Magnetic monopoles at sixties

Old age is usually associated with wisdom and similar virtues. In my case this association unfortunately fails and therefore the first morning at sixties gives me authority to free associations about everything under the heaven, and magnetic monopoles are a good place to start from. The evidence for condensed matter monopoles is accumulating (see this and this) and the question is whether they really represent some new physics. Perhaps this is the case.

Dirac monopoles are mathematically singular and cannot be therefore tolerated in elite circles of theoretical physics appreciating good manners coded by gauge invariance. Since I frantically want to belong to the elite, I am happy that TGD provides me with homological monopoles, which can exist gracefully because of the homological non-triviality of CP₂. Homological non-triviality means that CP₂ has non-contractible 2-surfaces such as spheres: this does not mean that it would have a hole as a lazy popularizer usually says. Rather, this kind of sphere is a 2-dimensional analog of a circle around torus not allowing contraction to a point without cutting. The imbedding of CP₂ to some higher dimensional space would contain a hole in some sense.

The weak form of electric-magnetic duality- a purely TGD based notion- implies that all elementary particles correspond to pairs of wormhole contacts. Each contact has two throats carrying magnetic monopole charge and each throat is connected to the corresponding throat of second contact. This makes altogether four wormhole throats so that graviton can be constructed in this manner. The length of the magnetic flux tube defining string like object corresponds to the weak length scale about 10^-17 m. All particles would be this kind of string like objects, "weak" strings.

Emergence gives excellent hopes about the realization of exact Yangian invariance and twistor Grassmannian program without infrared and UV divergences (see this). Emergence states that at the fundamental level there are only massless(!) wormhole throats carrying many-fermion states identifiable in terms of representations for the analog of space-time super-symmetry algebra with generators identified as fermionic oscillator operators. Masslessness applies also to the building blocks of virtual particles meaning a totally new interpretation of loop corrections and manifest UV finiteness. Also the vibrational degrees of freedom of partonic 2-surfaces are present as bosonic degrees of freedom and correspond to orbital degrees of freedom for the spinor fields of world of classical worlds (WCW) whereas fermionic degrees of freedom define WCW spin degrees of freedom. The dark variants of the elementary particles having large value of hbar have zoomed up size and in living matter these scaled up elementary particles would be the key players in the drama of life.

Quite recently I realized that dark variants of elementary particles identified in this manner are more or less the same thing as the wormhole magnetic fields that I introduced for more than decade ago (see this) and suggested that their Bose-Einstein condensates and coherent states could be crucial for understanding living matter. At that time I did not of course realize the connection with ordinary elementary particle physics and proposed these exotics as new kind of particle like objects. These flux tubes have become the basic structures in TGD inspired quantum biology. For instance, the model for DNA as topological quantum computer assumes that the nucleotides of DNA and lipids of cell membrane are connected by this kind of flux tubes with quarks at their ends and the braiding of the flux tubes codes for topological quantum computations.

If this picture is correct, quantum biology might be to high degree a collection of zoomed up variants of elementary particle physics at very high density! Also the super-partners and scaled up hadrons would be present. If this is true we would be able to study elementary particle interiors by zooming up them to the scales of living matter! There would be no need for the followers of LHC! Living matter could be an enormous particle physics laboratory providing physicists with incredibly refined research facilities;-). But are these facilities meant for us after we finally have realized that we ourselves are the most refined laboratory? Or are the physicists already there? If so, who these physicists from higher levels of self hierarchy might be;-)?

By the way, this crazy speculation might have been inspired also by the earlier finding that the model of dark nucleons allows to map the spectrum of nucleon states to RNA, DNA, tRNA triplets and aminoacids and also reproduces vertebrate genetic code in a very natural manner (see this and this).

Tau-pions again but now in galactic center

The standard view about dark matter is that it has only gravitatitonal interactions with ordinary matter so that high densities of dark matter are required to detect its signatures. On the average the density of dark matter is about 80 per cent of ordinary matter. Clearly, Milky Way's center is an excellent place for detecting the signatures of dark matter. The annihilation of pairs of dark matter particles to gamma rays is one possible signature and one could study the anomalous features of gamma ray spectrum from the galactic center (a region with radius about 100 light years).

Europe's INTEGRAL satellite launched in 2002 indeed found bright gamma ray radiations coming from the center of galaxy with energy of .511 MeV, which is slightly above electron mass (see the references below). The official interpretation is that the gammas are produced in the annihilations of particles of positrons and electrons in turn created in dark matter annihilations. TGD suggests much simpler mechanism. Gamma rays would be produced in the decay of what I call electropions having mass which is slightly larger than m=2m_e.

The news of the day was that the data from Fermi Gamma Ray telescope give analyzed by Dan Hooper and Lisa Goodenough gives evidence for a dark matter candidate with mass between 7.3-9.2 GeV decaying predominantly into a pair of τ leptons. The estimate for the mass region is roughly 4 times τ mass. What puts bells ringing that a mass of a charged lepton appears again!

Explanation in TGD framework

The new finding fits nicely to a bigger story based on TGD.

1. TGD predicts that both quarks and leptons should have colored excitations (see the chapter devoted to the leptohadron model). In the case of leptons lowest excitations are color octets. In the case of electro-pion this hypothesis finds support from the anomalous production of electron positron pairs in heavy ion collisions discovered already at seventies but forgotten for long ago since the existence of light particle at this mass scale simply was in total complete with standard model and what was known about the decay widths of intermediate gauge bosons. Also ortopositronium decay width anomaly -forgotten also-has explanation in terms of leptopion hypothesis (see the references below)

2. The colored leptons would be dark in TGD sense, which means that they live in dark sector of the "world of classical worlds" (WCW) meaning that they have no direct interactions (common vertices of Feynman diagrams) with ordinary matter. They simply live at different space-time sheets. A phase transition which is geometrically a leakage between dark sector and ordinary sector are possible and make possible interactions between ordinary and dark matter based on exchanged particles suffering this phase transition. Therefore the decay widths of intermediate gauge bosons do not kill the model. TGD based model of dark matter in terms of hierarchy of values of Planck constants coming as multiples of its smallest possible value (the simplest option) need not to be postulated separately and can be regarded as a prediction of quantum TGD reflecting directly the vacuum degenerarcy and extreme non-linearity of Kähler action (Maxwell action for induced CP₂ Kähler form).

3. CDF anomaly which created a lot of discussion in blogs for two years ago can be understood in terms of taupion. Taupion and its p-adically scaled up versions with masses about 2^km_τ, k=1,2,3 and m_τ≈ 1.8 GeV explains the findings reported by CDF in TGD framework. The masses of taupions would be 3.6 GeV, 7.2 GeV, and 14.2 GeV in good approximation and come as octaves of the mass of tau-lepton pair.

Predictions

The mass estimate for the dark matter particle suggests by Fermi Gamma Ray telescope corresponds to k=2 octave for taupion and the predict mass is about 7.2 GeV which at the lower boundary of the range 7.3-9.2 GeV. Also dark matter particles decaying to tau pairs and having masses 3.6 GeV and 14.2 GeV should be found.

Also muo-pion should exist there and should have mass slightly above 2m_μ= 210.4 MeV so that a gamma rays peak slightly above the energy μ=105.2 MeV should be discovered. Also octaves of this mass are possible. There is also evidence also for the existence of muopion (around 2007, see the links below).

LHC should provide excellent opportunities to test tau-pion and muo-pion hypothesis. Electro-pion was discovered in heavy ion collisions and also at LHC they study have heavy ion collisions but at much higher energies generating the required very strong non-orthogonal electric and magnetic fields for which the "instanton density" defined as the inner product of electric and magnetic fields is large and rapidly varying. I do not of course consider for a second the possibility that the mighty ones at LHC would take seriously what some ridiculed TGD guy without any academic affiliation suggests. As an optimist I hope that muo-pion and tau-pion could be discovered despite the fact that their decay signatures are very different from those for ordinary particles and despite that fact that at these energies one must know precisely what one is trying to find in order to disentangle it from the enormous background.

Also DAMA, CoGeNT, and PAMELA give indications for tau-pion

Note that also DAMA suggests the existence of dark matter particle in this mass range but it is not clear whether it can have anything to do with tau-pion state. One could of course imagine that dark tau-pions are created in the collisions of highly energetic cosmic rays with the nuclei of atmosphere. Also Coherent Germanium Neutrino Technology (CoGeNT) experiment has released data that are best explained in terms of a dark matter particle with mass in the range 7-11 GeV.

The decay of tau-pions produce lepton pairs, mostly tau but also muons and electrons. The subsequent decays of tau-leptons to muons and electrons produce also electrons and positrons. This relates interestingly to the positron excess reported by PAMELA collaboration at the same time as CDF anomaly was reported (my second birth days gift;-). The anomaly started at positron energy about 3.6 GeV, which is one just one half of 7. 2 GeV for tau-pion mass! What was remarkable that no antiproton excess predicted by standard dark matter candidates was observed. Therefore the interpretation as decay products of tau-pions seems to make sense! A short comment about sociology of science

By the way, CDF anomaly published two years ago meant quite an intensive drama in my life as a lonely dissident. The announcement of CDF about the anomaly happened to come just at the eve of my birth day and I took it as a birth day gift;-). Amusingly, also this news deserves to be called a birthday gift (New Scientists dates the article at October 28 and I will be 60 years old October 30. Note however that the eprint has been added to arXiv October 13). The explanation of the CDF anomaly was of course a great victory for TGD and meant a period of intense work lasting for several months. I had an excellent reason to participate blog discussions and this induced an extremely hostile attacks from the besserwissers of science in Resonaances. Probably also because the first evidence for electropions is from seventies and the neglect of all this data for a period of decades just because it does not conform with standard moded is a scandal. To put it mildly.

