5 TeV bump at CMS?

Lubos Motl tells about indications for a bump in dijet spectrum at CMS. The decay to dijets suggests interpretation as a meson like states consisting of exotic quarks. I already told about evidence for a bump at 2 TeV, whose decay signatures suggests interpretation as similar exotic meson state.

I talked in the earlier posting about the possible interpretation of 2 TeV bump as pions of M_G,79 hadron physics with masses obtained by scaling with a factor 2¹⁴. Both charged and neutral pion are predicted and the splitting of the bump to two with splitting of order 2.5 GeV serves as signature. A possible problem is that the naive scaling of the mass of ordinary pion gives mass 2.2 TeV, which is 10 per cent too high. If the mass is scaled up from the mass of M_G,89, which could have made itself visible through gamma pairs coming from galactic center one would obtain 4.4 TeV.

What about the interpretation of 5.15 TeV bump? It is easy to scale up the masses of ordinary mesons by multiplying them by factor 512 for M₈₉ and by 2¹⁴ for M_G,79. This gives a rough estimate but one can try it first in order to get at least order of magnitude estimates. The list of mesons can be found here.

Consider first M_G,79 hadron physics. m(K(79)) = 8 TeV is considerably higher than 5 TeV so that the interpretation in terms of M_G,79 hadron physics is not favored.

Consider next the interpretation as a meson of M_89> hadron physics.

1. m(π(89))= 67 GeV by naive scaling. There are indications for a meson like state with mass of about 135 GeV coming from gamma rays arriving from galactic center. p-Adic length scale hypothesis allows however to consider octaves of the masses and there are even slight indications for their occurrence. One can of course play with the possibility that a pionlike state with mass with about 67 GeV could have escaped detection? ρ(89) would have mass m(ρ(770, 89) = 385 GeV by naive scaling and if additioanal scaling by two is indeed present one would
   obtain 770 GeV.
   
   
2. Kaon mass would scale up to m(K(89))= 250 GeV. The search with "bump at 250 GeV" in Google produces search items in which 250 GeV bump indeed appears. It might well be that I have also commented this. The counterpart of spin 1 kaon K^*(891)would have mass about 445 GeV.
   
   
3. The counterpart of D meson with mass 2 GeV would have mass around 1.00 TeV. Strange D meson would have mass 1.05 TeV. The counterpart of J/Psi would have mass around 1.5 TeV. This is considerably lower than 2 GeV.
   
   
4. There are ccbar resonances Ψ and X around 4 GeV: for instance, Ψ(4160) would scale up to 2.08 TeV and could serve as a candidate for 2 TeV bump. It would be however more natural to have ground state meson and J/Psi candidate has only 1.5 TeV mass. Maybe the interpretation as M(G,79) pion is more appropriate.
   
   
5. B meson with mass 5.3 GeV would scale up to 2.65 TeV. Charmed B meson would have mass 3.14 TeV.
   
   
6. The naive scaling of the mass about 9.5 GeV bbar (Upsilon) meson would give 4.75 GeV - ten percet smaller than 5.15 GeV. If one scales up t quark mass for M₈₉ one obtains 3.6 TeV. If constituent quark mass squared is additive as p-adic mass calculations suggest, one obtains for ttbar meson mass 5.1 TeV! Note that ordinary top quark does not form hadrons since the life time against weak decays is shorter than timescale of strong interactions. For M₈₉ physics the situation might be different.
   

The ultracautious conclusion is that if the bumps are real (they need not be), the 2 GeV bump provides support for M(G,79) hadron physics and 5 GeV bump support for M₈₉ hadron physics.

Are bacteria able to induce phase transition to super fluid phase?

Claims about strange experimental findings providing support for TGD have started to accumulate in accelerating pace. During about week I have learned about four anomalies! The identification of the dark matter as h_eff phases is the common denominator of the explanations of these findings.

1. First I learned about 2 TeV bump at LHC providing evidence for M_G,79 hadron physics (I had realized that it might show itself at LHC only few weeks earlier!
   
   
2. Then emerged the finding that the knockdown of genes need not affect gene expression providing support for the vision that dark analogs of basic bio-molecules identifiable in terms of dark proton states are behind the biochemistry serving only as a shadow for the deeper quantum biology.
   
   
3. Two days ago I learned about the discoveries about Pluto by New Horizons space probe and having explanation in terms of the same model that justifies Expanding Earth hypothesis in TGD framework explaining among other things the mysteries of Cambrian explosion in biology.
   
   
4. Today I learned from Nature News that a team led by H. Auradou reports in the article "Turning Bacteria Suspensions into Superfluids" published in Phys Rev Letters that bacterium swimming in fluid do not only reduce its viscosity associated with shear stress (viscous force parallel to the surface) but makes it to behave in super-fluid like manner above a critical concentration of bacteria.
   

As the number of bacteria (E. coli) was increased, the viscosity associated with shear stress (the viscous force parallel to the surface) dropped: this in accordance with theoretical expectations. Adding about 6 billion cells (the fluid volume is not mentioned but it seems that the effect occurs above critical density of bacteria), the apparent viscosity dropped to zero - or more precisely, below the experimental resolution. The super-fluid like behavior was preserved above the critical concentration. What is important that this did not happen for dead bacteria: bacteria play an active role in the reduction of viscosity.

Researchers are not able to identify the mechanism leading to the superfluid-like behavior but some kind of collective effect is believed to be in question. The findings suggest that the flagellae - kind of spinning hairs used by the bacteria to propel themselves - should play an essential part in the phenomenon. As bacteria swim, they fight against current, decreasing the local forces between molecules that determine the fluid's viscosity. Above critical density the local effects would somehow become global.

Cates et al have proposed this kind of phenomenon: see the article "Shearing Active Gels Close to the Isotropic-Nematic Transition". The authors speak in the abstract about zero apparent viscosity.

1. The title of the article of Cates et al tells that the phenomenon occurs near isotropic-nematic transition. Nematic is defined as a liquid crystal for which the molecules are thread-like and parallel. I dare guess that in the recent case the approximately parallel flagellae would be modelled as liquid crystal like 2-D phase at the surface of bacterium. In the isotropic phase the orientations of the flagellae would be uncorrelated and long range orientational correlations would emerge in the phase transition to nematic phase.
   
   
2. Also the notions of contractile and extensile gels are introduced. Contraction and extension of gels are though to occur through molecular motors. The transformation of the fluid to apparent superfluid would require energy to run the molecular motors using metabolic energy and ordinary superfluidity would not be in question.
   
   
3. The model predicts divergence of viscosity for contractile gels. For extensile gels a zero of apparent viscosity is predicted. There is a hydrodynamical argument for how this would occur but I did not understand it. The active behavior of the bacteria would means that the gel like surface phase (nematic liquid crystal) formed by the flagellae extends to reduce viscosity. If I have understood correctly, this applies only to the behavior of single bacterium and is about the reduction of viscosity in the immediate vicinity of cell.
   
   

My deep ignorance about rheology allows me freedom to speculate freely about the situation in TGD framework.

1. In TGD inspired biology gel phase corresponds to a phase, which involves flux tube connections between basic units. Flux tubes contain dark matter with non-standard value h_eff=n× h. The h_eff changing phase transitions scaling the lengths of flux tubes proportional to h_eff are responsible for the contractions and extensions of gel.
   

   The extension of the gel should lead to a reduction of viscosity since one expects that dissipative effects are reduced as h_eff increases and quantum coherence is established in longer scales. Large h_eff phases are associated with criticality. Now the criticality would be associated with isotropic-nematic phase transition. The parallelization of flagellae would be due to the quantum coherence assignable with the flagellae.
   

   Note that the mechanism used by bacteria to control the liquid flow would be different since now molecular motors are replaced by h_eff changing phase transitions playing key role in TGD inspired view about biochemistry. For instance, reacting biomolecules find each other by h_eff reducing phase transition contracting the flux tubes connecting them.
   
   

2. This model does not yet explain the reduction of apparent viscosity to zero in the entire fluid occurring above a critical density of bacteria. What could happen could be analogous to the emergence of high T_c superconductivity according to TGD. Below pseudo gap temperature the emergence of magnetic flux tube pairs makes possible super-conductivity in short scales. At critical temperature a phase transition in which flux tubes reconnect to form larger thermodynamically stable networks occurs. One can speak about quantum percolation.
   

   The reduction of viscosity for a single bacterium could be based on the phase transition of liquid molecules to dark molecules flowing along the resulting flux tubes with very small friction (large heff) but only below certain scale smaller than the typical distance between bacteria. This would be the analog for what happens below pseudo gap. Above critical density he magnetic flux tubes associated with bacteria would reconnect and forming a net of connected flux tube paths at scale longer than inter-bacterial distances. This would be the counterpart for the emergence of superconductivity by percolation in long scales.
   
   

For a summary of earlier postings see Links to the latest progress in TGD.

New Horizons about Pluto

New Horizons is a space probe that has just been passing by Pluto and has taken pictures about the surface of Pluto and its Moon Kharon. The accuracy of the pictures is at best measured in tens of meters. Pluto has lost its status as a genuine planet and is now regarded as dwarf planet in the Kuiper belt - a ring of bodies beyond Neptune. Using Earthly unis its radius, mass (from New Horizons data), and distance from Sun are R=.18R_E, M= .0022× M_E and d= 40 d_E.

Pictures have yielded a lot of surprises. Pluto is not the geologically dead planet it was though to be. The following summarizes what I learned by reading a nice popular article by Markku Hotakainen in finnish weekly journal ("Suomen Kuvalehti") and also represents a TGD based interpretation of the findings.

1. Surprisingly, the surface of the Pluto is geologically young: the youngest surface shapes have age about 10⁸ years that is .1 billion years. This is strange since the temperature is about -240 ^oC at the cold side and it receives from Sun only 1/1000 of the energy received by Earth. Textbook wisdom tells that everything should have been geologically totally frozen for billions of years.
   
   
2. There is a large champaign in Pluto - one guess is that it has born as an asteroid or comet has collided with the surface of Pluto. The region is now officially called Tombaugh Regio. The reader can Google the reason for this. The flat region does not seem to have any craters so that it should be rather young. The boundary of this lowland area is surrounded by high (up to 3.5 km) mountains. Also these formations seem to be young. Nitrogen, methane and CO-ice cannot form so high formations.
   

   Several explanations have been imagined for the absence of craters: maybe there are active processes destroying the craters very effectively. Maybe there is tectonic activity. This however requires energy source. Radioactivity inside Pluto? Underground oceans liberating heat? Or maybe tidal forces: the motions of Pluto and its moon Kharon are locked and they turn always the same side towards each other. There is a small variation in the distance of Kharon causing tidal forces. Could this libration deform Pluto and force the liberation of heat produced by frictional forces?
   
   

3. The flat region decomposes to large polygons with diameter of 20-30 km. The mechanism producing the polygons is a mystery. Also their presence tells that the surface is geologically young: at some places only .1 billion years old.
   
   
4. The atmosphere of Pluto has also yielded a surprise. About 90 per cent of atmosphere (78 per cent at Earth) is nitrogen but it is estimated to leak with a rate of 500 tons per hour since the small gravitational acceleration (6 per cent of that on Earth) cannot prevent the gas molecules from leaking out. How Pluto manages to keep so much nitrogen in its atmosphere?
   
