Does the quantization of Kähler coupling strength reduce to the quantization of Chern-Simons coupling at partonic level?

Kähler coupling strength associated with Kähler action (Maxwell action for the induced Kähler form) is the only coupling constant parameter in quantum TGD, and its value (or values) is in principle fixed by the condition of quantum criticality since Kähler coupling strength is completely analogous to critical temperature. The quantum TGD at parton level reduces to almost topological QFT for light-like 3-surfaces. This almost TQFT involves Abelian Chern-Simons action for the induced Kähler form.

This raises the question whether the integer valued quantization of the Chern-Simons coupling k could predict the values of the Kähler coupling strength. I considered this kind of possibility already for more than 15 years ago but only the reading of the introduction of the recent paper by Witten about his new approach to 3-D quantum gravity led to the discovery of a childishly simple argument that the inverse of Kähler coupling strength could indeed be proportional to the integer valued Chern-Simons coupling k: 1/α_K=4k if all factors are correct. k=26 is forced by the comparison with some physical input. Also p-adic temperature could be identified as T_p=1/k.

1. Quantization of Chern-Simons coupling strength

For Chern-Simons action the quantization of the coupling constant guaranteing so called holomorphic factorization is implied by the integer valuedness of the Chern-Simons coupling strength k. As Witten explains, this follows from the quantization of the first Chern-Simons class for closed 4-manifolds plus the requirement that the phase defined by Chern-Simons action equals to 1 for a boundaryless 4-manifold obtained by gluing together two 4-manifolds along their boundaries. As explained by Witten in his paper, one can consider also "anyonic" situation in which k has spectrum Z/n² for n-fold covering of the gauge group and in dark matter sector one can consider this kind of quantization.

2. Formula for Kähler coupling strength

The quantization argument for k seems to generalize to the case of TGD. What is clear that this quantization should closely relate to the quantization of the Kähler coupling strength appearing in the 4-D Kähler action defining Kähler function for the world of classical worlds and conjectured to result as a Dirac determinant. The conjecture has been that g_K² has only single value. With some physical input one can make educated guesses about this value. The connection with the quantization of Chern-Simons coupling would however suggest a spectrum of values. This spectrum is easy to guess.

1. The U(1) counterpart of Chern-Simons action is obtained as the analog of the "instanton" density obtained from Maxwell action by replacing J wedge *J with J wedge J. This looks natural since for self dual J associated with CP₂ extremals Maxwell action reduces to instanton density and therefore to Chern-Simons term. Also the interpretation as Chern-Simons action associated with the classical SU(3) color gauge field defined by Killing vector fields of CP₂ and having Abelian holonomy is possible. Note however that instanton density is multiplied by imaginary unit in the action exponential of path integral. One should find justification for this "Wick rotation" not changing the value of coupling strength and later this kind of justification will be proposed.

2. Wick rotation argument suggests the correspondence k/4π = 1/4g_K² between Chern-Simons coupling strength and the Kähler coupling strength g_K appearing in 4-D Kähler action. This would give

   g_K²=π/k .

   The spectrum of 1/α_K would be integer valued

   1/α_K=4k.

   The result is very nice from the point of number theoretic vision since the powers of α_K appearing in perturbative expansions would be rational numbers (ironically, radiative corrections might vanish but this might happen only for these rational values of α_K!).

3. It is interesting to compare the prediction with the experimental constraints on the value of α_K. The basic empirical input is that electroweak U(1) coupling strength reduces to Kähler coupling at electron length scale (see this). This gives α_K= α_U(1)(M₁₂₇)≈ 104.1867, which corresponds to k=26.0467. k=26 would give α_K= 104: the deviation would be only .2 per cent and one would obtain exact prediction for α_U(1)(M₁₂₇)! This would explain why the inverse of the fine structure constant is so near to 137 but not quite. Amusingly, k=26 is the critical space-time dimension of the bosonic string model. Also the conjectured formula for the gravitational constant in terms of α_K and p-adic prime p involves all primes smaller than 26 (see this).

4. Note however that if k is allowed to have values in Z/n², the strongest possible coupling strength is scaled to n²/4 if hbar is not scaled: already for n=2 the resulting perturbative expansion might fail to converge. In the scalings of hbar associated with M⁴ degrees of freedom hbar however scales as 1/n² so that the spectrum of α_K would remain invariant.

3. Justification for Wick rotation

It is not too difficult to believe to the formula 1/α_K =qk, q some rational. q=4 however requires a justification for the Wick rotation bringing the imaginary unit to Chern-Simons action exponential lacking from Kähler function exponential.

In this kind of situation one might hope that an additional symmetry might come in rescue. The guess is that number theoretic vision could justify this symmetry.

1. To see what this symmetry might be consider the generalization of the Montonen-Olive duality obtained by combining theta angle and gauge coupling to single complex number via the formula

   τ= θ/2π+i4π/g².

   What this means in the recent case that for CP₂ type vacuum extremals (see this) Kähler action and instanton term reduce by self duality to Kähler action obtained by the replacement g² with -iτ/4π. The first duality τ→τ+1 corresponds to the periodicity of the theta angle. Second duality τ→-1/τ corresponds to the generalization of Montonen-Olive duality α→ 1/α. These dualities are definitely not symmetries of the theory in the recent case.

2. Despite the failure of dualities, it is interesting to write the formula for τ in the case of Chern-Simons theory assuming g_K²=π/k with k>0 holding true for Kac-Moody representations. What one obtains is

   τ= 4k(1-i).

   The allowed values of τ are integer spaced along a line whose direction angle corresponds to the phase exp(i2π/n), n=4. The transformations τ→ τ+ 4(1-i) generate a dynamical symmetry and as Lorentz transformations define a subgroup of the group E² leaving invariant light-like momentum (this brings in mind quantum criticality!). One should understand what is so special in this line.

3. This formula conforms with the number theoretic vision suggesting that the allowed values of τ belong to an integer spaced lattice. Indeed, if one requires that the phase angles are proportional to vectors with rational components then only phase angles associated with orthogonal triangles with short sides having integer valued lengths m and n are possible. The additional condition that the phase angles correspond to roots of unity! This leaves only m=n and m=-n>0 into consideration so that one would have τ= n(1-i) from k>0.

4. Notice that theta angle is a multiple of 8kπ so that a trivial strong CP breaking results and no QCD axion is needed (this of one takes seriously the equivalence of Kähler action to the classical color YM action).

4. Is p-adicization needed and possible only in 3-D sense?

The action of CP₂ type extremal is given as S=π/8α_K= kπ/2. Therefore the exponent of Kähler action appearing in the vacuum functional would be exp(kπ) known to be a transcendental number (Gelfond's constant). Also its powers are transcendental. If one wants to p-adicize also in 4-D sense, this raises a problem.

