Wednesday, November 26, 2014

New book about TGD inspired theory of consciousness and quantum biology

During last year I have been working hardly with two book projects: one book about TGD inspired theory of consciousness and quantum biology and second one about TGD proper as a unification of fundamental interactions. One motivation for the books is that a lot has happened during since the publishing of the earlier book about TGD. The books try to condense the rather extensive amount of material appearing as 17 online books at my homepage.

The project has been extremely fruitful: I dare say that the basic principles and interpretation of TGD are now well-understood. In particular, the relationship of TGD to GRT and standard model. Also the notion of self is now formulated in simple and clear manner and the relationship between geometric time and experienced time follows in elegant manner from zero energy ontology based generalisation of quantum measurement theory.

The first book is now finished and in print. It has title "TGD Based View about Consciousness and Living Matter". The 666-page book serves as a summary about the key ideas and implications of TGD inspired theory of consciousness and of living matter.

Lambert Publishing House is the publisher. The book can be ordered at

Tuesday, November 25, 2014

Surprising finding about gamma ray bursts

I received an interesting link (thanks to Ulla) about "too high" circular polarization observed for gamma radiation arriving from the after glow assignable to the afterglow of gamma ray burst assignable to a shockwave in the proposed models (see this). The amount of energy emitted in the bursts is gigantic if the emission takes place in all directions.

  1. I have proposed a model for gamma ray bursts based on magnetic flux identified as thickened cosmic strings in which the emission takes along the flux tube and is detected only if the flux tubes happens to intersect the region where the radiation is detected. Magnetic energy would be liberated as gamma ray burst. As a matter fact, all particles would have resulted in the decay of this magnetic energy assignable to monopole flux carrying flux tubes and taking the role of the dark energy in TGD.

  2. What would be the mechanism liberating the magnetic energy? This is the key question to be answered if one assumes that ordinary matter results from the dark energy identifiable as the magnetic energy of flux tubes. Something happens to the flux tube: the natural assumption is that it gets thicker since this process occurring repeatedly would gradually lead to the recent relatively weak values of magnetic fields.

    Flux must be conserved in the process. If the p-adic length scales characterizing the flux tube increases the field strength must scale down like B ∝ 1/L(k)2 so that the field energy density per unit length proportional to B2S, S the cross section of the flux tube, scales down like 1/L(k)2. Magnetic energy is liberated and this would be transformed to the energy of dark photons arriving along the flux tube and transform partially to ordinary photons as they are detected.

Consider now the mechanism possibly generating circular polarization. By looking at Wikipedia one learns that it is not easy to get circularly polarized light by natural mechanisms. For instance, in atmosphere multiple scattering of light can produce small circular polarization and it has been suggested that this circular polarization might have induced chiral selection in biology. Two mechanisms come into mind.

  1. The first mechanism generating circularly polarized gamma rays did not come first into my mind. Photons could be created as cyclotron photons in the transitions of dark cyclotron electron (say) condensate at the flux tube. If the spin direction of the charged particles is same (spontaneous magnetization) spin flips occur in same direction spin direction and produced photons of definite helicity. The problem is that the polarization would be circular! Could this be a mechanism generating dark circularly polarized photons along the flux tube? This kind of circularly polarized photons could play also a role in the generation of chiral selection in biology.

  2. What came first to into my non-professional mind was circular dichroism. Circular polarisations have handedness: left or right. The medium in which they move could absorb second handedness more strongly and leave only the other one. [Alternatively, the propagation velocities could differ for two orthogonal directions and this would lead to a phase difference between orthogonal components of linear polarization and thus circular polarization (or elliptic more generally)]. In biology the handedness of bio- molecules is detected by different absorption of left and right polarizations. One can express the linearly polarized light entering to this kind of medium as a superposition of opposite circular polarizations. If second polarization is absorbed more strongly a circular polarization is expected.

There are two difficult questions to be answered and I try to answer these questions by using the TGD based model of chiral selection in living matter and the TGD based model for the gamma ray bursts as a starting point.

  1. How to obtain the chiral media? Could it be that there are one or more helical magnetic flux tubes with preferred chirality along which the radiations propagates as cyclotron radiation and helicality favors generation of circular polarization just as helical molecules do in living matter? Breaking of chirality analogous to that in living matter is needed: large large enough value of heff=n× h provides it in TGD framework by making possible large parity breaking effect due to weak interactions but in scale which is n times the weak scale of order 10-17 meters.

