The flatness of the rotation curve of the Milky Way is challenged

Sabine Hossenfelder (see this) told about the recent findings challenging the view that the rotation curve of the Milky Way is flat. The findings are discussed in the article "The rotation Curve of the Milky Way: State of the Art, the Keplerian Decline Debate, and Implications for Dark Matter" by Alexandro Melchiorri and Ruchika (see this).

Here is part of the abstract of the article:

For four decades, the roughly flat rotation curve (RC) of the Milky Way (MW) stood as local evidence for an extended dark matter (DM) halo. Gaia DR3 has changed the picture: several analyses now find a velocity decline beyond R ≈ 15 kpc, and the most radical interpretation claims a nearly Keplerian fall-off (v ∝ R^-1/2) that excludes a flat RC at 3σ and implies a total dynamical mass of only ≈ 2 × 10¹¹M_sun-three to five times below pre-Gaia estimates. Taken at face value, this would make the MW exceptional among comparable spirals and challenge both ΛCDM and MOND. It would also alter predictions for direct-detection experiments, although the local DM density is not fixed by virial mass alone.

The findings challenge not only the ΛCDM model and MOND but also the TGD view of the galaxies, galactic dark matter, and galaxy formation (this).

The TGD based model (see this) for the formation of galaxies and of also smaller structures relies on the notions of cosmic string and flux tube.

1. Galactic dark matter is identified as the volume energy and Kähler magnetic energy assignable to long cosmic strings orthogonal to the galactic plane. Also cosmic strings parallel to the plane can be considered and collisions of nearly orthogonal cosmic strings could have given rise to spiral galaxies.

   Galaxies would correspond to tangles along the cosmic strings. Thickening of the cosmic string would have liberated energy and produced ordinary matter somewhat like in the decay of the inflaton field in cosmic inflation. The cylindrical geometry of the model predicts flat velocity spectrum but also implies testable deviations from the halo model.

2. The radius of the visible part of the Milky way is about R=100,000 ly. The critical distance at which the rotation curve ceases to be flat is 15 kpc, that is 48,923 light-years, roughly R/2. The average distance between galaxies is L= 1-few million ly and suggests that the average distance of galaxies along cosmic strings is roughly L.
3. In the modification of Λ CDM, the dark mass halo should be concentrated near the centre. This implies that the dark matter of the galaxy is about 3/4 of the recent estimate and smaller than the cosmological average. For MOND the challenge is much more difficult to overcome. In TGD the galactic dark matter is along the long cosmic string so that the problem disappears.

How to explain the finding in the TGD framework?

The TGD based model  for the formation of galaxies and of  also smaller structures relies on the notions of cosmic string and flux tube.  

1.  Galactic dark matter is identified as volume energy and K\"ahler magnetic energy assignable to long  cosmic strings transversal (not necessarily orthogonal) to the galactic plane. Also cosmic strings parallel to the plane can be  considered and collisions of transversal cosmic strings could have given rise to spiral galaxies \cite{btart/3pieces}.

   Galaxies would correspond to tangles along the cosmic strings. Thickening of the cosmic string would have liberated energy and produced ordinary matter somewhat like in the decay of the inflaton field in cosmic inflation. The cylindrical geometry of the model predicts flat velocity spectrum but also implies testable deviations from the halo model.

2. The radius of the visible part of the Milky way is  about  R=100,000 ly. The critical distance at which the rotation curve ceases to be flat is  15 kpc, that is  48,923  light-years, roughly R/2. The average distance between galaxies is L= 1-few million ly and suggests that the average distance of galaxies along cosmic strings is roughly L.
3. In the modification of ΛCDM, the dark mass halo  should be concentrated near the centre.  This implies that the dark matter of the galaxy is about 3/4 of the recent estimate and smaller than the cosmological average. For MOND the challenge is much more difficult to overcome. In TGD the galactic dark matter is along the long cosmic string.

One can consider several modifications of this model  as an explanation of the findings.