Before considering this problem, consider first the 4-D p-adicization more generally.

1. The definition of Kähler action and Kähler function in p-adic case can be obtained only by algebraic continuation from the real case since no satisfactory definition of p-adic definite integral exists. These difficulties are even more serious at the level of configuration space unless algebraic continuation allows to reduce everything to real context. If TGD is integrable theory in the sense that functional integral over 3-surfaces reduces to calculable functional integrals around the maxima of Kähler function, one might dream of achieving the algebraic continuation of real formulas. Note however that for lightlike 3-surface the restriction to a category of algebraic surfaces essential for the re-interpretation of real equations of 3-surface as p-adic equations. It is far from clear whether also preferred extremals of Kähler action have this property.

2. Is 4-D p-adicization the really needed? The extension of light-like partonic 3-surfaces to 4-D space-time surfaces brings in classical dynamical variables necessary for quantum measurement theory. p-Adic physics defines correlates for cognition and intentionality. One can argue that these are not quantum measured in the conventional sense so that 4-D p-adic space-time sheets would not be needed at all. The p-adic variant for the exponent of Chern-Simons action can make sense using a finite-D algebraic extension defined by q=exp(i2π/n) and restricting the allowed lightlike partonic 3-surfaces so that the exponent of Chern-Simons form belongs to this extension of p-adic numbers. This restriction is very natural from the point of view of dark matter hierarchy involving extensions of p-adics by quantum phase q.

If one remains optimistic and wants to p-adicize also in 4-D sense, the transcendental value of the vacuum functional for CP₂ type vacuum extremals poses a problem (not the only one since the p-adic norm of the exponent of Kähler action can become completely unpredictable).

1. One can also consider extending p-adic numbers by introducing exp(π) and its powers and possibly also π. This would make the extension of p-adics infinite-dimensional which does not conform with the basic ideas about cognition. Note that e^p is not p-adic transcendental so that extension of p-adics by powers e is finite-dimensional and if p-adics are first extended by powers of π then further extension by exp(π) is p-dimensional.

2. A more tricky manner to overcome the problem posed by the CP₂ extremals is to notice CP₂ type extremals are necessarily deformed and contain a hole corresponding to the lightlike 3-surface or several of them. This would reduce the value of Kähler action and one could argue that the allowed p-adic deformations are such that the exponent of Kähler action is a p-adic number in a finite extension of p-adics. This option does not look promising.

5. Is the p-adic temperature proportional to the Kähler coupling strength?

Kähler coupling strength would have the same spectrum as p-adic temperature T_p apart from a multiplicative factor. The identification T_p=1/k is indeed very natural since also g_K² is a temperature like parameter. The simplest guess is

T_p= 1/k.

Also gauge couplings strengths are expected to be proportional to g_K² and thus to 1/k apart from a factor characterizing p-adic coupling constant evolution. That all basic parameters of theory would have simple expressions in terms of k would be very nice from the point of view quantum classical correspondence.

If U(1) coupling constant strength at electron length scales equals α_K=1/104, this would give 1/T_p≈ 1/26. This means that photon, graviton, and gluons would be massless in an excellent approximation for say p=M₈₉, which characterizes electroweak gauge bosons receiving their masses from their coupling to Higgs boson. For fermions one has T_p=1 so that fermionic lightlike wormhole throats would correspond to the strongest possible coupling strength α_K=1/4 whereas gauge bosons identified as pairs of light-like wormhole throats associated with wormhole contacts would correspond to α_K=1/104. Perhaps T_p=1/26 is the highest p-adic temperature at which gauge boson wormhole contacts are stable against splitting to fermion-antifermion pair. Fermions and possible exotic bosons created by bosonic generators of super-canonical algebra would correspond to single wormhole throat and could also naturally correspond to the maximal value of p-adic temperature since there is nothing to which they can decay.

A fascinating problem is whether k=26 defines internally consistent conformal field theory and is there something very special in it. Also the thermal stability argument for gauge bosons should be checked.

What could go wrong with this picture? The different value for the fermionic and bosonic α_K makes sense only if the 4-D space-time sheets associated with fermions and bosons can be regarded as disjoint space-time regions. Gauge bosons correspond to wormhole contacts connecting (deformed pieces of CP₂ type extremal) positive and negative energy space-time sheets whereas fermions would correspond to deformed CP₂ type extremal glued to single space-time sheet having either positive or negative energy. These space-time sheets should make contact only in interaction vertices of the generalized Feynman diagrams, where partonic 3-surfaces are glued together along their ends. If this gluing together occurs only in these vertices, fermionic and bosonic space-time sheets are disjoint. For stringy diagrams this picture would fail.

To sum up, the resulting overall vision seems to be internally consistent and is consistent with generalized Feynman graphics, predicts exactly the spectrum of α_K, allows to identify the inverse of p-adic temperature with k, allows to understand the differences between fermionic and bosonic massivation, and reduces Wick rotation to a number theoretic symmetry. One might hope that the additional objections (to be found sooner or later!) could allow to develop a more detailed picture.

For more details see the chapter Is it Possible to Understand Coupling Constant Evolution at Space-Time Level? of "Towards S-matrix".

Schwartschild horizon for a rotating blackhole like object as a 3-D lightlike surface defining wormhole throat

The metric determinant at Schwartschild radius is non-vanishing. This does not quite conform with the interpretation as an analog of a light-like partonic 3-surface identifiable as a wormhole throat for which the determinant of the induced 4-metric vanishes and at which the signature of the induced metric changes from Minkowskian to Euclidian.

An interesting question is what happens if one makes the vacuum extremal representing imbedding of Schwartshild metric a rotating solution by a very simple replacement Φ→ Φ+nΦ, where Φ is the angle angle coordinate of homologically trivial geodesic sphere S² for the simplest vacuum extremals, and Φ the angle coordinate of M⁴ spherical coordinates. It turns out that Schwartschild horizon is transformed to a surface at which det(g₄) vanishes so that the interpretation as a wormhole throat makes sense. If one assumes that black hole horizon is analogous to a wormhole contact, only rotating black hole like structures with quantized angular momentum are possible in TGD Universe.

For details see the chapter TGD and GRT of "Classical Physics in Many-Sheeted Space-time".

Strings 2007 is not only about strings

Peter Woit and Kea commented Witten's talk in Strings 2007 about his new ideas related to 3-D quantum theory of gravity having very little to do with strings.

The little I know about LQG is that it is 3+1-D theory with 3-geometries as basic objects expressed in terms of loop variables. Witten considers 3-D theory with Chern Simons action: in this case 2-geometries would be the basic dynamical objects. Witten himself made clear that he has no idea about how to generalize the theory to 4-D context.

A connection to 4-D theory in TGD framework is obtained if one brings in holography, replaces 3-metrics with light-like 3-surfaces (light-likeness constraint is possible by 4-D general coordinate invariance), and accepts the new view about S-matrix implied by the zero energy ontology.