    Weak scale should be scaled up to something like wave length of gamma rays , which should roughly be of the order of the thickness of helical flux tubes. This requires quite a big value of heff/h=n. In biology n=about 1012 would bring weak scale to about 10-5 meters , which corresponds to size scale of cell (in biology this would also predict that dark photons at ELF frequencies have energies in bio-photon range). In fact, this value of n follows if the heff is identified as gravitational Planck constant, which is indeed done in the recent view about dark photons in living matter. The value of heff=h gr for a particle of mass m would be GMm/v0, where M is the mass of bigger object, now perhaps magnetar, m is the mass of particle, and v0< c is a characteristic velocity parameter for the system. hgr depends on particle but gravitational Compton length is same for all particles: a prerequisite for quantum coherence in the scale of R= GMmc/v0, which would represent the size scale of say magnetar. In fact, v0 might be estimated from this condition.

    This parity breaking could be analogous to that proposed by experimentalists to occur in heavy ion collisions for what was originally thought to be quark gluon plasma: I wrote a blog posting about this some time ago. I wrote also a posting about chiral selection in living matter. The proposed mechanisms are based also on large heff and dark magnetic flux tubes.

  2. There is also second problem related to the mechanism involving helical flux tubes. Dimensional magic suggests that the generation of circular polarization is maximal if the wavelength is of same order of magnitude as the thickness of the helical flux tube along which the radiation would arrive. For gamma rays with MeV energy the wavelength is however of order of order 10-12 meters, electron Compton length: this for the ordinary value of Planck constant. Wikipedia mentions magnetic fields strengths of order 1010 Tesla for magnetars also generating gamma ray bursts. If the magnetic flux through the tube is quantized and has minimal value (assuming that flux tubes carries monopole flux, which is possible in TGD Universe and explains the existence of magnetic fields in all scales), the estimate R &asymp: 10-13 meters follows for the radius of the flux tubes. The radius of the helical flux tube could be of course much larger.

  3. The wavelength is measured in longitudinal direction rather than in transversal direction unless large heff could strengths dark gamma ray photons only in the direction of the flux tube. Flux tube thickness need not be scaled up in h→ heff. The value of the flux quantum is proportional to heff is dictated by flux quantization. By replacing h with heff in the unit of flux quantum proportional to Planck constant, the flux quantum scales by n and the radius of the flux tube by n1/2 rather than n.

    For heff/h=n the wavelength is scaled up by n and for the values of n suggested by biology n would be of order 1012. One MeV gamma ray wave length would scale up to about .1 meters. The flux tube radius would scale to about 10-7 meters - happens to be a biological scale - 10 times the thickness of DNA coil of 10 nm. Nothing prevents assuming that that the radius of the helix is about .1 meter and thus of the same order of magnitude as wavelength.
Fractality of TGD Universe forces to ask whether there could be a connection with the findings of BICEP which have been questioned. BICEP reported an unexpectedly high linear -not circular- polarization of the cosmic ray background. The interpretation was in terms of graviton photons scattering. BICEPs findings have been questioned by Planck observatory suggesting that dust could produce the polarization. It has been also observed that graviton scattering produces an effect definitely differing from the observed one (see this). Also the applicablity of quantum field theory underlying the inflatonary models is highly questionable.

The generation of ordinary matter during TGD counterpart of inflationary period is also based on the decay of dark magnetic energy to dark photons. Could a small circular polarization of CMB serve as a signature of this process? I have already earlier considered the possibility that the magnetic fields assignable to the flux tubes could somehow be responsible for linear polarization. The above mechanism would however give circularly polarized component. I do not understand the experimental side: It seems implausible that experiments could fail to detect circular polarization.

To sum up, a possible candidate for the new physics required by the circular polarization of the afterglow would be that of dark matter in TGD sense. According to the earlier proposal, gamma ray bursts could be assigned with with decay of magnetic energy for thickened cosmic strings. The dark photon radiation could be generated at the flux tube or move along a helical thickened cosmic string and helicality could induce the circular polarization. The only justification for this picture is that it fits to the overall vision.

Thursday, November 20, 2014

How visual percepts are constructed?