1.  The monopole flux tubes and cosmic strings as extremely thin flux tubes  are necessarily closed.  If the return flux is along a single parallel monopole flux tube, there would be a violation of the planar  asymmetry in the rotation curve caused by the weakening  of gravitational force at one  side  and strengthening at the other side. The effect would increase at large distances and cause an approximate Keplerization. The rotation velocity would  have a strong dependence  on  the direction in the galactic plane.
2.    Could one think that the return   flux is  branched to less heavier flux tubes returning  along  a wall or  could be also along thin cylindrical flux sheets? In this case one can however argue that  the effect of a constant cylindrical mass distribution would however vanish in the entire interior so that this option fails.
3. The most plausible option is that a lattice of parallel cosmic strings transversal to a plane  defined by the galactic plane  causes Keplerization.  Monopole flux tubes bring in mind ferromagnets and antiferromagnets. The cancellation of the gravitational fields of neighboring cosmic strings would cause approximate Keplerization of the velocity curve.

What kind of lattice?

One can consider several kinds of 2-D lattices of cosmic strings.

1. Triangular and hexagonal lattices having the same symmetries, rectangular lattices with or without center points, and oblique lattices, can be considered.  The lattices spanned by a parallelogram appear as moduli spaces of toric conformal structures and  of elliptic Riemannian surfaces \cite{btart/Weierstrass}.
2. The square lattice would conform with the approximate 4-fold rotation planar symmetry assignable to the quadrupole harmonics (l=2).  The quadrupole in the distribution of temperature fluctuations  can be visualized  as a collection of 4 charges at the vertices of parallelogram in the plane orthogonal to the Axis of Evil.

   Octupole 8  has charges at the vertices of a cube projecting to 3+3=6 charges in the plane dissecting the diagonal of the cube giving rise to a hexagon. Axis of Evil is therefore in the direction of the diagonal of the cube which is in the plane of the solar system.  The hexagonal symmetry also suggests the possibility of a hexagonal lattice of cosmic strings.

3. The fluctuation patterns for the CMB temperature   (quadrupole and octopole) on the sky and divide the sky to two hemispheres relative to us. The octupole variation reflects itself as a division of the ecliptic  to 8 angular sectors such that  hot and cool sectors alternate.

The TGD view of dark matter as a phase with a larger h_eff suggests  an interpretation of this kind of lattice.

1. Many-sheeted-ness with respect to CP₂ (space-time surface as multi-sheeted graph over CP₂) could mean this kind of lattice: different flux tubes would be sheets over CP₂. This option could be consistent with the cosmic estimate for the density of the dark matter.
2. 15 kpc=  48,923 ly   gives an idea about the density of parallel cosmic strings orthogonal to the galactic plane.   The distance of cosmic strings should be larger but not too much so.  The radius for the visible part of the  Milky Way radius    is  100,000 ly  and roughly twice this scale so that the distance between cosmic strings should be larger than the radius of the visible galaxy.    
3. One could image    a  lattice of parallel cosmic strings with lattice spacing  of 100-200 ly.    Cosmic strings would have galaxies as tangles along them with average separation of 1-few million ly.    The distance  between parallel cosmic strings  would be roughly by  factor  1/10 smaller if it corresponds to galactic radius. Cylindrical symmetry is however violated. The effect is largest at large enough distances and should reflect the symmetry of the planar lattice.
4. Could   the galaxies along cosmic strings form  3-dimensional lattice like  structure, at least in an approximate sense? The typical distance between galaxies along the string would be about 1 million years and about 10 times larger than the distance between cosmic strings so that cubes would be stretched along the body diagonal to form a rhombohedron, which can have the same edge lengths as a cube.

Axis of Evil

Cosmic microwave background has a mysterious  property,  which is in conflict with the  cosmological principle.