• Light-like 3-surfaces can be regarded as solutions vacuum Einstein equations with vanishing cosmological constant (Witten considers solutions with non-vanishing cosmological constant). The effective 2-D character of the induced metric is what makes this possible.

• Zero energy ontology is also an essential element: quantum states of 3-D theory in zero energy ontology correspond to generalized S-matrices: Matrix or M-matrix might be a proper term. Matrix is a "complex square root" of density matrix -matrix valued generalization of Schrödinger amplitude - defining time like entanglement coefficients. Its "phase" is unitary matrix and might be rather universal. Matrix is a functor from the category of Feyman cobordisms and matrices have groupoid like structure.

• Theory becomes genuinely 4-D because S-matrix is not universal anymore but characterizes zero energy states.

• 4-D holography is obtained via the Kähler metric of the world of classical worlds assigning to light-like 3-surface a preferred extremal of Kähler action as the analog of Bohr orbit containing 3-D lightlike surfaces as submanifolds (analogs of blackhole horizons and lightlike boundaries). Interiors of 4-D space-time sheets corresponds to zero modes of the metric and to the classical variables of quantum measurement theory (quantum classical correspondence). The conjecture is that Dirac determinant for the modified Dirac action associated with partonic 3-surfaces defines the vacuum functional as the exponent of Kähler function with Kähler coupling strength fixed completely as the analog of critical temperature so that everything reduces to almost topological QFT.

• The counterpart of ordinary S-matrix is between zero energy states. I call it U-matrix. It has nothing to do with particle reactions. It is crucial for understanding consciousness via moment of consciousness as quantum jump identification.

For more details see the chapter Construction of Quantum Theory: S-matrix of "Towards S-matrix".

New Developments in TGD and Their Implications for TGD Inspired Theory of Consciousness

There have been quite an impressive development in the understanding of quantum TGD at the basic level, and the interaction of the new ideas with TGD inspired theory of conciousness and model of quantum biology will be a fascinating adventure. The first task was to write a chapter summarizing the updatings and develop a systematic overall view about the consequences for TGD inspired theory of consciousness. I glue the abstract of the chapter here.

The conflict between the non-determinism of state function reduction and determinism of time evolution of Schrödinger equation is serious enough a problem to motivate the attempt to extend physics to a theory of consciousness by raising the observer from an outsider to a key notion also at the level of physical theory. Further motivations come from the failure of the materialistic and reductionistic dogmas in attempts to understand consciousness in neuroscience context.

There are reasons to doubt that standard quantum physics could be enough to achieve this goal and the new physics predicted by TGD is indeed central in the proposed theory. The developments in quantum TGD during last years have led to a fusion of real and p-adic physics by using generalization of number concept, to the realization of the crucial role of hyper-finite factors of type II₁ for quantum TGD, to the generalization of the imbedding space implying hierarchy of quantized values of Planck constant, to so called zero energy ontology, and to the reduction of quantum TGD to parton level with parton understand as 2-D surface whose orbit is light-like 3-surface, and to the realization that quantum TGD can be formulated as almost topological quantum field theory using category theoretical framework.

These developments have considerably simplified the conceptual framework behind both TGD and TGD inspired theory of consciousness and provided justification for various concepts of consciousness theory deduced earlier from quantum classical correspondence and properties of many-sheeted space-time.

The notions of quantum jump and self can be unified in the recent formulation of TGD relying on dark matter hierarchy characterized by increasing values of Planck constant. Negentropy Maximization Principle serves as a basic variational principle for the dynamics of quantum jump and must be modified to the case of hyper-finite factors of type II₁ The new view about the relation of geometric and subjective time together with zero energy ontology leads to a new view about memory and intentional action. The quantum measurement theory based on finite measurement resolution and realized in terms of hyper-finite factors of type II₁ justifies the notions of sharing of mental images and stereo-consciousness deduced earlier on basis of quantum classical correspondence. A new element is finite resolution of quantum measurement and cognitive and sensory experience. Qualia reduce to quantum number increments associated with quantum jump. Self-referentiality of consciousness can be understood from quantum classical correspondence implying a symbolic representation of contents of consciousness at space-time level updated in each quantum jump. p-Adic physics provides space-time correlates for cognition and intentionality.

For details see the new chapter New Developments in TGD and Their Implications for TGD Inspired Theory of Consciousness.

Declaration of Academic Freedom

The recent crackpot hunting activities have their comic aspects but what looks comedy from a safe distance, is a tragedy when seen from nearby. A public defame literally in a global scale can produce a lot of suffering to their victims and their friends and relatives. The young crackpot hunters seems to be quite blind to this human aspect.

Many western intellectuals accept Physical Integrity as a basic value. For some reason these people however see nothing bad in the violation of what might be called Intellectual Integrity or Emotional Integrity. The events in comment sections of some blogs indeed bring in mind a story about how primitive tribes treated the individuals who broke the taboo: the taboo breaker was literally torn in pieces in a bloody orgy.

The crackpot hunting is of course only a tip of iceberg. The censorship applied by so called respected journals and by electronic archives such as arXiv.org plus academic discrimination prevents very effectively the communitation of new ideas.

There is an organization known as Archive Freedom founded for few years ago by the victims of these activities. It has also electronic archive to which people censored out of Archiv.org and unable to publish in so called respected journals can post their papers.

Kea had added to her blog a piece of the Declaration of Academic Freedom to her blog. I think that this piece of text deserves to be added also here.

Article 2: Who is a scientist

A scientist is any person who does science. Any person who collaborates with a scientist in developing and propounding ideas and data in research or application is also a scientist. The holding of a formal qualification is not a prerequisite for a person to be a scientist.

Article 4: Freedom of choice of research theme

Many scientists working for higher research degrees or in other research programmes at academic institutions such as universities and colleges of advanced study, are prevented from working upon a research theme of their own choice by senior academic and/or administrative officials, not for lack of support facilities but instead because the academic hierarchy and/or other officials simply do not approve of the line of inquiry owing to its potential to upset mainstream dogma, favoured theories, or the funding of other projects that might be discredited by the proposed research. The authority of the orthodox majority is quite often evoked to scuttle a research project so that authority and budgets are not upset. This commonplace practice is a deliberate obstruction to free scientific thought, is unscientific in the extreme, and is criminal. It cannot be tolerated.

A scientist working for any academic institution, authority or agency, is to be completely free as to choice of a research theme, limited only by the material support and intellectual skills able to be offered by the educational institution, agency or authority. If a scientist carries out research as a member of a collaborative group, the research directors and team leaders shall be limited to advisory and consulting roles in relation to choice of a relevant research theme by a scientist in the group.

