Do we need a theory of Everything?

There is an interview of Lisa Randall in New Scientist about building of theories of everything. Phil Gibbs wrote a nice commentary of the interview, and this posting is an extension of my comment on this posting. Quantum gravity and TOEing relate very closely and there is a very nice critical article about the recent situation in quantum gravity from the perspective of particle physics by Nicolai.

Eventually TOErs must take also consciousness seriously and this leads to the fundamental questions about quantum measurement theory. What is interesting that Weinberg has changed his views about Copenhagen interpretation better known as "shut-up-and-calculate" dogma. I will say something about Nicolai's views, the comments by Weinberg, and Lisa Randall's interview in the following.

The views of Nicolai about quantum gravity as seen from particle physics perspective

Part of the Nicolai's message is that the best manner to make progress in quantum gravity is to understand why standard model gauge group is so special. To this question the existing approaches have not answered or not even tried to answer. Separation of quantum gravity from other interactions is the worst thing to do. The next worst thing to do is to see recent day physics as nothing but low energy phenomenology, which happens to described by a more or less random gauge group applying in this particular corner of the multiverse. I cannot but agree with Nicolai.

As Nicolai expresses it, in standard model the fine tuning of Higgs mass in order to sail through the extremely narrow strait between the Scylla of vacuum instability and the Kharybdis of Landau pole causing Higgs self coupling to become infinite. This feat requires a correlation between Planck scale physics and TeV scale physics so that low energy physics becomes very relevant for understanding of Planck length scale physics. Nicolai suggests that some kind of negative feedback making it possible to sail through this strait, and suggests that conformal invariance is the symmetry (broken in quantum theory automatically) making this feedback possible. Usually supersymmetry is though to be the stabilizer but LHC has posed very severe limits on N=1 SUSY. This is of course only the simplest option and TGD leads to its own view about SUSY.

In TGD framework p-adic physics is what causes the correlation between various length scales. The standard reductionistic vision about the reduction of physics to Planck length scale is replaced with fractality meaning that there is entire infinite hierarchy of physics which are fractal variants of each other. The 3-surfaces representing particles can have arbitrarily large size scale - not only Planck scale as in standard dogma. Also the hierarchy of effective Planck constants and hierarchy of size scales associated with causal diamonds define length scale hierarchies. This strongly correlates the physics in long length scales with the physics in short length scales.

Nicolai suggests that conformal invariance acts as stabilizer. Super-conformal invariance generalized by replacing 2-D basic objects with 3-D light-like surfaces is indeed a basic pillar of TGD. In fact, the notion of complex structure generalizes from 2-D case to 4-D space-time level. For Euclidian regions it means 4-D complex structure and for Minkowskian regions to what I have christened as Hamilton-Jacobi structure. Rather remarkably, the preferred extremal property can be formulated without any reference to Kähler action and also minimal surface equations and Einstein-Maxwell equations with cosmological term hold true with G and Lambda coming as predictions.

Full D=4 generalized super-conformal symmetry applies to purely right handed neutrinos delocalized along entire space-time surfaces. Ordinary 2-D super-conformal invariance applies at string world sheets at which other spinor modes are localized. These infinite-D symmetries are crucial for the very mathematical existence of the "world of classical worlds" and therefore also for the physics. Conformal invariance generalizes scale invariants so that very strong correlation between physics in ultrashort and long length scales is expected.

Something wrong with Copenhagen interpretation?

A second interesting comment came from Weinberg (discussed by Lubos). At the age about 80 years he has been able to change his views about "interpretations" of QM and admits that there is something wrong here. The history of physics shows that single anomaly or even paradox is infinitely more valuable and tons of data. Therefore standard TOErs make a fatal error when they pretend that Copenhagen interpretation is the final one. At some day we must include conscious observer as part of the physical system, and the interpretational problems of QM give strong clue how to do it.

The interpretational problems of TGD forced to take quantum measurement theory seriously. This lead to radically news about basic ontology forcing to give up the materialistic dogma seeing consciousness as one particular property of physical state. The basic paradox of state function can be solved without totally giving up the notion of objective reality defined as "solution of field equations" but accepting that the defining property of consciousness is that it replaces this reality with a new one. Zero energy ontology is one crucial implication of this picture. Also a radically new view about time explaining the different character of subjective time and geometric time of physicist emerges.

Questions posed to Lisa Randall about unification

Also some comments relating to the questions posed to Lisa Randall are in order.

1. The first three questions can be lumped together. Is TOE the dream of every physicist and isn't it a myth? Isn't beautiful mathematics supposed to lead to the truth? Isn't it then a problem that our best theories are so messy?
   

   TOE of is a must for every theoretician with imagination and the passion to understand. What TOE means depends on the mathematics available (besides mathematical abilities of the TOEr;-)). Mathematics evolves so that TOEing poses evolutionary pressures also on mathematics itself.
   