1. The fluctuation patterns (dipole, quadrupole and octupole)  characterized by moments are are aligned along the same direction, the Axis of Evil \cite{bcast/AxisofEvil}, which is defined as the normal vector for these planar fluctuation patterns and is directed along the  ecliptica and  points toward the constellations Leo and Virgo.  Since CMB was created much before the solar system, this kind of correlation is impossible in the standard cosmology.  
2. Galactic plane and the plane of the solar system (ecliptic) are tilted and intersect  at an  angle about 60 degrees.     If the Axis of Evil as direction of cosmic strings is transversal to the galactic plane and parallel to the ecliptic it has an angle of 60 degree with respect to the galactic plane.  
3. Is it possible to understand why this angle is 60 degrees? Cube has  8  face diagonals which do not intersect the main diagonal and have an angle of 60 degrees with it. The directions of diagonals of opposite faces are the same, which leaves 3 directions defining normals of 3 planes.  One of these 3 face diagonals  could  be the  direction of the normal of the  galactic plane.

What could cause the Axis of Evil?

1. Axis of Evil as direction of cosmic strings would be along  the ecliptic and  the projection to  the ecliptic would consist of hot and cool lobes.  
2. Axis of Evil means that temperature and mass density fluctuations break   translational symmetry along   the direction of  cosmic strings.  If  this direction were  normal to the galactic plane, a large mass in the galactic plane could explain the asymmetry. Could the galaxies along  the cosmic strings, having  a typical distance of million light years, somehow give rise to the anomaly?

   Could the distances of the nearest galaxies at opposite sides  be different and cause a local anomaly? Or could the linear density of galaxies vary in the direction of the Axis of Evil causing global anomaly. Why so?  Could one think that  the formation of galaxies  was a wave, a kind of phase transition, propagating in the direction of cosmic strings?

An interesting question relates to the length scale in which the cosmic strings are parallel.

1. In the TGD framework, the cosmic strings would have existed already before the formation of galaxies. The planes assignable to galaxies, in particular the Milky Way, and stellar system would  be determined to a high degree by this primordial cylindrical symmetry.  
2. The plane of ecliptic as  a preferred plane   appears  in cosmic scales, which suggests that it must have existed before the time when CMB was generated and reflects the presence of an effective 2-dimensionality  of the Universe. If the density of galaxies  varies  along the  cosmic strings,   the CMB fluctuations would reflect this variation.

See the article About the recent TGD based view concerning cosmology and astrophysics or the chapter with the same title.

The 2s rhythm of human speech appears in all animal communications

Some time ago I wrote an article (see this) motivated by the article "A widespread animal communication tempo may resonate with the receiver's brain" by Balasubramanian et al (see this) about the finding that 2 Hz seems to define a universal rhythm in animal communications. As a matter of fact, there is an entire range of [.5,2] Hz involved with the communications.

Now I learned about an article "Rhythm Across Species: Situating Human Speech in a Comparative Framework" of Burchardt et al (see this) telling about animal communications at.5 Hz frequency. The study, carried out in Geisteswissenschaftliche Zentren Berlin e.V. (GWZ), has been published today in the journal Annals of the New York Academy of Sciences.

The popular article (see this gives the following summary about the findings.

1. The analysis focused on so-called inter-onset intervals : contiguous segments of speech including a following pause. This unit is also used in research into animal communication signals, thereby enabling a direct comparison between humans and animals. The data set comprised the Language Documentation Reference Corpus (DoReCo), which contains speech recordings from numerous, often under-researched languages, as well as various rhythmic metrics for animals already described in the literature.
2. The study analysed over 100,000 such intervals and revealed a strikingly similar duration of around 2 seconds across all 48 languages. This consistency held true regardless of language family or the individual characteristics of the speakers. A subsequent comparison with data from research into animal communication revealed that the human speech rhythm falls within the range also described, for example, the Cape fur seal, the brown meagre, or the skylark.
3. The research team cites physiological factors, such as breathing rhythm, which limits the length of contiguous intervals, as a possible explanation for the observed regularity. Limitations of working memory could also play a role. The results suggest that the fundamental temporal organisation of human communication may stem from mechanisms shared by humans and other animal species.

How the 2 sec rhythm appears in human brain?

Google Gemini informs that the 2 sec rhythm appears in several ways in the human brain. In neuroscience, a 2 sec cycle manifests in the brain in several distinct neurobiological and psychological ways: (see this and this).

