Concentric circles in WMAP and Penrose's vision about pre Big-Bang

Phil Gibbs told in Vixra log about the new paper by Penrose and Gurzadyan entitled Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity. I do not really understood how the circles of enhanced coherence for temperature fluctuations could follow from Penrose's theory. Probably so because I do not even understand Penrose's theory;-). Ulla asked in Vixra log about the possibility that they could have Big-Bang origin. One can also ask whether they could have post Big-Bang origin. The following is the typo free version of my comment in Vixra log with some little additions.

If one allows more general 1-D curves as curves of coherence one can perhaps consider something like this.

1. These curves should correspond to intersections of 2-D surfaces at which the inhomogenities of mass density causing the temperature fluctuations tend to be concentrated. There would be enhanced coherence along these surfaces if mass density at these surfaces is reasonably constant.

2. The intersections of these 2-D surfaces with the sphere from which the radiation comes from for a given red-shift would define 1-D circles of exceptional coherence. Concentric circles of coherence look something too specific.

3. More concretely, what comes in mind at the level of experimental facts are the large voids of scale 10⁸ light years having galaxies at their boundaries. If one believes in fractal universe these kind of honeycomb like structures should appear in a hierarchy of discrete length scales..

One can continue even further to the murky depths of TGD.

1. Suppose that one believes that the flatness of 3-space is not due to inflation but due to a period of quantum criticality (dark matter energy as phases with gigantic value of Planck constant). Criticality is characterized by long range fluctuations and fractality. Therefore one indeed expects a fractal honeycomb manifesting itself as a hierarchy of coherence circles in WMAP.

2. Diving still deeper and taking seriously p-adic length scale hypothesis, zero energy ontology, and causal diamonds, one would end up with the possibility that the fractal honeycomb with preferred size scales of cells coming as half octaves or powers of two or subset of them. This fractal structure would expand in various scales by discrete jumps involving perhaps the increase of gravitational hbar as the size of CD is scaled up by two.

3. We are now very deep -near to the bottom- and there is still some oxygen left which we can waste to our last speculations. Could it be that these astro quantum jumps have occurred even at the planetary level: could large hbar quantum version of Expanding Earth Theory make sense;-). Now we have no oxygen anymore. I am sorry. Maybe I should have warned;-).

Speaking seriously, one can ask whether these reckless speculations could share something with Penrose's theory. Minkowskian conformal invariance is an essential element of Penrose's theory. Minkowskian conformal symmetry is important also in the recent proposal for how twistors diagrams generalize in TGD framework so that a connection at some abstract level can be imagined.

1. Causal diamonds are defined as intersections of future and past directed light-cones and bring very strongly in mind Penrose diagrams. They indeed define causal units and thus serve as their analogs with upper and lower light-like surfaces of CD serving as the analogs of the conformal infinities at which the positive and negative energy parts of zero energy states reside. Negative/positive energy part of zero energy state looks big crunch or big bang depending on which time direction one looks.

2. There would be fractal hierarchy of these CDs within CDs - a fractal hierarchy of cosmologies within cosmologies. Note however that the notion of cosmology is somewhat generalized to include also elementary particles at the lower end of hierarchy;-). For electron with ordinary value of Planck constant this sub-cosmology has duration of .1 seconds in Minkowski time, which happens to correspond to the fundamental bio-rhythm.

Addition: I listened a popular science program about inflation yesterday in radio. These programs are very conservative as is science in Finland but of high quality, which cannot be said about many popular science TV programs made with big money at the other side of ocean.

The possible failure of Gaussianity - meaning a complete absence of long range correlations in the spectrum of temperature (mass density) fluctuations - is the hot topic of cosmology nowadays and the data from Planck satellite might resolve the problem within two years. The claim of Penrose and Gurzadyan is that these correlations are visible already in WMAP data. Note that the appearance of bon-Gaussian correlations is different from what one would expect from field theory models on basis of correlation functions since the prediction is correlations on 2-D surfaces. An interesting possibility is that holography allows ot interpret these surfaces as structures assignable to partonic 2-surfaces.

I learned that the presence of these correlations would kill all inflationary models with only single inflaton field. Theoreticians are however skilled and in the worst horror scenario this could lead to a decades of resuscitation attempts by bringing in more and more complexity. Already now there exists huge number of almost working inflationary scenarios.