Also the powerholders of Finnish theoretical physics decided to give their own birthday gift: I lost sthe right to use the memory of university computer for my homepage which had served as a symbolic support hoped to keep my silent! Small nuisance after all but a nuisance in any case since I had to be quick since the deadline was absolute. The situation today in Finnish theoretical physics has become rather surreal. I am mentioned in the list of fifty world-wide known finnish scientists in Wikipedia among two other living finnish physicists but absolutely no one in the academic environment dares to know about my existence publicly! An excellent opportunity for a gifted writer to create a brilliant satire about the madness of the academic world.

For the details of leptohadron hypothesis see the chapter Recent Status of Leptohadron Hypothesis of "p-Adic length Scale Hypothesis and Dark Matter Hierarchy". I have listed below publications related to lepto-pion anomaly.

1. Electropion anomaly

1. W. Koenig et al(1987), Zeitschrift fur Physik A, 3288, 1297.
2. A.T. Goshaw et al(1979), Phys. Rev. Lett. 43, 1065.
3. P.V. Chliapnikov et al(1984), Phys. Lett. B 141, 276.
4. K. Dantzman et al (1989), Phys. Rev. Lett., 62, 2353.
5. C. I. Westbrook ,D. W Kidley, R. S. Gidley, R. S Conti and A. Rich (1987), Phys. Rev. Lett. 58 , 1328.
6. S. Barshay (1992) , Mod. Phys. Lett. A, Vol 7, No 20, p. 1843.
7. J.Schweppe et al.(1983), Phys. Rev. Lett. 51, 2261.
8. H.Tsertos et al. (1985) , Phys. Lett. 162B, 273, H.Tsertos et al.(1987) , Z. Phys. A 326, 235.
9. P. Salabura et al (1990), Phys. Lett. B 245, 2, 153.
10. A. Chodos (1987) , Comments Nucl. Part. Phys., Vol 17, No 4, pp. 211, 223.
11. L. Kraus and M. Zeller (1986), Phys. Rev. D 34, 3385.
12. M. Clemente et al. (1984), Phys. Rev. Lett. 137B, 41.
13. S. Judge et al (1990) , Phys.Rev. Lett., 65(8), 972.
14. T. Cowan et al.(1985), Phys. Rev. Lett. 54, 1761 and T. Cowan et al.(1986), Phys. Rev. Lett. 56, 444.

2. Electro-pions as a candidate for dark matter in galactic center

1. G. Weidenspointner et al (2006), The sky distribution of positronium annihilation continuum emission measured with SPI/INTEGRAL, Astron. Astrophys. 450, 1013, astro-ph/0601673.
2. E. Churazov, R. Sunyaev, S. Sazonov, M. Revnivtsev, and D. Varshalovich, Positron annihilation spectrum from the Galactic Center region observed by SPI/INTEGRAL, Mon. Not. Roy. 17. Astron. Soc. 357, 1377 (2005), astro-ph/0411351.

3. Ortopositronium anomaly

R. Escribabno,E. Masso, R. Toldra (1995), Phys. Lett. B. 356, 313-318.

4. Muopion anomaly

1. X.-G. He, J. Tandean, G. Valencia (2007), Has HyperCP Observed a Light Higgs Boson?,Phys. Rev. D74. http://arxiv.org/abs/hep-ph/0610274 .
2. X.-G. He, J. Tandean, G. Valencia (2007), Light Higgs Production in Hyperon Decay, Phys. Rev. Lett. 98. http://arxiv.org/abs/hep-ph/0610362.

5. Taupion anomaly

1. CDF: T. Daniels et al (1994), Fermilab-Conf-94/136-E; Fermilab-Conf-94/212-E.
2. CDF Collaboration (2008), Study of multi-muon events produced in p-pbar collisions at sqrt(s)=1.96 TeV. http://arxiv.org/PS_cache/arxiv/pdf/0810/0810.0714v1.pdf.
3. T. Dorigo (2008), Some notes on the multi-muon analysis - part I. http://dorigo.wordpress.com/2008/11/08/some-notes-on-the-multi-muon-analysis-part-i/.

6. Taupions as a candidate for dark matter in galactic center

D. Hooper and L. Goodenough (2010), Dark Matter Annihilation in The Galactic Center As Seen by the Fermi Gamma Ray Space Telescope. http://arxiv.org/pdf/1010.2752v1.

DAMA collaboration (2010), Results from DAMA/LIBRA at Gran Sasso, Found. Phys. 40, p. 900. http://people.roma2.infn.it/~dama/web/publ10.html.

CoGENT collaboration (2010), Results from a Search for Light-Mass Dark Matter with a P-type Point Contact Germanium Detector. http://arxiv.org/abs/1002.4703. PAMELA Collaboration (2008), Observation of an anomalous positron abundance in the cosmic radiation. http://arxiv.org/abs/1002.4703. M. Boexio (2008), talk represented at IDM 2008, Stockholm, Sweden.

Topological explanation of family replication phenomenon

One of the basic ideas of TGD approach has been genus-generation correspondence: boundary components of the 3-surface should be carriers of elementary particle numbers and the observed particle families should correspond to various boundary topologies. Last summer meant quite a progress in the understanding of quantum TGD, which forced also the updating of the views about the topological explanation of family replication phenomenon.

With the advent of zero energy ontology the original picture changed somewhat. It is the wormhole throats identified as light-like 3-surfaces at with the induced metric of the space-time surface changes its signature from Minkowskian to Euclidian, which correspond to the light-like orbits of partonic 2-surfaces. One cannot of course exclude the possibility that also boundary components could allow to satisfy boundary conditions without assuming vacuum extremal property of nearby space-time surface. The intersections of the wormhole throats with the light-like boundaries of causal diamonds (CDs) identified as intersections of future and past directed light cones (CD × CP₂ is actually in question but I will speak about CDs) define special partonic 2-surfaces and it is the comformal moduli of these partonic 2-surfaces which appear in the elementary particle vacuum functionals naturally.

The first modification of the original simple picture comes from the identification of physical particles as bound states of pairs of wormhole contacts and from the assumption that for generalized Feynman diagrams stringy trouser vertices are replaced with vertices at which the ends of light-like wormhole throats meet. In this picture the interpretation of the analog of trouser vertex is in terms of propagation of same particle along two different paths. This interpretation is mathematically natural since vertices correspond to 2-manifolds rather than singular 2-manifolds which are just splitting to two disjoint components. Second complication comes from the weak form of electric-magnetic duality forcing to identify physical particles as weak strings with magnetic monopoles at their ends and one should understand also the possible complications caused by this generalization.

These modifications force to consider several options concerning the identification of light fermions and bosons and one can end up with a unique identification only by making some assumptions. Masslessness of all wormhole throats- also those appearing in internal lines- and dynamical SU(3) symmetry for particle generations are attractive general enough assumptions of this kind. This means that bosons and their super-partners correspond to wormhole contacts with fermion and antifermion at the throats of the contact. Free fermions and their superpartners could correspond to CP₂ type vacuum extremals with single wormhole throat. It turns however that dynamical SU(3) symmetry forces to identify massive (and possibly topologically condensed) fermions as (g,g) type wormhole contacts.

Do free fermions correspond to single wormhole throat or (g,g) wormhole?

The original interpretation of genus-generation correspondence was that free fermions correspond to wormhole throats characterized by genus. The idea of SU(3) as a dynamical symmetry suggested that gauge bosons correspond to octet and singlet representations of SU(3). The further idea that all lines of generalized Feynman diagrams are massless poses a strong additional constraint and it is not clear whether this proposal as such survives.

1. Twistorial program assumes that fundamental objects are massless wormhole throats carrying collinearly moving many-fermion states and also bosonic excitations generated by super-symplectic algebra. In the following consideration only purely bosonic and single fermion throats are considered since they are the basic building blocks of physical particles. The reason is that propagators for high excitations behave like p^-n, n the number of fermions associated with the wormhole throat. Therefore single throat allows only spins 0,1/2,1 as elementary particles in the usual sense of the word.

2. The identification of massive fermions (as opposed to free massless fermions) as wormhole contacts follows if one requires that fundamental building blocks are massless since at least two massless throats are required to have a massive state. Therefore the conformal excitations with CP₂ mass scale should be assignable to wormhole contacts also in the case of fermions. As already noticed this is not the end of the story: weak strings are required by the weak form of electric-magnetic duality.

3. If free fermions corresponding to single wormhole throat, topological condensation is an essential element of the formation of stringy states. The topological condensation of fermions by topological sum (fermionic CP₂ type vacuum extremal touches another space-time sheet) suggest (g,0) wormhole contact. Note however that the identification of wormhole throat is as 3-surface at which the signature of the induced metric changes so that this conclusion might be wrong. One can indeed consider also the possibility of (g,g) pairs as an outcome of topological conensation. This is suggested also by the idea that wormhole throats are analogous to string like objects and only this option turns out to be consistent with the BFF vertex based on the requirement of dynamical SU(3) symmetry to be discussed later. The structure of reaction vertices makes it possible to interpret (g,g) pairs as SU(3) triplet. If bosons are obtained as fusion of fermionic and antifermionic throats (touching of corresponding CP₂ type vacuum extremals) they correspond naturally to (g₁,g₂) pairs.

4. p-Adic mass calculations distinguish between fermions and bosons and the identification of fermions and bosons should be consistent with this difference. The maximal p-adic temperature T=1 for fermions could relate to the weakness of the interaction of the fermionic wormhole throat with the wormhole throat resulting in topological condensation. This wormhole throat would however carry momentum and 3-momentum would in general be non-parallel to that of the fermion, most naturally in the opposite direction.

   p-Adic mass calculations suggest strongly that for bosons p-adic temperature T=1/n, n>1, so that thermodynamical contribution to the mass squared is negligible. The low p-adic temperature could be due to the strong interaction between fermionic and antifermionic wormhole throat leading to the "freezing" of the conformal degrees of freedom related to the relative motion of wormhole throats.