1. Delta Waves and Slow-Wave Sleep. The absolute slowest major brainwave category is the delta band, which ranges from 0.5 to 4 Hz. The absolute lowest threshold of this band (0.5 Hz) is a 2-second rhythm. This rhythm dominates the neocortex during deep non-REM sleep and is critical for memory consolidation, neural tissue repair, and glymphatic waste clearance (see this, this, this, and this).
2. Infra-Slow Oscillations (ISOs). These fluctuations that occur at or below 0.5 Hz are known as infra-slow oscillations. These 2-second (and longer) rhythms act as a macro-level "pacemaker" for the brain. They modulate higher-frequency brain activity (like alpha or beta waves) and coordinate long-range communication between distant neural networks (see this, this, this).
3. The 2-Second Perceptual Window. Psychological and cognitive research shows that human temporal processing has a threshold of roughly 2 seconds. When we listen to a melody, track a train of thought, or rhythmically move, our brain binds sensory inputs into a singular, cohesive experience only if they occur within a 2-second window. If a gap exceeds 2 seconds, the brain's working memory activation decays, and it treats the next stimulus as an entirely separate event rather than a continuation (see this, this and this).

The TGD view of .5 Hz and 2Hz rhythms

The rhythms in the frequency range [.5,2] Hz have been reported as a universal rhythm in animal communications and the 2 seconds and 2Hz rhythm seem to represent lower and upper bounds for the rhythm. The proposed explanation is in terms of physiological factors and certainly they are involved. TGD inspired quantum biology based on the new view of space-time, classical fields and quantum ontology suggests that the explanation is at a deeper level and physiology just adapts rather than determines. I have proposed a model for the findings about 2 Hz rhythm (see the article "Universal rhythm for communications between animals?" and the blog article.

The notion of magnetic/field body is in a central role in TGD inspired quantum biology. The magnetic body would act as controller of the biological body and communications and control would rely on dark photon signals with very large value of effective Planck constant so that the energies of photons even in EEG frequency scale would have energies about thermal energy, in particular, in the range of biophotons.

The monopole magnetic field with strength about .2 Gauss (2/5 of the Earth's magnetic field strength) assignable to Earth, proposed by Blackman and christened by him as endogenous magnetic field is important. TGD suggests that also the octaves of this field and even the Pythagorean scale are involved so that the cyclotron frequencies associated with the monopole flux tubes give rise to a musical harmony. The TGD based model of the genetic code assigning to codons 3-chords defining what I call bio-harmonies, relies on this vision (see for instance this).

What is remarkable is that DNA cyclotron frequency is 1 Hz for $B_{end}=.2$ Gauss. The frequencies .5 Hz,1 Hz and 2 Hz correspond to octaves of .5 Hz and 1 Hz is the geometric mean of .5 Hz and 3 Hz. If the bioharmony hypothesis is accepted also 2 octaves spanning Pythagorean scales are involved. Are the communications between animals based on singing! What is important is that the fundamental explanation would be at the level of DNA, more precisely "dark" DNA.

See the article Universal rhythm for communications between animals? and the chapterThe recent view of TGD inspired theory of consciousness and quantum biology.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Has LUX-ZEPLIN found a scaled up variant of electron with mass of 256 GeV behaving like dark matter?

LUX-ZEPLIN (LZ) experiment at the Sanford Underground Research Facility in Lead, South Dakota reports 3 sigma evidence for a dark matter particle candidate at mass above 200 GeV, WIMP as it is called. See the popular article, the Nature commentary and the research article.

TGD predicts a hierarchy of hadron physics labelled by ordinary Mersenne primes M_k= 2^k/-1 and their Gaussian counterparts. k=107 corresponds to ordinary hadron physics and k=89 to hadron physics with mass scales of hadrons which are expected to be by factor 512 higher. They should be reachable at LHC and there exist pieces of evidence for resonances identifiable as M₈₉ mesons (see for instance this, this and this).