   
5. Kharon - the largest moon of Pluto - has radius which is half of that for Pluto. Also the surface texture of Kharon exhibits signs about upheavals and has similarities to that in Pluto. Craters seem to be lacking. North Pole has great dark region - maybe crater. Equator is surrounded by precipices with depths of hundreds of meters, maybe up to kilometers. If they are torn away so should have been also the precipices.
   
   

Can one understand the surface texture of Pluto and Kharon? For years I proposed a model for the finding that the continents of Earth seem to fit nicely to form a single supercontinent if the radius of Earth is taken to be one half of its recent radius. This led to a TGD variant of Expanding Earth theory.

1. It is known that cosmic expansion does not occur locally. In many-sheeted space-time of TGD this could mean that the space-time sheets of astrophysical objects comove at the the large space-time sheet representing expanding background but do not themselves expand. Another possibility is that they expand in rapid jerks by phase transitions increasing the radius. p-Adic length scale hypothesis suggests that scaling of the radius by two is the simplest possibility.
   
   
2. If this kind of quantum phase transition occurred for the space-time sheet of Earth about .54 billion years ago it can explain the weird things associated with Cambrian explosion. Suddenly totally new life forms appeared as from nowhere to only disappear soon in fight for survival. Could highly evolved life in underground seas shielded from UV radiation and meteoric bombardment have burst to the surface. The process would have also reduced the value of the gravitational acceleration by factor 1/4 and increased the length of the day by factor 4. The reduction of the surface gravity might have led to emergence of various gigantic lifeforms such as dinosauri, which later lost the evolutionary battle because of their small brains. Climate would have changed dramatically also and the Snowball Earth model is replaced by a new view.
   
   

If these sudden quantum phase transitions at the level of dark matter (h_eff=n× h phases of ordinary matter) is the manner how cosmic expansion universally happens then also Pluto might so the signs of this mechanism.

1. The surface of Pluto is indeed geologically young: the age is measured in hundreds of millions of years. Could the sudden jerkwise expansion have occurred - not only for Earth but - for objects in some region surrounding Earth and containing also Pluto?
   
   
2. The polygonal structure could be understood as a ripping of the surface of Pluto in the sudden expansion involving also cooling of magma and its compression (the analogy is what happens to the wet clay as it dries and becomes solid). The lowland region could correspond to the magma burst out from the interior of Pluto being analogous to the magma at the bottom of oceans at Earth. The young geological age of this region would explain the absence of craters. Also the surface texture of Kharon could be understood in the similar manner.
   
   

Could one understand the presence of nitrogen?

1. If the gravitational acceleration was 4 times larger (24 percent of that in Earth) before the explosion, the leakage would have been slower before it. Could this make it easier to understand why Pluto has so much nitrogen? Could the burst of material from the interior have increased the amount of nitrogen in the atmosphere? Geochemist could probably answer these questions.
   
   
2. A more radical explanation is that primitive life forms have prevented the leakage by binding the nitrogen to organic compounds like methane. If underground oceans indeed existed (and maybe still exist) in Pluto as they seem to exist in Mars, one can wonder whether life has been evolving as an underground phenomenon also in Pluto - as so many nice things in this Universe must do;-). Could these lifeforms have erupted to the surface of Pluto in the sudden expansion from underground seas and could some of them - maybe primitive bacteria - have survived. Nitrogen is essential for life and binds the nitrogen to heavier chemical compounds so that its leakage slows down. Could there exist an analog of nitrogen cycle meaning that underground life bind the nitrogen from the atmosphere of Pluto and slow down its leakage?
   
   

For background see the chapter Expanding Earth Model and Pre-Cambrian Evolution of Continents, Climate, and Life of "Genes and Memes".

For a summary of earlier postings see Links to the latest progress in TGD.

Direct evidence for dark DNA?!

This morning I learned in Sciencedaily about extremely interesting finding related to DNA. The finding is just what breakthrough discovery should be: it must be something impossible in the existing world view.

What has been found is that knock-out (removing parts of gene to prevent transcription to mRNA) and knock-down of gene (prevent protein translation) seem to have different consequences. Removing parts of gene need not have the expected effect at the level of proteins! Does this mean that somehow DNA as a whole can compensate the effects caused by knock-out but not those by knock-down?

Could this be explained by assuming that genome is a hologram as Gariaev et al have first suggested? Also TGD leads to a vision about living system as a conscious hologram. Small local changes of genes could be compensated. Somehow the entire genome would react like brain to a local brain damage: other regions of brain take the duties of the damaged region.

Could the idea about DNA double strand as nano-brain having left and right strands instead of hemispheres help here. Does DNA indeed act as a macroscopic quantum unit? The problem is that transcription is local rather than holistic process. Something very simple should lurk behind the compensation mechanism.

Could transcription transform dark DNA to dark mRNA?

Also the TGD based notion of dark DNA comes in mind (see this and this). Dark DNA consists of dark proton sequences for which states of single DNA proton correspond to those of DNA, mRNA, aminoacids, and tRNA. Dark DNA is one of the speculative ideas of TGD inspired quantum biology getting support from Pollack's findings . Ordinary biomolecules would only make their dark counterparts visible: dark biomolecules would serve as a template around which ordinary biomolecules such as DNA strands are formed in TGD Universe.

Although ordinary DNA is knocked out of ordinary gene, dark gene would still exist! If dark DNA actually serves as template for the transcription to mRNA, everything is still ok after knockout! Could it be that we do not understand even transcription correctly? Could it actually occur at the level of dark DNA and mRNA?! Dark mRNA would attach to dark DNA after which ordinary mRNA would attach to the dark mRNA. One step more!

Damaged DNA could still do its job! DNA transcription would would have very little to do with bio-chemistry! If this view about DNA transcription is correct, it would suggest a totally new manner to fix DNA damages. These damages could be actually at the level of dark DNA, and the challenge of dark genetic engineering would be to modify dark DNA to achieve a proper functioning.

Could dark genetics help to understand the non-uniqueness of the genetic code?

Also translation could be based on pairing of dark mRNA and dark tRNA. This suggests a fresh perspective to some strange and even ugly looking features of the genetic code. Are DNA and mRNA always paired with their dark variants? Do also amino-acids and anticodons of tRNA pair in this manner with their dark variants? Could the pairings at dark matter level be universal and determined by the pairing of dark amino-acids with the anticodons of dark RNA? Could the anomalies of the code be reduced to the non-uniqueness of the pairing of dark and ordinary variants of basic bio-molecules (pairings RNA--dark RNA, amino-acid-- dark amino-acid, and amino-acid--ordinary amino-acid in tRNA).

1. There are several variants of the genetic code differing slightly from each other: correspondence between DNA/mRNA codons and amino-acids is not always the same. Could dark-dark pairings be universal? Could the variations in dark anticodon - anticodon pairing and dark amino-acid-amino-acid pairing in tRNA molecules explain the variations of the genetic code?
   
   
2. For some variants of the genetic code a stop codon can code for amino-acid. The explanation at the level of tRNA seems to be the same as in standard framework. For the standard code the stop codons do not have tRNA representatives. If stop codon codes for amino-acids, the stop codon has tRNA representation. But how the mRNA knows that the stop codon is indeed stop codon if the tRNA associated with it is present in the same cell?
   

   Could it be that stop codon property is determined already at the level of DNA and mRNA? If the dark variant of genuine stop codon is missing in DNA and therefore also in mRNA the translation stops if it is induced from that at the level of dark mRNA. Could also the splicing of mRNA be due to the splitting of dark DNA and dark mRNA? If so genes would be separated from intronic portions of DNA in that they would pair with dark DNA. Could it be that the intronic regions do not pair with their dark counterparts. They would be specialized to topological quantum computations in the TGD inspired proposal.
   

   Start codon (usually AUG coding met) serves as a start codon defining the reading frame (there are 3 possible reading frames). Dark DNA would naturally begin from this codon.
   
   

3. Also two additional amino-acids Pyl and Sec appear in Nature. Gariaev et al have proposed that the genetic code is context dependent so that the meaning of DNA codon is not always the same. This non-universality could be reduced to the non-uniqueness of dark amino-acid--amino-acid pairing in tRNA if genetic code is universal.

Could dark genetics help to understand wobble base pairing?

Wobble base pairing is second not-so-well understood phenomenon. In the standard variant of the code there are 61 mRNAs translated to amino-acids. The number of tRNA anticodons (formed by the pairs of amino-acid and RNA molecules) should be also 61 in order to have 1-1 pairing between tRNA and mRNA. The number of ordinary tRNAs is however smaller than 61 in the sense that the number of RNAs associated with them is smaller than 45. tRNA anticodons must be able to pair with several mRNA codons coding for given amino-acid. This is possible since tRNA anticodons can be chosen to be representative for the mRNA codons coding a given amino-acid in such that all mRNA codons coding for the same amino-acid pair with at least one tRNA anticodon.

1. This looks somewhat confusing but is actually very simple: genetic code can be seen as a composite of two codes: first 64 DNAs/mRNAs to are coded to N<45 anticodons in tRNA, and then these N anticodons are coded to 20 amino-acids. One must select N anticodon representatives for the mRNAs in the 20 sets of mRNA codons coding for a given amino-acid such that each amino-acid has at least one anticodon representative. A large number of choices is possible and the wobble hypothesis of Crick pose reduce the number of options.
   
   
2. The wobble hypothesis of Crick states that the nucleotide in the third codon position of RNA codon of tRNA has the needed non-unique base pairing: this is clear from the high symmetries of the third basis. There is exact U-C symmetry and approximate A-G symmetry with respect to the third basis of RNA codon (note that the conjugates of RNA codons are obtained by A↔U and C↔G permutations).
   
   
3. The first two basis in the codon pair in 1-1 manner to the second and third basis of anticodon. The third basis of anticodon corresponds to the third letter of mRNA codon. If it is A or C the correspondence is assumed to be 1-to-1: this gives 32 tRNAs. If the first basis of anticodon is G or U the 2 mRNA basis can pair with it: they would be naturally A for G and C for U by symmetry. One would select A from A-G doublet and C from U-C double. This would give 16 anticodons: 48 anticodons altogether, which is however larger than 45. Furthermore, this would not give quite the correct code since A-G symmetry is not exact.
   

   Smaller number of tRNAs is however enough since the code has almost symmetry also with respect to A and C exchange not yet utilized. The trick is to replace in some cases the first basis of anticodon with Inosine I, which pairs with 3 mRNA basis. This replacement is possible only for those amino-acids for which the number of RNAs coding the amino-acid is 3 or larger (the amino-acids coded by 4 or 6 codons).
   
   

4. It can be shown at least 32 different tRNAs are needed to realize genetic code by using wobble base pairing. Full A-C and G-U symmetry for the third basis of codon would give 16+16=32 codons. Could one think that tRNA somehow realizes this full symmetry?
   
   

How dark variants of could help to understand wobble base pairing? Suppose for a moment that the visible genetics be a shadow of the dark one and fails to represent it completely. Suppose the pairing of ordinary and dark variants of tRNA anticodons resp. amino-acids and that translation proceeds at the level of dark mRNA, dark anticodons, and dark amino-acids, and is made visible by its bio-chemical shadow. Could this allow to gain insights about wobble base pairing? Could the peculiarities of tRNA serve for some other - essentially bio-chemical - purposes?

The basic idea would be simple: chemistry does not determine the pairing but it occurs at the level of the dark mRNA codons and dark tRNA anticodons. There would be no need to reduce wobble phenomenon to biochemistry and the only assumption needed would be that chemistry does not prevent the natural dark pairing producing standard genetic code apart from the modifications implied by non-standard dark amino-acid--amino-acid pairing explaining for different codes and the possibility that stop codon can in some situation pair with dark mRNA.