   First example from TGD. The geometrization program of Einstein generalizes to infinite-D context and leads to the notion of "world of classical worlds", whose very existence as Kähler geometry requires the existence of infinite-D isometry group (the property of being union of infinite-D symmetric spaces) and strongly suggests the uniqueness of the geometry (already for loop spaces Kähler geometry is unique). This is extremely abstract mathematics but leads to the vision that infinite-dimensional existence and therefore also physics is unique, an encouraging news for a TOEr. What is amusing is that in this approach holography reduces to general coordinate invariance and Bohr orbitology usually regarded as approximation generalizes and becomes an exact part of quantum theory. In infinite-D context also Born rules are the only possibility for purely mathematical reasons. Also Fermi statistics finds a geometrization.
   

   Second example from TGD. The idea about number theoretical universality of physics is very powerful guideline in attempts to fuse real and p-adic number based mathematics to something more general. The problems are very concrete: for instance, how to integrate in p-adic context?! This mathematics will certainly be beautiful and abstract but the need for it is forced by physics at the concrete experimental level (in TGD framework the original motivation comes from mass calculations based on p-adic thermodynamics plus super-conformal invariance). Number theoretical vision involves naturally also quaternions and octonions and they relate very intimately to standard model symmetries. Standard modely looks messy only if one has no idea about the meaning of the underlying symmetries and sees the group as just one choice among infinity of other choices.
   
   

2. Was the discovery of Higgs a surprise?
   

   Whether Higgs exists or not in TGD Universe has been one of the key questions from the very beginning of TGD, and I have considered very many scenarios. It is now clear that Higgs like state is there and is indeed possible in TGD Universe and even that Higgs vacuum expectation has a space-time correlate in TGD Universe. This conclusion came only during last year when I realized the solutions of the modified Dirac equation are localized at 2-D string world sheets for fermion modes which are not pure right-handed neutrinos - this from the condition that spinor modes have well-defined em charge. If string world sheet is minimal surface in space-time, it is not in general minimal surface in the imbedding space and CP₂ part of its second fundamental form defines a dimensional parameter whose value for the ends of braid strands carrying fermion number could correspond to Higgs vacuum expectation at QFT limit.
   

   The story Higgs taught to me how valuable experimental input is for theoretician, and how important it is to see how theory-dependent our interpretations of data really are. What we are doing is explaining the data in terms of Higgs: we do not see a particle carrying a label "Higgs"! Higgs mechanism could well be the only possible description of massivation in QFT context but is just a mimicry. For instance, the proportionality of Higgs-fermion couplings to fermion mass follows automatically if couplings is derivative coupling so that the assumption about Higgs vacuum expectation only effectively explains fermion masses! The predictive description must be in terms of a microscopic theory and if this theory has QFT limit then Higgs mechanism is the phenomenological parametrization this limit. Nothing more!
   
   

3. What would an extra dimension look like?
   

   This question is a teaser to Lisa Randall who has been proposing large extra dimensions now excluded by LCH. In TGD framework extra dimensions are not additional space-time dimensions but dimensions of the imbedding space containing space-time surfaces as 4-D sub-manifolds. This is very important distinction between TGD and string models. 3-branes (4-D surfaces) in M-theory are analogous to space-time surface but the dynamics is totally different. The new dimensions in TGD framework are neither large nor have Planck scale. The size scale of CP₂ is about 10⁴ Planck lengths and roughly corresponds to the unification scale for GUTs.
   

   This prediction comes from p-adic mass calculations: the prediction for electron mass assuming that it corresponds to Mersenne prime M₁₂₇ fixes the size scale of CP₂, and the overall success of calculations supports this identification of electron's p-adic length scale (largest non-super-astrophysical Mersenne prime length scale is in question, Gaussian Mersennes give rise to additional length scales and four of them are between 10 nm and 2.5 micrometers, the biological most important length scales).
   
   
   

4. What if we not see any new physics at LHC?
   

   It is quite well possible that we have been seen it for years but our theoretical conditioning - forced by methods comparable to those applied by Pavlov to his poor dogs - prevents to realize that we see it. The too high rate for the decays of Higgs to gamma pairs could be due to an additional wide resonance decaying to gamma pairs. Fermi satellite has reported 135 GeV bump which the existing paradigm wants to interpret as dark matter particle and this leads to problems. Perhaps the most important finding was made by RHIC for seven years ago: the production of charged particle pairs for which members tend to have parallel or antiparallel momenta as if they were produced in decays of string like objects. This is not at all consistent with perturbative QCD predicting QCD plasma but people soon introduced the notion of color glass phase to save QCD. My personal bet is that M₈₉ hadron physics (as I call it) with general mass scale 512 times higher than that for ordinary hadron physics is doing its best to inform the stubborn theoreticians about its presence.
   

What p-adic icosahedron could mean? And what about p-adic manifold?

I have been working for a couple of weeks with the problem of defining the notion of p-adic manifold: this is one of the key challenges of TGD. The existing proposals by mathematicians are rather complicated and it seems that something is lacking. To my opinion, to identify this something it is essential to make the question "What p-adic numbers are supposed to describe?". This question has not bothered either matheticians or theoretical physicists proposing purely formal p-adic counterparts for the scattering amplitudes.