How does visual system analyze the incoming visual information and reconstruct from it a (highly artistic) picture of the external world? I encountered this problem for the first time for about 35 years ago while listening some lecture about what happens in retina. I was working with my thesis as an unemployed in a job with the purpose to make me capable of getting a job in a real world (as a person suffering from a tendency to use my brains to thinking I was (and still am) labelled as a kind of socially handicapped person: in former Soviet Union I would have been labelled as a paranoid). The job itself was a purely formal duty and I was allowed to prepare my thesis rather freely (this would not be possible nowadays). I had also opportunity to listen lectures and this particular lecture series about neuroscience by Kari Kaila has teased me since then.

In the visual cortex there are so called orientation columns. They are sensitive to lines of the visual field in a specific direction. This sounded very strange to me. Why not divide visual field to small cycles or squares and be sensitive to the light in a particular square defining the bit? I learned that there are also simple and complex cells. Simple cells are sensitive to a particular line. Complex cells are sensitive to all lines with same direction.

I was also told that ganglions in retina have receptive fields. There are ganglions with on-center and off-center receptive fields. There is also a saccadic motion which is essential for visual consciousness: if it is prevented, subject persons first begins to see just darkness and eventually the visual consciousness fades away.

How to integrate these pieces to a coherent picture? During morning hours this problem popped up in my mind and I got some ideas and decided to check from Wikipedia what is known. I of course thought that this whole thing has been well-understood for decades and maybe it is! If so, I am making myself a fool: it does not however matter much at this age! I found an article about orientation columns containing a brief mention about a model for how the orientation map is constructed.

So called Moire interference of identical or nearly identical patters rotated with respect to each other by an angle produces a non-localized representation of a definite orientation. By putting the visual representation associated with approximately hexagonal lattices formed by on-centre and off-centre ganglions, one would obtain a representation of orientation somehow. I must be honest: I did not understand the idea at all! There was a reference to an article in Nature: Paik, S., Ringach, D. L. (2011): Retinal origin of orientation maps in the visual cortex. Nature Neuroscience, 14(7), 919-925. I do not have access to this article so that I can continue making naive questions and stupid arguments.

  1. What are the simplest possible visual representations of the external world? Drawings of course. Painters make first a a sketch. We have cartoons. Visualizations are typically 2-D drawings. It would not be surprising if visual system would not obey the same strategy. In finite resolution they consist of pieces of lines forming what looks like continuous structures when the length of basic piece is short enough as anyone who has used drawing programs knows. Maybe brain and retina first build this kind of representation and add colours and other details later.

  2. Could ganglia or possible linear structures formed from them effectively see through slits? They would be specialized to detect the presence of this kind of lines of some minimal length defining the resolution and going through through the centre of retina. When the line is parallel to the slit associated with the detector, the line detector sends nerve pulses to brain.

  3. There is a problem. If the orientation of eye remains fixed, the line detector sees only the lines going through the normal of the retina at its centre and usually sees nothing. Most of visual field would remain unseen.

    Saccadic motion saves the situation. When the normal of the line detector intersects the line of visual field with a proper orientation, it detects a line. For a given light intensity the input is maximal if the line is longer than the maximal length of line source for which detector is sensitive. The total intensity of incoming light through the slit is enough to build the representation. The output is bit telling whether a piece of line is there or not.

  4. These inputs from slit detectors would be the basic inputs fed to the complex cells forming representations of the lines. In visual cortex the information from the orientation of retina combined with the bits produced by slit detectors during a saccadic motion lasting so long a period that large enough number of orientations of normal are scanned, are combined to a drawing.

    T= .1 seconds is the croon of time for sensory percepts. and is the natural guess for this period of integration. The maximal angular speed of saccadic motion is for humans about 900 degrees/second making 90 degrees per time interval T (see this).

    Certainly there must exist a feedback from brain favoring preferred saccades using already existing information about the distribution of lines so that for targets which are stationary saccades would go along the lines of the already existing picture and detect if changes have occurred.

  5. If the object remains in good approximation at rest during this period, a drawing about the external world is obtained as an outcome. The simplest guess is that orientation column at particular point of visual cortex corresponds to a point in the visual field and if there is line of defined direction going through that point of visual field, simple cell sensitive to that orientation receives input.

  6. Could ganglia themselves see the world through a slit? One can argue that if this were the case, it would have been observed experimentally. I tend to agree. One can of course ask whether saccadic motion necessary for visual consciousness effective blurs the visual field of the ganglion so that it is disk of radius defined by the maximal length of line for which ganglion is sensitive.

    The simplest and probably the correct assumption is that ganglia indeed detect spots of light or absence of it. Line detectors would correspond to lines formed by ganglia or perhaps similar structures at higher levels of the neural hierarchy.