One can consider two options.

1. The number of dark tRNAs is 64 and the pairings between dark mRNA and dark anticodons and dark anticodons and dark amino-acids are 1-to-1 and only the pairing between dark RNA codons and anticodons in tRNA is many-to-1.
   
   
2. The model of dark genetic code) suggests that there are 40 dark proton states, which could serve as dark analogs of tRNA. This number is larger than 32 needed to realize the genetic code as a composite code. I have cautiously suggested that the proposed universal code could map dark mRNA states of the same total spin (there is breaking of rotational symmetry to that around the axis of dark proton sequences) to dark tRNA/dark amino-acid states with the same total spin. The geometric realization would in terms of color flux tubes connecting the dark protons of corresponding dark proton sequences. Also in ordinary nuclei nucleons are proposed to be connected by color flux tubes so that they form nuclear strings and dark proton sequences would be essentially dark variants of nuclei.
   

One should understand the details of the dark mRNA--tRNA anticodon correspondence. One can also ask whether the dark genetic code and the code deduced from the geometric model for music harmony in terms of Platonic solids are mutually consistent. This model implies the decomposition of 60+4 DNA codons to 20+20+20+4 codons, where each "20" corresponds to one particular icosahedral Hamilton's cycle with characteristic icosahedral symmetries. "4" can be assigned to tetrahedron regarded either disjoint from icosahedron or glued to it along one of its faces. This allows to understand both the standard code and the code with two stop codons in which exotic amino-acids Pyl and Sec appear. One should understand the compositeness 64→ 40\→20 of the dark genetic code and and whether it relates to the icosatetrahedral realization of the code.

I have proposed that dark variants of transcription, translation, etc.. can occur and make possible kind of R&D laboratory so that organisms can test the consequences of variations of DNA. If ordinary translation and transcription are induced from their dark variants and if dark biomolecules could also appear as unpaired variants, these processes could occur as purely dark variants. Organisms could indeed do experimentation in the virtual world model of biology and pairing with ordinary bio-molecules would make things real.

For background see the chapter Quantum Gravity, Dark Matter, and Prebiotic Evolution.

For a summary of earlier postings see Links to the latest progress in TGD.

Further evidence that 2 TeV bump could be MG,79 pion

For few days ago I told about 3.5 local sigma local evidence for a bump at about 2 TeV observed both at ATLAS and CMS. The title of the posting was "Pion of MG,79 hadron physics at LHC?". I learned about the bump from the posting of Lubos. Lubos was enthusiastic about left-right symmetric variant of the standard model as an explanation of the bump.

Lubos is five days later more enthusiastic about superstring inspired explanation of the bump . The title of the posting of Lubos is The 2 TeV LHC excess could prove string theory. The superstringy model involves as many as six superstring phenomenologists as chefs and the soup contains intersecting branes and anomalies as ingredients.

The article gives further valuable information about the bump also for those who are not terribly interested on intersecting branes and addition of new anomalous factors to the standard model gauge group. The following arguments show that the information is qualitatively consistent with the TGD based model.

1. Bump is consistent with both ZZ, WZ, and according to Lubos also Zγ final states and is in the range 1.8-2.1 TeV. Therefore bump could involve both charged and neutral states. If the bump corresponds to neutral elementary particle such as new spin 1 boson Z^' as proposed by superstring sextet, the challenge is to explain ZZ and Zγ bumps. WZ pairs cannot result from primary decays.
   
   
2. There is dijet excess, which is roughly by a factor of 20 larger than weak boson excesses. This would suggest that some state decays to quarks or their excitations and the large value of QCD coupling strength gives rise to a the larger excess. This also explains also why no lepton excess is observed.
   

   For the superstring inspired model the large branching fraction to hadronic dijets suggesting the presence of strong interactions is a challenge: Lubos does not comment this problem. Also the absence of leptonic pairs is problematic and model builders deduce that Z^' suffers syndrome known as lepto-phobia.
   
   

3. Neutral and charged M_G,79 pions can decay to virtual M_G,79 or M₈₉ quark pair annihilating further to a pair of weak bosons (also γγ pair is predicted) or by exchange of gluon to M_G,79, M₈₉ (or M₁₀₇) quark pair producing eventually the dijet. This would explain the observations qualitatively. If the order of magnitude for the relative mass splitting between neutral and charged M_G,79 pion is same as for ordinary pion one, the relative splitting is of order Δ M/M≈ 1/14 - less that 10 per cent meaning Δ M<.2 TeV. The range for the position of the bump is about .3 TeV.
   
   
4. The predictions of TGD model are in principle calculable. The only free parameter is the M_G,79 color coupling strength so that the model is easy to test.
   

For more details see the chapter New Particle Physics Predicted by TGD: part I of "p-Adic Length Scale Hypothesis" or the article What is the role of Gaussian Mersennes in TGD Universe?

For a summary of earlier postings see Links to the latest progress in TGD.

Topological order and quantum TGD

Topological order is a rather advanced concept of condensed matter physics. There are several motivations for the notion of topological order in TGD.

1. TGD can be seen as almost topological QFT. 3-D surfaces are by holography equivalent with 4-D space-time surfaces and by strong form of holography equivalent with string world sheets and partonic 2-surfaces. What make this duality possible is super-symplectic symmetry realizing strong form of holography and quantum criticality realized in terms of hierarchy of Planck constants characterizing hierarchy of phases of ordinary matter identified as dark matter. This hierarchy is accompanied by a fractal hierarchy of sub-algebras of supersymplectic algebra isomorphic to the entire algebra: Wheeler would talk about symmetry breaking without symmetry breaking.
   
   
2. h_eff=n× h hierarchy corresponds to n-fold singular covering of space-time surface for which the sheets of the covering co-incide at the boundaries of the causal diamond (CD), and the n sheets together with superconformal invariance give rise n additional discrete topological degreees of freedom - one has particles in space with n points. Kähler action for preferred extremals reduces to Abelian Chern-Simons terms characterizing topological QFT. Furthermore, the simplest example of topological order - point like particles, which can be connected by links - translates immediately to the collections of partonic 2-surfaces and strings connecting them.
   
   
3. There is also braiding of fermion lines/magnetic flux tubes and Yangian product and co-product defining fundamental vertics, quantum groups associated with finite measurement resolution and described in terms of inclusions of hyper-finite factors.
   

In the article Topological order and Quantum TGD topological order and its category theoretical description are considered from TGD point of view - category theoretical notions are indeed very natural in TGD framework. The basic finding is that the concepts developed in condensed matter physics (topological order, rough description of states as tangles (graphs imbedded in 3-D space), ground state degeneracy, surface states protected by symmetry or topology) fit very nicely to TGD framework and has interpretation in terms of the new space-time concept. This promises applications also in the conventional areas of condensed matter physics such as more precise description of solid, liquid, and gas phases.

See the chapter Criticality and dark matter of "Hyper-finite Factors, p-Adic Length Scale Hypothesis, and Dark Matter Hierarchy"

For a summary of earlier postings see Links to the latest progress in TGD.

Congruence subgroups of SL(2,R), Monster Moonshine, Gaussian Mersennes, and p-adic physics

Stephen Crowley made a very interesting observation about Gaussian Mersennes in the comment section of the posting Pion of M_G,79 hadron physics at LHC?. I glue the comment below.

Matti, why Low Gaussian primes? Your list of primes is a subset of the factors of the dimension of the friendly giant group.

The monster group was investigated in the 1970s by mathematicians Jean-Pierre Serre, Andrew Ogg and John G. Thompson; they studied the quotient of the hyperbolic plane by subgroups of SL2(R), particularly, the normalizer Γ₀(p)₊ of Γ₀(p) in SL(2,R). They found that the Riemann surface resulting from taking the quotient of the hyperbolic plane by Γ₀(p)₊ has genus zero if and only if p is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59 or 71. When Ogg heard about the monster group later on, and noticed that these were precisely the prime factors of the size of Monster, he published a paper offering a bottle of Jack Daniel's whiskey to anyone who could explain this fact (Ogg (1974)).

I must first try to clarify to myself some definitions so that I have some idea about what I am talking about.

1. Congruence group Γ₀(p) is the kernel of the modulo homomorphism mapping SL(2,Z) to SL(2,Z/pZ) and thus consists of SL(2,Z) matrices which are are unit matrices modulo p. More general congruence subgroups SL(2,Z/nZ) are subgroups of SL(2,Z/pZ) for primes p dividing n. Congruence group can be regarded as subgroup of p-adic variant of SL(2,Z) with elements restricted to be finite as real integers. One can give up the finiteness in real sense by introducing p-adic topology so that one has SL(2,Z_p). The points of hyperbolic plane at the orbits of the normalizer of Γ₀(p)₊ in SL(2,C) are identified.
   
   
2. Normalizer Γ₀(p)₊ is the subgroup of SL(2,R) commuting with Γ₀(p) but not with its individual elements. The quotient of hyperbolic space with the normalizer is sphere for primes k associated with Gaussian Mersennes up to k=47. The normalizer in SL(2,Z_p) would also make sense and an interesting question is whether the result can be translated to p-adic context. Also the possible generalization to SL(2,C) is interesting.
   

First some comments inspired by the observation about Gaussian Mersennes by Stephen.

1. Gaussian primes are really big but the primes defining them are logarithmically smaller. k=379 defines scale slightly large than that defined by the age of the Universe. Larger ones exist but are not terribly interesting for human physicists for a long time.
   

   Some primes k define Gaussian Mersenne as M_G,k= (1+i)^k-1 and the associated real prime defined by its norm is rather large - rather near to 2^k and for k= 79 this is already quite big. k=113 characterises muon and nuclear physics, k=151,157,163,167 define a number theoretical miracle in the range cell membrane thickness- size of cell nucleus. Besides this there are astro-physically and cosmoplogically important Gaussian Mersennes (see the earlier posting).
   
   

2. The Gaussian Mersennes below M₈₉ correspond to k=2, 3, 5, 7, 11, 19, 29, 47, 73. Apart from k=73 this list is indeed contained by the list of the lowest monster primes k= 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71. The order d of Monster is product of powers of these primes: d= 2⁴⁶× 3²⁰× 5⁹× 7⁶× 11²× 13³× 17× 19× 23× 29× 31× 41× 47× 59× 71 .
   

   Amusingly, Monster contains subgroup with order, which is product of exactly those primes k associated with Gaussian Mersennes, which are definitely outside the reach of LHC! Should one call this subgroup Particle Physics Monster? Number theory and particle physics would meet each other! Or actually they would not!
   

   Speaking seriously, could this mean that the high energy physics above M_G,79 energy is somehow different from that below in TGD Universe? Is k=47 somehow special: it correspond to energy scale 17.6× 10³ TeV=17.6 PeV (P for Peta). Pessimistic would argue that this scale is the Monster energy scale never reached by human particle physicists.
   

The continuations of congruence groups and their normalizers to the p-adic variants SL(2,Z_p) of SL(2,Z+iZ) (SL(2,C) are very interesting in TGD framework and are expected to appear in the adelization. Now hyperbolic plane is replaced with 3-D hyperbolic space H³ (mass shell for particle physicist and cosmic time constant section for cosmologist).

1. One can construct hyperbolic manifolds as spaces of the orbits of discrete subgroups in 3-D hyperbolic space H³ if the discrete subgroup defines tesselation/lattice of H³. These lattices are of special interest as the discretizations of the H³ parametrizing the position for the second tip of causal diamond (CD) in zero energy ontology (ZEO), when the second tip is fixed. By number theoretic arguments this moduli space should be indeed discrete.
   