Without any answer to this question there are simply quite too many alternatives to consider and one ends up to the garden of branching paths. I wrote already earlier a posting about this topic - essentially the introduction to the article What p-adic icosahedron could mean? And what about p-adic manifold? and of the new chapter of Physics as generalized Number theory with same title. The text below is this introduction in an updated form.

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This article was originally meant to be a summary of what I understand about the article "The p-Adic Icosahedron" in Notices of AMS. The original purpose was to summarize the basic ideas and discuss my own view about more technical aspects - in particular the generalization of Riemann sphere to p-adic context which is rather technical and leads to the notion of Bruhat Tits tree and Berkovich space. About Bruhat-Tits tree there is a nice web article titled p-Adic numbers and Bruhat-Tits tree describing also basics of p-adic numbers in a very concise form.

The notion of p-adic icosahedron leads to the challenge of constructing p-adic sphere, and more generally p-adic manifolds and this extended the intended scope of the article and led to consider the fundamental questions related to the construction of TGD.

Quite generally, there are two approaches to the construction of manifolds based on algebra resp. topology.

1. In algebraic geometry manifolds - or rather, algebraic varieties - correspond to solutions of algebraic equations. Algebraic approach allows even a generalization of notions of real topology such as the notion of genus.
   
   
2. Second approach relies on topology and works nicely in the real context. The basic building brick is n-ball. More complex manifolds are obtained by gluing n-balls together. Here inequalities enter the game. Since p-adic numbers are not well-ordered they do not make sense in purely p-adic context unless expressed using p-adic norm and thus for real numbers. The notion of boundary is also one of the problematic notions since in purely p-adic context there are no boundaries.
   

The attempt to construct p-adic manifolds by mimicking topological construction of real manifolds meets difficulties

The basic problem in the application of topological method to manifold construction is that p-adic disks are either disjoint or nested so that the standard construction of real manifolds using partially overlapping n-balls does not generalize to the p-adic context. The notions of Bruhat-Tits tree, building, and Berkovich disks and Berkovich space are represent attempts to overcome this problem. Berkovich disk is a generalization of the p-adic disk obtained by adding additional points so that the p-adic disk is a dense subset of it. Berkovich disk allows path connected topology which is not ultrametric. The generalization of this construction is used to construct p-adic manifolds using the modification of the topological construction in the real case. This construction provides also insights about p-adic integration.

The construction is highly technical and complex and pragmatic physicist could argue that it contains several un-natural features due to the forcing of the real picture to p-adic context. In particular, one must give up the p-adic topology whose ultra-metricity has a nice interpretation in the applications to both p-adic mass calculations and to consciousness theory.

I do not know whether the construction of Bruhat-Tits tree, which works for projective spaces but not for Q_pⁿ (!) is a special feature of projective spaces, whether Bruhat-Tits tree is enough so that no completion would be needed, and whether Bruhat-Tits tree can be deduced from Berkovich approach. What is remarkable that for M⁴× CP₂ p-adic S² and CP₂ are projective spaces and allow Bruhat-Tits tree. This not true for the spheres associated with the light-cone boundary of D≠ 4-dimensional Minkowski spaces.

Two basic philosophies concerning the construction of p-adic manifolds

There exists two basic philosophies concerning the construction of p-adic manifolds: algebraic and topological approach. Also in TGD these approaches have been competing: algebraic approach relates real and p-adic space-time points by identifying common rationals. Finite pinary cutoff is however required to achieve continuity and has interpretation in terms of finite measurement resolution. Canonical identification maps p-adics to reals and vice versa in a continuous manner but is not consistent with field equations without pinary cutoff.

1. One can try to generalize the theory of real manifolds to p-adic context. Since p-adic balls are either disjoint or nested, the usual constuction by gluing partially overlapping balls fails. This leads to the notion of Berkovich disk obtained as a completion of p-adic disk having path connected topology (non-ultrametric) and containing p-adic disk as a dense subset. This plus the complexity of the construction is heavy price to be paid for path-connectedness. A related notion is Bruhat-Tits tree defining kind of skeleton making p-adic manifold defining its boundary path connected. The notion makes sense for the p-adic counterparts of projective spaces, which suggests that p-adic projective spaces (S² and CP₂ in TGD framework) are physically very special.
   
   
2. Second approach is algebraic and restricts the consideration to algebraic varieties for which also topological invariants have algebraic counterparts. This approach is very natural in TGD framework, where preferred extremals of Kähler action can be characterized purely algebraically - even in a manner independent of the action principle - so that they make sense also p-adically.
   

   At the level of WCW algebraic approach combined with symmetries works: the mere existence of Kähler geometry implies infinite-D group of isometries and fixes the geometry uniquely. One can say that infinite-D geometries are the final victory of Erlangen program. At space-time level it however seems that one must have correspondence between real and p-adic worlds since real topology is the "lab topology". Canonical identification should enter the construction.
   