Also TGD -or at least a big and beautiful part of it- is in a danger zone. The absence of long range correlations would kill the explanation of flatness of three-space as a consequence of quantum criticality - long range correlations in large range of scales are after all the basic prediction of criticality.

Addition: Lubos Motl wrote a second posting about the finding of Penrose and Gurzadyan. Lubos claims that Penrose and Gurzadyan have rediscovered the already known WMAP excess at L=40 partial wave, which indeed represents deviation from the predictions of the inflationary scenario. This additional exceptionally large harmonic would produce the circles but what is the origin of this harmonics? But could it be just what Penrose and Gurzadyan are claiming or something or just single partial wave which is especially strong and what does this mean? Concentric surfaces intersection the z=constant sphere?

Addition: The preprints of Moss et al and Wehus et al claim that the concentric circles of Penrose and Gurzadyan can be reproduced in simulations. Penrose and Gurzadyan have responded the critics and claim that the simulations cannot reproduce the entire series of circles and that there are also other delicate misinterpretations. Personally I remain confused.

I would be happy if someone would list the reasons for believing that exponential expansion is the only explanation for the flatness of 3-space. Is there convincing evidence for exponential expansion? Or is it only flatness which is seen as evidence for the inflation?

Of course, exponential expansion would smooth out the inhomogenities but Lorentz invariance of the space-time sheet representing cosmological evolution could alone explain this since ground states tend to be highly symmetric. There is also a sequence quantum jumps replacing quantum superposition of cosmologies in 4-D sense (making sense in TGD framework where strong form of holography holds true) with a new one in each quantum jump and this evolution could lead to a situation in which the superposition involves only small deformations of Lorentz invariant cosmology. Kind of approach to highly symmetric ground state but in 4-D sense.

Mickelson-Morley experiment revisited again

For almost year ago I told about a variant of Mickelson Morley experiment performed by Martin Grusenick. He found that the interference pattern changed during vertical rotation. The experiment generated enthusiasm in people taking seriously the notion of aether although the explanation in terms of aether was excluded by very simple considerations. I proposed a possible explanation of the effect (assuming it is real) in terms of new gravitational physics possibly provided by TGD. The model involved one parameter whose size determined whether the effect is there or not.

I am grateful for Frank Pearce for informing me almost year later (20.11. 2010) that he has carried out the Grusenick experiment again. There is small movement of the interference pattern during vertical rotation but nothing comparable to that detected by Grusenick so that the effect is very probably an artifact due to instabilities associated with the central mirror. An excellent video Vertical Michelson Morley Interferometer Experiment 11 12 2010 about Pearce's version of the experiment can be found here.

What might be the origin of Fermi bubbles?

Fermi-LAT satellite has product new interesting data about Milky Way central region commented already by Lubos. The following is the abstract of the article Giant Gamma-ray Bubbles from Fermi-LAT: AGN Activity or Bipolar Galactic Wind? by Meng Su, Tracy R. Slatyer and Douglas P. Finkbeiner.

Data from the Fermi-LAT reveal two large gamma-ray bubbles, extending 50 degrees above and below the Galactic center, with a width of about 40 degrees in longitude. The gamma-ray emission associated with these bubbles has a significantly harder spectrum (dN/dE ≈&E^-2) than the IC emission from electrons in the Galactic disk, or the gamma-rays produced by decay of pions from proton-ISM collisions. There is no significant spatial variation in the spectrum or gamma-ray intensity within the bubbles, or between the north and south bubbles. The bubbles are spatially correlated with the hard-spectrum microwave excess known as the WMAP haze; the edges of the bubbles also line up with features in the ROSAT X-ray maps at 1.5-2 keV. We argue that these Galactic gamma-ray bubbles were most likely created by some large episode of energy injection in the Galactic center, such as past accretion events onto the central massive black hole, or a nuclear starburst in the last ≈&10 Myr. Dark matter annihilation/decay seems unlikely to generate all the features of the bubbles and the associated signals in WMAP and ROSAT; the bubbles must be understood in order to use measurements of the diffuse gamma-ray emission in the inner Galaxy as a probe of dark matter physics. Study of the origin and evolution of the bubbles also has the potential to improve our understanding of recent energetic events in the inner Galaxy and the high-latitude cosmic ray population.