Article 8: Freedom to publish scientific results:

A deplorable censorship of scientific papers has now become the standard practice of the editorial boards of major journals and electronic archives, and their bands of alleged expert referees. The referees are for the most part protected by anonymity so that an author cannot verify their alleged expertise. Papers are now routinely rejected if the author disagrees with or contradicts preferred theory and the mainstream orthodoxy. Many papers are now rejected automatically by virtue of the appearance in the author list of a particular scientist who has not found favour with the editors, the referees, or other expert censors, without any regard whatsoever for the contents of the paper. There is a blacklisting of dissenting scientists and this list is ommunicated between participating editorial boards. This all amounts to gross bias and a culpable suppression of free thinking, and are to be condemned by the international scientific community.

All scientists shall have the right to present their scientific research results, in whole or in part, at relevant scientific conferences, and to publish the same in printed scientific journals, electronic archives, and any other media. No scientist shall have their papers or reports rejected when submitted for publication in scientific journals, electronic archives, or other media, simply because their work questions current majority opinion, conflicts with the views of an editorial board, undermines the bases of other current or planned research projects by other scientists, is in conflict with any political dogma or religious creed, or the personal opinion of another, and no scientist shall be blacklisted or otherwise censured and prevented from publication by any other person whomsoever. No scientist shall block, modify, or otherwise interfere with the publication of a scientist's work in the promise of any presents or other bribes whatsoever.

P.S. In n-Category Cafe there is a nice posting of David Corfield expressing what science is at best: a spiritual endeavour rather than fight for academic positions.

S-matrix as a functor and the groupoid like structure formed by S-matrices

In zero energy ontology S-matrix can be seen as a functor from the category of Feynman cobordisms to the category of operators. S-matrix can be identified as a "complex square root" of the positive energy density matrix S= ρ^1/2₊S₀, where S₀ is a unitary matrix and ρ₊ is the density matrix for positive energy part of the zero energy state. Obviously one has SS^*=ρ₊. S^*S=ρ_- gives the density matrix for negative energy part of zero energy state. Clearly, S-matrix can be seen as a matrix valued generalization of Schrödinger amplitude. Note that the "indices" of the S-matrices correspond to configuration space spinors (fermions and their bound states giving rise to gauge bosons and gravitons) and to configuration space degrees of freedom (world of classical worlds). For hyper-finite factor of II₁ it is not strictly speaking possible to speak about indices since the matrix elements are traces of the S-matrix multiplied by projection operators to infinite-dimensional subspaces from right and left.

The functor property of S-matrices implies that they form a multiplicative structure analogous but not identical to groupoid. Groupoid has associative product and there exist always right and left inverses and identity in the sense that ff^-1 and f^-1f are defined but not identical in general, and one has fgg^-1=f and f^-1fg= g.

The reason for the groupoid like property is that S-matrix is a map between state spaces associated with initial and final sets of partonic surfaces and these state spaces are different so that inverse must be replaced with right and left inverse. The defining conditions for the groupoid are however replaced with more general ones. Associativity holds also now but the role of inverse is taken by hermitian conjugate. Thus one has the conditions fgg^*=fρ_{g,+} and f^*fg= ρ_f,-g, and the conditions ff^*=ρ₊ and f^*f=ρ_- are satisfied. Here ρ_f+/- is density matrix associated with positive/negative energy parts of zero energy state. If the inverses of the density matrices exist, groupoid axioms hold true since f^-1_L=f^*ρ_f,+^-1 satisfies ff^-1_L= Id₊ and f_R^-1=ρ_f,-^-1f^* satisfies f^-1_Rf= Id_-.

There are good reasons to believe that also tensor product of its appropriate generalization to the analog of co-product makes sense with non-triviality characterizing the interaction between the systems of the tensor product. If so, the S-matrices would form very beautiful mathematical structure bringing in mind the corresponding structures for 2-tangles and N-tangles. Knowing how incredibly powerful the group like structures have been in physics one has good reasons to hope that groupoid like structure might help to deduce a lot of information about the quantum dynamics of TGD.

A word about nomenclature is in order. S has strong associations to unitarity and it might be appropriate to replace S with some other letter. The interpretation of S-matrix as a generalized Schrödinger amplitude would suggest Ψ-matrix. Since the interaction with Kea's M-theory blog (with M denoting Monad or Motif in this context) helped to realize the connection with density matrix, also M-matrix might work. S-matrix as a functor from the category of Feynman cobordisms in turn suggests C or F. Or could just Matrix denoted by M in formulas be enough? Certainly it would inspire feeling of awe but create associations with M-theory in the stringy sense of the word but wouldn't it be fair if stringy M-theory could leave at least some trace to physics;-)!

For details see the chapter Construction of Quantum Theory: S-matrix of "Towards S-matrix".

It is time for crackpot hunting

Summer time seems to be especially active period for young crackpot hunters and the best season has begun. Only a few days ago Lubos revealed that Tommaso Dorigo is a "small crackpot". The scientific justification was that Tommaso had visited several times in Peter Woit's Not-Even-Wrong (Peter Woit is the "black crackpot" to be distinguished from Lee Smolin, the "blue crackpot"). As Tommaso noticed, the fact that Lubos knew about these visits, revealed that also Lubos had visited the same place, from which Lubos himself can make the obvious conclusion and come out of closet. Note that Lubos has also a special message for anyone trying to get to the blog of Lubos from Not-Even-Wrong.

For some time ago I saw commented Sean Carroll's idea that cosmology explains second law. Lubos Motl had already commented the idea and quite correctly pointed out the most obvious flaw in Sean's thinking, namely the failure to realize that cosmological time scale is totally different than the time scale of second law in laboratory environment. Lubos also concluded that Sean Carroll is a crackpot. What I did in the posting Second law and cosmology was some analysis of basic flaws in the thinking of not only Carroll and Lubos but entire community basically due to the refusal to return to roots and concentrate seriously on the fundamental conceptual problems instead of crackpot hunting. I commented the sad situation also from the point of view of particle physics in the posting About landscape: what's the real problem? .

I did not call anyone crackpot since I would regard scientific argumentation based on ad hominem attacks as a criterion number one for crackpot-ness if crackpot hunting were my hobby. Only the contents matter and if someone lacks the substance needed for a serious discussion, he (as a rule he and almost as a rule from US) should listen and learn rather than argue.

Both these young fellows seem to lack the courage and arguments to attack directly against me: this would be also against the politics of total silence about serious competitors of super string hegemony. However, a comment from someone outside Harward, US, and even academy showing a lack of deep unjustified respect towards anything declared by someone from the academic heights of Sean Carrol or Lubos Motl was too much for the vanity of these young bloggers and empire stroke back indirectly this morning. Sean Carroll devoted his posting to the identification criteria of alternative scientists and also Lubos used opportunity and emphasize that "alternative scientist", the characterization that he uses about me in his article to Physicists category of Wikipedia, is his polite expression for a crackpot. Lubos forgot that he himself is very alternative climate scientist.