Number theoretical universality and the construction of p-adic manifolds

Construction of p-adic counterparts of manifolds is also one of the basic challenges of TGD. Here the basic vision is that one must take a wider perspective. One must unify real and various p-adic physics to single coherent whole and to relate them. At the level of mathematics this requires fusion of real and p-adic number fields along common rationals and the notion of algebraic continuation between number fields becomes a basic tool.

The number theoretic approach is essentially algebraic and based on the gluing of reals and various p-adic number fields to a larger structure along rationals and also along common algebraic numbers. A strong motivation for the algebraic approach comes from the fact that preferred extremals are characterized by a generalization of the complex structure to 4-D case both in Euclidian and Minkowskian signature. This generalization is independent of the action principle. This allows a straightforward identification of the p-adic counterparts of preferred extremals. The algebraic extensions of p-adic numbers play a key role and make it possible to realize the symmetries in the same manner as they are realized in the construction of p-adic icosahedron.

The lack of well-ordering of p-adic numbers implies strong constraints on the formulation of number theoretical universality.

1. The notion of set theoretic boundary does not make sense in purely p-adic context. Quite, generally everything involving inequalities can lead to problems in p-adic context unless one is able to define effective Archimedean topology in some natural manner. Canonical identifcation inducing real topology to p-adic context would allow to achieve this.
   
   
2. The question arises about whether real topological invariants such as genus of partonic 2-surface make sense in the p-adic sector: for algebraic varieties this is the case. One would however like to have a more general definition and again Archimedean effective topology is suggestive.
   
   
3. Integration poses problems in p-adic context and algebraic continuation from reals to p-adic number fields seems to be the only possible option making sense. The continuation is however not possible for all p-adic number fields for given surface. This has however a beautiful interpretation explaining why real space-time sheets (and elementary particles) are characterized by some p-adic prime or primes. The p-adic prime determining the mass scale of the elementary particle could be fixed number theoretically rather than by some dynamical principle formulated in real context (number theoretic anatomy of rational number does not depend smoothly on its real magnitude!).
   A more direct approach to integration could rely on canonical integration as a chart map allowing to define integral on the real side.
   
   
4. Only those discrete subgroups of real symmetries, which correspond matrices with elements in algebraic extension of p-adic numbers can be realized so that a symmetry breaking to discrete subgroup consistent with the notion of finite measurement resolution and quantum measurement theory takes place. p-Adic symmetry groups can be identified as unions of elements of discrete subgroup of the symmetry group (making sense also in real context) multiplied by a p-adic variant of the continuous Lie group. These genuinely p-adic Lie groups are labelled by powers of p telling the maximum norm of the Lie-algebra parameter. Remarkably, effective values of Planck constant come as powers of p. Whether this interpretation for the hierarchy of effective Planck constants is consistent with the interpretation in terms of n-furcations of space-time sheet remains an open question.
   

How to achieve path connectedness?

The basic problem in the construction of p-adic manifolds is the total disconnectedness of the p-adic topology implied by ultrametricity. This leads also to problems with the notion of p-adic integration. Physically it seems clear that the notion of path connectedness should have some physical counterpart.

The notion of open set makes possib le path connectedness possible in the real context. In p-adic context Bruhat-Tits tree and Berkovich disk are introduced to achieve the same goal. One can of course ask whether Berkovich space could allow to achieve a more rigorous formulation for the p-adic counterparts of CP₂, of partonic 2-surfaces, their light-like orbits, preferred extremals of Kähler action, and even the "world of classical worlds" (WCW). To me this construction does not look promising in TGD framework but I could be wrong.

TGD suggests two alternative approaches to the problem of path connectedness. They should be equivalent.

p-Adic manifold concept based on canonical identification

The TGD inspired solution to the construction of path connectd p-adic topology is based on the notion of canonical identification mapping reals to p-adics and vice versa in a continuous manner.

1. Canonical identification is used to map the predictions of p-adic mass calculations to map the p-adic value of the mass squared to its real counterpart. It makes also sense to map p-adic probabilities to their real counterparts by canonical identification. In TGD inspired theory of consciousness canonical identification is a good candidate for defining cognitive representations as representations mapping real preferred extremals to p-adic preferred extremals as also for the realization of intentional action as a quantum jump replacing p-adic preferred extremal representing intention with a real preferred extremal representing action. Could these cognitive representations and their inverses actually define real coordinate charts for the p-adic "mind stuff" and vice versa?
   
   
2. The trivial but striking observation was that it satisfies triangle inequality and thus defines an Archimedean norm allowing to induce real topology to p-adic context. Canonical identification with finite measurement resolution defines chart maps from p-adics to reals (rather than p-adics!) and vice versa and preferred extremal property allows to complete the discrete image to hopefully unique space-time surface so that topological and algebraic approach are combined. Without preferred extremal property one can complete to smooth real manifold (say) but the completion is much less unique - which indeed conforms with finite pinary resolution.
   
   
3. Also the notion of integration can be defined. If the integral for - say- real curve at the map leaf exists, its value on the p-adic side for its pre-image can be defined by algebraic continuation in the case that it exists. Therefore one can speak about lengths, volumes, action integrals, and similar things in p-adic context. One can also generalize the notion of differential form and its holomomorphic variant and their integrals to the p-adic context. These generalizations allow a generalization of integral calculus required by TGD and also provide a justification for some basic assumptions of p-adic mass calculations.
   