    Since I love magnetic flux tubes, I cannot resist the temptation to connect the ganglia by flux tubes to form these lines so that one would have a grid lines of ganglia analogous to a the radial lines of a coordinate grid of cylindrical coordinates with origin at the centre of retina. Peripheral regions would correspond to a poorer resolution if this is the case. Maybe macroscopic quantum coherence would enter the stage here and allow to bind the percepts about spots to a percept about line.

Of, course this idea is just a first guess reflecting my deep ignorance about how visual representations are formed, and certainly the details, if not the whole idea, are wrong.

Wednesday, November 19, 2014

Mysterious long range correlations between spins of distant quasars

The European Southern Observatory announced today (November 19, 2014) that its Very Large Telescope in Chile has revealed something downright odd. That is, the rotation axes of the central supermassive black holes in a sample of quasars are parallel to each other over distances of billions of light-years (see this, thanks for Ulla for the link).This kind of long range correlations look indeed very strange in the framework of standard cosmology where local thermal equilibrium should destroy all long range correlations.

I remember that analogous findings have been made for spin directions of distant stars but now distances are indeed enormous, larger than the length scale .1 billion years for the large voids. Also the stars are aligned along lines.

TGD explanation is one of the oldest pieces of TGD inspired cosmology and was originally proposed as an explanation for why galaxies are arranged like pearls in necklace. Key players in the model are of course cosmic strings thickened to flux tubes during cosmic evolution so that their magnetic fields and energy densities reduced. Living matter would be full of them! This would be the new element needed to explain the findings.

The cosmic strings preceded the visible matter resulting in their partial decay when space-time in the usual sense formed from the soup of cosmic strings (string-like 4-D surfaces with only 2 big dimensions). String gas condensed to form space-time (analog of inflationary period) and radiation dominated cosmology emerged. Elementary particles emerged as energy of cosmic string. In inflation theory they are believed to emerge from inflation fields for which there is however no support.

Expanding cosmic strings would be still there ands since they carry topological monopole fluxes (made possible by CP2 geometry) give rise to magnetic fields in all scales without need for currents to create them: the existence of these magnetic fields is a mystery in standard cosmology. Their magnetic energy is the mysterious dark energy and their description in TGD framework requires small cosmological constant. Also galactic dark matter could be mostly dark magnetic energy assignable to the galactic dark string going through the galaxy: this explains elegantly the constant velocity spectrum of distant stars in galactic plane.

Quasars and also other matter in scale of billions of light years results as decay products of cosmic strings and quasars formed kind of pearls in necklaces defined by cosmic strings. The interactions of primordial quasars with cosmic strings and each other at time when they were near to each other implies strong correlations between spins of these objects. The main deviation from standard cosmology is that the seeds of stars existed already during transition to radiation dominated era.

The parallel spins of quasars could originate from that of cosmic string. The simplest cosmic string is at rest in comoving coordinates (Robertson-Walker coordinates) and is parallel to x axis as one goes to plus/minus infinity but has kink near origin (sigma curve) (see this). In local Minkowski coordinates it appears to be differentially rotating since cosmic radial coordinate r is expressible as r= rM/a, a the cosmic time, and therefore depends on time since angle coordinate Φ along string is function of r and thus of rM/a, and therefore of cosmic time.

The quasars could be generated in the region in two strings have made a close encounter: the center of Milky Way gives support for this. The angular momentum and energy lost by cosmic string goes to the quasars and they start to spin in the same direction as cosmic strin rotates locally. Analogous mechanism could explain why planets tend to rotate in same direction.

Tuesday, November 18, 2014

Evidence for astrophysical phase transitions of ordinary matter to dark matter?

I received a link to an interesting article about the problem of unseen neutron stars. According to current astrophysical and cosmological models, several hundred pulsars should be orbiting the supermassive blackhole believed to reside at the heart of the Milky Way. The searches for these pulsars by looking for radio waves has found none. This is known as missing pulsar problem.

Researchers suggest that dark matter could destroy these neutron stars by transforming the to black holes. In a region of high particle density an enormous amount of dark matter particles could accumulate in a pulsar, causing it to grow massive enough to collapse and form black hole.