5. The weak form of electric-magnetic duality forces second wormhole throat with opposite magnetic charge and the light-like momenta could sum up to massive momentum. In this case string tension corresponds to electroweak length scale. Therefore p-adic thermodynamics must be assigned to wormhole contacts and these appear as basic units connected by Kähler magnetic flux tube pairs at the two space-time sheets involved. Weak stringy degrees of freedom are however expected to give additional contribution to the mass, perhaps by modifying the ground state conformal weight. A nice implication is that all elementary particles -not only gravitons- correspond to pairs of wormhole throats connected by magnetic flux tubes to form "weak strings". This has obvious implications at LHC.

Dynamical SU(3) fixes the identification of fermions and bosons and fundamental interaction vertices

For 3 light fermion families SU(3) suggests itself as a dynamical symmetry with fermions in fundamental N=3-dimensional representation and N× N=9 bosons in the adjoint representation and singlet representation. The known gauge bosons have same couplings to fermionic families so that they must correspond to the singlet representation. The first challenge is to understand whether it is possible to have dynamical SU(3) at the level of fundamental reaction vertices.

This is a highly non-trivial constraint. For instance, the vertices in which n wormhole throats with same (g₁,g₂) glued along the ends of lines are not consistent with this symmetry. The splitting of the fermionic worm-hole contacts before the proper vertices for throats might however allow the realization of dynamical SU(3). The condition of SU(3) symmetry combined with the requirement that virtual lines resulting also in the splitting of wormhole contacts are always massless, leads to the conclusion that massive fermions correspond to (g,g) type wormhole contacts transforming naturally like SU(3) triplet. This picture conformsl with the identification of free fermions as throats but not with the naive expectation that their topological condensation gives rise to (g,0) wormhole contact.

The argument leading to these conclusions runs as follows.

1. The question is what basic reaction vertices are allowed by dynamical SU(3) symmetry. FFB vertices are in principle all that is needed and they should obey the dynamical symmetry. The meeting of entire wormhole contacts along their ends is certainly not possible. The splitting of fermionic wormhole contacts before the vertices might be however consistent with SU(3) symmetry. This would give two a pair of 3-vertices at which three wormhole lines meet along partonic 2-surfaces (rather than along 3-D wormhole contacts).

2. Note first that crossing gives all possible reaction vertices of this kind from F(g₁)Fbar(g₂)→ B(g₁,g₂) annihilation vertex, which is relatively easy to visualize. In this reaction F(g₁) and Fbar(g₂) wormhole contacts split first. If one requires that all wormhole throats involved are massless, the two wormhole throats resulting in splitting and carrying no fermion number must carry light-like momentum so that they cannot just disappear. The ends of the wormhole throats of the boson must glued together with the end of the fermionic wormhole throat and its companion generated in the splitting of the wormhole. This means that fermionic wormhole first splits and the resulting throats meet at the partonic 2-surface.

   This requires that topologically condensed fermions correspond to (g,g) pairs rather than (g,0) pairs. The reaction mechanism allows the interpretation of (g,g) pairs as a triplet of dynamical SU(3). The fundamental vertices would be just the splitting of wormhole contact and 3-vertices for throats since SU(3) symmetry would exclude more complex reaction vertices such as n-boson vertices corresponding the gluing of n wormhole contact lines along their 3-dimensional ends. The couplings of singlet representation for bosons would have same coupling to all fermion families so that the basic experimental constraint would be satisfied.

3. Both fermions and bosons cannot correspond to octet and singlet of SU(3). In this case reaction vertices should correspond algebraically to the multiplication of matrix elements e_ij: e_ij e_kl = δ_jk e_il allowing for instance F(g₁,g₂) +Fbar(g₂,g₃)→ B(g₁,g₃) . Neither the fusion of entire wormhole contacts along their ends nor the splitting of wormhole throats before the fusion of partonic 2-surfaces allows this kind of vertices so that BFF vertex is the only possible one. Also the construction of QFT limit starting from bosonic emergence led to the formulation of perturbation theory in terms of Dirac action allowing only BFF vertex as fundamental vertex.

4. Weak electric-magnetic duality brings in an additional complication. SU(3) symmetry poses also now strong constraints and it would seem that the reactions must involve copies of basic BFF vertices for the pairs of ends of weak strings. The string ends with the same Kähler magnetic charge should meet at the vertex and give rise to BFF vertices. For instance, FFbarB annihilation vertex would in this manner give rise to the analog of stringy diagram in which strings join along ends since two string ends disappear in the process.

If one accepts this picture the remaining question is why the number of genera is just three. Could this relate to the fact that g≤ 2 Riemann surfaces are always hyper-elliptic (have global Z₂ conformal symmetry) unlike g>2 surfaces? Why the complete bosonic de-localization of the light families should be restricted inside the hyper-elliptic sector? Does the Z₂ conformal symmetry make these states light and make possible delocalization and dynamical SU(3) symmetry? Could it be that for g>2 elementary particle vacuum functionals vanish for hyper-elliptic surfaces? If this the case and if the time evolution for partonic 2-surfaces changing g commutes with Z₂ symmetry then the vacuum functionals localized to g≤ 2 surfaces do not disperse to g>2 sectors.

These and many other questions are discussed in the chapters of p-Adic length scale hypothesis and dark matter hierarchy, in particular in the chapter Elementary Particle Vacuum Functionals.

By the way, I have performed and updating of several books about TGD in order to achieve a more coherent representation. I have also added three new chapters to the book Topological Geometrodynamics: an Overview discussing TGD from particle physics perspective (see this, this, and this).

Also the chapters of p-Adic length scale hypothesis and dark matter hierarchy are heavily updated.

Quark compositeness nowhere near: what about weak strings?

We are living exciting times. At least I have full reason to feel like this;-). LHC has already given evidence for deviations from QCD possibly due to the fact that QCD plasma resides at long entangled color magnetic flux tubes. Then came first rumors about indications for supersymmetric partners.

As I saw Tommaso's posting about quark compositeness I was for a moment absolutely sure that quark compositeness in the sense of TGD has been discovered. Unfortunately my wishful thinking (or rather feeling!) was wrong. What has been found that there is no substructure at energy scales below 4 TeV. In any case it is worth of summarizing what compositeness would mean in TGD framework since the concept of substructure is a delicate notion.

The weak form of electric-magnetic duality, last summer's big theoretical discovery in TGD, forces to conclude that elementary particles in TGD Universe correspond to "weak strings", which are essentially magnetic flux tubes carrying opposite magnetic charges at their ends. The fermion at the first end is accompanied by a neutrino antineutrino pair at second end. The neutrino pair neutralizes weak isospin and in this manner causes weak confinement and screening which closely relates to TGD counterpart for particle massivation. I have explained at my blog gauge boson massivation based on this picture: see this.

One highly suggestive conclusion is that also photon gets massive by eating the remaining component of Higgs ( consisting of SU(2) triplet and singlet as gauge bosons rather than complex doublet) so that there would be no Higgs to be found at LHC.

What should be found (among other things) would be compositeness of both quarks, leptons, and intermediate gauge bosons. All of them would be string like objects -magnetic flux tubes with wormhole contacts with two throats at their ends of length of order weak scale. The weak string tension is the crucial parameter which does not however make itself visible through the masses of elementary particles which correspond to the lowest states. The first guess is in terms of weak mass scale in which case new physics would be easy to observe and might have been already observed. The second natural guess is that Mersenne prime M_89 characterizing weak bosons determines the tension. If so the tension would be 2⁹=512 times hadronic string tension and by p-adic length scale hypothesis would correspond to about 512 times 1 GeV = .5 TeV.

I have also proposed that ordinary hadron physics characterized by Mersenne prime M₁₀₇ has a scaled up variant of characterized by M₈₉ with about 512 GeV string tension. The proposal is inspired by the observation that Mersenne primes seem to correspond to hadron like physics in TGD Universe: leptons e and tau correspond to Mersenne primes M₁₂₇ and M₁₀₇ and muon to Gaussian Mersenne with k=113 and there is evidence for leptopion like states formed by color octet excitations of these states for all three leptons. For electron evidence comes from seventies, for tau CDF anomaly provides the evidence, and there is also evidence in case of muon. It remains to be seen if both M₈₉ hadronic physics and/or weak stringy physics is or neither of them are there. For details see this.

What makes the situation exciting since I do not have enough understanding to conclude whether the results say anything about the notion of weak string. One can say that below the length scale one would see quarks and leptons as particles without the weak screening is this what we have seen already for a long time above weak energy scale. Only time will show.

What before Big Bang?

Both Phil Gibbs and Lubos have commented a BBC documentary in which the familiar old names and also two younger not so namy cosmologists told about their answers to the question "What before Big Bang". I must admit that I enjoyed the aggressive rhetoric of Lubos's commentary although I do not share his ultra-conservative views and belief in inflation. Most of these approaches shared something with my own approach although all of them are conceptually primitive and involve a lot of hand waving. The reason is that these theoreticians remain in the framework of General Relativity where the new ideas do not have a natural place.

1. Probably Penrose was the only one who raised the question whether the question "What before Big Bang" makes sense at all. His earlier answer to the question had been negative in general relativity context but unfortunately he had changed his view. If one leaves GRT framework, the situation changes.

   For instance, if one decides to take TGD seriously and identifies space-times as 4-D surfaces of M⁴× CP₂, it takes only five years to end up with the notion of world of classical worlds (WCW), and only 27 years with zero energy ontology (ZEO);-). In ZEO WCW decomposes to a union of sub-WCWs consisting of space-time surfaces located inside causal diamonds (CD, essentially the intersection of future and past directed light-cones) carrying zero energy states with positive and negative energy parts of the state at the light-like boundaries of the causal diamond. One can form unions of CDs and CDs can also intersect. In this framework one has a hierarchy of CDs beginning from elementary particle level and extending up to Russian doll hierarchy of cosmologies.