The article contains a long highly technical description of findings. I of course do not have real understanding about this side. The results however seem to be rather clear. There is bubble and its mirror image (bringing in the mind of Lubos infinity symbol) with a center in the galactic nucleus. In these regions there is no significang spatial variation of the gamma ray intensity. The radius of the bubbles is about 5 kparsecs. The X-ray maps in energy range 1.5-2 keV suggest features consistent with the identification as Fermi bubbles. Also the WMAP microwave excess known as microwave haze is consistent with Fermi bubbles.

What could be the mechanism producing the gamma rays?

1. I do not regard the explanation in terms of a catastrophic event terribly convincing since I find it difficult to understand the symmetry with respect to the galactic plane for this option. Rather, the notion of many-sheeted space-time would suggest that quasi-static structures are involved.

2. Fractality of TGD Universe would encourage to consider analogies with the physics of stellar objects, maybe even planets. The nearest and best known example is Earth itself with its magnetic fields and associated van Allen radiation belts. Could Fermi bubbles correspond to a dipole magnetic field with dipole in the direction of galactic plane? Could the dipole correspond to the galactic bar? The estimates for its size vary in surprisingly large range of 1-5 kparsecs but are reasonably near to the size scales of the bubbles which is around 10 kparsecs.

3. One could perhaps imagine the analogs of van Allen radiation belts with very energetic particles originating from the galactic bar a nd traveling along flux quanta (back and forth?) and radiating gamma rays, whose energies would vary up to 100 GeV at least. In the magnetohydrodynamic approximation the charged particles would move along the field lines of the magnetic field. There is however energy conserving Lorentz force present (plus possibly the Coulomb force caused by electric field) and this causes the emission of radiation.

4. In TGD framework the decay of string like object defined by bar could generate extremely energetic particles -say electrons- propagating along the flux quanta. The emission of gamma rays would be especially intensive near turning points where the direction of motion of charged particle is changing most intensely. This would occur near galactic plane where the direction of the magnetic field is changing.

One could bring more TGD to this picture.

1. In TGD vision galaxies are like pearls in the necklace represented by long cosmic strings. These cosmic strings are not the cosmic strings are in GUTs but string like 3-surfaces predicted by TGD dominating the very early cosmolgy and gradually developing an increasing size for their Minkowski space projection with in the ideal case is 2-D. These cosmic strings would be responsible for the magnetic fields filling the Universe but very poorly understood in the standard cosmology. The jet orthogonal to the plane of galaxy would be associated with the "big cosmic string" defining the necklace.

2. Also the galaxies themselves could correspond to decay producs of cosmic strings. They could be closed or open: maybe the two cases correspond to elliptic and spiral galaxies. The galactic bar for spiral galaxies could correspond to decay products of open cosmic string. A straight cosmic string with length L corresponds to an object with mass which is roughly 10^-4 times the mass of black hole with radius L. If the cosmic string is highly entangled, its mass can approach to that of black hole and supermassive galactic black hole with a size of about 150 light seconds could correspond to a highly entangled piece of cosmic string.

3. Open cosmic strings could decay to ordinary matter at their ends. During quasar phase this process would be especially effective and could be partially responsible for gamma ray beams in the direction of the string and producing gamma ray bursts. Kind of cosmic fire crackers would be in question and galactic bar could represent remnants of this kind of fire-cracker still emitting matter travelling along the flux quanta of the galactic magnetic field and producing the gamma radiation.

4. There should be strong magnetic fields associated with these objects. In TGD Universe they would correspond to space-time sheets defining flux tubes or flux sheets of magnetic field. Charged particles would travel along these flux sheets and dissipate their energy by emitting gamma rays.

An interesting question is whether it makes sense to speak about cyclotron states at the flux tubes of the magnetic field and assign the X rays or microwaves with the cyclotron emission.

1. The d'Alembertian for a relativistic motion in constant magnetic field reduces to free motion in longitudinal direction and harmonic oscillator in the transversal directions. By generalizing the non-relativistic formula one one obtain the dispersion relation

   E = (p²+2n × h× eB)^1/2 .

   Here p is the momentum parallel to the flux tube. The magnetic contribution to the energy is completely neglibible in gamma ray range unless magnetic field is very strong.

