Tuesday, August 09, 2022

Ultradiffuse galaxies as a problem of cold dark matter and MOND scenarios

The existence of ultra-diffuse galaxies for which the velocity of distant rotating stars is extremely low (see this), 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 have been proposed as a support for MOND, but also MOND has grave difficulties with them.

In the TGD framework (see this, this, and this), 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. No dark matter halo is needed. 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 the inflaton field.

Whereas the dark halo model predicts that any rotation plane for the distant stars is possible, TGD allows only the galactic plane orthogonal to the long cosmic string, and distant stars move in the general case along helical orbits along the cosmic string.

The TGD view also allows us to understand why MOND works in some cases: in the TGD framework the critical acceleration acr, suggested originally to be constant of Nature, is replaced with string tension.

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 rotation velocity is possible. Ordinary bound states of matter are not necessary since the gravitational force of the flux tubes binds the stars to the flux tube. This might explain why the galaxy can be ultradiffuse.

For a summary of earlier postings see Latest progress in TGD.

Articles related to TGD.

Is pair creation really understood in the twistorial picture?

Twistorialization leads to a beautiful picture about scattering amplitudes at the level of M8 (see this). 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.

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 M8-H duality to a geodesic of M4 starting from either vertex of the causal diamond (CD) . Uncertainty Principle at classical level requires inversion so that one has a= ℏeff/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 H3⊂ M4⊂ M8.

The geodesic would intersect the a=ℏeff/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.

One can however criticize this framework. Does it really allow us to understand pair creation at the level of the space-time surfaces X4⊂ H?

  1. 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.
  2. 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.
  3. 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 M4⊂ H and M4⊂ M8? Only the first problem will be considered in the following.
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.

One can first try to identify the key ingredients of the possible solution of the problem.

  1. 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?
  2. At the level of H, particles have CP2 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.

    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.

    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.

  3. 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 X4. Could the topological 3-vertex be enough to avoid the introduction of the 4-fermion vertex?
Could one modify the definition of the particle line as a geodesic of H to a geodesic of the space-time surface X4 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 M8 picture tachyons are building bricks of physical particles identified as Galois singlets.
  1. 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.
  2. 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.

    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?

  3. It is not clear whether one can assign a conserved space-like M4 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.

    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 M4 mass squared, the geodesic must be space-like and therefore tachyonic.

    The non-conservation of M4 momentum at single particle level (but not classically at n-particle level) would be due to the interaction with the classical fields.

  4. In the M8 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 M8 level, correspond to tachyonic geodesics along wormhole throats possibly returning backwards along the another wormhole throat?
How does this picture relate to p-adic thermodynamics (see this) as a description of particle massivation?
  1. 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.

    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 X4.

  2. 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.
  3. 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.

    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.

  4. It should be noted however that the roots of the polynomials in M8 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.
See the article About TGD counterparts of twistor amplitudes: part II or the chapter About TGD counterparts of twistor amplitudes.

For a summary of earlier postings see Latest progress in TGD.

Articles related to TGD.

Monday, August 08, 2022

Universe 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 this) 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 this). A lot has happened during these two decades and it is interesting to take a fresh TGD inspired view.

In the TGD framework, one can imagine two starting points concerning the explanation of the findings.

  1. Could there be a connection with the redshift quantization along some lines ("God's fingers"") proposed by Halton Arp (see this) and Fang-Sato. I have considered several explanations for the quantization. In TGD cosmic=time constant surface corresponds to hyperbolic 3-space H3 of Minkowski space in TGD. H3 allows an infinite number of tessellations (lattice-like structures).

    I have proposed an explanation for the redshift quantization in terms of tessellations of H3. The magnetic bodies (MBs) of astrophysical objects and even objects themselves could tend to locate at the unit cells of the tessellation.

  2. Icosa-tetrahedral tessellation (lattice-like structure in hyperbolic space H3) plays a key role in the TGD model of genetic code (see this) 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.
In the sequel I will consider only the latter option.
  1. 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 heff. 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).
  2. 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.]

    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?

Could the possible dark part of the CMB radiation diffract in local tessellations assigned with the local MBs?
  1. 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?
  2. The gravitational Planck constant ℏgr =GMm/β0, where M is large mass and m a small mass, say proton mass (see this, this, this, this and this). Both masses are assignable to the monopole flux tubes mediating gravitational interaction. β0=v0/c is velocity parameter and near to unity in the case of Earth.
  3. The size scale of the unit cell of the dark gravitational crystal would be naturally given by Λgr = ℏgr/m= GM/β0 and would be depend on M only and would be rather large and depend on the local large mass M, say that of Earth. Λgr does not depend on m (Equivalence Principle).
  4. For Earth, the size scale of the unit cell would be of the order of Λgr= GME0 ≈ .45 cm, where β0= 0=v0/c ≈ 1 is near unity from the experimental inputs emerging from quantum hydrodynamics (see this) and quantum model of EEG (see this) and quantum gravitational model for metabolism (see this and this). Λgr could define the size of the unit cell of the icosa-tetrahedral tessellation. Note that Earth's Schwartschild radius rS=2GM≈ .9 cm.