   I would have been happy if at least one of the visionaries had said something about the relationship between experienced time and geometric time of physicist. These times are not one and the same thing as even child realizes. Unfortunately the academic habit is to think that they are. I have become convinced that the proper understanding of this difference will mean enormous progress both in the quantum theory of consciousness and in quantum physics defined in standard manner (the extension of physics to a quantum theory of consciousness is natural in the wider framework).

   Unfortunately Penrose's arguments were so popular that I could not get any idea about the mathematics behind it. My approximation for what Penrose said is that when the density of matter gets sufficiently low the space-time somehow begins to look like a good candidate for the first moment of a new Big Bang. I failed to understand. Note however that in TGD framework the mass per comoving volume for critical and string dominated cosmologies goes to zero as linear function of the scaling factor of 3-metric and identified as the light-cone proper time in TGD framework. I have talked about a silent whisper amplified to big bang as a more approriate description of TGD inspired cosmology than Big Bang which is a mathematical singularity.

   Penrose's intuition can be actually justified in TGD context. The canonical imbedding of empty Minkowski space to M⁴× CP₂ is maximally critical in the sense that Kähler action is fourth order in small deformations so that perturbative quantum field theory is impossible: this was the problem which lead to the notion of WCW and eventually to the notion of hierarchy of Planck constants. Criticality has also interpretation as criticality against deformations assignable to zero energy states representing sub-cosmologies in very long length scales. Note also that there is analogy with Higgs potential in the sense that the point at the origin of Mexican hat potential is replaced with the infinite-dimensional space of vacuum extremals.

2. As a full day zero energy ontologists I liked Michio Kaku's vision about the fusion of Buddhist's vision about complete emptiness as source of everything and of the Christian "Let there be light" idea. ZEO solves many deep philosophical problems. For instance, the classical question about what was the initial state and the quantal question about what where the values of the conserved net quantum numbers associated with the initial state becomes irrelevant. ZEO is also consistent with crossing symmetry of quantum field theories and leads to an elegant generalization of thermal quantum field theories. At practical level one ends up to an opening of the black box of virtual particle and a manifestly finite version of Feynman diagrammatics emerges with massless fermions serving as fundamental building bricks of all particles, including stringy objects. Twistor approach is absolutely essential element of this approach.

   As a representative of Christian culture I find it amusing that the basic objects would be light-like 3-surfaces so that the statement "Let there be light" receives an additional hidden meaning! Maybe Christian God is Great Humorist after all although Bible does not suggest this. Of course, this is not the only manner to say it. By general coordinate invariance one can equivalently speak about space-like 3-surfaces. This implies effective 2-dimensionality and strong form of holography: partonic 2-surfaces and the 4-D tangent space data of the space-time surfaces at them code for the quantum physics.

3. Linde is an inflationary theorist wanting to give up the notion of Big Bang altogether and replace it with eternal inflation."What before Big Bang?" transforms to "What before Inflation?" so that not much has been gained. The basic problem of inflationary scenarios is that it involves GUTs and thus arbitrary amounts of Higgs like stuff with a lot Higgs potentials with a lot of parameters so that everything can be fitted but nothing predicted. Some of us -even Lubos- regard this as a success. Linde tested the limits of plausibility by claiming that their calculations have led to some gigantic number involving many exponents equal to 10. The highest exponent in the impressive tower of exponents was - surprise surprise- number 7! Why just 7? Sensitive listener could perhaps argue that the number seven as the number of mystic world views must be coded to the basic laws of physics and this is how it achieved;-). This number was supposed to be number of possible universes if I got it correctly.

   What makes me astonished that theoretical cosmologists still fail to realize that the flatness of 3-space could be also seen as a correlate of quantum criticality. Quantum criticality means universality and one can forget all fiddling with Higgs potentials. Indeed, in TGD framework criticality plus imbeddability to M⁴× CP₂ fixes the cosmology apart from the value of the parameter fixing its duration as I have repeatedly tried to tell. A model for critical periods involving only a single parameter would be easy to kill or shown to be the cosmological counterpart of Nordström metric. One prediction is a fractal hierarchy of long range correlations in cosmological scales reflecting the hierarchy of Planck constants having gigantic values in astrophysical systems and assignable to dark matter and to the counterpart of dark energy.

   What made me happy that one experimentalist involved is interested in testing of the presence of this kind of correlations! There is actually already indications for these correlations: for instance, copies of astrophysical object appearing at same line of sight. If they are actual this suggest lattice like structures if cosmological scales. They could be also artefacts resulting from a circulation of the light coming from the object around circular path several times before being detected.

   In any case, all hope is not lost since the experimentalists are still among us!

4. Neil Turok criticized inflation and proposed an M-theory inspired model of pre Big Bang era assuming the presence of two branes which then collided. These kind of models are of course non-predictive but if cosmologists get interested they can produce endless number of fits and conclude that on basis of the amount of literature written on the subject this is the only game in the town.

   What connects this with TGD is that if one necessarily wants so, one can call 3-surfaces and 4-surfaces branes also in TGD framework. I still do not know how much of inspiration for the second superstring revolution came from TGD and whether the hope was that M-theory would work and TGD as a predecessor of the idea could be safely buried in sands of time. This hope was not realized. TGD is making detailed predictions to LHC whereas M-theorists remain remarkably silent.

5. Param Singh was second non-namy cosmologist allowed to tell about his views. He proposed that instead of big bang there is a series of bounces: almost big crunch followed by almost big bang. Planck scale would be the scale where GRT based cosmology would fail and super-string models would somehow come in rescue. I am afraid that super-string models do not have time to help since they are fighting with their very severe personal problems.

   In TGD framework CD could be visualized as big bang followed by a big crush (or better to say, a silent whisper amplified to a lot of noise eventually calming down and ending with a silent last breath). In ZEO a more approriate manner to interpret the big crush would be as a big bang in reversed time direction. It is also quite possible that partonic 2-surfaces at boundaries of CDs can continue as light-like 3-surfaces in both directions and this is essential for generalized Feynman diagrammatics. Could this define something which could be regarded as the analog of the bounce?

6. Lee Smolin represented his idea of cosmological evolution and suggested that the collapse of star to black hole is somehow followed by a creation of new cosmology inside black hole. The idea about natural selection in cosmological scales is quite interesting and I ended up with it fifteen years ago through the p-adic calculations of elementary particle masses. The calculations made one key assumption or better to say observation: elementary particles correspond to p-adic primes which are near to powers of two and Mersenne primes and their Gaussian counterparts turned out to be especially important.

   Zero energy cosmology combined with number theoretical universality can give at least a partial justification for this hypothesis. The proper time distances between the tips of CDs would come as octaves of CP₂ time and correspond to what I am used to call secondary p-adic length/time scales. For instance, in the case of electron one obtains .1 second which is fundamental biological length scale! The idea that there is natural selection also in elementary particle length scales selecting p-adic length scales characterized by favored p-adic primes as those for which particles are long lived looks very natural. Also TGD inspired quantum biology and theory of consciousness imply evolution in all length and time scales. Mersenne primes emerge also in quantum information theory as special ones.

7. Laura Mersini-Houghton talked about "waves" in cosmology. I was unable to understand a single word of it but looked at web and found that she is proposing that the notion of wave function could make sense in M-theory landscape. Probably she had realized that string landscape is not a very sexy word nowadays and decided to avoid its use.

   It seems M-theorists have finally begun to think of the possibility that one could speak about quantum states in landscape. Wheeler talked about wave functions in super space for aeons ago and I talked about wave functions in the space of 3-surfaces already in my thesis around 1982, and ended up to the notion of configuration space (WCW) geometry and the modes of classical configuration space spinor field as a general representation of the quantun states of Universe around 1985. Around 1990 I ended up with the realization that general coordinate invariance forces to identify Kähler function of configuration space as Kähler action for a preferred extremal defining the counterpart of Bohr orbit and realizing holography. This almost incredibe delay in the natural evolution of ideas is an excellent lesson about how dangerous it is to censor out a bottle neck ideas.

First rumors about super partners in LHC

Lubos reports the first rumors from LHC concerning super-partners. The estimates for the masses are 200 GeV for scalar super partner (higgsino) and 160 GeV for fermion superpartner (I guess selectron). Being an incurable optimist I suppose that the rumors from LHC are more trustworthy than the physics blog rumors usually. If so, can one understand these masses in TGD framework and what can one conclude about them? Also this posting has been replaced with a new one since I finally ended up with the understaning of how the TGD based variant of gauge boson massivation could explain how gauge bosons get their longitudinal components and how the ratio of W and Z masses could result in this framework in terms of weak string picture.

Consider first the theoretical background in light p-adic mass calculations, the weak form of electric-magnetic duality, and TGD based view about supersymmetry.

1. The simplest possibility is that the p-adic length scale of the super-partner differs from that of partner but the p-adic thermodynamical contributions to the mass squared obey the same formula.

2. If the p-adic prime p≈ 2^k of super-partner is smaller than M₈₉=2⁸⁹-1, the weak length scale must be scaled down and M₆₁=2⁸⁹-1 is the next Mersenne prime. Scaled up variant of QCD for M₈₉ would naturally correspond to M₆₁ weak physics and would have hadronic string tension about 2¹⁸ GeV² by scaling the ordinary hadronic string tension of about 1 GeV². This scaled up variant of hadronic physics is an old prediction of TGD. As noticed, also weak string tension could have the same value. Quite generally, the pairs of weak and hadronic scales predicted to form a hierarchy could correspond to pairs of subsequent (possibly Gaussian) Mersenne primes.

3. What happens for k=89? Can the particle topologically condense at the same p-adic scale that characterizes its weak flux tube? Or should one assume that the p-adic prime corresponds to k< 89 assuming that the particle has standard weak interactions. If so then the superpartners of light fermions would have k< 89. This is a strong prediction if superpartners obey the same mass formula as particles. In the case of weak gluinos and also QCD gluinos the bound would be k≤ 89 and even stronger bound would be k=89 so that the masses of wino and zino would be same as W and Z.

