSY. The new duality and relates 6-gluon amplitude for the forward scattering to a 3-gluon form factor of stress tensor analogous to a quantum field describing a scalar particle. This amplitude can be identified as a contribution to the scattering amplitude h+g→ g+g at the soft limit when the stress tensor particle scatters in forward direction. The result is somewhat mysterious since in the standard model strong and electroweak interactions are completely separate.
</p><p>
In TGD, there are indeed quite a number of pieces of evidence for this kind of duality but the possibility that only electroweak or color interactions could provide a full description of scattering amplitudes. The number-theoretical view of TGD could however come into rescue.
</p><p>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/antipodalTGD.pdf">Antipodal duality and TGD</A> or the chapter <a HREF= "https://tgdtheory.fi/pdfpool/twisttgd.pdf">About TGD counterparts of twistor amplitudes</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A></p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-40237385367592675502022-08-03T01:47:00.002-07:002022-08-03T01:47:10.721-07:00Quantization of cosmic redshifts in the TGD framework
In a FB discussion Jivan Coquat asked for my opinion about Halton Arp (see <A HREF="https://en.wikipedia.org/wiki/Halton_Arp">this</A>).
</p><p>
Halton Arp brings to my mind redshift quantization along lines, which has been considered also by Fang-Sato, who talked of "God's fingers". I have considered several explanations for the quantization.
<OL>
<LI> To my opinion, the most convincing explanation is in terms of lattice-like structures, tessellations, in hyperbolic space H<sup>3</sup>, which corresponds to cosmic time a= constant hyperboloid of future light-one (see <A HREF="https://tgdtheory.fi/pdfpool/selforgac.pdf">this</A>).
<LI> H<sup>3</sup> allows an infinite number of tessellations, which correspond to discrete subgroups of Lorentz group SO(1,3) having as covering SL(2,C) (spinors). In E<sup>3</sup> only 17 lattices are possible. The so called icosa-tetrahedral tessellation is in a key role in TGD model of genetic code realized at a deeper level in terms of dark (h<sub>eff</sub>=nh<sub>0</sub>>h) proton triplets and flux tubes of magnetic body (see <A HREF="https://tgdtheory.fi/public_html/articles/TIH.pdf">this</A>).
<LI> For lattices in the Euclidean space E<sup>3</sup>, the radial distance from origin is quantized. For H<sup>3</sup> redshift proportional to H<sup>3</sup> distance replaces Euclidian radial distance and the tessellation gives redshift quantization. Astrophysical objects would tend to be associated with the unit cells of the tessellation.
<LI> The tessellation itself could be associated with the magnetic (/field) body carrying dark matter in the TGD sense as h<sub>eff</sub>=nh<sub>0</sub>>h phases: this is a prediction of number theoretic vision about physics as dual of geometric vision. Very large values of h<sub>eff</sub> =h<sub>gr</sub>= GMm/v<sub>0</sub> (Nottale hypothesis for gravitational Planck constant, see <a HREF= "https://tgdtheory.fi/pdfpool/astro.pdf">this</A>) assignable to gravitational flux tubes are possible, and this makes these tessellations possible as gravitationally quantum coherent structures even in cosmological scales. This is a diametric opposite to what superstring models where quantum gravitation appears only in Planck length scale, suggests.
</OL>
See the chapter (see <A HREF="https://tgdtheory.fi/pdfpool/selforgac.pdf">Quantum Theory of Self-Organization</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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A></p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-72560576467718720062022-08-03T01:26:00.001-07:002022-08-03T01:26:37.680-07:00The mysterious precession of the Earth's spin axis from the TGD point of view
These comments were inspired by two interesting Youtube videos by Sören Backman (see <A HREF="https://www.youtube.com/watch?v=-oPE3l5E8uk">this</A> and
<A HREF="https://www.youtube.com/watch?v=kLfoy5V7CRE">this</A>) with a provocative title "Gravity's biggest failure - precession, what is it hiding". The precession of the Earth's spin axis cannot be explained as an effect caused by other planets and Sun and even the nearest stars are too far in order to explain the precession as an effect caused by them. Precession is therefore a real problem for the standard view of gravitation.