Could path connectedness have quantal description?

The physical content of path connectedness might also allow a formulation as a quantum physical rather than primarily topological notion, and could boil down to the non-triviality of correlation functions for second quantized induced spinor fields essential for the formulation of WCW spinor structure. Fermion fields and their n-point functions could become part of a number theoretically universal definition of manifold in accordance with the TGD inspired vision that WCW geometry - and perhaps even space-time geometry - allow a formulation in terms of fermions.

The natural question of physicist is whether quantum theory could provide a fresh number theoretically universal approach to the problem. The basic underlying vision in TGD framework is that second quantized fermion fields might allow to formulate the geometry of "world of classical worlds" (WCW) (for instance, Kähler action for preferred extremals and thus Kähler geometry of WCW would reduce to Dirac determinant. Maybe even the geometry of space-time surfaces could be expressed in terms of fermionic correlation functions.

This inspires the idea that second quantized fermionic fields replace the K-valued (K is algebraic extension of p-adic numbers) functions defined on p-adic disk in the construction of Berkovich. The ultrametric norm for the functions defined in p-adic disk would be replaced by the fermionic correlation functions and different Berkovich norms correspond to different measurement resolutions so that one obtains also a connection with hyper-finite factors of type II₁. The existence of non-trivial fermionic correlation functions would be the counterpart for the path connectedness at space-time level. The 3-surfaces defining boundaries of a connected preferred extremal are also in a natural manner "path connected": the "path" is defined by the 4-surface. At the level of WCW and in zero energy ontology (ZEO) WCW spinor fields are analogous to correlation functions having collections of these disjoint 3-surfaces as arguments. There would be no need to complete p-adic topology to a path connected topology in this approach.

It must be emphasized that this apporach should be consistent with the first option and that it is much more speculative that the first option.

About literature

It is not easy to find readable literature from these topics. The Wikipedia article about Berkovich space is written with a jargon giving no idea about what is involved. There are video lectures about Berkovich spaces. The web article about Berkovich spaces by Temkin seems too technical for a non-specialist. The slides however give a concise bird's eye of view about the basic idea behind Berkovich spaces.

Topics of the article

The article was originally meant to discuss p-adic icosahedron. Although the focus was redirected to the notion of p-adic manifold - especially in TGD framework - I decided to keep the original starting point since it provides a concrete manner to end up with the deep problems of p-adic manifold theory and illustrates the group theoretical ideas.

• In the first section icosahedron is described in real context. In the second section the ideas related to its generalization to the p-adic context are introduced. After that I discuss how to define sphere in p-adic context.
  
  
• In the section about algebraic universality I consider the problems related to the challenge of defining p-adic manifolds TGD point of view, which is algebraic and involves the fusion of various number fields and number theoretical universality as additional elements.
  
  
• The key section of the article describes the construction of p-adic space-time topology relying on chart maps of p-adic preferred extremals defined by canonical identification in finite measurement resolution and on the completion of discrete chart maps to real preferred extremals of Kähler action. The needed path-connected topology is the topology induced by canonical identification defining real chart maps for p-adic space-time surface. Canonical identification allows also the definition of p-adic valued integrals and definition of p-adic differential forms crucial in quqantum TGD.
  
  
• Last section discusses in rather speculative spirit the possibility of defining space-time surfaces in terms of correlation functions of induced fermion fields.
  

For the article and chapter see the links in the beginning of the posting.

Strange pulsar

The following abstract summarizes the discovery of a pulsar showing behavior which challenges all pulsar emission theories.

Pulsars emit from low-frequency radio waves up to high-energy gamma-rays, generated anywhere from the stellar surface out to the edge of the magnetosphere. Detecting correlated mode changes across the electromagnetic spectrum is therefore key to understanding the physical relationship among the emission sites. Through simultaneous observations, we detected synchronous switching in the radio and x-ray emission properties of PSR B0943+10. When the pulsar is in a sustained radio-"bright" mode, the x-rays show only an un-pulsed, non-thermal component. Conversely, when the pulsar is in a radio-"quiet" mode, the x-ray luminosity more than doubles and a 100 per cent pulsed thermal component is observed along with the non-thermal component. This indicates rapid, global changes to the conditions in the magnetosphere, which challenge all proposed pulsar emission theories.

The first explanation that comes in mind in TGD framework relies on the notion of magnetic body as a representation for the magnetic field for an object considered. This is topologically quantized and consists of flux tubes and sheets having onion-like structure. In TGD inspired quantum biology magnetic body carrying dark matter as phases with large effective value of Planck constant is the key concept and its size even in the case of human body can be astrophysical. The magnetic body describing the magnetosphere of the pulsar could behave like a single coherent unit even in quantum sense. If it contains dark matter, the outcome could be a coherent non-thermal emission of X rays.

Is there an inert neutrino there?