A TGD variant of this explanation would be that ordinary matter in neutron stars suffers a phase transition to dark matter, which in TGD framework corresponds to a phase of ordinary matter with non-standard value of Planck constant heff= n×h and becomes invisible. As a matter of fact, blackholes in TGD Universe would most naturally consist of dark matter. Also the interior of blackhole would be different: at the space-time sheet defining the should-be blackhole the metric would have Euclidian signature: an enormous wormhole contact with size scaled up by heff/h to a size above Schwartschild radius would be in question carrying matter at its boundary. Also astrophysical objects consisting of ordinary matter would have formed around dark matter seeds. For instance, planetary orbits could have contained torus-like accumulations of dark matter and might still do so.

One can couple this assumption with the proposal of Nottale introducing gravitational Planck constant hgr= GMm/v0, where v0 corresponds rotational velocity scale in a system of masses M and m. The gravitational Compton length does Lgr=hgr/m= GM/v0 does not depend on particle mass at all, which makes the situation ideal for macroscopic quantum coherence. Note that the radius is larger than the Schwartschild radius rs= 2GM for v0/c<1/2. Upper bound might be actually light velocity: at this time of day I am too tired to to check the numerical factor, sorry!;-)

One of the basic predictions relates to gravitational radiation: low frequency dark gravitons would have energies scaled up by a factor heff/h= n from their values for ordinary gravitons. The detection of dark graviton would require a phase transition of the dark graviton into a high energy ordinary graviton or a bunch of ordinary gravitons. Without this decay dark gravitons are not observed at all. All these options could mean that LIGO will not observe gravitons at all since ordinary and dark gravitons behave very differently!

If m is some elementary particle mass, the values Planck constant are of the same order of magnitude as needed in TGD inspired model of living matter. The proportionalty of heff/h to m implies that cyclotron energies of charged particles do not depend on the particle mass at all and the spectrum of energies is universal. This would mean in living matter that the energy scale is in the range of visible and UV energies for photons guaranteeing that the effects on organic molecules are maximal. Bio-photons would result in a phase transition transforming them to ordinary photons with ordinary value of Planck constant.

Monday, November 17, 2014

Harmony, music, and religious myths

I have talked about the notion of harmony based on icosahedral representation of 12-note scale and its connection with biology and consciousness coming from the observation that the number of faces of icosahedron is 20 - the number of amino-acids. The link connecting music with biology would be via the geometry of Platonic solids: icosahedron and also tetrahedron.

The 12 vertices of icosahedron correspond to the notes of the 12-note scale and to some Hamilton's cycle defining a closed curved connecting nearest neighbour vertices: it is closed by octave equivalence and does not intersect itself. Quint cycle assigns to each vertex a note of the scale and thus also to every face (triangle) of the icosahedron a chord. These chords define the harmony and there are 11 cycles/harmonies allowing symmetries (6 cycles without symmetries). They fall in three types corresponding to symmetry group Z6= Z3rot× Z2refl, Z4=Z2rot× Z2refl , and Z2= Z2rot or Z2=Z2refl, which is subgroup of icosahedral isometries A5× Z2refl having 2× 60 elements. Just these groups appeared in the model of genetic code inspired by observations about the structure of the code table telling the numbers N(d) of amino-acids coded by d codons.

These symmetries define a hierarchy of symmetry breakings. This hierarchy has amazing connections with the myths, which I believe to reflect deep facts about consciousness and biology at fundamental level. The story of genesis is a good representative in this respect.

  1. The hierarchy of symmetry breakings proceeding from Z6 down to Z2refl brings strongly in mind evolution as loss of innocence. For Z6 one as 4 orbits. One orbit contains 2 triangles (chords, DNA codons assignable to ile). The other orbits correspond to six codons assignable to amino-acids ser, arg, and leu. The chords at the orbits are major chords and 7-chords, and minor chords and 6-chords for the inverse of the harmony.

    There are no dissonant chords in 0-quint sector: dissonances appear only for the remaining groups as 0-quint chords. This is musical representation of paradize. This harmony is based on 6-note scale for the basic notes of the chords and used by impressionistic composers. Amino-acids correspond to selections of preferred chord from each orbit and there are only four different chords: this sub-harmony is very simple. Life in paradize is simple!