   One must be however very cautious with this kind of arguments since one is dealing with quantum theory. For instance, quarks inside proton have masses in 10 MeV scale and their Compton lengths are much larger than the Compton size of proton and even atomic nucleus. The interpretation is that for the corresponding space-time sheets is in terms of the color magnetic body of quark. These large space-time sheets are essential in the model of the Lamb shift anomaly of muonic hydrogen.

4. In TGD framework Higgs and its pseudo-scalar companion define electroweak triplet and singlet and Higgs could be eaten completely by electro-weak gauge bosons if the TGD based mechanism of massivation is correct. The condition of exact Yangian symmetry demands the cancellation of IR divergences requiring a small mass for all gauge bosons and graviton. The twistorially natural assumption that gauge bosons are bound states of massless fermion and antifermion implies that the three-momenta of fermion and antifermion are in opposite directions so that all gauge bosons -even photon- and graviton would be massive. Super-symmetry strongly suggests that gauginos eat Higgsinos as they become massive so that only massive gauge bosons and gauginos and possible pseudoscalar Higgs and its superpartner would remain to be discovered at LHC. Similar mechanism can indeed work also in the case of gluons expected to have colored scalar counterparts. Gluon would be massless below the scale corresponding to QCD Λ and massive above this scale.

What does this picture give when compared with the rumors about super-partners of fermion and scalar. If selectron corresponds to the not necessarily allowed M₈₉=2⁸⁹-1, and obeys otherwise the same mass formula as electron, the mass should be 250 GeV, which is too large. For k=88 which is the smallest value allowed by the above argument, one would obtain 177 GeV not far from 160 GeV. Therefore the interpretation as selectron could make sense. In the case of super-partner of scalar one can consider several options.

1. The first observation is that 200 GeV mass does not satisfy the proposed upper bound k> 89 for higgsinos and gauginos suggested by the condition that the weak string cannot have p-adic length scale longer than the p-adic length scale at which the particle condensed topologically. Hence neither higgsino nor longitudinal polarization of gaugino can be in question.
2. If one gives up the upper bound m_Z=91.2 GeV on mass but takes the twistorially motivated and mathematically beautiful horror scenario for LHC seriously, the 200 GeV particle can only correspond to a longitudinal polarization of Zino or photino.

One can of course forget the upper bound on mass and give up the horror scenario for a moment and look what one obtains.

1. If photonic Higgs is not eaten by photon, one would obtain k(Higgs)= k(Higgsino)+n. n=1,2,3 would give Higgs mass equal to (141,100, 71) GeV for m(Higgsino)= 200 GeV. On basis of experimental data mildly suggesting that neutral Higgs appears in two mass scales I have considered the possibility that Higgs indeed appears at two p-adic length scales corresponding to about 130 GeV and 92 GeV related by square root of two factor. 130 GeV would give m(Higgsino)= 184 GeV: I dare guess that this is consistent with the estimate 200 GeV.
2. For W and Z⁰ Higgsinos the mass mass would be p-adically scaled up variant of W or Z⁰ mass and for Z⁰ mass about 91.2 GeV Z⁰ Higgsino mass would be 182.4 GeV for n=2. For W Higgsino the mass would be around 160.8 GeV.

I have already earlier considered the predictions of p-adic length scale hypothesis for super partners on basis of single very strange scattering event (see the section "Experimental indication for space-time supersymmetry"). This kind of considerations must of course be taken as a mere blog entertainment. The hypothesis assuming that the mass formulas for particles and sparticles are same but p-adic length scale is possibly different, combined with kinematical constraints fixes the masses of TGD counterparts of selectron, higgsino, and Z⁰-gluino to be 131 GeV (just at the upper bound allowed kinematically), 45.6 GeV, and 91.2 GeV (Z⁰ mass) respectively. The masses are consistent with the bounds predicted by the MSSM inspired model. Selectron mass would be by a factor factor 2^-1/2 smaller than 177 GeV and presumably consistent with the 160 GeV rumor. Higgsino mass would be one half of Z⁰ mass and would satisfy the proposed constraint k< 89. Z⁰ gluino mass would be equal to Z⁰ mass also in accordance with the proposed constraint. W gluino is predicted to have same mass as W. In the case of photino the upper bound to the mass would be given by weak boson mass scale. Could it be that the life would be so simple? Could these predictions make it easy to discover super partners at LHC? Well-informed reader might be able to answer these questions.

For background see the new section of p-Adic Mass Calculations: New Physics.

Higgs and massivation in TGD framework

The view about about particle massivation in TGD Universe has evolved considerably during the last half year thanks to the discovery of the weak form of electric-magnetic duality and in the following I try to explain it. The piece of text is actually a reply to a question by Ulla in Kea's blog. As I started to write the response my thoughts about Higgs mechanism in TGD framework were considerably different and this has forced to replace the posting with a new one. The core message is that one can really do without Higgs bosons and that it is quite possible and perhaps even unavoidable that photon eats the neutral Higgs boson getting very small mass so that only pseudoscalar counterpart of Higgs and Higgsinos would remain in the spectrum. This would mean that the search for Higgs at LHC would fail.

In TGD framework p-adic thermodynamics gives the dominating contribution to fermion masses, which is something completely new. In the case of gauge bosons thermodynamic contribution is small since the inverse integer valued p-adic temperature is T=1/2 for bosons or even lower: for fermions one has T=1.

Whether Higgs can contribute to the masses is not completely clear. In TGD framework Mexican hat potential however looks like trick. One must however keep in mind that any other mechanism must explain the ratio of W and Z⁰ masses and how these bosons receive their longitudinal polarizations. One must also consider seriously the possibility that all components for the TGD counterpart of Higgs boson are transformed to the longitudinal polarizations of the gauge bosons. Twistorial approach to TGD indeed strongly suggests that also the gauge bosons regarded usually as massless have a small mass guaranteing cancellation of IR singularities. As I started write to write this piece of text I believed that photon does not eat Higgs but had to challenge my beliefs. Maybe there is no Higgs to be found at LHC! Only pseudo-scalar partner of Higgs would and super partners of Higgs and pseudoscalar Higgs would remain to be discovered.

The weak form of electric magnetic duality implying that each wormhole throat carrying fermionic quantum numbers is accompanied by a second wormhole throat carrying opposite magnetic charge and neutrino pair screening weak isospin and making gauge bosons massive. Concerning the implications the following view looks the most plausible one at this moment.

1. Neutral Higgs-if not eaten by photon- could develop a coherent state meaning vacuum expectation value and this is naturally proportional to the inverse of the p-adic length scale as are boson masses. This contribution can be assigned to the magnetic flux tube mentioned above since it screens weak force - or equivalently - makes them massive. Higgs expectation would not cause boson massivation. Rather, massivation and Higgs vacuum expectation would be caused by the presence of the magnetic flux tubes. Standard model would suffer from a causal illusion. Even a worse illusion is possible if the photon eats the neutral Higgs.

2. The "stringy" magnetic flux tube connecting fermion wormhole throat and the wormhole throat containing neutrino pair would give to the vacuum conformal weight a small contribution and therefore to the mass squared of both fermions and gauge bosons (dominating one for the latter). This contribution would be small in the p-adic sense (proportional 1/p² rather than 1/p). I cannot calculate this "stringy" contribution but stringy formula in weak scale is very suggestive.

3. In the case of light fermions and massless gauge bosons the stringy contribution must vanish and therefore must correspond to n=0 string excitation (string does not vibrate at all) : otherwise the mass of fermion would be of order weak boson mass. For weak bosons n=1 would look like a natural identification but also n=0 makes sense since h+/- 1 states corresponds opposite three-momenta for massless fermion and antifermion so that the state is massive. The mechanism bringing in the h=0 helicity of gauge boson would be the TGD counterpart for the transformation of Higgs component to a longitudinal polarization. n> 0 excited states of fermions and n> 1 excitations of bosons having masses above weak boson masses are predicted and would mean new physics becoming possibly visible at LHC.

Consider now the identification of Higgs in TGD framework.

1. In TGD framework Higgs particles do not correspond to complex SU(2) doublets but to triplet and singlet having same quantum numbers as gauge bosons. Therefore the idea that photon eats neutral Higgs is suggestive. Also a pseudo-scalar variant of Higgs is predicted. Let us see how these states emerge from weak strings.

2. The two kinds of massive states corresponding to n=0 and n=1 give rise to massive spin 1 and spin 2 particles. First of all, the helicity doublet (1,-1) is necessarily massive since the 3-momenta for massless fermion and anti-fermion are opposite. For n=L=0 this gives two states but helicity zero component is lacking. For n=L=1 one has tensor product of doublet (1,-1) and angular momentum triplet formed by L=1 rotational state of the weak string. This gives 2× 3 states corresponding to J=0 and J=2 multiplets. Note however than in spin degrees of freedom the Higgs candidate is not a genuine elementary scalar particle.

3. Fermion and antifermion can have parallel three momenta summing up to a massless 4-momentum. Spin vanishes so that one has Higgs like particle also now. This particle is however pseudo-scalar being group theoretically analogous to meson formed as a pair of quark and antiquark. p-Adic thermodynamics gives a contribution to the mass squared. By taking a tensor product with rotational states of strings one would obtain Regge trajectory containing pseudoscalar Higgs as the lowest state.

Consider now the problem how the gauge bosons can eat the Higgs boson to get their longitudinal component.

1. (J=0,n=1) Higgs state can be combined with n=0 h=+/- 1 doublet to give spin 1 massive triplet provided the masses of the two states are same. This will be discussed below.

2. Also gauge bosons usually regarded as massless can eat the scalar Higgs so that Higgs like particle could disappear completely. There would be no Higgs to be discovered at LHC! But is this a real prediction? Could it be that it is not possible to have exactly massless photons and gluons? The mixing of M⁴ chiralities for Chern-Simons Dirac equation implies that also collinear massless fermion and antifermion can have helicity +/- 1. The problem is that the mixing of the chiralities is a signature of massivation!