   
2. In TGD inspired cosmology the positions of dark astrophysical objects could tend to be localized in hyperbolic lattice and visible matter could condense around dark matter. There are infinite number of different lattices assignable to the discrete subgroups of SL(2,C). Congruence subgroups and/or their normalizers might define p-adically natural tesselations. In ZEO this kind of lattices could be also associated with the light-like boundaries of CDs obtained as the limit of hyperbolic space defined by cosmic time constant hyperboloid as cosmic time approaches zero (moment of big bang). In biology there is evidence for coordinate grid like structures and I have proposed that they might consist of magnetic flux tubes carrying dark matter.
   

   Only a finite portion of the light-cone boundary would be included and modulo p arithmetics refined by using congruence subgroups Γ₀(p) and their normalizers with the size scale of CD identified as secondary p-adic time scale could allow to describe this limitation mathematically. Γ(n) would correspond to a situation in which the CD has size scale given by n instead of prime: in this case, one would have multi-p p-padicity.
   
   

3. In TGD framework one introduces entire hierarchy of algebraic extensions of rationals. Preferred p-adic primes correspond to so called ramified primes of the extension, and also p-adic length scale hypothesis can be understood and generalized if one accepts Negentropy Maximization Principle (NMP) and the notion of negentropic entanglement. Given extension of rationals induces an extension of p-adic numbers for each p, and one obtains extension of of ordinary adeles. Algebraic extension of rationals leads also an extension of SL(2,Z). Z can be replaced with any extension of rationals and has p-adic counterparts associated with p-adic integers of extensions of p-adic numbers. The notion of primeness generalizes and the congruence subgroups Γ₀(p) generalize by replacing p with prime of extension.
   
   

Above I have talked only about algebraic extensions of rationals. p-Adic numbers have however also finite-dimensional algebraic extensions, which are not induced by those of rational numbers.

1. The basic observation is that e^p exists as power series p-adically as p-adic integer of norm 1 - e^p cannot be regarded as a rational number. One can introduce also roots of e^p and define in these manner algebraic extensions of p-adic numbers. For rational numbers the extension would be algebraically infinite-dimensional.
   

   In real number based Lie group theory e is in special role more or less by convention. In p-adic context the situation changes. p-adic variant of a given Lie group is obtained by exponentiation of elements of Lie algebra which are proportional to p (one obtains hierarchy of sub-Lie groups in powers of p) so that the Taylor series converges p-adically.
   

   These subgroups and algebraic groups generate more interesting p-adic variants of Lie groups: they would decompose into unions labelled by the elements of algebraic groups, which are multiplied by the p-adic variant of Lie group. The roots of e are mathematically extremely natural serving as hyperbolic counterparts for the roots of unity assignable to ordinary angles necessary if one wants to talk about the notion of angle and perform Fourier analysis in p-adic context: actually one can speak only about trigonometric functions of angles p-adically but not about angles. Same is true in hyperbolic sector.
   
   

2. The extension of p-adics containg roots of e could even have application to cosmology! If the dark astrophysical objects tend to form hyperbolic lattices and visible matter tends to condensed around lattice points, cosmic redshifts tend to have quantized values. This tendency is observed. Also roots of e^p could appear. The recently observed evidence for the oscillation of the cosmic scale parameter could be understood if one assumes this kind of dark matter lattice, which can oscillate. Roots of e² appear in the model! (see the posting Does the rate of cosmic expansion oscillate?). Analogous explanation in terms of dark matter oscillations applies to the recently observed anomalous periodic variations of Newton's constant measured at the surface of Earth and of the length of day (Variation of Newton's constant and of length of day).
   
   
3. Things can get even more complex! e^Π converges Π-adically for any generalized p-adic number field defined by a prime Π of an algebraic extension and one can introduce genuinely p-adic algebraic extensions by introducing roots e^Π/n! This raises interesting questions. How many real transcendentals can be represented in this manner? How well the hierarchy of adeles associated with extensions of rationals allowing also genuinely p-adic finite-dimensionals extensions of p-adics is able to approximate real number system? For instance, can one represent Π in this manner?
   
   

See the chapter More about TGD inspired cosmology of "Physics in Many-Sheeted Space-time"

p> For a summary of earlier postings see Links to the latest progress in TGD.

Pion of MG,79 hadron physics at LHC?

For some time ago I wrote about Gaussian Mersennes M_G,n=(1+i)ⁿ-1 in cosmology, biology, and nuclear and particle physics. In particle physics paragraph appears the following line about new ultra high energy physics - perhaps scaled up copies of hadron physics.

n∈{2, 3, 5, 7, 11, 19, 29, 47, 73} correspond to energies not accessible at LHC. n= 79 might define new copy of hadron physics above TeV range - something which I have not considered seriously before. The scaled variants of pion and proton masses (M₁₀₇ hadron physics) are about 2.2 TeV and 16 TeV. Is it visible at LHC is a question mark to me.

Today I saw the posting of Lubos suggesting that M_G,79 pion might have been already seen!! Lubos tells about a bump around 2(!)TeV energy observed already earlier at ATLAS and now also at CMS. See the article in Something goes bump in Symmetry Magazine. The local signficance is about 3.5 sigma and local significance about 2.5 sigma. Bump decays to weak bosons.

Many interpretations are possible. An interpretation as new Higgs like particle has been suggested. Second interpretation - favored by Lubos - is as right-handed W boson predicted by left-right- symmetric variants of the standard model. If this is correct interpretation, one can forget about TGD since the main victory of TGD is that the very strange looking symmmetries of standrad model have an elegant explanation in terms of CP₂ geometry, which is also twistorially completely unique and geometrizes both electroweak and color quantum numbers.

Note that the masses masses of M_G,79 weak physics would be obtained by scaling the masses of ordinary M₈₉ weak bosons by factor 2^(89-79)/2)= 512. This would give the masses about 2.6 TeV and 2.9 TeV.

There is however an objection. If one applies p-adic scaling 2^(107-89)/2=2⁹ of pion mass in the case of M₈₉ hadron physics, M₈₉ pion should have mass about 69 GeV (this brings in mind the old and forgotten anomaly known as Aleph anomaly at 55 GeV). I proposed that the mass is actually an octave higher and thus around 140 GeV: p-adic length scale hypothesis allows to consider octaves. Could it really be that a pion like state with this mass could have slipped through the sieve of particle physicists? Note that the proton of M₈₉ hadron physics would have mass about .5 TeV.

I have proposed that M₈₉ hadron physics has made itself visible already in heavy ion collisions at RHIC and in proton- heavy ion collisions at LHC as strong deviation from QCD plasma behavior meaning that charged particles tended to be accompanied by particles of opposite charged in opposite direction as if they would be an outcome of a decay of string like objects, perhaps M₈₉ pions. There has been attempts - not very successful - to explain non-QCD type behavior in terms of AdS/CFT. Scaled up variant of QCD would explain them elegantly. Strings would be in D=10. The findings from LHC during this year probably clarify this issue.

See the chapter New particle physics predicted by TGD: part I of "p-Adic Length Scale Hypothesis" or the article What is the role of Gaussian Mersennes in TGD Universe?

For a summary of earlier postings see Links to the latest progress in TGD.

What music can teach about consciousness?

Recently I have been reading the book of Oliver Sacks titled "Musicophilia" dealing with various aspects of music experience. Humans as a species indeed have a very special relation to music. But is it really genuine characteristic of human consciousness? One can even ask whether consciousness emerges only in higher species or whether it could be in some form a characteric of any living or even inanimate system? I am not the only quantum consciousness theorists forced to consider panpsychism in some form. In this framework one can ask whether music like aspects of conscious experience could be universal and only especially highly developed in humans?

I restrict the consideration to those stories of Musicophilia, which I find of special interest from the point of view of TGD inspired theory of consciousness. The outcome is a more precise formulation for the general TGD inspired vision about brain based on basic ideas of quantum TGD.

Zero Energy Ontology (ZEO) implies a new view about the relation between geometric and experienced time and allowing to generalize quantum measurement theory to a theory of consciousness.

Strong form of holography implies the analog of AdS/CFT duality between 2-D representation of physics based on string world sheets and partonic 2-surfaces and 4-D space-time representations. This duality is not tautology and this inspires the idea that these two representations correspond to two modes for consciousness motivating "Left brain talks, right brain sings" metaphor.

1. Language and music could relate to two dual representations of conscious information - local and holistic, cognitive and sensory. Discretization of function/its Fourier transform as a collection of its values at discrete set values of time/frequencies would correspond local/holistic approximations of function. In principle any conscious entity - self- could utilize these two representational modes at appropriate quantum criticality.
   
   
2. The holistic "musical consciousness" is assignable to right brain hemisphere and according to the stories of Sacks seems to characterized by episodal sensory memories. TGD based view about memories relies on ZEO: the memories would be mental images with sensory input from geometric past, genuine sensory experiences of time reversed sub-selves! This picture simplifies considerably and one can see all memories - sensory, cognitive, or emotional - as analogs of phantom pain, which would be also a sensory memory and even more a genuine sensory experience. It is even possible that our biological bodies are used by two selves: right brain hemisphere sleeps when we are awake and vice versa. Even the experiences of epileptics about having double consciousness could be understood.
   
   
3. A more concrete realization of "Left brain talks, right brain sings" metaphor relies on the assumption that "magneto-anatomy" is universal. Only the "magneto-physiology"> characterized by the values of h_eff characterizing quantum criticality and defining a kind of intelligence quotient dictating the span of long term memory and planned action varies.
   

   h_eff would differ for the magnetic bodies of various brain areas, and the spectrum of h_eff for right and left brain would differ and characterize their specializations. For instance, the value of h_eff would be large (small) for the cognitive areas of left (right) brain and small (large) for some higher sensory areas of right (left) brain. Magnetic bodies form a fractal hierarchy and one can characterize even individual cells and neurons by the value of h_eff associated with them. The spectrum for h_eff allows also to distinguish between members of the same species since it defines the skill profile. This obviously goes far beyond the genetic determinism.
   

See the chapter What music can teach about consciousness? of "TGD and EEG" or the article What music can teach about consciousness?

.

For a summary of earlier postings see Links to the latest progress in TGD.

Strange behavior of SmB6 and new mechanism of quantum bio-control

The idea that TGD Universe is quantum critical, is the corner stone of quantum TGD and fixes the theory more or less uniquely since the only coupling constant parameter of the theory - Kähler coupling strength - is analogous to critical temperature. Also more than one basic parameters are in principle possible - maximal quantum criticality fixes the values of all of them - but it seems that only Kähler coupling strength is needed. TGD Universe is a quantum critical fractal: like a ball at the top of hill at the top of hill at.... Quantum criticality allows to avoid the fine tuning problems plaguing as a rule various unified theories.

Quantum criticality

The meaning of quantum criticality at the level of dynamics has become only gradually clearer. The development of several apparently independent ideas generated for about decade ago have led to the realization that quantum criticality is behind all of them. Behind quantum criticality are in turn number theoretic vision and strong forms of general coordinate invariance and holography.

1. The hierarchy of Planck constants defining hierarchy of dark phases of ordinary matter corresponds to a hierarchy of quantum criticalities assignable to a fractal hierarchy of sub-algebras of super-symplectic algebra for which conformal weights are n-ples of those for the entire algebra, n corresponds to the value of effective Planck constant h_eff/h=n. These algebras are isomorphic to the full algebra and act as gauge conformal algebras so that a broken super-conformal invariance is in question.
   