    Encouragingly, the wavelength of CMB intensity as a function of wavelength around .5 cm to be compared with Λgr ≈ .45 cm! Quantum gravitational diffraction might take place for dark CMB and give rise to the diffraction peaks!

  5. 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 this), 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.
  6. 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 ℏgr/ℏ =(GMEm/β0)/ℏ ≈ 3.5× 1012 for proton. This gives Λ=1.75 × 107 km, to be compared with the radius of Earth about 6.4× 106 km.
See the chapter TGD and cosmology.

For a summary of earlier postings see Latest progress in TGD.

Articles related to TGD

Thursday, August 04, 2022

Antipodal 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 N=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.

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.

See the article Antipodal duality and TGD or the chapter About TGD counterparts of twistor amplitudes.

For a summary of earlier postings see Latest progress in TGD.

Articles related to TGD

Wednesday, August 03, 2022

Quantization of cosmic redshifts in the TGD framework

In a FB discussion Jivan Coquat asked for my opinion about Halton Arp (see this).

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.

  1. To my opinion, the most convincing explanation is in terms of lattice-like structures, tessellations, in hyperbolic space H3, which corresponds to cosmic time a= constant hyperboloid of future light-one (see this).
  2. H3 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 E3 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 (heff=nh0>h) proton triplets and flux tubes of magnetic body (see this).
  3. For lattices in the Euclidean space E3, the radial distance from origin is quantized. For H3 redshift proportional to H3 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.
  4. The tessellation itself could be associated with the magnetic (/field) body carrying dark matter in the TGD sense as heff=nh0>h phases: this is a prediction of number theoretic vision about physics as dual of geometric vision. Very large values of heff =hgr= GMm/v0 (Nottale hypothesis for gravitational Planck constant, see this) 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.
See the chapter (see Quantum Theory of Self-Organization.

For a summary of earlier postings see Latest progress in TGD.

Articles related to TGD

The 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 this and this) 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.

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 this).

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.

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.

  1. 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.
  2. Flux tubes relate to the model for the emergence of galaxies (see this and this) and explain galactic jets propagating along flux tubes (see this). Dark energy and possible matter assignable to the cosmic strings predicts correctly the flat velocity spectrum of stars around galaxies.
  3. In the MOND model it is assumed that the gravitational force transforms for certain critical acceleration from 1/r2 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/rho2 force. The predictions of MOND TGD are different since in TGD the motion takes place in the plane orthogonal to the cosmic string.
  4. 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 M4 projections and 2-D E3 projections (time= constant) (also an example of "non-Einsteinian" space-time surface).
  5. 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.
  6. 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.
A possible TGD inspired solution of the precession problem relies on the TGD view about the formation of galaxies and stellar systems.
  1. 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.
  2. 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.
  3. 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.
  4. 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 this and this .
  5. 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 heff=nh0 which can be much larger than h, even so large that gravitational quantum coherence is possible in astrophysical and even cosmological scales.
See the the chapter TGD and astrophysics.

For a summary of earlier postings see Latest progress in TGD.

Articles related to TGD.

MOND and TGD view of dark matter

The 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 acr =about 10-11g, where g is the gravitational acceleration at the Earth. MOND theory assumes that Newtonian laws are modified below acr.
  1. In TGD, dark energy plus magnetic energy would be associated with cosmic strings, which are "non-Einsteinian" 4-surfaces of M4× CP2 with 2-D M4 projection. Cosmic strings are unstable agains thickening of the M4 projection so that one obtains Einsteinian monopole flux tube.

    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 this, this, and this).

  2. 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.
  3. If 1/r2 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 this).
  4. The critical acceleration predicted would correspond to acceleration of the same order of magnitude as the acceleration caused by cosmic string. From M2/Rcr= GM/R2cr= TG/Rcr (assuming that dark matter dominates) one obtains the estimate Rcr=M/T and acr =GT2/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=(acrM/G)1/2 so that the visible mass would scale like M∝ T2 if acr is constant of Nature.

See the chapter TGD and astrophysics.

For a summary of earlier postings see Latest progress in TGD.

Articles related to TGD