</p><p>
The proposal for the explanation of the precession of Earth discussed in the videos is inspired by the notion of Electric Universe, and has several similarities with the TGD inspired model. I could expect this from my earlier discussions with the proponents of Electric Universe. About 3 years ago, I wrote a chapter inspired by these discussions (see <A HREF ="https://tgdtheory.fi/public_html/articles/electricuniverse.pdf">this</A>).
</p><p>
My view is that the extremist view that gravitation reduces to electromagnetism is wrong but that electromagnetism, in particular magnetic fields, have an important role even in cosmological scales. In standard physics, magnetic fields in long scales would require coherent currents, which tend to be random and dissipate. Even the understanding of the stability of the magnetic field of Earth is a challenge, to say nothing of the magnetic fields able to survive in cosmological scales. In TGD, monopole flux tubes define magnetic fields which need no currents as sources.
</p><p>
Consider first monopole flux tubes, which are present in all length scales in the TGD Universe and distinguish TGD from both Maxwell's electrodynamics and general relativity.
<OL>
<LI> Flux tubes can carry monopole flux, in which case they are highly stable. The cross section is not a disk but a closed 2-surface so that no current is needed to create the magnetic flux. The flux tubes with vanishing flux are not stable against splitting.
<LI> Flux tubes relate to the model for the emergence of galaxies (see <A HREF="https://tgdtheory.fi/public_html/articles/meco.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/galaxystars.pdf">this</A>) and explain galactic jets propagating along flux tubes (see <A HREF="https://tgdtheory.fi/public_html/articles/galjets.pdf">this</A>). Dark energy and possible matter assignable to the cosmic strings predicts correctly the flat velocity spectrum of stars around galaxies.
<LI> In the MOND model it is assumed that the gravitational force transforms for certain critical acceleration from 1/r<sup>2</sup> to 1/r force. In TGD this would mean that the 1/ρ forces caused by the cosmic string would begin to dominate over the 1/rho<sup>2</sup> force. The predictions of MOND TGD are different since in TGD the motion takes place in the plane orthogonal to the cosmic string.
<LI> The flux tubes can appear as torus-like circular loops. Also flux tube pairs carrying opposite fluxes, resembling a DNA double strand, are possible and might be favoured by stability. Flux tubes are possible in all scales and connect astrophysical structures to a fractal quantum network. The flux tubes could connect to each other nodes, which are deformations of membrane-like entities having 3-D M<sup>4</sup> projections and 2-D E<sup>3</sup> projections (time= constant) (also an example of "non-Einsteinian" space-time surface).
<LI> Pairs of monopole flux tubes with opposite direction of fluxes can connect two objects: this could serve as a prerequisite of entanglement. The splitting of a flux tube pair to a pair of U-shaped flux tubes by a reconnection in a state function reduction destroying the entanglement. Reconnection would play an essential role in bio-catalysis.
<LI> Flux tube pairs can form helical structures and stability probably requires helical structure. Cosmic analog of DNA could be in question: fractality and gravitational quantum coherence in arbitrarily long scales are a basic prediction of TGD so that monopole flux tubes should appear in all scales. Also flux tubes inside flux tubes inside and hierarchical coilings as for DNA are possible.
</OL>
A possible TGD inspired solution of the precession problem relies on the TGD view about the formation of galaxies and stellar systems.
<OL>
<LI> Just like galaxies, also the stellar systems would have been formed as local tangles of a long monopole flux tube (thickened cosmic string), which itself could be part of or have been reconnected from a tangle of flux tube giving rise to the galaxy. The thickening liberates dark energy of cosmic strings and gives rise to the ordinary matter and is the TGD counterpart of inflation involving no inflaton fields.
<LI> In the same way as galaxies, stellar systems would be like pearls along string. This predicts correlations in the dynamics and positions of distant stars and galaxies and there is evidence for these correlations.
<LI> The flux tubes could connect the solar system to some distant stellar system. A good candidate for this kind of system is Pleiades, a star cluster located at a distance of 444 light years (the nearest star has a distance of 4 light years). There would also be an analog of solar wind along this flux tube giving for the solar magnetosphere a bullet-like shape.
<LI> The transversal gravitational force of the flux tube would cause the precession of the solar system around the flux tube. The entire solar system, as a tangle of the flux tube, would precess like a bullet-like top around the direction of this flux tube. The details of this picture are discussed in <A HREF="https://tgdtheory.fi/pdfpool/astro.pdf">this</A> and <A HREF="https://tgdtheory.fi/pdfpool/TGDcosmo.pdf">this</A> .