2. The unit of transversal magnetic energy corresponding to Δ n=1 in the formula for the energy is h× eB/E obtained by replacing mass with energy in the classical formula. For relativistic energies these energies form a continuum. Magnetic confinement suggests that the value of the galactic magnetic field should be such that the transversal contribution to the energy is comparable to the longitudinal energy. For magnetic field of 1 Tesla L= sqrt(h/eB) corresponds to magnetic length of order nm which corresponds to energy of order 10² eV. For ordinary value of Planck constant 100 GeV would require a magnetic field with magnitude of order 10⁹ Tesla. 10⁸ Tesla is the value of B assigned with typical pulsars but there is also a class of pulsars with 1000 stronger magnetic field. One might expect magnetic fields with at strength of at least 10⁸ Tesla in the galactic nucleus.

3. How the scaling of scaling of Planck constant for dark matter affects the situation? Large values of Planck constant correspond to integer multiples h=nh₀ of ordinary Planck constants and coverings of the imbedding space. This would suggest that the total magnetic flux remains constant and is only divided between N sheets so that the formula for the energy is unaffected for a given sheet of the covering.

Octonions at Institute of Advanced Study

Atiyah should have given last week a talk entitled Quantum Gravity and the Riemann Hypothesis in Instutute of Advance Study. This talk was canceled and Kea tells that the title of the talk was Octonions and the four forces of Physics. In the conference program the title of his talk held at Friday November fifth was Exploring the Geometry Behind the Quantum Universe. So what Atyiah did really talk about? Kea also informs that Atiyah concluded his talk with

You can regard what I say as nonsense, or you can claim that you know it already, but you cannot make these two claims together.

This does not give any clue.

Why I am worrying about what Atiyah really did at Friday November fifth is very TGD-centered. As you should already know, TGD is more or less what I am - or more precisely, what has been left of me under the squeeze of cruel academic forces. If Atiyah indeed talked about octonions, I have the courage (in my pitifully crackpottish manner of course) to wonder whether my humble and shy octonionic message from the bottomest bottom of the hierarchy could have reached the Olympian heights so that even Atiyah gets interested;-). In my heart I of course know that I must understand that I am just a poor classless pariah as compared to these Brahmins of Science and it is incredibly blasphemous to even imagine that they might be interested on something that I have said!

The basic problem with octonions and quaternions has been how to bring them to physics in a manner consistent with what we already know.

1. One should build a connection with standard model quantum numbers. Here the solution comes from the observation that SU(3) subgroup of octonion automorphisms can take the role of color group. This observation leads in TGD to what I call M⁸-M⁴× CP₂ duality giving M⁴× CP₂ and therefore standard model symmetries a unique number theoretic status.

2. The signature of the imbedding space metric and space-time remains the problem and here complexified octonions and hyper-octonionic sub-spaces with Minkowskian signature is here a way out and means the replacement of number field with algebra. Same about hyper-quaternions.

3. Non-associativity is the third tough problem: the ideas about octonionic and quaternionic quantum do not work. Here however a simple solution suggests itself: associativity as the number theoretical realization of the fundamental variational principle selecting the 4-D space-time surface as quaternionic and thus associative sub-manifolds of an 8-D space-time with octonionic structure. Everything would reduce to number theory: space-time dimension, standard model symmetries, dynamics, and much more.

4. A further tough problem is what octonionic and quaternionic structure really means. The attempts to make sense of the notions of quaternion/ octonion analyticity (restricted to real analyticity) lead to conflict with what we know about wave equations. The notion of (hyper-) quaternionic and (hyper-)octonionic representations of gamma matrices turned out to be the optimal solution to the question what one means with quaternionic and octonionic structures. The first guess is that induced gamma matrices span quaternionic subspace at each point of space-time surface.

   This works if volume defines the action behind space-time dynamics but not for Kähler action. One must replace the induced gammas with modified gammas. Modified gamma matrices would span a hyper-quaternionic sub-space of octonionic gammas at each point of space-time surface. Do these surfaces define preferred extremals of Kähler action (does the same holds for any general coordinate invariance action principle)? This is the question.

Addition. From Gil Kalai's blog I learned that Atyiah indeed talked about classical number fields and physics and proposed that the four number fields could correspond to fundamental interactions with gravitation assigned with octonions. This idea looks to me more like a numerology. Notice however that other interactions than gravitation could be described in field theory framework using 4-D Minkowski space which can be interpreted in terms of hyper-quaternionic flat space. When gravitation comes into play one must have more general hyper-quaternionic sub-manifolds of hyper-octonionic space with hyper-quaternionicity defined in terms of modified gamma matrices and their octonionic representation.