These particles are predicted to be dark in the sense that the value of the effective Planck constant h_eff is larger than the value of ordinary Planck constant so that they do not appear in the same vertices as ordinary particles. M₈₉ hadrons would be created as their dark variants having the same Compton length as their M₁₀₇ counterparts. The strange properties of quark gluon plasma would reflect the quantum criticality for a transitions from M₁₀₇ hadron physics to M₈₉ hadron physics (see this and this).

This hierarchy applies also to leptons. The M₈₉ counterpart of electron would have mass 2^(127-89)/2 m_e= 256 GeV. If has h_eff/h equal to the ratio (M₁₂₇ /M₈₉)^1/2= 2¹⁹, it would behave like a dark matter particle and have the same Compton length as ordinary electron: this would be a prerequisite for quantum criticality. Note that also the existence of M₁₀₇ dark electron with mass of 500 MeV and M_G,113 dark electron with mass of 64 MeV is suggested.

See the article Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Is Nature a mathematician proving theorems by holography

We had an interesting discussion with Tuomas Sorakivi about metamathematics yesterday. For a mainstream physicist, mathematics is "maths": a box from which you can draw calculational methods. The physical reality behind the models is real to the physicist, and mathematics is just a tool for creating models for it.

For a Platonist, on the other hand, mathematics is real. What the mathematician himself is, remains an open question in both views. A theory of consciousness is needed. TGD proposes such a theory (see for instance this and this).

In TGD, physics represents mathematics rather than vice versa. The view of the standard physicist is turned upside down. Mathematics is Platonia identified as the "world of classical worlds" (WCW) consisting of space-time surfaces in H=M⁴× CP₂. In zero energy ontology, space-time surfaces obeying holography would represent numbers and more general mathematical objects, even theorems. Theorems can be identified as space-time surfaces which obey an almost deterministic holographic time evolution. If determinism were perfect, there would be only a single theorem - not very interesting mathematics - but this is not the case, so several theorems corresponding to different time evolutions follow from the given premises. This happens naturally. In the TGD Universe, the task of the mathematician is to become aware of the proofs that Nature produces.

This solves the problem caused by the combinatorial explosion encountered in attempts to mechanize mathematical proofs. Theorems are deduced from the axioms by rules that are analogous to the dynamic equations of classical physics. One can speak of truth-preserving dynamics. Boolean logic crystallizes these traffic rules. The problem is that these traffic rules are very weak. From given premises, a huge number of theorems can be deduced in an infinite number of ways. In practice, a mathematical machine is therefore impossible.

The combinatorial explosion can be illustrated by the set-theoretic representation of Boolean algebra. The premises correspond to the set A. The logical implication A→B corresponds to the fact that B is a subset of A. The number of subsets increases exponentially as the number of elements of A increases. There are 2^N elements among the subsets if A has N elements. The result is a combinatorial explosion.

How are human mathematicians able to derive any theorems at all? Could one think that physics comes to rescue and replaces the Boolean traffic rules with holographic dynamics for proving. Could the laws of Nature define not only the axioms but also proofs of the theorems as holographic time evolutions. Given premises A would lead to a finite number of consequences B, provided that the holographic dynamics is slightly nondeterministic. The quantum-platonism of TGD would realize this dream.

See the article G&oum;del, Lawvere, and TGD or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Cosmic birefringence in TGD framework

In Big Think Ethan Siegel has an article titled "Cosmic birefringence: the signal that could upend cosmology" (see this). I have considered the generalization of birefringence in the TGD framework in case of neutrinos (see this). The original proposal for bireferengence for neutrinos came from Anca Tureanu (see this).

What makes this so interesting is that from Atama Cosmology Telescope (ACT) collaboration, a new set of analyses has arrived (see this). From ACT alone, the significance rules out zero rotation angle (β=0°) at 2.9σ, and by jointly combining WMAP, Planck, and ACT data together, a new paper accepted in Physical Review D in August of 2026 claims to see β=0.277° +/- 0.057°, which is non-zero at 4.8σ significance.

Ordinary birefringence in condensed matter occurs because orthogonal linear polarizations travel with different velocities. This causes phase difference between polarizations visible as a rotation of the polarization plane.