Amusingly, someone in the comment section of Lubos noticed Lubos had deemed also Carroll as a crackpot in his comments about Carroll's cosmic explanation of second law. Lubos indeed admitted that poor Sean, the discoverer of the new brilliant crackpot identification criteria, becomes the first victim of his own method. If my proposal that ad hominem attacks as a substitute for a scientific argumentation is also basic signature of crackpot-ness is accepted then both these crackpot hunters suffer the same fate. Perhaps scientists using so much valuable time to the hunting of crackpots deserve this.

P.S. Could one consider some kind of mind police of theoretical physics analogous to KGB in Soviet Union, where professionals would take care of crackpot hunting so that super string theorists could concentrate on deducing new predictions from M-theory;-)?

Empirical support for TGD based model of long term memories

Quite recently I learned about empirical support for the TGD inspired model of long term memories. Experiments with mice have shown that loss of long-term memory can be reversed with drugs that seem to trigger the rewiring of brain cells. The findings suggest ways of treating dementia and other neuro-degenerative diseases that are associated with impaired learning and memory loss, says Li-Huei Tsai of the Massachussetts Institute of Technology. Tsai and her team studied mice genetically engineered to express a protein called p25 when their diet contained an antibiotic. The protein has been implicated in some neuro-degenerative diseases.

The mice were first placed in a tank of water and trained to find their way to a platform just below the surface. Next, the team ensured that the task was stored in the mice's long-term memory by waiting for a few weeks. Then they induced the mice to produce p25, leading to loss of neurons, learning ability and memory. When the mice were replaced in an environment rich of various stimuli the memories were restored.

The first interpretation is that the memories are stored in the ordinary sense but not to synaptic contacts but somewhere else, say to RNA inside cell nuclei known now to be coded in large quantities by the intronic portion of DNA (see the recent article in New Scientist). Stable storage of memories in the conventional sense of the word seems however to require that these RNA molecules remain in the nucleus which need not make sense.

TGD based model of long term memories for which zero energy ontology provides a justification, provides an alternative explanation. The basic ideas are following.

• Long term sensory or episodal memories making possible memory feats correspond to either sharing of mental images of the geometric past by time-like entanglement.

• This storage mechanism is not very efficient and a more efficient mechanism would be based on communication with geometric past. Memory recall would be represented as a signal sent from magnetic body at appropriate level of onionlike hierarchy of magnetic bodies to the brain of the geometric past and realized as phase conjugate negative energy dark photons. Memory would be communicated to the geometric future by using analogous positive energy signal. This time mirror mechanism is also the key mechanism of remote metabolism and mechanism of intentional action and explains the findings of Libet about strange time delays of consciousness.

• The problems due to the extremely low photon energies are circumvented if photons are dark and thus correspond to so large value of Planck constant that their energies are above thermal energy at room temperature. EEG represents only a small portion of frequencies involved and corresponds to time scale which is fraction of second. Much longer time scales are involved with what we are used to call long term memories.

The model makes un-necessary explicit storage mechanisms and memories as such are intact in the geometric past apart from the possible changes induced by quantum jumps and only the ability to recall them is lost as a consequence of treatment and it would be this ability which is restored in the stimulus rich environment. This option allows the representation of memories in terms of RNA without requiring the stability of RNA molecules. Also the long microtobuli associated with axons are excellent candidates for providing representations of memories.

In fact, almost any quantum dynamical event of the geometric past in the living body could serve as a memory storage. Nerve pulse patterns would serve only as symbolic "digital" representations of memories. This representation would be much more economic and than the representation as sensory memories localizable at the level of primary sensory organs.

Introns transcribed to RNA inside cell nuclei

The last issue of New Scientist contains an article about the discovery that only roughly one half of DNA expresses itself as aminoacid sequences. The article is published in Nature (thanks for Doug for the link). The Encyclopedia of DNA Elements (ENCODE) project has quantified RNA transcription patterns and found that while the "standard" RNA copy of a gene gets translated into a protein as expected, for each copy of a gene cells also make RNA copies of many other sections of DNA. In particular, intron portions ("junk DNA", the portion of which increases as one climbs up in evolutionary hierarchy) are transcribed to RNA in large amounts. What is also interesting that the RNA fragments correspond to pieces from several genes which raises the question whether there is some fundamental unit smaller than gene.

In particular, intron portions ("junk DNA", the portion of which increases as one climbs up in evolutionary hierarchy) are transcribed to RNA in large amounts. What is also interesting that the RNA fragments correspond to pieces from several genes which raises the question whether there is some fundamental unit smaller than gene.

None of the extra RNA fragments gets translated into proteins, so the race is on to discover just what their function is. TGD proposal is that it gets braided and performs a lot of topological quantum computation (see this). Topologically quantum computing RNA fits nicely with replicating number theoretic braids associated with light-like orbits of partonic 2-surfaces and with their spatial "printed text" representations as linked and knotted partonic 2-surfaces giving braids as a special case (see this). An interesting question is how printing and reading could take place. Is it something comparable to what occurs when we read consciously? Is the biological portion of our conscious life identifiable with this reading process accompanied by copying by cell replication and as secondary printing using aminoacid sequences?

This picture conforms with TGD view about pre-biotic evolution. Plasmoids [1], which are known to share many basic characteristics assigned with life, came first: high temperatures are not a problem in TGD Universe since given frequency corresponds to energy above thermal energy for large enough value of hbar. Plasmoids were followed by RNA, and DNA and aminoacid sequences emerged only after the fusion of 1- and 2-letter codes fusing to the recent 3-letter code. The cross like structure of tRNA molecules carries clear signatures supporting this vision. RNA would be still responsible for roughly half of intracellular life and perhaps for the core of "intelligent life".

I have also proposed that this expression uses memetic code which would correspond to Mersenne M₁₂₇=2¹²⁷-1 with 2 ¹²⁶ codons whereas ordinary genetic code would correspond to M₇=2⁷-1 with 2⁶ codons. Memetic codons in DNA representations would consist of sequences of 21 ordinary codons. Also representations in terms of field patterns with duration of .1 seconds (secondary p-adic time scale associated with M ₁₂₇ defining a fundamental biorhythm) can be considered.

A hypothesis worth of killing would be that the DNA coding for RNA has memetic codons scattered around genome as basic units. It is interesting to see whether the structure of DNA could give any hints that memetic codon appears as a basic unit.

1. In a "relaxed" double-helical segment of DNA, the two strands twist around the helical axis once every 10.4 base pairs of sequence. 21 genetic codons correspond 63 base pairs whereas 6 full twists would correspond to 62.4 base pairs.