   
2. Quantum criticality in turn reduces to the number theoretic vision about strong form of holography. String world sheets carrying fermions and partonic 2-surfaces are the basic objects as far as pure quantum description is considered. Also space-time picture is needed in order to test the theory since quantum measurements always involve also the classical physics, which in TGD is an exact part of quantum theory.
   

   Space-time surfaces are continuations of collections of string world sheets and partonic 2-surfaces to preferred extremals of Kähler action for which Noether charges in the sub-algebra of super-symplectic algebra vanish. This condition is the counterpart for the reduction of the 2-D criticality to conformal invariance. This eliminates huge number of degrees of freedom and makes the strong form of holography possible.
   
   

3. The hierarchy of algebraic extensions of rationals defines the values of the parameters characterizing the 2-surfaces, and one obtains a number theoretical realization of an evolutionary hierarchy. One can also algebraically continue the space-time surfaces to various number fields - reals and the algebraic extensions of p-adic number fields. Physics becomes adelic. p-Adic sectors serve as correlates for cognition and imagination. One can indeed have string world sheets and partonic 2-surfaces, which can be algebraically continued to preferred extremals in p-adic sectors by utilizing p-adic pseudo constants giving huge flexibility. If this is not possible in the real sector, figment of imagination is in question! It can also happen that only part of real space-time surface can be generated: this might relate to the fact that imaginations can be seen as partially realized motor actions and sensory perceptions.
   
   

Quantum criticality and TGD inspired quantum biology

In TGD inspired quantum biology quantum criticality is in crucial role. First some background.

1. Quantum measurement theory as a theory of consciousness is formulated in zero energy ontology (ZEO) and defines an important aspect of quantum criticality. Strong form of NMP states that the negentropy gain in the state function reduction at either boundary of causal diamond (CD) is maximal. Weak form of NMP allows also quantum jumps for which negentropic entanglement is not generated: this makes possible ethics (good and evil) and morally responsible free will: good means basically increase of negentropy resources.
   
   
2. Self corresponds to a sequence state function reductions to the same boundary of CD and h_eff does not change during that period. The increase of h_eff (and thus evolution!) tends to occur spontaneously, and can be assigned to the state function reduction to the opposite boundary of CD in zero energy ontology (ZEO). The reduction to the opposite boundary means death of self and living matter is fighting in order to avoid this even. To me the only manner to make sense about basic myth of Christianity is that death of self generates negentropy.
   
   
3. Metabolism provides negentropy resources for self and hopefully prevents NMP to force the fatal reduction to the opposite boundary of CD. Also homeostasis does the same. In this process self makes possible evolution of sub-selves (mental images dying and re-incarnating) state function by state function reduction so that the negentropic resources of the Universe increase.
   
   

A new mechanism of quantum criticality

Consider now the mechanisms of quantum criticality. The TGD based model (see this) for the recent paradoxical looking finding (see this) that topological insulators can behave like conductors in external magnetic field led to a discovery of a highly interesting mechanism of criticality, which could play a key role in living matter.

1. The key observation is that magnetic field is present. In TGD framework the obvious guess is that its flux tubes carry dark electrons giving rise to anomalous currents running in about million times longer time scales and with velocity, which is about million times higher than expected. Also supra-currents can be considered.
   

   The currents can be formed of the cyclotron energies of electrons are such that they correspond to energies near the surface of the Fermi sphere: recall that Fermi energy for electrons is determined by the density of conduction electrons and is about 1 eV. Interestingly, this energy is at the lower end of bio-photon energy spectrum. In the field of 10 Tesla the cyclotron energy of electron is .1 mV so that the integer characterizing cyclotron orbit must be n≅ 10⁵ if conduction electron is to be transferred to the cyclotron orbit.
   
   

2. The assumption is that external magnetic field is realized as flux tubes of fixed radius, which correspond to space-time quanta in TGD framework. As the intensity of magnetic field is varied, one observes so called de Haas-van Alphen effect used to deduce the shape of the Fermi sphere: magnetization and some other observables vary periodically as function of 1/B.

   
   This can be understood in the following manner. As B increases, cyclotron orbits contract. For certain increments of 1/B n+1:th orbit is contracted to n:th orbit so that the sets of the orbits are identical for the values of 1/B, which appear periodically. This causes the periodic oscillation of say magnetization.
   
   

3. For some critical values of the magnetic field strength a new orbit emerges at the boundary of the flux tube. If the energy of this orbit is in the vicinity of Fermi surface, an electron can be transferred to the new orbit. This situation is clearly quantum critical.
   

   If the quantum criticality hypothesis holds true, h_eff/h=n dark electron phase can generated for the critical value of magnetic fields. This would give rise to the anomalous conductivity perhaps involving spin current due to the spontaneous magnetization of the dark electrons at the flux tube. Even super-conductivity based on the formation of parallel flux tube pairs with either opposite or parallel directions of the magnetic flux such that the members of the pair are at parallel flux tubes, can be considered and I have proposed this a mechanism of bio-superconductivity and also high Tc super-conductivity
   
   

A new mechanism of quantum criticality and bio-control

The quantum criticality of the process in which new electron orbit emerges near Fermi surface suggests a new mechanism of quantum bio-control by generation of super currents or its reversal.

1. In TGD inspired quantum biology magnetic body uses biological body as motor instrument and sensory receptor and EEG and its fractal variants with dark photons with frequencies in EEG range but energy E=h_efff in the range of bio-photon energies make the necessary signalling possible.
   
   
2. Flux tubes can become braided and this makes possible quantum computation like processes. Also so called 2-braids - defined by knotted 2-surfaces imbedded in 4-D space-time surface - are possible for the string world sheets defined by flux tubes identified to be infinitely thin, are possible. As a matter fact, also genuine string world sheets accompany the flux tubes. 2-braids and knots are purely TGD based phenomenon and not possible in superstring theory or M-theory.
   
   
3. It is natural to speak about motor actions of the magnetic body. It is assumed that the flux tubes of the magnetic body connect biomolecules to form a kind of Indra's web explaining the gel like character of living matter. h_eff reducing phase transitions contract flux tubes connecting biomolecules so that they can find each other by this process and bio-catalysis becomes possible. This explains the mysterious looking ability of bio-molecules to find each other in the dense molecular soup. In fact the dark matter part is far from being soup! The hierarchy of Planck constants and h_eff=h_gr hypothesis imply that dark variants of various particles with magnetic moment are neatly at their own flux tubes like books in shelf.
   

   Reconnection of the U-shaped flux tubes emanating from two subsystems generates a flux tube pair between them and gives rise to supracurrents flowing between them. Also cyclotron radiation propagating along flux tubes and inducing resonant transitions is present. This would be the fundamental mechanism of attention.
   
   

4. I have proposed that the variation of the thickness of the flux tubes could serve as a control mechanism since it induces a variation of cyclotron frequencies allowing to get in resonance or out of it. For instance, two molecules could get in flux tube contact when the cyclotron frequencies are identical and this can be achieved if they are able to vary their flux tube thickness. The molecules of immune system are masters in identifying alien molecules and the underlying mechanism could be based on cyclotron frequency spectrum and molecular attention. This would be also the mechanism behind water memory and homeopathy (see this), which still is regarded as a taboo by mainstreamers.
   
   
5. Finally comes the promised new mechanism of bio-control! The variation of the magnetic field induced by that of flux tube thickness allows also to control whether there is quantum criticality for the generation of dark electron supra currents of electrons. The Fermi energy of the conduction electrons at the top of Fermi sphere is the key quantity and dictated by the density of these electrons. This allows to estimate the order of magnitude of the integers N characterizing cyclotron energy for ordinary Planck constant and the maximal value of h_eff/h=n cannot be larger than N.
   
   

See the chapter Criticality and Dark Matter of "Hyper-finite Factors and Hierarchy of Planck Constants" or the article A new control mechanism of TGD inspired quantum biology.

For a summary of earlier postings see Links to the latest progress in TGD.

Does the physics of SmB6 make the fundamental dynamics of TGD directly visible?

The group of Suchitra Sebastian has discovered very unconventional condensed matter system which seems to be simultaneously both insulator and conductor of electricity in presence of magnetic field. Science article is entitled "Unconventional Fermi surface in an insulating state". There is also a popular article "Paradoxical Crystal Baffles Physicists" in Quanta Magazine summarizing the findings. I learned about the finding first from the blog posting of Lubos
(I want to make absolutely clear that I do not share the racistic attitudes of Lubos towards Greeks. I find the discussions between Lubos and same minded blog visitor barbarians about the situation in Greece disgusting).

Observations

The crystal studied at superlow temperatures was Samarium hexaboride - briefly SmB₆. The high resistance implies that electron cannot move more that one atom's width in any direction. Sebastian et al however observed electrons traversing over a distance of millions of atoms- a distance of orde 10^-4 m, the size of a large neuron. So high mobility is expected only in conductors. SmB₆ is neither metal or insulator or is both of them! The finding is described by Sebastian as a "big schock and as a "magnificent paradox by condensed matter theorists Jan Zaanen. Theoreticians have started to make guesses about what might be involved but according to Zaanen there is no even remotely credible hypothesis has appeared yet.

On basis of its electronic structure SmB₆ should be a conductor of electricity and it indeed is at room temperature: the average number conduction electrons per SmB₆ is one half. At low temperatures situation however changes. At low temperatures electrons behave collectivly. In superconductors resistance drops to zero as a consequence. In SmB₆ just the opposite happens. Each Sm nucleus has the average 5.5 electrons bound to it at tight orbits. Below 223 degrees of Celsius the conduction electrons of SmB₆ are thought to "hybridize" around samarium nuclei so that the system becomes an insulator. Various signatures demonstrate that SmB₆ indeed behaves like an insulator.

During last five years it has been learned that SmB₆ is not only an insulator but also so called topological insulator. The interior of SmB₆ is insulator but the surface acts as a conductor. In their experiments Sebastian et al hoped to find additional evidence for the topological insulator property and attempted to measure quantum oscillations in the electrical resistance of their crystal sample. The variation of quantum oscillations as sample is rotated can be used to map out the Fermi surface of the crystal. No quantum oscillations were seen. The next step was to add magnetic field and just see whether something interesting happens and could save the project. Suddenly the expected signal was there! It was possible to detect quantum oscillations deep in the interior of the sample and map the Fermi surface! The electrons in the interior travelled 1 million times faster than the electrical resistance would suggest. Fermi surface was like that in copper, silver or gold. A further surprise was that the growth of the amplitude of quantum oscillations as temperature was decreased, was very different from the predictions of the universal Lifshitz-Kosevich formula for the conventional metals.

Could TGD help to understand the strange behavior of SmB₆?

There are several indications that the paradoxical effect might reveal the underlying dynamics of quantum TGD. The mechanism of conduction must represent new physics and magnetic field must play a key role by making conductivity possible by somehow providing the "current wires". How? The TGD based answer is completely obvious: magnetic flux tubes.

One should also understand topological insulator property at deeper level, that is the conduction along the boundaries of topological insulator. One should understand why the current runs along 2-D surfaces. In fact, many exotic condensed matter systems are 2-dimensional in good approximation. In the models of integer and fractional quantum Hall effect electrons form a 2-D system with braid statistics possible only in 2-D system. High temperature super-conductivity is also an effectively 2-D phenomenon.One should also understand topological insulator property at deeper level, that is the conduction along the boundaries of topological insulator.