   Could it really be that even the gauge bosons regarded as massless have a small mass characterized by the length scale of the causal diamond defining the physical IR cutoff and that the remaining Higgs component would correspond to the longitudinal component of photon? This would mean the number of particles in the final states for a particle reaction with a fixed initial state is always bounded from above. This is important for the twistorial aesthetics of generalized Feynman diagrammatics implied by zero energy ontology. Also the vanishing of IR divergences is guaranteed by a small physical mass. Maybe internal consistency allows only pseudo-scalar Higgs.

The weak form of electric-magnetic duality suggests strongly the existence of weak Regge trajectories.

1. The most general linear mass squared formula with spin-orbit interaction term M²_L-SL• S reads as

   M²= nM₁²+ M₀² +M²_L-SL• S , n=0,2,4 or n=1,3,5,... .

   M₁² corresponds to string tension and M₀² corresponds to the thermodynamical mass squared and possible other contributions. For a given trajectory even (odd) values of n have same parity and can correspond to excitations of same ground state. From ancient books written about hadronic string model one vaguely recalls that one can have several trajectories (satellites) and if one has something called exchange degeneracy, the even and odd trajectories define single line in M²-J plane. As already noticed TGD variant of Higgs mechanism combines together n=0 states and n=1 states to form massive gauge bosons so that the trajectories are not independent.

2. For fermions, possible Higgs, and pseudo-scalar Higgs and their super partners also p-adic thermodynamical contributions are present. M₀² must be non-vanishing also for gauge bosons and be equal to the mass squared for the n=L=1 spin singlet. By applying the formula to h=+/- 1 states one obtains

   M₀²= M²(boson) .

   The mass squared for transversal polarizations with (h,n,L)=(+/- 1,n=L=0,S=1) should be same as for the longitudinal polarization with (h=0, n=L=1, S=1, J=0) state. This gives

   M₁²+M₀²+ M²_L-SL• S= M₀² .

   From L• S= [ J(J+1)-L(L+1)-S(S+1)]/2= -2 for J=0, L=S=1 one has

   M_L-S²= -M₁²/2 .

   Only the value of weak string tension M₁² remains open.

3. If one applies this formula to arbitrary n=L one obtains total spins J= L+1 and L-1 from the tensor product. For J=L-1 one obtains

   M²= (2n+1)M₁²+ M₀².

   For J=L+1 only M₀² contribution remains so that one would have infinite degeneracy of the lightest states. Therefore stringy mass formula must contain a non-linear term making Regge trajectory curved. The simplest possible generalization which does not affect n=0 and n=1 states is of from

   M²= n(n-1)M₂²+ (n-L• S/2)M₁²+ M₀².

The challenge is to understand the ratio of W and Z⁰ masses, which is purely group theoretic and provides a strong support for the massivation by Higgs mechanism.

1. The challenge is to understand the ratio of W and Z⁰ masses, which is purely group theoretic and provides a strong support for the massivation by Higgs mechanism. The above formula and empirical facts require

   M₀²(W)/M₀²(Z)= cos²(θ_W) .

   Since this parameter measures the interaction energy of the fermion and antifermion decomposing the gauge boson depending on the net quantum numbers of the pair, it would look very natural that one would have

   M₀²(W)= g_W²M_SU(2)² ,

   M₀²(Z)= g_Z²M_SU(2)² .

   Here M_SU(2)² would be the fundamental mass squared parameter for SU(2) gauge bosons. p-Adic thermodynamics of course gives additional contribution which is vanishing or very small for gauge bosons.

2. The required mass ratio would result in an excellent approximation if one assumes that the mass scales associated with SU(2) and U(1) factors suffer a mixing completely analogous to the mixing of U(1) gauge boson and neutral SU(2) gauge boson W₃ leading to γ and Z⁰. Also Higgs, which consists of SU(2) triplet and singlet in TGD Universe, would very naturally suffer similar mixing. Hence M₀(B) for gauge boson B would be analogous to the vacuum expectation of corresponding mixed Higgs component. More precisely, one would have

   M₀(W)= M_SU(2) ,

   M₀(Z)= cos(θ_W) M_SU(2)+ sin(θ_W) M_U(1) ,

   M₀(γ)= -sin(θ_W) M_SU(2)+ cos(θ_W) M_U(1) .

   The condition that photon mass is very small and corresponds to IR cutoff mass scale gives

   M₀(γ)=ε cos(θ_W)M_SU(2),

   where ε is very small number, and implies

   M_U(1)/M(W)=tan(θ_W) +ε ,

   M(γ)/M(W)= ε× cos(θ_W) ,

   M(Z)/M(W)= [1+ε × sin(θ_W)cos(θ_W)]/cos(θ_W) .

   There is a small deviation from the prediction of the standard model for W/Z mass ratio but by the smallness of photon mass the deviation is so small that there is no hope of measuring it. One can of course keep mind open for ε=0. The formulas allow also an interpretation in terms of Higgs vacuum expectations as it must. The vacuum expectation would most naturally correspond to interaction energy between the massless fermion and antifermion with opposite 3-momenta at the throats of the wormhole contact and the challenge is to show that the proposed formulas characterize this interaction energy. Since CP_2 geometry codes for standard model symmetries and their breaking, it woul not be surprising if this would happen. One cannot exclude the possibility that p-adic thermodynamics contributes to M₀²(boson). For instance, ε might characterize the p-adic thermal mass of photon.

   If the mixing applies to the entire Regge trajectories, the above formulas would apply also to weak string tensions, and also photons would belong to Regge trajectories containing high spin excitations.

3. What one can one say about the value of the weak string tension M₁²? The naive order of magnitude estimate is M₁²≈ m_W²≈ 10⁴ GeV² is by a factor 1/25 smaller than the direct scaling up of the hadronic string tension about 1 GeV²scaled up by a factor 2¹⁸. The above argument however allows also the identification as the scaled up variant of hadronic string tension in which case the higher states at weak Regge trajectories would not be easy to discover since the mass scale defined by string tension would be 512 GeV to be compared with the recent beam energy 7 TeV. Weak string tension need of course not be equal to the scaled up hadronic string tension. Weak string tension - unlike its hadronic counterpart- could also depend on the electromagnetic charge and other characteristics of the particle.

For background see the new section of p-Adic Mass Calculations: New Physics.

Some thoughts inspired by graphene

In viXra log there has been some discussion inspired by Phil's posting about the Nobel prize of physics received by Andre Geim and Konstantin Novoselov for discovering graphene. The discussion had the effect that I clicked "graphene" in Wikipedia to refresh my mental images about graphene.

By looking at Wikipedia article, one realizes that graphene is an extremely interesting from the perspective of theoretical physicist willing to challenge the reductionistic belief that everything above weak length scale is perfectly understood by recent day physics (for a really extreme position bringing in mind the days before quantum mechanics see the article of Sean Carroll and a reaction to it by Johannes Koelman).

Addition: I have made some corrections to the text below afer listening the excellent lecture straightenint out some mis-understandings due to the rather informal style of the Wikipedia article.

Quantum Hall effect and graphene

From Wikipedia one learns that quantum Hall effect (QHE) in graphene corresponds to the multiples N= 4× (2r+1)/2 of minimal transversal conductivity σ_xy. This could be understood as integer quantum Hall effect (QHE) allowing only even integers. Why even integers? This one should understand. This is possible. I learned from a nice lecture about graphene by Eva Andrei here that the formula for N is well-understood. The overall factor g=4 corresponds to the degeneracy of edge states and 1/2 in half odd integer comes from the effective masslessness of electrons at the lowest Landau level meaning that only second chirality for a given momentum is possible. This is so called γ₅ anomaly having analog in particle physics. From the lecture one learns that also FQHE has been observed by Eva Andrei and her group for n=1/3 and there are excellent reasons to expect that it will be found also for other values of n. Also the prospects for graphene super-conductivity are excellent. Therefore the following TGD based explanation of FQHE in terms of quantization of Planck constant is well motivated.

I have considered several variants for the quantization of Planck constant in TGD framework.

The first option postulates the quantization of Planck constant as a first principle and in this case the spectrum of Planck constants would be given by rational numbers: hbar= q× hbar₀ in the most general case but their are arguments favoring rationals for which the quantum phases exp(iq2π) are algebraically simple, say those representable in terms of square root operation alone (rules and compass integers as denominators of q). For q= 1/2 so that Planck constant would be hbar₀/2, one would obtain even integer QHE but this explanation is not needed by the above facts from Eva Andrei's lecture.

There is a slight indication for fractional quantization of Planck constant from hydrino atom of Mills for which the energy levels of hydrogen are claimed to be scaled up by a square of integer. Since energies are proportional to 1/hbar² this would follow from rational quantization of hbar. One can however explain the anomaly also by replacing the Laguerre equation for radial parts of the solutions of Schrödinger equation for hydrogen atom with is q-counterpart. Therefore there is no pressing need to assume fractional values of hbar.

This makes me happy since I have a competing argument reducing the quantization of Planck constant to the basic TGD without introducing it as a separate postulate. This option is of course the one which is more attractive since minimalism is an excellent guideline for a theoretician. This option is highly attractive also from the point of view of biology since integer valuedness means that it is possible to understand evolution in terms of drifting in the space of Planck constants to ever larger Planck constants. This is like difficusion in half-space. For rational values one would have analogy with diffusion along real axis to the directions of both small and large Planck constants and no direction of evolution.

For this option the hierarchy of Planck constants gives a straightforward explanation for FQHE since integer multiple hbar=n× hbar₀ implies that the transversal conductivity σ_xy proportional to alpha proportional to 1/hbar is proportional to 1/n and thus fractionized as multiples of 1/n.

The argument giving quantization of Planck constant as integer multiples of ordinary Planck constant goes as follows.