Cosmic birefringence occurs because circular polarizations travel with different velocities.

1. The reason why for circular polarizations is that initial polarizations are linear with a fixed direction caused by the density perturbations (E-mode) with quadrupole character.

   E-mode polarization is generated by density perturbations such as sound waves, which are scalars. Quadrupole (4 poles) is realized as two pairs of sources of radiation in orthogonal directions and photons coming from these sources experience Thomson scattering from charged particles such as electrons. The scattering is dominantly in right angles. If the other source is more intense (hotter) the polarization (as statistical parameter) is linear and along the axis connecting the more intense source pair.

2. Also B-mode polarization is in principle possible and would be created by gravitational waves interacting with matter and inducing to the energy momentum tensor non-diagonal components. This would cause B-modes for which the distribution of scattering angles are characterized by spherical harmonics Y₂^+/-2 rather than Y₂^+/-1,0 as for E-modes. Y₂^+/-2 has characteristic sin(2φ) or cos(2φ) dependence implying cross-shaped polarization pattern with 4 angle maxima.
3. Cosmic birefringence would emerge in the following way. The original linear polarization can be expressed as the sum of circular polarizations. These travel with different velocities and this causes a phase shift. When the polarizations combine in a telescope, the resulting linear polarization is rotated by some angle by interference. Quantum effect in cosmic scales is in question and would require a revolution in cosmology and entire quantum physics.

The TGD explanation involves two new elements.

1. Quantum coherence is required in arbitrarily long, perhaps even cosmological length scales. The hierarchy of Planck constants, which includes gravitational Planck constant, makes this possible. So called massless extremals (MEs) as geometric counterparts of massless radiation realize precisely targeted propagation of photons along MEs as dark photons. Darkness means a very large value of gravitational Planck constant making possible very long quantum coherence length. The MEs can be also associated with the monopole flux tubes arriving from distant sources.
2. Also a polarization dependent light-velocityd ue to interactions with environment is required.

The possibility of warping is one of the basic differences between GRT and TGD. It makes possible reduced light velocity and the polarization dependence of the light velocity.

1. Warped space-time surfaces are flat like Minkowski space but the light-velocity is reduced because 3-space can be said to rotate along CP₂ geodesic. This notion emerged already during the first years of TGD but are only during last year (see this and this)). I have started to realize how deep its implications are. Warping effect occurs also for the fermion lines associated with the 3-D light-like parton orbits containing them.
2. Fermion line is a light-like geodesic of H = M⁴×CP₂ and also of space-time surface but its M⁴ projection is time-like geodesic of M⁴ and characterized by mass. Therefore warping gives rise to a space-time description of particle massivation.

3. Also Allais anomaly and the variation of gravitational constant could be understood (see this). In condensed matter physics refraction and reflection of light would involve change of the reduced light-velocity at the boundary between differently warped space-time regions.
4. Space-time surfaces are small deformations of these warped gravitational vacua (for warped gravitational vacua the g_tt component of the induced metric is constant deviating from unity and defines constant gravitational potential as analog of constant electric potential). Warping can be generalized to the level of Hamilton-Jacobi structure (see this).

Cosmic birefringence would emerge in the following way.

1. The MEs assigned to the photons arriving from a distant source are different from opposite circular polarizations because ME allows only single polarization which can be local. The linear polarized ME can be decomposed to a superposition of MEs with circular polarizations and the photons associated with these MEs propagate with different velocity and cause the rotation of the polarization plane observed in the measurement in which linear polarization is the outcome.
2. Cosmic birefrience also implies parity violation in cosmic scales. The hierarchy of effective Planck constants allows the weak parity violation to occur in arbitray long scales.

Consider now objections against this picture. In the standard picture the quantum superposition for linear polarizations corresponds to the superpositions for gauge potentials and this correspondence fails since the YM type field equations of the standard model are not linear. Can one accept this approximation?

TGD is strongly non-linear and linear superposition for the induced gauge potentials fails in the general case. Massless extremals (MEs) are however an exception.