<LI> The TGD analogs of Birkeland currents and the analogy of solar wind would flow along the monopole flux tubes, perhaps as dark particles in the TGD sense, that is having effective Planck constant h<sub>eff</sub>=nh<sub>0</sub> which can be much larger than h, even so large that gravitational quantum coherence is possible in astrophysical and even cosmological scales.
</OL>
See the the chapter <A HREF="https://tgdtheory.fi/pdfpool/astro.pdf">TGD and astrophysics</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A>.</p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-48406793176241907612022-08-03T00:51:00.001-07:002022-08-03T00:51:47.243-07:00MOND and TGD view of dark matterThe TGD based model explains the MOND (Modified Newton Dynamics) model of Milgrom for the dark matter. Instead of dark matter, the model assumes a modification of Newton's laws. The model is based on the observation that the transition to a constant velocity spectrum in the galactic halos seems to occur at a constant value of the stellar acceleration equal to a<sub>cr</sub> =about 10<sup>-11</sup>g, where g is the gravitational acceleration at the Earth. MOND theory assumes that Newtonian laws are modified below a<sub>cr</sub>.
<OL>
<LI> In TGD, dark energy plus magnetic energy would be associated with cosmic strings, which are "non-Einsteinian" 4-surfaces of M<sup>4</sup>× CP<sub>2</sub> with 2-D M<sup>4</sup> projection. Cosmic strings are unstable agains thickening of the M<sup>4</sup> projection so that one obtains Einsteinian monopole flux tube.
</p><p>
In accordance with the observations of Zeldovich, galaxies would correspond to tangles along a long cosmic string at which the string has thickened and liberated its energy as ordinary matter (TGD counterpart for the decay of the inflaton field). The flux tubes create 1/ρ type gravitational field orthogonal to string and this gives rise to the observed flat velocity spectrum (see
<A HREF="https://tgdtheory.fi/public_html/articles/meco.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/galaxystars.pdf">this</A>, and <A HREF="https://tgdtheory.fi/public_html/articles/galjets.pdf">this</A>).
<LI> In MOND theory, it is assumed that gravitation starts to behave differently when it becomes very weak and predicts the critical acceleration. In the TGD framework, the critical acceleration would be of the same order of magnitude as the acceleration created by the gravitational field of the cosmic string and would also define a critical distance depending only on the string tension.
<LI> If 1/r<sup>2</sup> changes to 1/r in MOND, model one obtains the same predictions as in TGD for the planar orbits orthogonal to the long string along which galaxies correspond to a flux tube tangled. The models are not equivalent. In TGD, general orbit corresponds to a helical motion of the star along the cosmic string so that the concentration on a preferred plane is predicted. This has been recently reported as an anomaly of dark matter models (see <A HREF ="https://tgdtheory.fi/public_html/articles/twogalanos.pdf">this</A>).
<LI> The critical acceleration predicted would correspond to acceleration
of the same order of magnitude as the acceleration caused by cosmic string. From M<sup>2</sup>/R<sub>cr</sub></sub>= GM/R<sup>2</sup><sub>cr</sub>= TG/R<sub>cr</sub> (assuming that dark matter dominates) one obtains the estimate R<sub>cr</sub>=M/T and a<sub>cr</sub> =GT<sup>2</sup>/M, where M is the visible mass of the object - for instance the ordinary matter of a galaxy. If critical acceleration is always the same, one would have T=(a<sub>cr</sub>M/G)<sup>1/2</sup> so that the visible mass would scale like M∝ T<sup>2</sup> if a<sub>cr</sub> is constant of Nature.
</OL>
</p><p>
See the chapter
<A HREF="<A HREF="https://tgdtheory.fi/pdfpool/astro.pdf">TGD and astrophysics</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A></p><p>.
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-47860119150163815812022-07-31T23:02:00.008-07:002022-08-01T01:17:29.814-07:00Wheels and quantum arithmetics
Gary Ehlenberg gave a link to a Wikipedia article telling of Wheel theory (<A HREF="https://en.wikipedia.org/wiki/Wheel_theory">this</A>) and said that he now has a name for what he has been working with. I am sure that this kind of adventure is a wonderful mathematical experience.
</p><p>
I looked at the link and realized that it might be very relevant to the TGD inspired idea about quantum arithmetics (see <A HREF="https://tgdtheory.fi/public_html/McKayGal.pdf">this</A>).