1. Kähler action is extremely nonlinear and possesses enormous vacuum degeneracy since any space-time surface with CP₂ projection which is Lagrange sub-manifold (maximum dimension 2) is vacuum extremal (Kähler gauge potential is pure gauge).

   The U(1) gauge symmetry realized as symplectic transformations of CP₂ is not gauge symmetry but spin glass degeneracy and not present for non-vacuum extremals. TGD Universe would be 4-D spin glass and thus possess extremely rich structure of ground states. The failure of classical non-determinism for vacuum solutions would make possible to generalized quantum classical correspondence so that one would have space-time correlates also for quantum jump sequences and thus symbolic representations at space-time level for contents of consciousness (quantum jumps as moment of consciousness). Preferred extremal property guarantees both holography and generalized Bohr orbit property for space-time surfaces.

2. As a consequence, the correspondence between canonical momentum densities and time derivatives of the imbedding space coordinates is 1-to -many: 1-to-infinite for vacuum extremals. This spoils all hopes about canonical quantization and path integral approach and led within 6 years or so to the realization that quantum physics as geometry of the world of classical worlds vision generalizing Einstein's geometrization program is the only way out of the situation. Much later -during last summer- I realized that this 1-to-many correspondence could allow to understand the quantization of Planck constant as a consequence of quantum TGD rather than as independent postulate.

3. Different roots for the values of time derivatives in the extremely non-linear formulas for canonical momentum densities correspond to same values of canonical momentum densities and therefore also conserved currents and of Kähler action if the weak form of electric-magnetic duality is accepted reducing Kähler action to Chern-Simons term. It is convenient to introduce n-sheeted covering of imbedding space as a convenient tool to describe the situation. hbar= n× hbar₀ is the effective value of Planck constant at the sheets of covering.

4. Fractionization means simply division of Kähler action and various conserved charges between the n sheets. In this manner the amount of charge at given sheet is reduced by a factor 1/n and perturbation theory applies. One could say that the space-time sheet is unstable against this kind of splitting and in zero energy ontology the space-time sheets split at the boundaries of the causal diamond (intersection of future and past directed light-cones) to n sheets of the covering. One particular consequence is fractional quantum Hall effect. A very pleasant news for theoretician is that Mother Nature loves her theoreticing children and takes care that perturbative approach works!

Kähler Dirac equation and graphene: a useful mis-understanding

As I looked at Wikipedia article, I found that Dirac equation is applied by treating electron as a massless particle and by replacing light velocity with Fermi velocity. I must say, that I find it very difficult to believe that this description could be deduced from first principles. This skeptic thought led to the realization that here might be the natural physical interpretation of formally massless Kähler Dirac equation in space-time interior.

Addition: Here again Eva's lecture clarified a lot. The spinors in question are not genuine Dirac spinors. There are two sub-lattices in graphene such that the wave functions of electron are localized to either of them. This is conveniently described in terms of spinors: the value of spin corresponds to a localization to either sub-lattice. Condensed matter physics uses rather informal Wikipedia terminology! "Schrödinger spinor" mentioned in the lecture would help enormously the random Wikipedia visitor. To avoid possible confusions let us stress that the linear dispersion relation has absolutely nothing to do with the dispersion relation of real electron in relativistic theory and and reflects only the dependence of electrons non-relativistic energy on momentum. Also spin is only a formal concept in this context.

This irritatingly informal use of the notion of spinor caused very useful mis-understanding since it forced to ask whether these strange spinors describing effectively massless electrons could have a first principle counterpart in TGD. They do not and there is not need for this that but one ends up with a proposal for the physical interpretation of the Kähler Dirac equation for the induced spinor fields in the interior of space-time surface.

To begin with, Dirac equation appears in three forms in TGD.

1. The Dirac equation in world of classical worlds codes for the super Virasoro conditions for the super Kac-Moody and similar representations formed by the states of wormhole contacts forming the counterpart of string like objects (throats correspond to the ends of the string. This Dirac generalizes the Dirac of 8-D imbedding space by bringing in vibrational degrees of freedom. This Dirac equation should gives as its solutions zero energy states and corresponding M-matrices generalizing S-matrix and their collection defining the unitary U-matrix whose natural application appears in consciousness theory as a coder of what Penrose calls U-process.

2. There is generalized eigenvalue equation for Chern-Simons Dirac operator at light-like wormhole throats. The generalized eigenvalue is pslash. The interpretation of pseudo-momentum p has been a problem but twistor Grassmannian approach suggests strongly that it can be interpreted as the counterpart of equally mysterious region momentum appearing in momentum twistor Grassmannian approach to N=4 SYM. The pseudo-/region momentum p is quantized (this does not spoil the basics of Grasssmannian residues integral approach) and 1/pslahs defines propagator in lines of generalized Feynman diagrams. The Yangian symmetry discovered generalizes in a very straightforward manner and leads alsoto the realization that TGD could allow also a twistorial formulation in terms of product CP₃ ×CP₃ of two twistor spaces. General arguments lead to a proposal for explicit form for the solutions of field equation represented identified as holomorphic 6-surfaces in this space subject to additional partial different equations for homogenenous functions of projective twistor coordinates suggesting strongly the quantal interpretation as analogs of partial waves. Therefore quantum-classical correspondence would be realize in beatiful manner.

3. There is Kähler Dirac equation in the interior of space-time. In this equation the gamma matrices are replaced with modified gamma matrices defined by the contractions of canonical momentum currents T^&alpha_k = ∂ L/∂_α h^k with imbedding space gamma matrices γ_k. This replacement is required by internal consistency and by super-conformal symmetries.

Could Kähler Dirac equation provide a first principle justification for the light-hearted use of effective mass and the analog of Dirac equation in condensed manner physics? This would conform with the holographic philosophy. Partonic 2-surfaces with tangent space data and their light-like orbits would give hologram like representation of physics and the interior of space-time the 4-D representation of physics. Holography would have in the recent situation interpretation also as quantum classical correspondence between representations of physics in terms of quantized spinor fields at the light-like 3-surfaces on one hand and in terms of classical fields on the other hand.

The resulting dispersion relation for the square of the Kähler-Dirac operator assuming that induced like metric, Kähler field, etc. are very slowly varying contains quadratic and linear terms in momentum components plus a term corresponding to magnetic moment coupling. In general massive dispersion relation is obtained as is also clear from the fact that Kähler Dirac gamma matrices are combinations of M⁴ and CP₂ gammas so that modified Dirac mixes different M⁴ chiralities (basic signal for massivation). If one takes into account the dependence of the induced geometric quantities on space-time point dispersion relations become non-local. Let us however add again that this dispersion relation has nothing to do with the dispersion relation for Schrödinger spinors in graphene.

Does energy metric provided the gravitational dual for condensed matter systems?

The modified gamma matrices define an effective metric via their anticommutators which are quadratic in components of energy momentum tensor (canonical momentum densities). This effective metric vanishes for vacuum extremals. Note that the use of modified gamma matrices guarantees among other things internal consistency and super-conformal symmetries of the theory. The physical interpretation has remained obscure hitherto although corresponding effective metric for Chern-Simons Dirac action has now a clear physical interpretation.

If the above argument is on the right track, this effective metric should have applications in condensed matter theory. In fact, energy metric has a natural interpretation in terms of effective light velocities which depend on direction of propagation. One can diagonalize the energy metric g_e^αβ (contravariant form results from the anticommutators) and one can denote its eigenvalues by (v₀,v_i) in the case that the signature of the effective metric is (1,-1,-1,-1). The 3-vector v_i/v₀ has interpretation as components of effective light velocity in various directions as becomes clear by thinking the d'Alember equation for the energy metric. This velocity field could be interpreted as that of hydrodynamic flow. The study of the extremals of Kauml;hler action shows that if this flow is actually Beltrami flow so that the flow parameter associated with the flow lines extends to global coordinate, Kähler action reduces to a 3-D Chern-Simons action and one obtains effective topological QFT. The conserved fermion current

Ψbar&Gamma_e^αΨ

has interpretation as incompressible hydrodynamical flow.

This would give also a nice analogy with AdS/CFT correspondence allowing to describe various kinds of physical systems in terms of higher-dimensional gravitation and black holes are introduced quite routinely to describe condensed matter systems: probably also graphene has already fallen in some 10-D black hole or even many of them.

In TGD framework one would have an analogous situation but with 10-D space-time replaced with the interior of 4-D space-time and the boundary of AdS representing Minkowski space with the light-like 3-surfaces carrying matter. The effective gravitation would correspond to the "energy metric". One can associate with it curvature tensor, Ricci tensor and Einstein tensor using standard formulas and identify effective energy momentum tensor associated as Einstein tensor with effective Newton's constant appearing as constant of proportionality. Note however that the besides ordinary metric and "energy" metric one would have also the induced classical gauge fields having purely geometric interpretation and action would be Kähler action. This 4-D holography would provide a precise, dramatically simpler, and also a very concrete dual description. This cannot be said about model of graphene based on the introduction of 10-dimensional black holes, branes, and strings chosen in more or less ad hoc manner.

This raises questions. Does this give a general dual gravitational description of dissipative effects in terms of the "energy" metric and induced gauge fields? Does one obtain the counterparts of black holes? Do the general theorems of general relativity about the irreversible evolution leading to black holes generalize to describe analogous fate of condensed matter systems caused by dissipation? Can one describe non-equilibrium thermodynamics and self-organization in this manner?

One might argue that the incompressible Beltrami flow defined by the dynamics of the preferred extremals is dissipationless and viscosity must therefore vanish locally. The failure of complete non-determinism of Kähler action however means generation of entropy since the knowledge about the state decreases gradually. This in turn should have a phenomenological local description in terms of viscosity which characterizes the transfer of energy to shorter scales and eventually to radiation. The deeper description should be non-local and basically topological and might lead to quantization rules. For instance, one can imagine the quantization of the ratio η/s of the viscosity to entropy density as multiples of a basic unit defined by its lower bound (note that this would be analogous to Quantum Hall effect). For the first M-theory inspired derivation of the lower bound of η/s see this. The lower bound for η/s is satisfied in good approximation by what should have been QCD plasma but found to be something different (RHIC and the first evidence for new physics from LHC: I have discussed TGD based understanding of these anomalies in previous posting).