1. MEs are characterized by two parameters: light-like wave vector k satisfying k· k=0 and polarization vector ε orthogonal to it satisfying k· ε=0. For the simplest MEs k and ε are constant. The inner product u=k·m of k with the vector m defined by linear Minkowski coordinates appears in the plane phase factor exp(ik·m).
2. This picture generalizes. One can assume a local light-like vector k(m) expressible as a gradient k(m)= ∇ u and thus defining tangents for coordinate curves of u. k· m→ u= ∫ ^m k(m)dm. Also ε can be made local polarization vector ε (m) as tangent vector to coordinate curves orthogonal to the local plane M² defined by light-like vector u.

   In the same way, the coordinate line parallel to ε (m) corresponds to v= ∫ ^m ε(m)dm. This would make possible local variants of polarization and light-like vector and make possible curvilinear photons.

   This picture was one motivation for introducing the notion of Hamilton-Jacobi (H-J)structure (see this) as a generalization of complex structure to M⁴. H-J structure involves a integrable distribution of hypercomplex planes defined by the local light-like vector and its dual and orthogonal complex planes defined by a complex local polarization vector and its conjugate.

3. For MEs, the superposition for waves propagating along ME in the same direction holds true and is only restricted by the condition that the amplitudes are small so that the CP₂ characterizing the induced fields are in the allowed range (say angle variable cos(θ) for geodesic sphere of CP₂. This restriction can be removed by using complex coordinates for CP₂. These coordinates are always possible and especially natural for CP₂ if holography = holomorphy hypothesis is satisfied (see this and this). Also waves with the same fixed local linear polarization can be superposed.
4. What about circular (elliptic) polarizations, which are superpositions of two linear polarizations which are not parallel? Are these possible?
   1. They could correspond to superpositions of solutions corresponding to two different polarization vectors ε₁(w) and ε₂(w) giving rise to complex polarization vectors ∫ ^mε₁(w)dw and ∫ ^mε₂(w)dw. Can these polarization vectors have phase difference?
   2. The second way to obtain circular polarization is as a rotating linear polarization. Could one assume that the local polarization ε depends on both w and u: ε ε(w,u)?
   I am unable to invent any obvious reason preventing either option.

One should also understand what happens when the linear superposition of two orthogonal linear polarizations assignable to a single ME transforms to superposition of differently warped MEs with different reduced light velocities.

1. The linear polarization can be expressed for ME with standard light velocity as a superposition of two circular polarizations with phase difference. The interaction with the environment must distinguish between these polarizations so that they must correspond to different MEs with different warping and reduced light-velocity.
2. This interaction must induce the entanglement of the circular polarization states with the environment. Entanglement must induce the warping of MEs and reduce the maximal signal velocity by giving to the photon a very small mass (see this). p-Adic thermodynamics indeed predicts this possibility (see this and this. The opposite circular polarizations would propagate with slightly different velocities so that the MEs must be different.

There is also the question about whether the photons from the remote source propagate in an entangled state all the way or whether state function reductions are possible during the travel.

1. Gravitational Planck constant characterizes a pair M,m of masses. The associated Compton length is proportional to the Schwartschild radius of the larger mass M associated with the pair of masses. For the Milky Way it is .47 ly and much shorter than the path travelled by photon in the case of cosmic birefringence. Therefore it seems that entanglement cannot be preserved during the entire trip. Quantum measurements during the travel can destroy it and interaction with the environment can transform it to superposition of circular polarizations re-entangling with the environment.
2. Zero energy ontology (ZEO) is forced by the slight non-determinism of the classical time evolution in TGD. ZEO solves the basic paradox of quantum measurement theory. In ZEO one can distinguish between two kinds of state function reductions (SFRs). The "small" ones (SSFRs) generalize the Zeno effect so that repeated quantum measurements do not leave the state invariant anymore. SSFRs are crucial for TGD inspired theory of consciousness and cognition and, somewhat surprisingly, also for the TGD description of fundamental interaction. The "big" SFRs (BSFRs) correspond to ordinary quantum measurements and they change the arrow of time. Either SSFRs or pairs of BSFRs changing the arrow of time temporarily could occur during the travel.