1. Many-sheeted space-time is second fundamental prediction TGD. The dynamics of single sheet of many-sheeted space-time should be very simple by the strong form of holography implying effective 2-dimensionality. The standard model description of this dynamics masks this simplicity since the sheets of many-sheeted space-time are replaced with single region of slightly curved Minkowski space with gauge potentials sums of induced gauge potentials for sheets and deviation of metric from Minkowski metric by the sum of corresponding deviations for space-time sheets. Could the dynamics of exotic condensed matter systems give a glimpse about the dynamics of single sheet? Could topological insulator and anyonic systems provide examples of this kind of systems?
   
   
2. Second basic prediction of TGD is strong form of holography: string world sheets and partonic 2-surfaces serve as kind of "space-time genes" and the dynamics of fermions is 2-D at fundamental level. It must be however made clear that at QFT limit the spinor fields of imbedding space replace these fundamental spinor fields localized at 2-surface. One might argue that the fundamental spinor fields do not make them directly visible in condensed matter physics. Nothing however prevents from asking whether in some circumstances the fundamental level could make itself visible.
   

   In particular, for large h_eff dark matter systems (, whose existence can be deduced from the quantum criticality of quantum TGD) the partonic 2-surfaces with CP₂ size could be scaled up to nano-scopic and even longer size scales. I have proposed this kind of surfaces as carriers of electrons with non-standard value of h_eff in QHE and FQHE.
   

   The long range quantum fluctuations associated with large, h_eff=n× h phase would be quantum fluctuations rather than thermal ones. In the case of ordinary conductivity thermal energy makes it possible for electrons to jump between atoms and conductivity becomes very small at low temperatures. In the case of large scale quantum coherence just the opposite happens as observed. One therefore expects that Lifshitz-Kosevich formula for the temperature dependence of the amplitude does not hold true.
   

   The generalization of Lifschitz-Kosevich formula to quantum critical case deduced from quantum holographic correspondence by Hartnoll and Hofman might hold true qualitatively also for quantum criticality in TGD sense but one must be very cautious.
   

   The first guess is that by underlying super-conformal invariance scaling laws typical for critical systems hold true so that the dependence on temperature is via a power of dimensionless parameter x=T/mu;, where μ is chemical potential for electron system. As a matter fact, exponent of power of x appears and reduces to first power for Lifshitz-Konsevich formula. Since magnetic field is important, one also expects that the ratio of cyclotron energy scale E_c∝ ℏ_eff eB/m_e to Fermi energy appears in the formula. One can even make an order of magnitude guess for the value of h_eff/h≅ 10⁶ from the facts that the scale of conduction and conduction velocity were millions times higher than expected.
   

   Strings are 1-D systems and strong form of holography implies that fermionic strings connecting partonic 2-surfaces and accompanied by magnetic flux tubes are fundamental. At light-like 3-surfaces fermion lines can give rise to braids. In TGD framework AdS/CFT correspondence generalizes since the conformal symmetries are extended. This is possible only in 4-D space-time and for the imbedding space H=M⁴× CP₂ making possible to generalize twistor approach.
   
   

3. Topological insulator property means from the perspective of modelling that the action reduces to a non-abelian Chern-Simons term. The quantum dynamics of TGD at space-time level is dictated by Kähler action. Space-time surfaces are preferred extremals of Kähler action and for them Kähler action reduces to Chern-Simons terms associated with the ends of space-time surface opposite boundaries of causal diamond and possibly to the 3-D light-like orbits of partonic 2-surfaces. Now the Chern-Simons term is Abelian but the induced gauge fields are non-Abelian. One might say that single sheeted physics resembles that of topological insulator.
   
   
4. The effect appears only in magnetic field. I have been talking a lot about magnetic flux tubes carrying dark matter identified as large h_eff phases: topological quantization distinguishes TGD from Maxwell's theory: any system can be said to possess "magnetic body, whose flux tubes can serve as current wires. I have predicted the possibility of high temperature super-conductivity based on pairs of parallel magnetic flux tubes with the members of Cooper pairs at the neighboring flux tubes forming spin singlet or triplet depending on whether the fluxes are have same or opposite direction.
   

   Also spin and electric currents assignable to the analogs of spontaneously magnetized states at single flux tube are possible. The obvious guess is that the conductivity in question is along the flux tubes of the external magnetic field. Could this kind of conductivity explains the strange behavior of SmB₆. The critical temperature would be that in which the parallel flux tubes are stable. The interaction energy of spin with the magnetic field serves as a possible criterion for the stability if the presence of dark electrons stabilizes the flux tubes.
   

The following represents an extremely childish attempt of a non-specialist to understand how the conductivity might be understood. The current carrying electrons at flux tubes near the top of Fermi surface are current carriers. h_eff=n×h and magnetic flux tubes as current wires bring in the new elements. Also in the standard situation one considers cylinder symmetric solutions of Schrödinger equation in external magnetic field and introduces maximal radius for the orbits so that formally the two situations seem to be rather near to each other. Physically the large h_eff and associated many-sheeted covering of space-time surface providing the current wire makes the situation different since the collisions of electrons could be absent in good approximation so that the velocity of charge carriers could be much higher than expected as experiments indeed demonstrate.

Quantum criticality is the crucial aspect and corresponds to the situation in which the magnetic field attains a value for which a new orbit emerges/disappears at the surface of the flux tube: in this situation dark electron phase with non-standard value of h_eff can be generated. This mechanism is expected to apply also in bio- superconductivity and to provide a general control tool for magnetic body.

1. Let us assume that flux tubes cover the whole transversal area of the crystal and there is no overlap. Assume also that the total number of conduction electrons is fixed, and depending on the value of h_eff is shared differently between transversal and longitudinal degrees of freedom. Large value of h_eff squeezes the electrons from transversal to longitudinal flux tube degrees of freedom and gives rise to conductivity.
   
   
2. Consider first Schrödinger equation. In radial direction one has harmonic oscillator and the orbits are Landau orbits. The cross sectional area behaves like πR²= n_Th_eff/2mω_c giving n_T∝1/h_eff. Increase of the Planck constant scales up the radii of the orbits so that the number of states in cylinder of given radius is reduced.
   

   Angular momentum degeneracy implies that the number of transversal states is N_T= n_T²∝ 1/h_eff². In longitudinal direction one has free motion in a box of length L with states labelled by integer n_L. The number of states is given by the maximum value N_L of n_L.
   
   

3. If the total number of states is fixed to N = N_LN_T is fixed and thus does not depend on h_eff, one has N_L ∝ h_eff². Quanta from transversal degrees of freedom are squeezed to longitudinal degrees of freedom, which makes possible conductivity.
   
   
4. The conducting electrons are at the surface of the 1-D "Fermi-sphere", and the number of conduction electrons is N_cond≅ dN/dε × δ ε≅dN/dε T= NT/2ε_F ∝ 1/h_eff⁴. The dependence on h_eff does not favor too large values of h_eff. On the other hand, the scattering of electrons at flux tubes could be absent. The assumption L∝h_eff increases the range over which current can flow.
   
   
5. To get a non-vanishing net current one must assume that only the electrons at the second end of the 1-D Fermi sphere are current carriers. The situation would resemble that in semiconductor. The direction of electric field would induce symmetry breaking at the level of quantum states. The situation would be like that for a mass in Earth's gravitational field treated quantally and electrons would accelerate freely. Schrödinger equation would give rise to Airy functions as its solution.
   

What about quantum oscillations in TGD framework?

1. Quantum oscillation refers to de Haas-van Alphen effect - an oscillation of the induced magnetic moment as a function of 1/B with period τ= 2πe/ℏS, where S is the momentum space area of the extremal orbit of the Fermi surface, in the direction of the applied field. The effect is explained to be due to the Landau quantization of the electron energy. I failed to really understand the explanation of this source and in my humble opinion the following arguments provide a clearer view about what happens.
   
   
2. If external magnetic field corresponds to flux tubes Fermi surface decomposes into cylinders parallel to the magnetic field since the motion in transversal degrees of freedom is along circles. In the above thought experiment also a quantization in the longitudinal direction occurs if the flux tube has finite length so that Fermi surface in longitudinal direction has finite length. One expects on basis of Uncertainty Principle that the area of the cross section in momentum space is given by S∝ h_eff²/πR², where S is the cross sectional area of the flux tube. This follows also from the equation of motion of electron in magnetic field. As the external magnetic field B is increased, the radii of the orbits decrease inside the flux tube, and in momentum space the radii increase.
   
   
   

   
   

3. Why does the induced magnetic moment (magnetization) and other observables oscillate?
   
   
   1. The simplest manner to understand this is to look at the situation at space-time level. Classical orbits are harmonic oscillator orbits in radial degree of freedom. Suppose that that the area of flux tube is fixed and B is increased. The orbits have radius r_n²= (n+1/2) × hbar/eB and shrink. For certain field values the flux eBA =n×hbar corresponds to an integer multiple of the elementary flux quantum - a new orbit at the boundary of the flux tube emerges if the new orbit is near the boundary of Fermi sphere providing the electrons. This is clearly a critical situation.
      
      
   2. In de Haas- van Alphen effect the orbit n+1 for B has same radius as the orbit n for 1/B+Δ (1/B): r_n+1(1/B) =r_n(1/B+Δ (1/B)). This gives approximate differential equation with respect to n and one obtains (1/B)(n)= (n+1/2)× Δ (1/B) . Δ (1/B) is fixed from the condition the flux quantization. When largest orbit is at the surface of the flux, tube the orbits are same for B(n) and B(n+1), and this gives rise to the de Haas - van Alphen effect.
      
      
   3. It is not necessary to assume finite radius for the flux tube, and the exact value of the radius of the flux tube does not play an important role. The value of flux tube radius can be estimated from the ratio of the Fermi energy of electron to the cyclotron energy. Fermi energy about .1 eV depending only on the density of electrons in the lowest approximation and only very weakly on temperature. For a magnetic field of 1 Tesla cyclotron energy is .1 meV. The number of cylinders defined by orbits is about n=10⁴.
      
      
4. What happens in TGD Universe in which the areas of flux tubes identifiable as space-time quanta are finite? Could quantum criticality of the transition in which a new orbit emerges at the boundary of flux tube lead to a large h_eff dark electron phase at flux tubes giving rise to conduction?
   
   
   1. The above argument makes sense also in TGD Universe for the ordinary value of Planck constant. What about non-standard values of Planck constant? For h_eff/h =n the value of flux quantum is n-fold so that the period of the oscillation in de Haas - van Alphen effect becomes n times shorter. The values of the magnetic field for which the orbit is at the surface of the flux tube are however critical since new orbit emerges assuming that the cyclotron energy corresponds is near Fermi energy. This quantum criticality could give rise to a phase transition generating non-standard value of Planck constant.
      

      What about the period for Δ (1/B)? For h_eff/h=n? Modified flux quantization for extremal orbits implies that the area of flux quantum is scaled up by n. The flux changes by n units for the same increment of Δ (1/B) as for ordinary Planck constant so that de Haas -van Alphen effect does not detect the phase transition.
      
      

   2. If the size scale of the orbits is scaled up by n1/2 as the semiclassical formula suggests the number of classical orbits is reduced by a factor 1/n if the radius of the flux tube is not changed in the transition h→ h_eff to dark phase. n-sheetedness of the covering however compensates this reduction.
      