There is a very interesting posting by Jester in Resonaances with title How many neutrinos in the sky?. Jester tells about the recent 9 years WMAP data and compares it with earlier 7 years data. In the earlier data the effective number of neutrino types was N_eff= 4.34 +/- 0.87 and in the recent data it is N_eff= 3.26 +/- 0.35. WMAP alone would give N_eff = 3.89 +/- 0.67 also in the recent data but also other data are used to pose constraings on N_eff.

To be precise, N_eff could include instead of fourth neutrino species also some other weakly interacting particle. The only criterion for contributing to N_eff is that the particle is in thermal equilibrium with other massless particles and thus contributes to the density of matter considerably during the radiation dominated epoch.

Jester also refers to the constraints on N_eff from nucleosynthesis, which show that N_eff∼ 4 us slightly favored although the entire range [3,5] is consistent with data.

It seems that the effective number of neutrinos could be 4 instead of 3 although latest WMAP data combined with some other measurements favor 3.

Addition:Later however a corrected version of the eprint appeared telling that the original estimate of N_eff contained a mistake and the correct estimate is N_eff=3.84+/- 0.40.

What could N_eff=4 mean in TGD framework?

1. One poses to the modes of the modified Dirac equation the following condition: electric charge is conserved in the sense that the time evolution by modified Dirac equation does not mix a mode with a well-defined em charge with those with different em charge. The implication is that all modes except pure right handed neutrino are restricted at string world sheets. The first guess is that string world sheets are minimal surfaces of space-time surface (rather than those of imbedding space). One can also consider minimal surfaces of imbedding space but with effective metric defined by the anti-commutators of the modified gamma matrices. This would give direct physical meaning for this somewhat mysterious effective metric.
   

   For the neutrino modes localized at string world sheets mixing of left and right handed modes takes place and they become massive. If only 3 lowest genera for partonic 2-surfaces are light, one has 3 neutrinos of this kind. The same applies to all other fermion species. The argument for why this could be the case relies on simple observation: the genera g=0,1,2 have the property that they allow for all values of conformal moduli Z₂ as a conformal symmetry (hyper-ellipticity). For g>2 this is not the case. The guess is that this additional conformal symmetry is the reason for lightness of the three lowest genera.
   
   

2. Only purely right-handed neutrino is completely delocalized in 4-volume so that one cannot assign to it genus of the partonic 2-surfaces as a topological quantum number and it effectively gives rise to a fourth neutrino very much analogous to what is called sterile neutrino. Delocalized right-handed neutrinos couple only to gravitation and in case of massless extremals this forces them to have four-momentum parallel to that of ME: only massless modes are possible. Very probably this holds true for all preferred extremals to which one can assign massless longitudinal momentum direction which can vary with spatial position.
   
   
3. The coupling of ν_R is to gravitation alone and all electroweak and color couplings are absent. According to standard wisdom delocalized right-handed neutrinos cannot be in thermal equilibrium with other particles. This according to standard wisdom. But what about TGD?
   

   One should be very careful here: delocalized right-handed neutrinos is proposed to give rise to SUSY (not N=1 requiring Majorana fermions) and their dynamics is that of passive spectator who follows the leader. The simplest guess is that the dynamics of right handed neutrinos at the level of amplitudes is completely trivial and thus trivially supersymmetric. There are however correlations between four-momenta.
   
   

   1. The four-momentum of ν_R is parallel to the light-like momentum direction assignable to the massless extremal (or more general preferred extremal). This direct coupling to the geometry is a special feature of the modified Dirac operator and thus of sub-manifold gravity.
      
      
   2. On the other hand, the sum of massless four-momenta of two parallel pieces of preferred extremals is the - in general massive - four-momentum of the elementary particle defined by the wormhole contact structure connecting the space-time sheets (which are glued along their boundaries together since this is seems to be the only manner to get rid of boundary conditions requiring vacuum extremal property near the boundary). Could this direct coupling of the four-momentum direction of right-handed neutrino to geometry and four-momentum directions of other fermions be enough for the right handed neutrinos to be counted as a fourth neutrino species in thermal equilibrium? This might be the case!
      

   One cannot of course exclude the coupling of 2-D neutrino at string world sheets to 4-D purely right handed neutrinos analogous to the coupling inducing a mixing of sterile neutrino with ordinary neutrinos. Also this could help to achieve the thermal equilibrium with 2-D neutrino species.

Addition: The recent (22.3. 2013) data from Planck satellite give updated view about cosmic microwave background. The data give N_eff=3.3 +/- .5 and do not favour inert neutrino. For a nice summary see Resonaances.

For background see the chapter http://tgdtheory.com/public_html/paddark/paddark.html#susychap of "p-Adic length scale hypothesis and dark matter hierarchy".

Robert Kiehn's ideas about Falaco solitons and generation of turbulent wake from TGD perspective

I have been reading two highly interesting articles by Robert Kiehn. The first article has the title "Hydrodynamics wakes and minimal surfaces with fractal boundaries". Second article is titled "Instability patterns, wakes and topological limit sets". There are very many contacts on TGD inspired vision and its open interpretational problems.