An encouraring sign comes from the observation that for so called massless extremals representing classically arbitrarily shaped pulses of radiation propagating without dissipation and dispersion along single direction the canonical momentum currents are light-like. The effective contravariant metric vanishes identically so that fermions cannot propate in the interior of massless extremals! This is of course the case also for vacuum extremals. Massless extremals are purely bosonic and represent bosonic radiation. Many-sheeted space-time decomposes into matter containing regions and radiation containing regions. Note that when wormhole contact (particle) is glued to a massless extremal, it is deformed so that CP₂ projection becomes 4-D guaranteing that the weak form of electric magnetic duality can be satisfied. Therefore massless extremals can be seen as asymptotic regions. Perhaps one could say that dissipation corresponds to a decoherence process creating space-time sheets consisting of matter and radiation. Those containing matter might be even seen as analogs blackholes as far as energy metric is considered.

Could warped imbeddings relate to graphene?

An interesting question is whether the reduction of light-velocity to Fermi velocity could be interpreted as an actual reduction of light-velocity at space-time surface. I have discussed this possibility for some years in some blog posting and the argument is also buried in some chapter of some of the seven books about TGD. The proposed interpretation of energy metric in terms of hydrodynamic velocities does not allow this interpretation. Rather, the velocity in question should be assigned to the ordinary radiation.

TGD allows infinite family of warped imbeddings of M⁴ to M⁴xCP₂. They are analogous to different imbeddings of flat plane to 3-D space. In real world the warped imbeddings of 2-D flat space are obtained spontaneously when you have a thin plane of metal or just a sheet of paper: it gets spontaneously warped. The resulting induced geometry is flat as long as no stretching occurs.

A very simple example of this kind of imbedding is obtained as graph of a map from M⁴ to the geodesic circle S¹ of CP₂ with angle coordinate Φ linear in M⁴ time coordinate t:

Φ= &omega× t.

What is interesting is that although their is no gravitation in the standard sense, the light velocity is in this simple situation reduced to

v =(g_tt)^1/2c= (1-R²ω²)^1/2c

in the sense that it takes time T=L/v to move from point A to B along light-like geodesic of warped space-time surface whereas along non-warped space-time surface the time would be only T= L/c. The reason is of course that the imbedding space distance travelled is longer due to the warping. One particular effect is anomalous time dilation which could be much larger than the usual special relativistic and general relativistic time dilations.

Suppose that Kähler Dirac equation and Kähler action itself can be used as a possible first principle counterpart for the phenomenological Dirac equation and Maxwell's equations in the modeling of condensed matter systems. This is kind of description might make sense for so called slow photons with very slow group velocity. These surfaces could provide a holographic description for the reduction of the light-velocity also in di-electrics caused by interactions between particles described in terms of light-like 3-surfaces.

Strongly warped space-time surfaces obtained as deformations of warped imbeddings of flat Minkowski geometries (vacuum extremals) do not seem to provide a natural model for graphene. The basic objection is that electrons are in question and this light velocity is associated with genuinely massless particles. As already proposed, one could however assign effective light-velocity also to the "energy" metric. This velocity could be assigned to electrons in condensed matter.

Is the new physics at LHC "approximately unavoidable"?

Tommaso Dorigo has written a summary about a highly interesting conference talk by Guido Altarelli in 2010 LHC Days in Split (slides can be found here).

The talk begins with the question "Is it possible that Higgs will not be found?". The general conclusion is that if Higgs is not found then some other new physics is "approximately unavoidable". One very general reason is that the unitarity of electroweak theory is otherwise spoiled. Altarelly saw also a reason for worry. The new physics should should emerge rather abruptly: the general view is that there is no evidence for it existence from the previous experimental work. How can it is possible that the new physics lurking just behind the corner manages to hide itself so completely?

TGD predict Higgs and supersymmetry and also weak confinement

This touched something inside me since the questions whether TGD predicts Higgs and standard space-time super-symmetry have shadowed my life for a long time. When the notions of bosonic emergence and understanding of super-conformal symmetry in terms of partons identified as wormhole throats emerged, it became clear that boson with quantum numbers of Higgs identified as wormhole contact with opposite throats carrying fermion and antifermion quantum numbers is bound to exist. Also an appropriate generalization of broken space-time supersymmetry exists and reduces to N=1 super-symmetry at low energy limit.

The emergence of the weak form of electric-magnetic duality during this year led to the realization that the wormhole throats behave like magnetic monopoles since the CP₂ projections of these 2-surfaces are homologically non-trivial. The only manner to avoid macroscopic magnetic monopole fields is magnetic confinement appearing as a side product of electro-weak symmetry breaking and possibly also of color confinement. In the case of electroweak symmetry breaking this would mean that a wormhole throat carrying lepton or quark quantum numbers is accompanied by second throat with opposite Kähler magnetic charge and carrying quantum numbers of neutrino and antineutrino neutralizing the weak charge of the elementary fermion and screening of weak force. One can speak of weak confinement. For quarks the neutralization of magnetic charge need not be complete and valence quarks could be Kähler magnetic monopoles giving rise to hadrons which have neither magnetic nor color charges.

Physical elementary particles would be string like objects with length of order weak length scale. This would certainly represent new physics which could become visible at LHC. This piece of new physics (TGD predicts also many other pieces) would resemble the good old hadron physics for which the predecessor of the recent super string theory provided a satisfactory description. Regge trajectories would be one striking signature of this physics both at the level of states and scattering amplitudes. The string tension of these trajectories would be enormous: in the first estimate 2^107-89=18 times higher than that for low energy hadrons. Mass scale would be about .512 TeV to be compared with the collision energy of 7 TeV of LHC. The proton of this physics would have mass of about .512 TeV (if one believes on naive p-adic scaling) and is expected to be unstable against decay to ordinary hadrons. Lifetime should be long since otherwise also the ordinary proton is expected to be unstable against decay to scaled down hadrons with say p-adic length scale of electron (, which corresponds to the largest Mersenne prime which does not define super-astrophysical p-adic length scale).

p-Adic thermodynamics and the emergence of string like objects from massless partons

While reading the summary about Guido's representation I realized that I have been talking for years about scaled up copy of hadron physics at electroweak length scale. What distinguishes the string like objects of this hadronic physics from those of electroweak physics? Or do they represent two different aspects of something more general? The obvious answer would be that color confinement is not involved with weak strings and that this is the basic distinction. This answer seems to be correct.

1. Dirac equation in M⁴×CP₂ predicts that free fermions -also leptons- in general correspond to in non-trivial color partial waves of CP₂ and that the correlation between color and electroweak quantum numbers is wrong although quarks correspond to triality t=1 and leptons to triality t=0. This was a strong objection against TGD until I realized that super-conformal invariance could resolve the problem. The lightest leptonic (quark) states are color singlets (triplets) and colored super-conformal generators can generated the anomalous color so that lightest leptons and quarks are colors singlets and triplets. p-Adic mass calculations are consistent with this picture. The contributions from enormous bare mass squared (conformal weight) whose values are dictated by the color partial waves of quarks and leptons are compensated by negative tachyonic mass squared (conformal weight) of the vacuum state.

2. p-Adic thermodynamics assumes that elementary particles correspond to representations of super-conformal algebra characterized by enormous string tension. Elementary particle mass scales emerge thermodynamically from a fundamental mass scale which corresponds to CP₂ mass, which is roughly 10^-4-10^-3 times Planck mass. Massless states with vanishing conformal weight are thermally mixed with those with non-vanishing conformal weight and enormous value of mass squared given by string mass formula.

3. Weak form of electric-magnetic duality, the basic facts about modified Dirac equation, and also twistorialization of quantum TGD force to conclude that both strings and bosons and their super-counterparts emerge from massless fermions moving collinearly at partonic two-surfaces. Stringy mass spectrum is consistent with this only if p-adic thermodynamics describes wormhole contacts. For instance, the three-momenta of massless wormhole throats could be in opposite direction so that wormhole contact would become massive. String like objects would therefore correspond to the wormhole contacts with size scale of order CP₂ length. Wormhole contacts would be the fundamental stringy objects and already these have the correct correlation between color and electroweak quantum numbers.

4. One can of course ask whether the anomalous color could be neutralized in the weak scale? This is not possible. p-Adic thermodynamics with string tension defined by electro-weak length scale would make completely unrealistic predictions.

How the new physics around the corner manages to hide so well?

The basic worry of Guido Altarelly is expressed by the question of the title and it seem that the new physics predicted TGD might provide a satisfactory answer to the question.

1. What seems to be a prediction is that the weak length scale serves as the confinement scale for the string like objects with second end containing neutrino pairs with electroweak isospin. Regge trajectories of weak bosons and Higgs is one consequence. The new physics would behind the corner would be made virtually invisible by weak confinement. The replacement of these neutrino pairs with more general states would give a lot of new physics.

2. Of course, Nature could choose to scale up the weak scale to say Mersenne prime M₆₁ meaning weak bosons with mass scale 512 higher than weak scale. This would be more or less equivalent with the disappearance of weak interactions and the new weak physics would emergence in discontinuous manner via phase transition. That an entire weak physics would just disappear from existence without any warning sounds of course weird! In reality of course the phase transition would take place for a small portion of the stuff created in the collisions. The scaled up weak bosons would also decay in time scale which is by a factor 1/512 shorter than than the life time of weak bosons. The challenge is therefore to detect very small signals from background.

3. Whether a scaled up counterpart of hadron physics exists at weak scale remains an open question. There is evidence for scaled up variants of leptohadrons for which both ends would contain charged leptons in color partial waves. For these states at p-adic mass scales characterizing ordinary leptons there indeed exists experimental evidence.