</p><p>
I understood that Wheel structure is special in the sense that division by zero is well defined and multiplication by zero gives a non-vanishing result. The wheel of fractions, discussed in the Wikipedia article as an example of wheel structure, brings into mind a generalization of arithmetics and perhaps even of number theory to its quantum counterpart obtained by replacing + and - with direct sum ⊕ and tensor product &otimes: for irreps of finite groups with trivial representation as multiplicative unit: Galois group is the natural group in TGD framework.
</p><p>
One could also define polynomial equations for the extension of integers (multiples of identity representation) by irreps and solve their roots.
</p><p>
This might allow us to understand the mysterious McKay correspondence. McKay graph codes for the tensor product structure for irreps of a finite group, now Galois group. For subgroups of SL(n,C), the graphs are extended Dynkin diagrams for affine ADE groups.
</p><p>
Could wheel structure provide a more rigorous generalization of the notion of the additive and multiplicative inverses of the representation somehow to build quantum counterparts of rationals, algebraic numbers and p-adics and their extensions?
<OL>
<LI> One way to achieve this is to restrict consideration to the quantum analogs of finite fields G(p,n): + and x would be replaced with ⊕ and ⊗ obtained as extensions by the irreps of the Galois group in TGD picture. There would be quantum-classical correspondence between roots of quantum polynomials and ordinary monic polynomials.
<LI> The notion of rational as a pair of integers (now representations) would provide at least a formal solution of the problem, and one could define non-negative rationals.
</p><p>
p-Adically one can also define quite concretely the inverse for a representation of form R=1 ⊕ O(p), where O(p) is proportional to p (p-fold direct sum) of a representation, as a geometric series.
<LI> Negative integers and rationals pose a problem for ordinary integers and rationals: it is difficult to imagine what direct sum of -n irreps could mean.
</p><p>
The definition of the negative of representation could work in the case of p-adic integers: -1 = (p-1)⊗ (1 ⊕ p*1 ⊕ p^2*1 ⊕...) would be generalized by replacing 1 with trivial representation. Infinite direct sum would be obtained but it would converge rapidly in p-adic topology.
<LI> Could 1/p<sup>n</sup> make sense in the Wheel structure so that one would obtain the analog of a p-adic number field? The definition of rationals as pairs might allow this since only non-negative powers of p need to be considered. p would represent zero but multiplication by p would give a non-vanishing result.
</OL>
See the article <a HREF= "https://<A HREF="http/tgdtheory.fi/public_html/articles/McKayGal.pdf">McKay Correspondence from Quantum Arithmetics Replacing Sum and Product with Direct Sum and Tensor Product?</A> or the <A HREF ="https://tgdtheory.fi/pdfpool/McKayGal.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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A></p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-40180005882587658262022-07-29T21:27:00.008-07:002022-07-31T00:16:48.080-07:00The first findings of the James Webb telescope might revolutionize the views of the formation of galaxies
The first preliminary findings of the James Webb telescope, the successor of the Hubble telescope, are in conflict with the standard view of the formation of galaxies. The YouTube video (see <A HREF="https://cutt.ly/OZc4lV7">this</A>) "James Webb Found Galaxies That Sort of Break Modern Theories" gives a good summary of these findings. The findings are also summarized in an article in Nature (see <A HREF="https://cutt.ly/lZc4clq">this</A>) with the title "Four revelations from the Webb telescope about distant galaxies".
</p><p>
The official story of the formation of galaxies goes roughly as follows.
<OL>
<LI> Around 3 minutes of cosmic time, the cosmic microwave background emerged as the first atoms formed and radiation decoupled from matter.
<LI> When the age of the Universe was more than about .1 billion years, the first stars were formed. They lived their life and exploded as supernovas and yielded interstellar hydrogen gas. Galaxies started to form. One can see this process as a gravitational condensation. What is essential is that this process went from long to short scales, just as the formation of stars in the earlier phase.
<LI> The model gives a stringent upper bound for the age of the galaxies. They should be younger than the oldest observed stars. This limit gives an upper bound for the distance of the galaxy, that is for its redshift.
</OL>
The first, preliminary, observations of the James Webb telescope were galaxies with redshifts up to 16. Even redsshift extending to 20 have been speculated in arXiv papers. Redshift 16 would correspond to the age of 250 million years and redshift of 20 to the age of 200 million years. They are too far to fit into the official picture. To get some perspective, note that the estimate for the age of the Universe is 13.8 billion years.