The notion of Falaco soliton has surprisingly close resemblance with Kähler magnetic flux tubes defining fundamental structures in TGD Universe. Fermionic strings are also fundamental structures of TGD accompanying magnetic flux tubes and this supports the vision that these string like objects could allow reduction of various condensed matter phenomena such as sound waves -usually regarded as emergent phenomena allowing only highly phenomenological description - to the fundamental microscopic level in TGD framework. This can be seen as the basic outcome of reading the articles.

Kiehn proposed a new description for the generation of various instability patterns of hydrodynamics flows (Kelvin-Helmholtz and Rayleigh-Taylor instabilities) in terms of hyperbolic dynamics so that a connection with wave phenomena like interference and diffraction would emerge. The role of characteristic surfaces as surfaces of tangential and also normal discontinuities is central for the approach. In TGD framework the characteristic surfaces have as analogs light-like wormhole throats at which the signature of the induced 4-metric changes and these surfaces indeed define boundaries of two phases and of material objects in general. This inspires a more detailed comparison of Kiehn's approach with TGD.

For details see the article Robert Kiehn's ideas about Falaco solitons and generation of turbulent wake from TGD perspective.

Anomalies, anomalies,...

Many interesting signals about new physics haved emerged during last week and all of could be signatures of the new physics predicted by TGD.

Cosmological principle questioned

One of the many hypes of the last year was that cosmological principle has been validated above some length scale. In other words, beyond certain length scale universe would appear homogenous and isotropic as cosmological principle assumes. From Wikipedia one lears that the scale is about 4 billion years. At that time I commented the announcement only in the comment section of some posting. Unfortunately, I do not remember the posting and could not find from web the appropriate link.

During the erate of hype situations however change very rapidly. Now we learn that cosmological principle is under severe threat: see this. A structure consisting of quasars with gigantic size of 4 billion light years has been discovered.

What says TGD? The notion of many-sheeted space-time means a revolution in cosmology based on TGD. In TGD cosmological principle is replaced by its fractal variant meaning Russian doll cosmology. In large enough scales space-time sheets are approximately Lorentz invariant (cosmological principle) and can be modelled by Robertson-Walker cosmologies. This is of course approximation using some length scale resolution. Furthermore, R-W cosmologies are vacuum extremals of Kähler action and as such non-physical except as models giving average energy momentum tensor via Einstein's equations. Einstein-Maxwell equations hold true for preferred extremals in all length scales- albeit with G and Λ comes as predictions rather than inputs.

Astrophysics and magnetic ropes

Magnetic flux ropes havr been discovered in the atmospheres of various planets, including Earth. Now they are discovered also
around Venus. They carry superheated plasma gas from the one side of the rope to another one. Earlier I told about magnetic ropes in much longer scales: see Giant dark matter bridge between galaxy clusters discovered. Magnetic flux tubes carrying dark matter would be in question.

Magnetic flux tubes in various scales define a basic prediction of TGD and they would have resulted as gradual thickening of "cosmic" strings predicted to be dominated primordial TGD inspired cosmology. These primordial cosmic strings have strictly 2-D Minkowski space projection. They would be what string model builders should be ore than happy abut but unfortunately they have nothing to do with superstrings.

Looming dark matter announcements

Lubos Motl has a posting summarizing several anomalous findings. For few years ago so called musket-ball galaxy cluster was discovered and the newest analysis of the data has yielded a surprise.

Two colliding galaxy clusters are in question. Scientists believe that the visible stars in these galaxies make up only about 2 percent of the total mass in the cluster. About 12 percent of the mass is found in hot gas, which shines in X-ray wavelengths, while the remaining roughly 86 percent is made of invisible dark matter. Because the galaxies make up so little of the mass of the system and the spaces between them are so large, they don’t really do much of the crashing. Odds are that they will simply sail by one another as the clusters merge. It’s mostly the gas that collides, causing it to slow down and fall behind the galaxies as trails. Same is expected in the case of dark matter which should have only gravitational interactions.

Astronomers were also able to make a maps of dark matter in musket ball galaxy using the bending of light in the field the galaxy as a diagnostic tool. The surprise was however that more precise measurements suggest that the dark matter does not behave as it should! The behaviour seems also now involve aspects similar to that of the gas phase, which is due to the short range forces- basically electromagnetic. Needless to say, this is in direct conflict with the dominating dark matter paradigm. Does this mean that the dark matter has also other than gravitational interactions with itself?!

TGD based view of dark matter differs from standard one. There is entire hierarchy of dark matter phases corresponding to a hierarchy of effective values of Planck constants. Different levels of the hierarchy correspond to different space-time sheets so that Feynman diagram at given space-time sheet can contain only particles with the same value of effective Planck constant. Therefore dark matterparticles in TGD sense can have samemutual interactions as ordinary matter and the particle quantum numbers spectrum can be the same.