2. Nucleosomes are fundamental repeating units in eukaryotic chromatin possessing what is known as 10 nm beads-on-string structure. They repeat roughly every 200 base pairs: integer number of genetic codons would suggest 201 base pairs. 3 memetic codons makes 189 base pairs. Could this mean that only a fraction p≈ 12/201, which happens to be of same order of magnitude as the portion of introns in human genome, consists of ordinary codons? Inside nucleosomes the distance between neighboring contacts between histone and DNA is about 10 nm, the p-adic length scale L(151) associated with the Gaussian Mersenne (1+i)¹⁵¹-1 characterizing also cell membrane thickness and the size of nucleosomes. This length corresponds to 10 codons so that there would be two contacts per single memetic codon in a reasonable approximation. In the example of Wikipedia nucleosome corresponds to about 146=126+20 base pairs: 147 base pairs would make 2 memetic codons and 7 genetic codons.

   The remaining 54 base pairs between histone units + 3 ordinary codons from histone unit would make single memetic codon. That only single memetic codon is between histone units and part of the memetic codon overlaps with histone containing unit conforms with the finding that chromatin accessibility and histone modification patterns are highly predictive of both the presence and activity of transcription start sites. This would leave 4 genetic codons and 201 base pairs could decompose as memetic codon+2 genetic codons+memetic codon+2 genetic codons. The simplest possibility is however that memetic codons are between histone units and histone units consist of genetic codons. Note that memetic codons could be transcribed without the straightening of histone unit occurring during the transcription leading to protein coding. Note that prokaryote genome lacks the histone units so that the transition from prokaryotes to eukaryotes would mean the emergence of memetic code.

[1] E. Lozneanu and M. Sanduloviciu (2003), Minimal-cell system created in laboratory by self-organization, Chaos, Solitons and Fractals, Volume 18, Issue 2, October, p. 335. See also Plasma blobs hint at new form of life, New Scientist vol. 179 issue 2413 - 20 September 2003, page 16.

For background see the chapter Topological Quantum Computation in TGD Universe of "TGD as a Generalized Number Theory" and the chapter Pre-biotic Evolution in Many-Sheeted Space-Time of "Genes and Memes".

In what sense tangles are realized in TGD Universe?

Kea gave a link to a highly interesting article of Kauffman and Lambropoulou about rational 2-tangles having commutative sum and product allowing to map them to rationals. The illustrations of the article are beautiful and make it easy to get the gist of various ideas. The theorem of the article states that equivalent rational tangles giving trivial tangle in the product correspond to subsequent Farey numbers a/b and c/d satisfying ad-bc=+/-1 so that the pair defines element of the modular group SL(2,Z).

1. The basic observation is that 2-tangles are 2-tangles in both "s- and t-channels". Product and sum can be defined for all tangles but only in the case of 2-tangles the sum, which in this case reduces to product in t-channel obtained by putting tangles in series, gives 2-tangle. The sum of M- and N-tangles is M+N-2-tangle and combines various N-tangles to a monoidal structure. Tensor product like operation giving M+N tangle looks to me physically more natural than the sum.

2. The reason why general 2-tangles are non-commutative although 2-braids obviously commute is that 2-tangles can be regarded as sequences of N-tangles with 2-tangles appearing only as the initial and final state: N is actually even for intermediate states. Since N>2-braid groups are non-commutative, non-commutativity results. It would be interesting to know whether braid group representations have been used to construct representations of N-tangles.

The article stimulated the question in what senses N-tangles could be obtained in TGD framework.

1. Tangles as number theoretic braids?

The strands of number theoretical N-braids correspond to roots of N:th order polynomial and if one allows time evolutions of partonic 2-surface leading to the disappearance or appearance of real roots N-tangles become possible. This however means continuous evolution of roots so that the coefficients of polynomials defining the partonic 2-surface can be rational only in initial and final state but not in all intermediate "virtual" states.

2. Tangles as tangled partonic 2-surfaces?

Tangles could appear in TGD also in second manner.

• Partonic 2-surfaces are sub-manifolds of a 3-D section of space-time surface. If partonic 2-surfaces have genus g>0 the handles can become knotted and linked and one obtains besides ordinary knots and links more general knots and links in which circle is replaced by figure eight and its generalizations obtained by adding more circles (eyeglasses for N-eyed creatures;-)).

• Since these 2-surfaces are space-like, the resulting structures are indeed tangles rather than only braids. Tangles made of strands with fixed ends would result by allowing spherical partons elongate to long strands with fixed ends. DNA tangles would the basic example, and are discussed also in the article. DNA sequences to which I have speculatively assigned invisible (dark) braid structures might be seen in this context as space-like "written language representations" of genetic programs represented as number theoretic braids.

For details see the chapter Hyper-Finite Factors and Construction of S-Matrix of "Towards S-Matrix".

Farey sequences, Riemann Hypothesis, and Platonia as the best possible world

Kea has mentioned Farey sequences in her blog couple of times (see this and this).

Some basic facts about Farey sequences demonstrate that they are very interesting also from TGD point of view.

1. Farey sequence F_N is defined as the set of rationals 0< q= m/n≤1 satisfying the conditions n≤ N ordered in an increasing sequence.

2. Two subsequent terms a/b and c/d in F_N satisfy the condition ad-bc=1 and thus define and element of the modular group SL(2,Z).

3. The number of terms in Farey sequence is given by

   F(N) =F(N-1)+ φ(N-1).

   Here φ(n) is Euler's totient function giving the number of divisors of n. For primes one has φ(p)=1 so that in the transition from p to p+1 the length of Farey sequence increases by one unit by the addition of q=1/(p+1) to the sequence.

The members of Farey sequence F_N are in one-one correspondence with the set of quantum phases q_n=exp(i2π/n) , 0≤ n≤ N. This suggests a close connection with the hierarchy of Jones inclusions, quantum groups, and in TGD context with quantum measurement theory with finite measurement resolutiona nd the hierarchy of Planck constants involving the generalization of imbedding space. Also the recent TGD inspired ideas about the hierachy of subgroups of rational modular group with subgroups labelled by N and in direct correspondence with the hierarchy of quantum critical phases would naturally relate to Farey sequence.

1. Riemann Hypothesis and Farey sequences

Farey sequences are used in two equivalent formulations of the Riemann hypothesis. Suppose the terms of F_N are a_n,N, 0 < n≤ m_N. Define d_n,N = a_n,N - n /m_N: in other words d_n,N is the difference between the n:th term of the N:th Farey sequence, and the n:th member of a set of the same number of points, distributed evenly on the unit interval. Franel and Landau proved that both of the two statements

• ∑_n=1,...,mNd_n,N =O(N^r) for any r>1/2.

• ∑_n=1,...,mN d_n,N² =O(N^r) for any r>1.

are equivalent with Riemann hypothesis.