</p><p>
The ages of these galaxies were few hundred million years and of the same order as the estimated ages of about 100 million years of the hypothetical population III stars (see <A HREF="https://cutt.ly/eZc4mr1">this</A>), which are thought to be the oldest stars but have not not (yet?) detected. The criterion for the age of the star is its metal content: the first stars should have contained only hydrogen and Helium and "metal" here means anything heavier than Helium.
The suggestive conclusion is that there was a significant population of star forming galaxies in the early universe. This challenges the standard view stating that stars came first and led to the formation of galaxies.
</p><p>
TGD proposes an unofficial view of the formation of galaxies (see <A HREF="https://tgdtheory.fi/public_html/articles/meco.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/galaxystars.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/galjets.pdf">this</A>).
<OL>
<LI> In the very beginning the Universe was dominated by cosmic strings, which were space-time surfaces in H=M<sup>4</sup>× CP<sub>2</sub> having 2-dimensional M<sup>4</sup> projection. They were not "Einsteinian" space-time surfaces with 4-D M<sup>4</sup> projection and have no counterpart in general relativity.
<LI> Cosmic strings were unstable against thickening of the M<sup>4</sup> projection to 4-D one. Phase transitions thickening the cosmic strings occurred and increased their thickness and reduced string tension so that part of their energy transformed to ordinary matter. This is the TGD counterpart for inflation.
</p><p>
This process led to radiation dominated Universe and the local description of the Universe as an Einsteinian 4-surface became a good approximation and is used in standard cosmology based on the standard model as a QFT limit of TGD.
</p><p>
At this moment the thickness of the thickened strings would be around 100 micrometers, which corresponds to a length scale around large neuron size. Water blob with this size has mass of order Planck mass. The connection with biology is suggestive \cite{btart/penrose,watermorpho,waterbridge}.
<LI> The liberated dark energy (and possible dark matter, dark in the TGD sense) assignable to cosmic strings produced quasars, which in the TGD framework are identified as time reversals of the ordinary galactic blackholes. They did not extract matter from the environment but feeded darl energy as matter to the environment as jets. Jets are observed and explained in terms of the magnetic field due to the rotation of the galaxy.
</p><p>
The jets are somewhat problematic in the GRT based cosmology since the simplest, non-rotating Schwarzschild blackholes do not allow them. The rotating blackholes identifiable as Kerr-Newman blackholes accompanied by magnetic fields, also have some interpretational problems. For instance, the arrow of time can be said to be different in the nearby and faraway regions and closed time-like geodesics are possible. In TGD, this could have an interpretation in terms of zero energy ontology (ZEO). The matter from the jets would have eventually led to the formation of atoms, stars, and galaxies.
<LI> What is essential is that the formation of galaxies proceeds from short to long scales rather than vice versa as in the standard cosmology. A second essential point is that the dark energy (and possible dark matter) concentrated at cosmic strings was added to the ordinary matter predicted by the standard model to be present in the radiation dominated cosmology. This led to the formation of galaxies. Therefore this picture is consistent with the standard story as far as the formation of atoms and emergence of CMB is considered.
</OL>
The possibility considered in the TGD framework (see <A HREF="https://tgdtheory.fi/public_html/articles/meco.pdf">this</A>, <A HREF="https://tgdtheory.fi/public_html/articles/galaxystars.pdf">this</A> and <A HREF="https://tgdtheory.fi/public_html/articles/galjets.pdf">this</A>) is that quasars are time reversed black-holes (this property can be formulated precisely in zero energy ontology (ZEO), which forms the basis of TGD based quantum measurement theory) (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/ZEOnumber.pdf">this</A>). Note that the time reversal property would hold true in long time scales at the magnetic body (MB) defined by the monopole flux tubes produced by the thickening of the cosmic strings. For ordinary matter, the scale for the time spent with a given arrow of time is very short but MB with a large gravitational Planck constant can force ordinary matter to effectively behave like its time reversed version.