Entropic gravity again

There has been a lot of talk about Verlinde's entropic gravity. The fashion and fancy hysteria familiar from the breakthough of super string models has begun. The enthusiasm is certainly partly because there are only few formulas and it is easy to tinker with them. I am also afraid that often the real motivation is the hope to deduce a formula giving a place in the history of theoretical physics with a minimum amount of hard work. Verlinde has received two million euro funding for the entropic gravity program. I hope that something emerges from entropic gravity but the horror scenario is that the story of superstrings repeats itself.

Some comments about the lectures if Verlinde

I listened the lecture of Verlinde and I must say that they failed to make me enthusiastic about the idea. I try to articulate the reasons for the lack of enthusiasm.

1. I see the identification of gravitation as a force of any kind as something horribly ugly. Everyone in the field one course knows that the realization that gravitational force is not actually a force at all was the fantastic discovery of Einstein which led to general relativity whose super-symmetric version promises to be the second candidate for the UV finite quantum field theories ever discovered. For me it is horribly light-hearted to give up General Coordinate Invariance and Equivalence Principle and replace them with some thermodynamical analogies and hopelessly fuzzy notion of emergent space.

2. In any case, the priority number one would be the formulation of entropic gravity in a general coordinate invariant manner or finding whether this is possible at all. Can the thermodynamics of holographic screens indeed lead to a genuine emergence of space-time with metric? Or is this notion of emergence actually similar self deception as the emergence of continuous space-time from something discrete?

   How to formulate thermodynamics treating space-time coordinates as macroscopic thermodynamical parameters such that general coordinate invariance for these parameters emerges. What dictates what thermodynamical parameters playing the role of space-time coordinates are allowed? What distinguishes between the space-time coordinates and other thermodynamical parameters? Why don't we experience any generalized thermodynamical coordinate as a coordinate analogous to space-time coordinate? What distinguishes between coordinate of screen and the coordinates of space-time interior? Why the dimension of the screen should be just two?

   How the space-time metric defining the distance between space-time points appearing as thermodynamical parameters emerges from thermodynamics in the case that this notion has some meaning? How can one formulate the theory at practical level without relying again and again on the basic notions of special and general relativity making the arguments hopelessly circular?

3. At least on the basis the lectures I got the impression that no dramatic progress in answering these questions has been made yet. Of course it could be that the lectures are "popular" and for this reason so fuzzy. In some arguments one takes black holes as starting point. One also brings stuff from M-theory suggesting that gravitational force between branes emerges from the interactions mediated by strings. At the same time the basic idea is however that no quantization of gravitation is needed since gravitation is indeed entropic force. The formula for the entropic force in the thermodynamics of polymers is discussed, there is good old Newton's formula for the gravitational force, and there is also Schwartschild metric and black hole horizon. How on Earth all this more or less contradictory ideas can be mutually consistent? Please, do not try to tell me that some duality brings in the harmony.

New theories have always emerged from a genuinely new ideas and new concepts. Formulas are the final outcome. To my humble opinion the tinkering with the formulas of existing theories is trying to bring life to dead bones and is dangerous because one forgets that the formulas make sense only in some context. The basic problem of the physics after the first super string revolution has been the increasing loss of conceptual economy. The loose use of dualities has led to a final loss of intellectual control and the field seems to have collapsed to a copious production of loose arguments. A thorough turnout is unavoidable sooner or later and I am afraid that both M-theory and entropic gravity end up to the recycle bin in this process.

Is 4-D holography enough?

The approach involves also holography in strong form and this is something beautiful. I see no need to complicate things by introducing fuzzy ideas about gravitation as entropic force. I have long time ago developed a beautiful theory in which space-time dimension four is completely unique.

1. The strong form of General Coordinate Invariance (GCI) plus sub-manifold gravity are all that is needed. GCI alone implies strong form of holography meaning that either light-like 3-surfaces or space-like 3-surfaces at boundaries of causal diamonds (CDs) defined as intersections of future and past directed light-cones) as basic dynamical objects. This implies effective 2-dimensionality: 2-D partonic surfaces and their 4-D tangent space data at boundaries of CDs dictate quantum physics.