      
   3. What about possible values of h_eff/h? The total value of flux seems to give the upper bound of h_eff/h=n_max, where n_max is the value of magnetic flux for ordinary value of Planck constant. For electron and magnetic field for B=10 Tesla and has n≤ 10⁵. This value is of the same order as the rough estimate from the length scale for which anomalous conduction occurs.
      
   Clearly, the mechanism leading to anomalously high conductivity might be the transformation of the flux tubes to dark ones so that they carry dark electrons currents. The observed effect would be dark, quantum critical variant of de Haas-van Alphen effect!

   Also bio-superconductivity is quantum critical phenomenon and this observation would suggests sharpening of the existing TGD based model of bio-super-conductivity. Super-conductivity would occur for critical magnetic fields for which largest cyclotron orbit is at the surface of the flux tube so that the system is quantum critical. Quantization of magnetic fluxes would quantify the quantum criticality. The variation of magnetic field strength would serve as control tool generating or eliminating supra currents. This conforms with the general vision about the role of dark magnetic fields in living matter.

To sum up, a breaktrough of TGD is taking place. I have written about thirty articles during this year - more than one article per week. There is huge garden there and trees contain fruits hanging low! It is very easy to pick them: just shatter and let them drop to the basket! New experimental anomalies having a nice explanation using TGD based concepts appear on weekly basis and the mathematical and physical understanding of TGD is taking place with great leaps. It is a pity that I must do all alone. I would like to share. I can only hope that colleagues could take the difficult step: admit what has happened and make a fresh start.

See the article Does the physics of SmB₆ make the fundamental dynamics of TGD directly visible?

For a summary of earlier postings see Links to the latest progress in TGD.

Deconstruction and reconstruction in quantum physics and conscious experience

Deconstruction means roughly putting something into pieces. Often deconstruction is thought to involve also the reconstruction. This process is applied in deconstructivistic architecture as one can learn by going to Wikipedia and also cubism brings in mind this kind of approach. Reconstruction organizes typical features of existing styles in new - one might even say "crazy" manner. There can be even a kind of "social interaction" between buildings: as if they were communicating by exchanging features. Similar recombination of elements from various styles have appeared also in music - neoclassicism comes in mind immediately.

Postmodernism is a closely related movement and claims that truths are social constructs: great narratives are dead. Nothing could irritate more the physicist who has learned how much mistakes, wrong tracks, and hard work are needed to distill the truth! Everything does not go! On the other hand, one can argue that the recent state of stagnation in the frontier of theoretical physics suggests that postmodernists are right. Superstrings and multiverse are definitely highly social constructs: superstrings were the only game in the town for decades but now American Mathematical Society is worried that super string theoreticians are spoiling the public image of science. Multiverse was in fashion only few years. Certainly one great narrative - the story or reductionism and materialism thought to find its final culmination as M-theory - is dead. It is however nonsense to claim that all great narratives are dead. That telling alternative great narratives in respected journals is impossible does not mean that they are dead!

But the association of deconstruction with postmodernism does not justify throwing away the ideas of deconstruction and reconstruction. Rather, one can ask whether they could be made part of a new great narrative about physical world and consciousness.

1. Deconstruction and reconstruction in perception, condensed matter physics and in TGD inspired theory of consciousness

Deconstruction and reconstruction appear in the construction of percepts, in condensed matter physics, and are also part of TGD inspired theory of consciousness.

1.1 Perception

The very idea of deconstruction in architectural sense is highly interesting from the perspective of both quantum physics and consciousness.

I was astonished as I learned for about 35 years ago that the buildup of our perception involves very concretely what I would now call deconstruction and reconstruction and I could not understand why this. First the sensory input is decomposed into features. Edges, corners, positions, motions analyzed to direction and velocity, colors,... Objects are replaced with collections of attributes: position, motion, shape, surface texture, color,.... Deconstruction occurs at lower cortical layers. After this reconstruction takes place: various kinds of features are combined together through a mysterious looking process of binding - and the outcome is a percept.

Reconstruction can occur also in "wrong" manner. This occurs in hallucinations, delusions, and dreams. Humour is based on association of "wrong" things together, making intentional category errors. Synesthesia involves association between different sensory modalities: note with a given pitch has characteristic color or numbers correspond to colors or shapes. I remember an article telling about how subject persons in hypnosis can experience what circle with four corners looks like. Some attribute can be lacking from the reconstruction: person can perceive the car as object but not its motion. The car is there now and a moment later it is here. Nothing between.

Also non - standard reconstructions are possible. Could these non-standard reconstructions define a key aspect of creativity? Could reconstruction create in some lucky situations new idea rather than hallucination or delusion?

For few years ago I listened a radio document about a professional, who builds soundscapes to movies and learned that the construction of soundscape is deconstruction followed by reconstruction. One starts from natural sounds but as such they are not very impressive: driving by car over some-one does not create any dramatic sound effect - just "splat" - nothing else. This is so non-dramatic that it has been be used to create black humour. In order to cure the situation the real sounds are analyzed to features and then reconstructed by amplifying some features and by throwing away the unessential ones. The fictive output sounds much more real than the real input. Actors are masters of this technique and this is why videos about ordinary people doing something funny is like looking autistic ghosts. And if you look at the collection of modules of video game you see modules with name "Aargh", "Auch", "Bangggg", etc..

Association is the neuroscientist's key notion allowing to get an idea about what happens in reconstruction. Reconstruction involves association of various features to form percepts. First this process occurs for various sensory modalities. These intermediate sensory percepts are then combined to full percept in association regions.

But what associations are at deeper level? What features are? Heretic could ask whether they could correspond to conscious experiences not conscious to us but conscious at lower sub-conscious level. Reader perhaps noticed that deconstruction and reconstruction took place here: the student is not supposed to ask this question since most theories of consciousness for some funny reason - maybe a pure accident - make the assumption that consciousness has no structure - no selves with subselves with sub-selves with... For physicist this kind deconstruction of consciousness is very natural. How do these features bind to our conscious percepts? Neuroscience alone cannot tell much about this since it is based on physicalism: "hard problem" articulates this dead end.

The following considerations represent deconstructions and reconstructions, and I will not explicitly mention when this happens - just warning.

1.2 Condensed matter physics

One must bring in some basic notions of quantum theory if one wants to reduce de- and reconstruction to quantum physics. The key mathematical fact is that in quantum theory each particle in many-particle state corresponds to a tensor factor of state space of the entire system. This notion is very difficult to explain without actually having a lecture series about quantum theory and I prove in the following that this is indeed the case.

1. The space of quantum states of system is the basic notion: technically it is known as Hilbert space, which can have finite or even infinite dimension and also infinite dimension (and this in many senses!).
   

   The basic idea is that one can build bigger Hilbert spaces as their tensor products. If you have Hilbert spaces of dimensions n₁ and n₂, the tensor product has dimension n₁× n₂. This is algebraically like multiplying numbers and one can indeed identify prime Hilbert spaces as those with prime dimension. Also direct sums of Hilbert spaces are possible.
   

   Hilbert spaces represent physical systems: say electron and proton. To describe a world consisting of proton and electron one forms the tensor product of electron and proton Hilbert spaces. This is somewhat like playing with legos.
   

   I was cheating a little bit. Life is not quite so simple. One can also form bound states of two systems - say hydrogen atom from proton and electron, and the bound states of hydrogen atom represent only a sub-space of the tensor product. Connes tensor product is more exotic example: only certain kind of entangled states in tensor product for which the composites are strongly correlated are allowed. As a matter of fact, also the gluing the legos together creates strong correlations between them so that it serves as a good analogy for Connes tensor product and tensor product assignable to bound states.
   
   

2. Even elementary particles have several degrees of freedom - say spin and charge - to which one can assign Hilbert spaces decomposing formally into tensor product of Hilbert spaces associated with these degrees of freedom. Sub-space of the full tensor product is allowed, and one can purely formally say that elementary particle is a bound state of even more elementary particles. Somewhat like written word having meaning to us consists of letters, which as such represent nothing to us (but could represent something to lower level conscious entities). Could it be possible to apply deconstruction to elementary particles?

Now comes the surprise: condensed matter physicists have discovered deconstruction long time ago)! Condensed matter electron can be deconstructed under some circumstances.

1. Electron in the valence band of conductor has three kinds of degrees of freedom labelled by spin, charge and orbital state - state of electron in atom - characterizing the valence band. The state of electron decomposes in purely formal sense to a bound state of spinon, chargon, and holon carrying spin, charge, and phase of electron wave function. Could one deconstruct this bound state to its composites? If so, one would have effectively three particles - three quantum waves moving with different velocities. For free electrons obeying Dirac equation this is certainly impossible. But this might be (and is!) possible in condensed matter.
   

   Instead of single wave motion there can be three free wave motions occurring with different velocities (wave vectors) corresponding to spinon, chargon and holon. In popular articles this process is called "splitting" of electron. The term is optimal choice if the purpose is to create profound mis-understandings in the layman reader associating naturally splitting with a geometric process of putting tiny ball into pieces. As already explained, it is Hilbert space, which is split into tensor factors, not the tiny ball. The correlations between factors forced by bound state property are broken in this divorce of degrees of freedom.
   
   

2. What condensed matter theorist propose is roughly following. The consideration is restricted to effectively one-dimensional systems - wires. Electron has spin, charge, and orbital degrees of freedom if in conduction band and delocalized and thus shared by the atoms. Usually these degrees of freedom are bound to single entity.
   

   The holy trinity of charge, spin, and orbital degrees of freedom can be however split under some circumstances prevailing in condensed matter. The phase of the spinor representing electron can vary along wire and defines wave motion with some velocity/wave vector assignable with the ordinary electric current. The spin of electron can rotate at each point and the phase of this rotation can vary along wire so that a quantum wave moving along wire with velocity different from that for charge: this is spin wave having as classical analog the rotation of bicycle pedals. If the wire is a linear lattice of atoms, the orbital excitation can also vary along the wire and a third quantum wave moving with its own velocity is possible. One has three particle like entities moving with different velocities! This kind of waves are certainly not possible for the solutions of Dirac equation representing freely moving fermions and particle physicists do not encounter them.
   
   

3. These wave motions are different from the wave motions associated with phonons and magnons. For sound it is periodic oscillation for the position of atom, which propagates in sound wave. For magnon it is change of spin value, which propagates and defines a spin 1 collective excitation. Spinon as a quasiparticle has spin 1/2 so that spinon and magnon are different things. Spinon is formal constituent of electron made visible by the condensed matter environment. Magnon is collective excitation of condensed matter system.
   

   Spin currents provide an example of a situation in which spin and charge currents can flow at different speeds and are becoming important in a new technology known as spintronics. Spin currents have very low resistance and the speculation is that they might relate to high T_c super conductivity.
   
   

From the articles that I have seen one might conclude that deconstruction is in practice possible only for effectively 1-dimensional systems. I do not see any obvious mathematical reason why the deconstruction could not occur also in higher-dimensional systems.

It is however true that 1-dimensional systems are very special physically. Braid statistics replaces ordinary statistics bringing in a lot of new effects. Furthermore, 2-D integrable gauge theories allow to model interactions as permutations of quantum numbers and lead to elegant models describing deconstructed degrees of fields as quantum fields in 2-D Minkowski space with interactions reducing to 2-particle interactions decribable in terms of R-matrix satisfying the Yang-Baxter equations. It is difficult to say how much the association of deconstruction to 1-D systems is due the fact that they are mathematically easier to handle than higher-D ones and there is existing machinery.