A long cosmic string containing galaxies along it like pearls in the necklace is the TGD basec explanation for galactic dark matter manifesting itself as constant velocity spectrum of distant stars. This spectrum follows automatically from the 1-D character of the distribution of magnetic energy of flux tubes identified as dark energy and serving as a source of gravitational field. Also dark matter in the above sense is expected to be present. There are certainly also non-gravitational interactions between the long magnetic strings associated with colliding galactic clusters occurring via Kähler magnetic fields.

Dark energy alternatives to Einstein are running of of room

It is known that the expansion of the universe is accelerating. Cosmological constant appearing in Einstein's equations as a fundamental constant is a straighforward formal explanation for the accelerated expansion. One can also explain cosmological constant in terms of dark energy - or more precisely, in terms of the energy momentum tensor assignable with dark vacuum energy proportional to metric. This dark energy is often called quintessence. The vacuum expectation values of scalar fields determining the cosmological constant gradually change and so does cosmological constant. Remakably, also proton/eleectron mass ratio depends on the vacuum expectation values.

It has become now possible to perform accurate enough measurements about proton/electron mass ratio and the recent analysis of the data shows that the ratio has not changed at all to one part in then million after a time when the universe was half about its current age, around 7 billion years ago. Huge variety of models for dark energy are excluded and the situation of inflationary scenario is becoming rather gloomy.

What says TGD? In TGD framework p-adic mass calculations in principle predict the proton/electron mass ratio and there are no rolling scalar fields responsible for inflation: there is simply no need for inflation in TGD Universe since quantum criticality explains at general level the flatness of 3-space. Dark energy corresponds to magnetic energy of magnetic flux tubes structures which originate from the primordial cosmology and magnetic tension gives rise to "negative pressure" responsible for accelerated expansion.

As a matter fact, TGD provides several descriptions of the accelerated expansion assignable to different scales of description. Einstein's equations with cosmological term are satisfied by all preferred extremals but G and Λ are now predictions rather than input parameters and depens in principle on space-time sheet. These equations could be called microscopic (the original interpretation was diametrical opposite of this!). Critical cosmology has imbedding as Robertson-Walker cosmology which is unique apart from its duration which is finite and corresponds to accelerated expansion with negative "pressure". Also overcritical cosmologies have finite duration.

D0 of the Tevatron reports a potential particle physics anomaly: new evicence for M₈₉ hadron physics?

D0 of the Tevatron reports a potential new physics anomaly. Below is the abstract of their preprint titled Measurement of the ratio of differential cross sections σ(ppbar → Z +b jet)/σ (ppbar → Z + jet) in ppbar collisions at sqrt(s)=1.96 TeV.

We measure the ratio of cross sections, σ(ppbar → Z +b jet)/σ(ppbar → Z + jet), for associated production of a Z boson with at least one jet. The ratio is also measured as a function of the jet transverse momentum, jet pseudorapidity, Z boson transverse momentum, and the azimuthal angle between the Z boson and the closest jet for events with at least oneb jet. These measurements use data collected by the D0 experiment in Run II of Fermilab's Tevatron ppbar Collider at a center-of-mass energy of 1.96 TeV, and correspond to an integrated luminosity of 9.7 fb^-1. The results are compared to predictions from next-to-leading order calculations and various Monte Carlo event generators.

The group reports that they have not been able able to build overall fit for the ratio of differential cross sections with respect to all variables in the entire region studied by using the Monte Carlos programs available.

Also Higgs contributes to the ratio studied via the decays H→ bbar following associated production of Z and H. If Higgs behaves as standard model Higgs the experiment can be seen as a test of perturbative QCD since apart from Z emission the Feynman graphs involve only strong interaction vertices. Therefore the claimed anomaly could be seen as a further indication for M₈₉ hadron physics in TGD framework. Lubos in turn hopes that the anomaly could be seen as evidence for a new Higgs like state predicted by N =1 SUSY in some form.

The Feynman graphs at the second page of W/Z +b jets: discussion of possible improvements and planned/ongoing activities represent the leading QCD contributions for the process ppbar→ W +b jet. By replacing W with Z one has the recent situation. In the first graph quark q and antiquark qbar annihilate to Z and gluon g, which annihilates to bbar. In the second graph incoming quark q emits Z and incoming gluon g decays to bbar. After that b and q exchange gluon.

Suppose that the decay of M₈₉ color magnetic flux tubes representing low energy M₈₉ mesons explains the production of correlated charged particle pairs moving in same or opposite directions. The same model predicts that M₈₉ gluons and quarks move along the flux tube: effectively one has QCD in 2-D Minkowski space if one considers only gluon exchanges parallel to the flux tube. The exchanged gluons could be however also transversal to the flux tube if they have large enough transversal momentum.

1. For istance, in 2-D QCD variant of the first diagram could correspond to q and qbar moving in opposite directions along the flux tube and kenooverlineq emitting parallel Z and recoiling in opposite direction and after annihilating with q to gluon decying to bbar.
   
   
2. The 2-D QCD variant of the first diagram would correspond to g and q moving in opposite directions. The decays g→ bbar and q → q+Z take place and a gluon moving parallel to flux tube is exchanged between b and q.
   

These diagrams would represent M₈₉ contributions to studied process and might explain the claimed discrepancy.