One can say that RH would guarantee that the numbers of Farey sequence provide the best possible approximate representation for the evenly distributed rational numbers n/m_N.

2. Farey sequences and TGD

Farey sequences seem to relate very closely to TGD.

1. The rationals in the Farey sequence can be mapped to the roots of unity by the map q→exp(i2π q). The numbers 1/m_N are in turn mapped to the numbers exp(i2π/m_N), which are also roots of unity. The statement would be that the algebraic phases defined by Farey sequence give the best possible approximate representation for the phases exp(in2π/m_N) with evenly distributed phase angle.

2. In TGD framework the phase factors defined by F_N corresponds to the set of quantum phases corresponding to Jones inclusions labelled by q=exp(i2π/n), n≤ N, and thus to the N lowest levels of dark matter hierarchy. There are actually two hierarchies corresponding to M⁴ and CP₂ degrees of freedom and the Planck constant appearing in Schrödinger equation corresponds to the ratio n_a/n_b defining quantum phases in these degrees of freedom. Z_{na× nb} appears as a conformal symmetry of "dark" partonic 2-surfaces and with very general assumptions this implies that there are only three fermion families in TGD Universe.

3. The fusion of physics associated with various number fields to single coherent whole requires algebraic universality. In particular, the roots of unity, which are complex algebraic numbers, should define approximations to continuum of phase factors. At least the S-matrix associated with p-adic-to-real transitions and more generally p₁ → p₂ transitions between states for which the partonic space-time sheets are p₁- resp. p₂-adic can involve only this kind of algebraic phases. One can also say that cognitive representations can involve only algebraic phases and algebraic numbers in general. For real-to-real transitions and real-to-padic transitions U-matrix might be non-algebraic or obtained by analytic continuation of algebraic U-matrix. S-matrix is by definition diagonal with respect to number field and similar continuation principle might apply also in this case.

4. The subgroups of the hierarchy of subgroups of the modular group with rational matrix elements are labelled by integer N and relate naturally to the hierarchy of Farey sequences. The hierarchy of quantum critical phases is labelled by integers N with quantum phase transitions occuring only between phases for which the smaller integer divides the larger one.

5. The 2-tangles known as rational tangles form are characterized by a rational number a/b (for detailed definitions see the article of Kaufmann and Lambropoulou). According to the result of the same article, two rational tangles labelled by a/b and c/d and possessing commutative sum and product combine to form an unknot if and only if a/b and c/d are two subsequent Farey numbers and therefore satisfy ad-bc=+/-1. An interesting question is whether the result somehow generalizes to the case of N-tangles and whether this generalization relates to the hierarchy of subgroups of the rational modular group obtained by replacing the generator τ→τ+1 with τ→ τ+1/N.

3. Interpretation of RH in TGD framework

Number theoretic universality of physics suggests an interpretation for the Riemann hypothesis in TGD framework. RH would be equivalent to the statement that the Farey numbers provide best possible approximation to the set of rationals k/m_N. Or to the statement that the roots of unity contained by F_N define the best possible approximation for the roots of unity defined as exp(ik2π/m_N) with evenly spaced phase angles. The roots of unity allowed by the lowest N levels of the hierarchy of Jones inclusions allows the best possible approximate representation for algebraic phases represented exactly at m_N:th level of hierarchy.

A stronger statement would be that the Platonia where RH holds true would be the best possible world in the sense that algebraic physics behind the cognitive representations would allow the best possible approximation hierarchy for the continuum physics (both for numbers in unit interval and for phases on unit circle). Platonia with RH would be cognitive paradise;-).

One could see this also from different view point. "Platonia as the cognitively best possible world" could be taken as the "axiom of all axioms": a kind of fundamental variational principle of mathematics. Among other things it would allow to conclude that RH is true: RH must hold true either as a theorem following from some axiomatics or as an axiom in itself.

For details see the chapter Hyper-Finite Factors and Construction of S-Matrix of "Towards S-Matrix".

Second law and cosmology

In his blog Lubos criticizes Sean Carrol's recent idea that cosmology explains second law.

Carroll is not completely wrong

Basically I agree with the criticism of Lubos. Carroll fails to realize that second law applies in all length scale and cosmology is only about largest scales. On the other hand, in the fractal Universe of TGD and in good mood;-) one can find in Carrol's idea something which cannot be said to be completely wrong. What I mean is follows.

In TGD framework one is forced to assign to incoming/outgoing elementary particles appearing in the generalized Feynman diagrams future/past directed lightcones analogous to mini-mini versions of big bang/crunch. These lightcones define geometric correlates for irreversibility and for the arrow of subjective time implied by the identification of the subjective time flow as sequence of quantum jumps. Therefore also second law can be said to have representation at space-time level.

The failure of complete classical determinism characterizing the basic variational principle of TGD is crucial for quantum classical correspondence also at level of quantum jumps. The representations of quantum jump sequences at space-time level make also possible symbolic representations for the contents of consciousness at space-time level and explain the "aboutness" character of consciousness: it is possible to become conscious about what one was conscious of (seeing red during this quantum jump and in next quantum jump becoming conscious that one was seeing red). These representations make possible a continual evolution of new reflective levels of consciousness via the feedback analogous to formulas written by a mathematician and inducing further ideas.

The basic fallacies

It is useful to list the fallacies of in the thinking of Lubos and Carroll since these fallacies allow to understand the recent dead end situation in theoretical physics.

• Both Lubos and Carroll and the entire string communitity stubbornly continue to miss the fractality of the Universe reflected as hierarchies of p-adic length scales and Planck constants in TGD framework. The p-adic hierarchy make itself especially visible in the widely different mass scales for elementary particles. Recall that the ratio of mass scales for top quark mass and neutrino is around 10¹¹: despite this the proponents of strings→ GUT at low energies vision try to force these particles inside the same multiplet of unifying gauge group!

• A lot of muddy thinking results from the refusal to reconsider quantum measurement theory. Just the introduction of finite quantum measurement resolution to the theory would help considerably and would give connection with quantum groups and hyper-finite factors.

• I mentioned in the beginning that quantum classical correspondence provides space-time correlates for the sequences of quantum jumps in TGD Universe. One could also ask what are the classical space-time correlates for the choice of quantization axes and end up with the hierarchy of Planck constants. M-theorists are ready to consider incredibly weird brane world scenarios but refuse to consider this kind of idea inspired by need to go forward from the position where the fathers of quantum theory left us.

• Lubos with his ultraconservative hbar=1 vision about Universe refuses to seriously consider the connection between consciousness and quantum theory. I believe that quantum is absolutely crucial for consciousness as is also the understanding of consciousness for quantum physics. Of course, I do not believe that simple wave mechanics could resolve the riddle of consciousness: something much more general is needed.