</p><p>
There is indeed quite recent support for the proposal that quasars are time reversals of blackhole-like objects identified in the TGD framework as monopole flux tube tangles. The Hubble telescope detected a dwarf galaxy at a distance of 30 million light years for which the number of stars is about 10 per cent for that in the Milky Way. Its center contains a blackhole-like object (see <A HREF="https://cutt.ly/kZc77B1">this</A>), which did not extract matter from the environment but did just the opposite by jets, which gave rise to a formation of stars.
</p><p>
The observations challenging the basic dogma of blackhole physics are not new and during the writing of an article about <A HREF="https://tgdtheory.fi/public_html/articles/galjets.pdf">galactic jets</A> I got the impression that one of the basic challenges is to explain why some blackholes do just the opposite of what they should do.
</p><p>
See the article <A HREF="https://tgdtheory.fi/public_html/articles/galjets.pdf">TGD View of the Engine Powering Jets from Active Galactic Nuclei</A> or the <A HREF="https://tgdtheory.fi/pdfpool/galjets.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>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A></p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0tag:blogger.com,1999:blog-10614348.post-80019137211993950602022-07-27T00:10:00.007-07:002022-08-31T22:23:47.190-07:00Dark 3N-resonances and quantum teleportation
Could the communication by dark 3N-resonances (see for instance <a HREF= "https://tgdtheory.fi/public_html/articles/watermorpho.pdf">this</A>), which is central for the TGD view about genetic code (see <a HREF= "https://tgdtheory.fi/public_html/articles/bioharmony2021.pdf">this</A> and <a HREF= "https://tgdtheory.fi/public_html/articles/TIH.pdf">this</A>), relate to quantum teleportation?
</p><p>
This is possible but requires modifying the previous assumption that
the states of dark proton sequences are fixed and correspond to those of
ordinary genes with which they are in energy resonance when communicating.
One must loosen this assumption.
<OL>
<LI> Give up the assumption that cyclotron states of the dark 3N-proton are always the same and correspond to a gene. Assume that in some time scale, perhaps of order cyclotron time, dark proton sequences representing genes decay to the ground state configuration defining an analog of ferromagnet.
<LI> Assume that some excited dark 3N-photon states, dark geme states, can be in energy resonance with ordinary genes, most naturally the nearest one if dark DNA strands are parallel to an ordinary DNA strand. Even this assumption might be unnecessarily strong. Dark 3N-proton would interact with its ordinary counterpart by energy resonance only when it corresponds to the dark variant of the gene.
</p><p>
Same applies to dark genes in general. Only identical dark genes can have resonance interaction. This applies also to the level of other fundamental biomolecules RNA,tRNA and amino acids.
<LI> What is this interaction in its simplest form? Suppose dark 3N- proton is in an excited state and thus defines a dark gene. Suppose that it decays by SFR to the ground state (magnetization) by emitting dark 3N-photon. If this 3N photon is absorbed in SFR by a dark proton sequence originally in ferromagnetic state, it excites by resonance the same gene. The transfer of entanglement takes place.
</p><p>
This is nothing but quantum teleportation but without Alice, doing Bell measurements and sending the resulting bit sequences to Bob , performing the reversals of Bell measurements to rebuild the entanglement.
</OL>
This suggests a modification of the earlier picture of the relation between dark and chemical genetic code and the function of dark genetic code.
<OL>
<LI> Dark DNA (DDNA) strand is dynamical and has the ordinary DNA strand associated with it and dark gene state can be in resonant interaction with ordinary gene only when it corresponds to the ordinary gene. This applies also to DRNA, DtRNA and DAA (AA is for amino acids).
</p><p>
This would allow DDNA, DRNA, DtRNA and DAA to perform all kinds of information processing such as TQC by applying dark-dark resonance in quantum communications. The control of fundamental biomolecules by their dark counterparts by energy resonance would be only one particular function.
<LI> One can also allow superpositions of the dark genes representing 6-qubit units. A generalization of quantum computation so that it would use 6-qubits units instead of a single qubit as a unit, is highly suggestive.
<LI> Genetic code code could be interpreted as an error code in which dark proteins correspond to logical 6-qubits and the DNA codons coding for the protein correspond to the physical qubits associated with the logical qubit.
<LI> The teleportation mechanism could make possible remote replication and remote transcription of DNA by sending the information about ordinary DNA strand to corresponding dark DNA strand by energy resonance. After that, the information would be teleported to a DNA strand in a ferromagnetic ground state at the receiver. After this, ordinary replication or transcription, which would also use the resonance mechanism, would take place.