2. Space-time interior defining the analog of Bohr orbit realizes quantum classical correspondence. This connection of GCI with quantum theory was something totally unexpected to say nothing about geometrization of fermion statistics in terms of gamma matrices of the world of classical worlds (the space of 3-surfaces).

3. In this framework it is also to see what goes wrong with the entropic gravity. In TGD Universe all interactions -also gravitation- can be described in terms of generalized Feynman graphs having as lines light-like 3-surfaces. The classical fields-including induced metric- at space-time surfaces provide classical correlates of these interactions required by quantum classical correspondence. The mere realization of the necessity of quantum classical correspondence might have saved us from the idea that gravitation is nothing but a macroscopic entropic force.

One might think that these discoveries alone could have some effect on colleagues but it seems that they are completely deaf to anything which does not come from the mouths of names. This opportunistic attitude is second basic disease of theoretical physics of today: it does not matter what you say, what matters who you are.

Constraint force instead of entropic force?

Entropic force does not solve the problems of general relativity based cosmology and it is only a matter of time when the claim that there is no microscopic gravitation will be shown to be wrong. There is also an article arguing that entropic gravity is in conflict with the behavior of ultracold neutrons in the gravitational field of Earth (see this) but this kind of voices are probably not heard by young career builders.

TGD however predicts a force which resolves the big problems of general relativity both at classical and quantum level. This force is the constraint force due to the condition that space-time surfaces are sub-manifolds of M⁴× CP₂. It is somewhat abstract force since it acts in the world of classical worlds. This force should replace entropic force as the hot topic of theoretical physics. As a matter fact, it should have become the hot topic already decades ago. Sub-manifold gravitation leads also to the geometrization of elementary particle quantum numbers and geometrization of classical gauge fields. Both the condition that standard model quantum numbers are obtained and number theoretic vision fix the imbedding space uniquely to M⁴× CP₂.

The huge number of unphysical degrees of freedom is the reason to the problems of both general relativity and M-theory and sub-manifold gravitation implies a huge reduction of degrees of freedom as compared to Einstein's theory. Let me represent some examples.

1. Sub-manifold constraint resolves the basic difficulty of GRT based cosmologies posed by the estimate for the natural value of cosmological constant which is by a factor of order 10¹²⁰ too large: the solutions with infinite duration are sub-critical simply by the embeddability condition. Critical and sub-critical solutions are determined apart from parameter coding for the finite duration of this kind of cosmology.

2. The mere quantum criticality requiring flatness of 3-space in TGD inspired cosmology replaces inflation whose failure was also basically due to the exponential increase of non-physical degrees of freedom. Quantum criticality also implies accelerating expansion during critical periods: the negative pressure term is essentially due to the sub-manifold constraint. As already noticed, criticality fixes the Robertson-Walker cosmology apart from a parameter characterizing its duration.

3. The landscape catastrophe of M-theory is also due to the inflationary growth of unobserved and very probably non-existing degrees of freedom.
   1. What one started from 26 years ago was string theory in 10-D background giving a nice description of what was believed to represent gravitonic scattering amplitudes in terms of Feynman diagrams.
   2. The problem was that our space-time is 4-dimensional. Instead of asking whether one could replace strings with 3-surfaces- something very natural and done by me 6 years before the first superstring revolution- the idea of spontaneous compactification was introduced. Besides stringy gravitation one had now also the classical 10-D gravitation instead of having just the 4-D gravitation of Einstein's theory. Impressive! The price to be paid for these additional degrees of freedom was that one had to understand why space-time looks 4-dimensional. Still no one knows the answer and the dreams about TOE have been buried long time ago!
   3. But even this did not work! One had to introduce also branes and the result was super-exponential increase of unobserved degrees of freedom and landscape catastrophe.
   4. Did you think that this was enough? No! It seems that F-theory with 12-D target space might give some hopes about reproducing standard model quantum number spectrum?
   God grief! Is it possible that no-one in the hegemony did realize what was happening?!

4. I hope that reader could get some impression about the deep frustration that I have felt during these years as I have been witnessing this odyssey from something might-be-reasonable to completely obvious non-sense. But even this is not enough! Gods really hate me! It is quite possible that I must wittness also the success of these so called phenomenological approaches to gravitation. Maybe the vision about gravitation as entropic force is some day the only game in the town! In any case, anyone need not come to me and tell that I did not warn!