The rise of superstring models certainly was to a high degree due to this technical easiness. As I tried to tell about 3-surfaces replacing strings as fundamental dynamical objects, the almost reflect like debunking of this idea was to say that super-conformal invariance of super-string models is lost and the theory is not calculable and does not even exist - period. It took indeed a long time to realize that super-conformal symmetry allows a huge generalization, when space-time is 4-D and imbedding space has Minkowski space as its Cartesian factor. Twistorial considerations fixed the imbedding space uniquely to M⁴× CP₂. The lesson is clear: theoretician should be patient and realize that theory building is much more than going to math library and digging the needed mathematics. Maybe colleagues are mature to learn this lesson some day.

1.3 TGD inspired theory of consciousness

The believer in quantum consciousness of course wonders what could be the quantum counterparts of de- and reconstruction as mechanism of perception. It would seem that analysis and synthesis of the sensory input deconstructs the mental image associated with it to features - perhaps simpler fundamental mental images - and reconstruct from these the percept as mental image. What does this correspond at the level of physics?

Before one can really answer one must understand what the quantum physical correlates of mental image are. How mental images die and are born? What features are as mental images? What their binding to sensory percepts does mean physically?

Here I can answer only on my own behalf and to do it I must introduce the basic notions and ideas of TGD inspired theory of consciousness. I will not go into details here because I have done this so many times and just suggest that the reading of some basic stuff about TGD inspired theory of consciousness. Suffice it to list just the basic ideas and notions.

1. Zero energy ontology (ZEO), the closely related causal diamonds (CDs), and hierarchy of Planck constants assignable to quantum criticality are basic notions. Number theoretic vision is also central. In particular, adelic physics fusing real physics and various p-adic physics as correlates for cognition is also a basic building brick.
   
   
2. TGD inspired theory of consciousness theory can be seen as a generalization of quantum measurement theory constructed to solve the basic problems of ordinary quantum measurement theory: observer becomes "self" - conscious entity - described by physics and part of physical system rather than being an outsider. Consciousness does not cause state function reduction: consciousness is state function reduction. Consciousness is therefore not in the world but between two worlds. This resolves the basic paradox of quantum measurement theory since there are two causalities: causality of consciousness and causality of field equations.
   

   Negentropy Maximization Principle (NMP) defines the basic variational principle. Strong form of NMP states that the negentropy gain in state function reduction is maximal. Weak form of NMP leaves for self free will in that self can choose also non-maximal negentropy gain. This makes possible universe with ethics and moral with good defined as something which increases negentropy resources of the Universe.
   

   Self hierarchy is the basic notion of TGD inspired theory of consciousness. Self experiences sub-selves as mental images. Self corresponds to a state function reduction sequence to the same boundary of causal diamond (CD). In standard quantum measurement theory this sequence does not change the state but in TGD framework the state at the opposite boundary of CD and even opposite boundary changes. This gives rise to the experience flow of time having the increases of the temporal distance between the tips of CD as a geometric correlate. Self dies as the first reduction to the opposite boundary takes place and re-incarnates at the opposite boundary as its time reversal. Negentropy Maximization Principle forces it to occur sooner or later. The continual birth and death of mental images supports this view if one accepts the idea about hierarchy. One can also consider a concrete identification for what the change of the arrow of time means for mental image (see this).
   
   

3. Magnetic bodies carrying dark matter identified as h_eff=n× h phases of ordinary matter define quantum correlates for selves. Magnetic body has hierarchical onion-like structure and it communicates with biological body using dark photons propagating along magnetic flux tubes. EEG and its fractal generalizations make possible both communication from/control of biological body to/by magnetic body. Dark matter hierarchy can be reduced to quantum criticality and this in turn has deep roots in the adelic physics. Magnetic body means an extension of the usual organism-environment double to triple involving magnetic body as intentional agent using biological body for its purposes.
   
   

What reconstruction could mean in TGD inspired theory of consciousness?

1. The restriction of deconstruction to the degrees of freedom of elementary particle i s un-necessarily restrictive. One can consider also larger units such a as ..., molecules, cells,... and corresponding magnetic bodies and their representations using tensor products.
   
   
2. Besides bound state formation also negentropic entanglement (NE) allows states which are almost stable with respect to NMP. One can imagine two kinds of NE, which can be metastable with respect to NMP. In the first case density matrix is a projector with n identical eigenvalues of density matrix. This state can be an outcome of a state function reduction since it is an eigenstate of the universal observable defined by the density matrix.
   

   Density matrix has matrix elements in an algebraic extension algebraic extension of rationals characterizing the system in the evolutionary hierarchy. It can also happen that the eigenvalues of the density matrix (probabilities) do not belong to this extension. One can argue that since diagonalization is not possible inside the extension, also state function reduction is impossible without a phase transition extending the extension and identifiable as a kind of evolutionary step. This is assumed - at least tentatively.
   

   Both kinds of NEs would have natural place in the world order. The first kind of NE would correspond to a kind of enlightened consciousness since any orthonormal state basis would define an eigenstate basis of density matrix. Schrödinger cat would be exactly half alive and half dead or exactly half of X and half of Y, where X and Y are any orthonormal superpositions of alive and dead. For the second kind of NE there would be a unique state basis. For instance, the cat could be 1/2^1/2 alive and 1 - 1/2^1/2 dead. The words dead and alive have meaning. This would correspond to a state of rational mind discriminating between things. If a phase transition bringing into daylight 2^1/2 takes place, state function reduction makes cat fully alive or fully dead.
   
   

3. In condensed matter example the velocity of quantal wave motion serves as a criterion allowing to tell whether the degrees of freedom bind or not. Velocity/wave fector is obviously too limited criterion for binding or its absence. In neuroscience the coherence of EEG is seen as a signature of binding: maybe oscillation with same EEG frequency could serve the signature of fusion of mental images to a larger one. In TGD inspired theory of consciousness EEG frequencies correspond to differences of generalized Josephson frequencies that is sums of Josephson frequency for the resting potential and of the difference of cyclotron frequencies for ions at different sides of cell membrane (see this, this, and this ).
   
   
4. At the level of magnetic flux tubes binding would correspond to a reconnection of magnetic flux tubes of synchronously firing region to form a larger structure for which the magnetic field strength is same for the composites and therefore also cyclotron frequencies are identical. Reconstruction would have a concrete geometric correlate at the level of magnetic flux tubes as a reconnection. Different parts of brain containing quantum states serving as mental images defining features would connected by flux tubes of the magnetic body and binding of mental images would take place.
   
   
5. In TGD inspired quantum biology dark matter identified as large h_eff=n× h phases give rise to a deconstruction if one accepts the hypothesis h_eff=h_gr =GMm/v₀, where M represents mass of dark matter and m particle mass (see this and this). Here h_gr is assigned with a flux tube connecting masses M and m and v₀ is a velocity parameter characterizing the system. This hypothesis implies that dark cyclotron energy is given E_c=h_grf_c, where f_c is cyclotron frequency, is independent of particle mass: universal cyclotron energy spectrum is the outcome. The dark cyclotron photons can transform to ordinary photons identified as biophotons having energy spectrum in visible and UV range, where also the energy spectrum of molecules is. Magnetic body could use dark photons to control bio-chemistry.
   

   What makes this also so remarkable is that particles with magnetic dipole moment possessing different masses correspond to different values of h_eff and reside at different magnetic flux tubes. This is mass spectroscopy - or deconstruction of matter by separating charged particles with different masses to their own dark worlds! Dark living matter would not be a random soup of particles: each charged particle (also neutral particles with magnetic dipole moment) would sit neatly at its own shelf labelled by h_gr! In TGD inspired theory of consciousness magnetic flux tubes can be associated with magnetic bodies serving as correlates of selves so that deconstruction for mental images would reduce to this process with each charged particle representing one particular combination and perhaps also a quale (see this).
   

What about re-construction in this framework?

1. In reconstruction flux tube connections between two subsystems representing sub-selves (experienced by self as mental images) would be formed so that they would fuse to single system characterized by the same cyclotron frequency. Flux tube connection would be formed by the reconnection of U-shaped flux tubes to form single pair of connecting flux tubes connecting the systems.
   

   Resonant exchange of dark cyclotron photons and also dark super-conductivity would accompany this process. This process would represent a correlate for directed attention and would take place already at bio-molecular level. I have proposed that bio-molecules with aromatic rings in which circulating electron pair currents generate magnetic bodies are especially important and in some sense fundamental level of the self hierarchy at molecular level \citeallb/pulse. In brain different brain regions could connect to single coherently firing region in this manner.
   
   

2. The magnetic bodies associated with brain regions representing features could be connected in this manner to larger sub-selves. Negentropic quantum entanglement - a purely TGD based notion - could define a further correlate for the binding. This entanglement could take place in discrete degrees of freedom related to the hierarchy h_eff=n× h of Planck constants having no correlate in standard physics. The discrete degree of freedom would correspond to n sheets of singular coverings representing space-time surfaces. The sheets would co-incide at the ends of causal diamonds (CDs): one possible interpretation (holography allows many of them) could be that entire closed 3-surfaces formed by the unions of space-like 3-surfaces at the boundaries of CD and light-like 3-surfaces connecting them serve as basic objects.
   
   
3. Reconstruction by negentropic quantum entanglement and flux tube connections inducing resonance could also lead to non-standard composites. Synesthesia could be understood in this manner and even the sensory experience about circle with four corners could be understood. The binding of left and right brain visual experiences to single one could take place through negentropic entanglement and effectively generate the experience of third dimension. The dimensions would not however simply add: 3-D experience instead of 4-D. The dream of a mathematician is to perceive directly higher dimensional objects. Could sensory perception of higher than 3-D objects be possible by a reconstruction fusing several visual percepts - maybe even from different brains - together? Could higher levels of self hierarchy carry out this kind of reconstruction? Could Mother Gaia fuse our experiences to single experience about what it is to be a human kind, species, or bio-sphere?

2. Could condensed matter physics and consciousness theory have something to share?

Magnetic bodies are present in all scales and one can ask whether consciousness theory and condensed matter physics might have something in common. Could the proposed picture of matter as consisting of selves with sub-selves with.... defining analogs of quasiparticles and collective excitations make sense even at the level of condensed matter? Could construction and reconstruction of mental images identifiable as sub-selves take place already at this level and have interpretation in terms of primitive information processing building standardized primitive mental images?

Deconstruction need not be restricted to electron and velocity could be replaced by oscillation frequency for various fields: at quantum level there is not actually real distinction since in quantum theory velocity defines wave vector. Also more complex objects, atoms, molecules, etc. could be deconstructed and the process could occur at the level of magnetic bodies and involve in essential manner reconnection and other "motor actions" of flux tubes. The notions of quasi-particle and collective excitation would generalized dramatically and the general vision about basic mechanism might help to understand this zoo of exotics.

Future condensed matter theorists might also consider the possibility of reconstruction in new manner giving rise to the analogs of synesthesia. Could features from different objects be recombined to form exotic quasi-objects having parts all around. Could dark matter in TGD sense be involved in an essential manner? Could cyclotron resonance or its absence serve as a correlate for the binding? Note that the disjoint regions of space would be in well-defined sense near to each other in the reconstructed state. Topology would be different: effective p-adic topology could provide a natural description for a situation: in p-adic topology systems at infinite distance in real sense can be infinitesimally close to each other p-adically.

See the aritcle Deconstruction and reconstruction in quantum physics and conscious experience

For a summary of earlier postings see Links to the latest progress in TGD.