</OL>
Could there be a connection with bioharmony as a model of harmony providing also a model of genetic code (see <a HREF= "https://tgdtheory.fi/public_html/articles/bioharmony2021.pdf">this</A> and <a HREF= "https://tgdtheory.fi/public_html/articles/TIH.pdf">this</A>)?
<OL>
<LI> In the icosa-tetrahedral model, the orbit of the face of icosahedron under the group Z<sub>6</sub>,Z<sub>4</sub>, Z<sub>2,rot</sub> or Z<sub>2,refl</sub> would correspond to single physical 6-qubit represented as dark protein.
</p><p>
This representation of the logical qubit would be geometric: orbit rather than sub-space of a state space. One could however assign to this kind of orbit a state space as wave functions defined at the orbit. This representation of Z<sub>6</sub>, Z<sub>4</sub>, Z<sub>2,rot</sub> or Z<sub>2,refl</sub> would correspond to a set of 6-qubits, which replaces a single 6-qubit.
<LI> The TGD proposal for TQC \cite{btart/TQCTGD,QCCC} is that the irreps of Galois groups could replace qubits as analogs of anyons. Could these orbits correspond to irreps of Galois groups or their subgroups, say isotropy groups of roots?
</p><p>
Another option is the finite subgroups G of quaternionic automorphisms, whose MacKay diagrams, characterizing the tensor products of irreps of G with the canonical 2-D irrep, give rise to extended Dynkin diagrams (see <a HREF= "https://tgdtheory.fi/public_html/articles/McKayGal.pdf">this</A>). What puts bells ringing is that Z<sub>6</sub>,Z<sub>4</sub>, Z<sub>2,rot</sub> or Z<sub>2,refl</sub> are subgroups of the icosahedral group, which corresponds to the Dynkin diagram of E<sub>8</sub>.
</p><p>
These alternatives need not be mutually exclusive. I have proposed (see <a HREF= "https://tgdtheory.fi/public_html/articles/McKayGal.pdf">this</A>) that Galois groups could act as the Weyl groups of extended ADE Dynkin diagrams given by McKay graphs of finite subgroups of SU(2) interpreted as the covering group for the automorphism group of quaternions. The Galois group and its subgroup would define a cognitive representation for the subgroup of the covering group of quaternion automorphisms.
</OL>
The communications by the modulation of frequency scale 3N-Josephson frequency scale are still possible.
<OL>
<LI> The 3N-resonance occurs when the receiver 3N-proton is in ferromagnetic ground state and the 3N-Josephson frequency corresponds to 3N-cyclotron frequency. If the time scale for the return to the ferromagnetic state is considerably shorter than the time scale of modulations, a sequence of resonance pulses results and codes for the frequency modulation as an analog of nerve pulse pattern. This communication can lead to communication if the ordinary gene accompanying the excited dark gene is in energy resonance with it.
<LI> It must be noticed that the communications by dark 3N-resonances are not possible in standard physics and are made possible only by. Galois confinement and h<sub>eff</sub> hierarchy. In standard physics only single photon fermion interactions would be present and would be relatively weak. In quantum computation, this suggests the possibility of quantum coherent manipulation of N-qubit states by dark N-photons instead of qubit-wise manipulations prone to errors and destroying the coherence. There is evidence for N-photon states with these properties (see <A HREF="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.127.10770">this</A> and <A HREF="https://www.nature.com/articles/s41567-022-01630-y">this</A>). For the TGD inspired comments see <a HREF= "https://tgdtheory.fi/public_html/articles/TGDcondmatshort.pdf">this</A>.
</OL>
See the article <a HREF= "https://tgdtheory.fi/public_html/articles/fluteteleport.pdf">Quantum biological teleportation using multiple 6-qubits</A> or
the chapter <a HREF= "https://tgdtheory.fi/pdfpool/watermorpho.pdf">TGD View about Water Memory and the Notion of Morphogenetic Field</A>.
</p><p>
For a summary of earlier postings see <a HREF= "https://tgdtheory.fi/public_html/articles/progress.pdf">Latest progress in TGD</A>.
</p><p>
<A HREF="https://www.tgdtheory.fi/tgdarticles/tgdarticlesall.html">Articles related to TGD</A></p><p>
Matti Pitkänenhttp://www.blogger.com/profile/13512912323574611883noreply@blogger.com0