See the article Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Challenging the interpretation of Zero Energy Ontology

In holography = holomorphy (H-H) principle the basic objects are not 3-D surfaces but their slightly non-deterministic Bohr orbits. This forces zero energy ontology (ZEO), which solves the basic problem of quantum measurement theory. Classical non-determinism is associated with the edges of the space-time surface and plays a fundamental role in both the TGD inspired theory of conscious experience and basic quantum TGD. It is assumed that edges correspond to "small" state function reductions (SSFRs) in which quantum decoherence is assumed to occur. This also occurs in "big" SFRs (BSFRs) as the TGD counterparts of ordinary state function reductions in which also the arrow of geometric time changes. There are. however several open questions related to ZEO.

1. Are SSFRs really SFRs associated with the edges of the space-time surface or does their sequence define a TGD finite counterpart of Feynman path integral so that no decoherence would occur?
2. There are also questions related to the details of the periods consisting of SSFRs. The increase of the size of causal diamond (CD) by scalings occurring in SSFRs would allow us to understand how subjective a sequence of SSFRs corresponds to geometric time as distance between the tips of CD.

   The alternative proposal is that CD shifts gradually to the direction of the active boundary of CD at which the states do not remain fixed in SSFRs. Which option is correct? Does the size of the CD increase indefinitely or does it reduce in BSFRs so that conscious entities would experience childhood after every BSFR? Is the breaking of T symmetry (and also CP symmetry) necessary for the gradual shift of CD to a fixed time direction?

3. The feed of metabolic energy is necessary for consciousness. Sleep and wakeup can be identified as conscious states with opposite arrows of geometric time. Does the periodically varying feed of the metabolic energy from the Sun as light ,making also possible direct visual perceptions, give rise to a stochastic resonance in which the state of consciousness corresponds to flips between the potential wells of a bistable system.

See the article Challenging the interpretation of Zero Energy Ontology or the chapter Zero Energy Ontology.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

Could expolanet K2-18b serve as a seat of life in TGD Universe?

I have just developed a model for the evolution of geology and biology of Earth and this leads to a criterion for whether life can evolve on the planet (or moon) (see this). The criterion relies heavily on new physics predicted by TGD. The margin is very narrow. The criterion is rather tight and not satisfied for planets with too large Schwartschild radius to radius, for instance giant gas planets of the Earth.

1. The p-adic transition k=139→ k=137 from ordinary atomic physics to scaled down atomic physics (for which Mills has found evidence), having 4 times higher atomic binding energy scale than ordinary atomic physics, would reduce the atomic radius by factor 1/2 and increase the density by factor 8. This transition would induce scaling of the radius of Earth by factor 1/2 and subsequent Cambrian Explosion in which it increases by factor 2. This transition would bring life from underground oceans to the surface of the Earth.
2. The liberated atomic and gravitational binding energies make it possible in the case of Earth to throw out a surface layer condensing to form the Moon and metabolic energy burst generating dark atoms, analogous to Rydberg atoms with very large size, making possible large scale quantum coherence inside Earth. This generates p-Adic length scales, which correspond to biologically important scales. Large scale quantum coherence makes possible the evolution of life in the interior of the Earth. The condition that the CE in which expansion to the original radius occurs, can take place requires that gravitational binding energy per proton is larger than the atomic binding energy. This gives for the lower bound of atomic weight A as A>.3 which is satisfied.

The recently found exoplanet K2-18b is regarded as a candidate for a seat of life. In particular, there are indications that it has water at its surface. Its distance is 124 light years. Its radius and mass are R=2.61R_E and M= 8.6M_E. This gives r_s/R= 8.6/2.61∼ 3.3. The condition for A in the case of the Earth is scaled up from A>.3 to estimate A>.99 satisfied already for hydrogen atoms. K2-18b would be just at the border line but the condition making possible the expansion and burst of life to the surface of K2-18b, would be satisfied.

See the article Could the notions of quantum geology and quantum biology make sense? or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.