  2. Next comes an intriguing observation. The number of amino-acids obtained as projections of the icosahedral DNA orbits is 19, not 20! One chord does not correspond to amino-acid: it is non-playable chord! Could it be impossible to have 20 amino-acids as projections of the orbits and that 19 is the maximum number? The reason for 19 is that the number of amino-acid of type Z6 is 3+1=4 rather than 5. Therefore there is one "non-playable" chord - located at the "paradize orbit" -, which does not correspond to any amino-acid. The natural identification of the non-playable chord is as one of the aug type chords (say CEG#, which is the last breath in many finnish tangos telling about unhappy love end - something between happy CM and sad Am, "raueta" is finnish word for this manner to come to an end: "expire" might be the nearest english counterpart). This chord is located at the 2-chord orbit related to the other chord of the orbit by half-octave shift (chords could be CEG# and F#BbD), the tritonus denied by church.

    One cannot avoid the associations between non-playable chord and the denied fruit hanging in the tree of good and bad knowledge in the story of Adam and Eve, and its analog in many fairy tales. The non-playable chord also brings in mind the hilarious story of Gödel-Escher-Bach about non-playable record (a truth unprovable in given axiom system).

  3. The hierarchy of symmetry breakings leading from Z6 to Z2refl encourages one to continue with the biblical analogies. Z6, Z4 and Z2rot cycles have half-octave shift as a symmetry: good and evil do not exist in paradise, but dissonances are already there for Z4 and Z2 harmonies - the evil snake! These states correspond to the consciousness of animals, children, and saints. Note that bio-harmony corresponds to the presence of one sub-harmony of type Zn, n=6,4,2.

  4. The banishing from the paradize takes place as Z2refl symmetric harmony replaces Z2rot harmony: half-octave shift is not a symmetry anymore, and one can tell between good and evil, and eventually church decides to deny tritonus as a symbol of evil! Paradise is left as icosahedral and tetrahedral code are fused to form the tetra-icosahedral code - the ordinary genetic code leading to the breaking of Z2refl symmetry.

  5. In banishment punct ("empty" amino-acid) as a counterpart of chord shared by tetrahedron and icosahedron emerges and means stopping of the music piece altogether. Death of the sinner! For unfused codes this chord is playable as Sec/Pyl and the music piece is never-ending: life is eternal in paradise! No notion of time, no sin, no death! Amusingly, impressionist music with 6-note scale is music of "now", attempt to catch this moment.

For details see the chapter Quantum model for hearing or the article Geometric theory of harmony.

Sunday, November 16, 2014

Neutrinos from the galactic center as a further piece of evidence for many-sheeted space-time?

One of the basic predictions of TGD is the variation of effective light velocity determined in terms of the time taken to travel from point A to B. This time depends on the space-time sheet along which the photon, neutrino or some other elementary particle propagates (note that neutrinos are not quite massless). This effect is one of the key signatures of many-sheeted space-time manifesting as anomalies of general relativity.

The space-time of general relativity corresponds to effective space-time obtained by replacing the sheets of space-time with single region of Minkowski space with metric replaced with the sum of empty space Minkowski metric with the deviations of the induced metrics of the space-time sheets (effects of classical fields on space-time sheets on test particle sum up since it touches all the space-time sheets: linear superposition of fields is replaced with that for their effects).

SN1987A supernova provides first evidence for the presence of several space-time sheets. Neutrinos came as two bursts and before photons. The variation of effective light-velocity was of order Δ c/c ≈ 2× 10-9. Opera experiment claimed much larger variation of order: Δ c/c ≈ 10-5: unfortunately there was an error in the analysis of the experiments. Now Lubos has a posting about galactic blackhole Sagittarius A as neutrino factory. Chandra X-ray observatory and also Nustar and Swift Gamma-Ray Burst Mission detected some X-ray flares from Sagittarius A. 2-3 hours earlier IceCube detected high energy neutrinos by IceCube on the South Pole. As a good conservative Lubos of course denies the effect as he denies also climate warming. He did not however claim that experimenters are communists;-).

Could neutrinos arrive from galactic center? If they move with the same (actually somewhat lower) velocity than photons, this cannot be the case. The neutrinos did the same trick as SN1987A neutrinos and arrived 2-3 hours before the X-rays! What if one takes TGD seriously and estimates Δ c/c for this event? The result is Δ c/c ∼ (1.25-1.40 )×10-8 for 3 hours lapse using the estimate r= 25,900+/- 1,400 light years (see this). Δ c/c is by a factor 4 larger than for SN1987A at distance about 168,000 light years (see this). This distance is roughly 8 times longer. This would suggests that the smaller the space-time sheets the nearer the velocity of neutrinos is to its maximal value. For photons the reduction from the maximal signal velocity is larger.