Why positrons are so shy?

There is really dramatic news in New Scientist. Positrium atoms consisting of positron and electron scatter particles almost as if they were lonely electrons! This is called cloaking effect for positron (the article is here). If this is not a bad joke, this is something totally devastating from the point of view of QED and all that we have believed until this day;-).

I have said the words "many-sheeted space-time" and "dark matter hierarchy" so many times that it should be easy to guess that the following arguments will be attempts to understand the cloaking of positron in terms of these notions.

1. Let us start with the erratic argument since it comes first in mind. If positron and electron correspond to different space-time sheets and if the scattered particles are at the space-time sheet of electron then they do not see positron's Coulombic field at all. The objection is obvious. If positron interacts with the electron with its full electromagnetic charge to form a bound state, the corresponding electric flux at electron's space-time sheet is expected to combine with the electric flux of electron so that positronium would look like neutral particle after all. Does the electric flux of positron return back to the space-time sheet of positronium at some distance larger than the radius of atom? Why should it do this? No obvious answer.

2. Assume that positron dark but still interacts classically with electron via Coulomb potential. In TGD Universe darkness means that positron has large hbar and Compton size much larger than positronic wormhole throat (actually wormhole contact but this is a minor complication) would have more or less constant wave function in the volume of this larger space-time sheet characterized by zoomed up Compton length of electron. The scattering particle would see pointlike electron plus background charge diffused in a much larger volume. If hbar is large enough, the effect of this constant charge density to the scattering is small and only electron would be seen.

3. As a matter fact, I have proposed this kind of mechanism to explain how the Coulomb wall which is the basic argument against cold fusion could be overcome by the incoming deuteron nucleus (see this). Some fraction of deuteron nuclei in the palladium target would be dark and have large size just as positron in the above example. It is also possible that only the protons of these nuclei are dark. I have also proposed that dark protons explain the effective chemical formula H_1.5O of water in the scattering by neutrons and electrons in attosecond time scale (see this). The connection with cloaked positrons is highly suggestive.

4. Also one of TGD inspired proposals for the absence of antimatter is that antiparticles reside at different space-time sheets as dark matter and are apparently absent (see this). Also the modified Dirac equation with measurement interaction term suggests that fermions and antifermions reside at different space-time sheets, in particulart that bosons correspond to wormhole contacts (see this). Cloaking positrons (shy as also their discoverer Dirac!) might provide an experimental supports for these ideas.

The recent view about the detailed structure of elementary particles forces to consider the above proposal in more detail.

1. According to this view all particles are weak string like objects having wormhole contacts at its ends and magnetically charged wormhole throats (four altogether) at the ends of the string like objects with length given by the weak length cale connected by a magnetic flux tube at both space-time sheets. Topological condensation means that these structures in turn are glued to larger space-time sheets and this generates one or more wormhole contacts for which also particle interpretation is highly suggestive and could serve as space-time correlate for interactons described in terms of particle exchanges. As far electrodynamics is considered, the second ends of weak strings containing neutrino pairs are effectively non-existing. In the case of fermions also only the second wormhole throat carrying the fermion number is effectively present so that for practical purposes weak string is only responsible for the massivation of the fermions. In the case of photons both wormhole throats carry fermion number.

2. An interesting question is whether the formation of bound states of two charged particles at the same space-time sheet could involve magnetic flux tubes connecting magnetically charged wormhole throats associated with the two particles. If so, Kähler magnetic monopoles would be part of even atomic and molecular physics. I have proposed already earlier that gravitational interaction in astrophysical scales involves magnetic flux tubes. These flux tubes would have o interpretation as analogs of say photons responsible for bound state energy. In principle it is indeed possible that the energies of the two wormhole throats are of opposite sign for topological sum contact so that the net energy of the wormhole contact pair responsible for the interaction could be negative.

3. Also the interaction of positron and electron would be based on topological condensation at the same space-time sheet and the formation of wormhole contacts mediating the interaction. Also now bound states could be glued together by magnetically charged wormhole contacts. In the case of dark positron, the details of the interaction are rather intricate since dark positron would correspond to a multi-sheeted structure analogous to Riemann surface with different sheets identified in terms of the roots of the equation relating generalized velocities defined by the time derivatives of the imbedding space coordinates to corresponding canonical momentum densities.