• A vision about the origin of second law (most naturally quantum jumps) is missing. The erratic identification of the geometric time and experienced time irrespective of the fact that these times are quite different (reversibility/irreversibility, etc.) relates closely to this. Some amount of quantum consciousness theorizing accepting Boolean logic as a starting point would help to get rid of obvious logical paradoxes but what one can do if someone has decided that the idea about connection between quantum and consciousness is dull - as Lubos states it.

• Penrose's conjecture about the special role of gravitation concerning consciousness corresponds in TGD Universe immense values of gravitational Planck constant implying macroscopic quantum coherence in astro length scales. Gravitational interaction becomes fundamental for consciousness and life in TGD Universe.

From above it should be clear that basic problems are conceptual and the development of mathematical methods instead of humble return to the roots is not the manner to make progress.

Second law in standard Big Bang cosmology and TGD inspired cosmology

The considerations of Carrol have roots in the problem of understanding second law in Big Bang cosmology. The necessity of low entropy during primordial times does not quite fit with the standard big bang picture. In TGD long string like objects represent primordial state and this phase has low entropy. Entropy is produced when these objects decay to elementary particles. Dominance of string like objects also means that gravitational mass per comoving volume vanishes linearly as a function of cosmic time (call it t) rather than diverging as 1/t as in radiation dominated cosmology. Big Bang is transformed to a silent whispher gradually amplified to a big roar.

The recent situation in Stanford

Wonderful weather and we are still able to enjoy it! It is a real experience to sit outside with eyes closed and mind wandering freely. Add to this garden of apple trees in full blossom and flowers.

In the middle of this all one should not go to web but it is difficult to avoid the usual blog around. The recent situation in Stanford had inspired Peter Woit to develop an interesting indirect argument against string models. Some homeless woman had found a roof above her head in Standord university in the same building as Leonard Susskind and Stanford model theory group. This has lasted as long as for four years. As a non-professional I failed to understand the details or even the gist of the argument leading to the conclusion that this poor woman was actually a string theorist and that something very strange was going also in Stanford theory group, which might relate to the recent situation in string theory. What would had come into my uneducated mind first that it is nice that even string theorist can feel compassion towards suffering human kind.

Also Lubos commented but did not point out any correlations with the recent situation in M-theory. Scott Aaronson also commented the situation in Stanford but from a pragmatic view point and crystallized his view as: "When we discover a stowaway on the great Ship of Science, why throw her overboard when we could make her swab the decks?"!

The crisis in Stanford inspired amazingly lively discussions about the groupies of science, as Scott Aaronson called them. The discussion left the overall impression that the ability to feel compassion towards those who suffer is something which I would not use to recognize a physicist from a big crowd of people. The topic also seemed to create group feeling: "we scientists in our departments in contrast to those non-scientists outside academy". This group feeling materialized in several serious questions. Should we tolerate among us also individuals who cannot do calculus? Could it be possible to teach the most intelligent individuals of groupie species to perform simple but useful activities such as writing popular scientific articles (rather than only swab the decks)?

What it is to be a theoretical physicist in Finland

I thought to tell something about about my life as theoretical physicist in Finland. I visited today the employment agency of state which formally tries to get me a job. Actually getting the job outside academic world would be a catastrophe but the criteria about what job I am forced to receive have allowed me to continue serious work as a physicist. Not because I would not like to have a job and enjoy salary and all that brings with it. The problem is that I simply have so much to give to this stupid human kind that I would regard myself as a criminal if I would start to do something just for money and leave my mission. Since the academic powerholders of Finland have for a long time ago made the firm decision that they will not in any imaginable circumstances provide the ridiculously small funding that I would need to continue my work, I am in a difficult situation.

Admittely there are also some comic aspects involved since there are two finnish physicists in the category "Physicists" with Einstein's picture as basic icon: the other one is Norström- a friend and competitor of Einstein- and the second one is me. Finnish academic decision makers do not let this to disturb them and do their best to look determined and intelligent.

In employment agency there has however been a continually increasing tension from the top to improve unemployment statistics by kicking out persons like me out and although individuals that I have met understand perfectly the silly situation but they cannot continue endlessly this formal employment procedure. This statistical tidying up procedure would mean getting money for food and rent from social office and living at the lowest step of the social ladder. The right wing won in the parliament election in the beginning of the year and I guessed correctly that the situation would worsen as a consequence. The inofficial term for the politics applied now is in finnish "panna köyhät kyykkyyn": the free translation is to "put poor people on their knees".

This policy means that I am forced to chose between the following options.

• I will receive my living expenses from social office just like the people having very bad personal problems. This might mean also a kind of David Star type humiliation: I must show a card telling that social office pays my living when I go to buy my daily food.

• I can also try to get some 1/2 period of unemployment work funded by government and hope that I could continue my work at least part of the time. I should find an intelligent employer who perhaps realizes that he has opportunity to get into history of science in the country which can be proud of having the silliest scientific decision makers in the known Universe.

• Then there is the possibility that I get a position as a trainee for some employer. These positions are usually meant for 18 year olds having problems with addictions, suffering from ADHD, or something like that but since I am so called hard-to-employ kind of person I might get it although I am 56 years old. I would not receive any salary except for the minimum unemployment money as hitherto. The purpose of this job would be to teach me the basic skills needed in the working life such as the ability to concentrate for 5 minutes to do one and same thing. Having worked with a unified theory for 28 years and produced 15 books I am optimistic about achieving the required skills during the trainee period. I am however afraid that I cannot be a trainee for the rest of my life so that the lowest step is still waiting there.

I must say that the last option - and why not- also the David Star option looks a fascinating possibility to make my memoirs a best steller. It would be even more wonderful to tell this in Stockholm and conclude with warm thanks to all finnish colleagues without whose generous help this great human comedy would not have been possible!

More seriously: I can blame only myself. I should have chosen politics as a tool to make word better. The people suffering political discrimation have Amnesty but there is nothing like this for scientists who happen to have brains in a wrong country.

About landscape: what's the real problem?

I have seen quite too much bullfighting in blogs so that I try to avoid saying negative things, and I have indeed enough to do in explaining the progress of TGD. In a situation in which string model hegemony is gradually replacing reality with M-theory landscape and making anthropic principle part of physics it is however difficult to remain silent. Therefore I make an exception from the rule.

Peter Woit commented the recent paradoxical situation in which most people in field deny of taking antropic principle and landscape seriously but increasing portion of people are working with it. What makes me disappointed that also Lubos is accepting the existence of landscape (fine!) but not admitting that something is badly wrong and suggesting a return to the roots.

Banal explanation and what to do?

Banal explanations are often the most realistic ones. Concerning the observation of Woit, the banal explanation is that the people working in the field can only one thing: to apply and develop the existing methodology. Landscape is certainly a treasure trove in this respect. Rapid production of formula rich publications is the basic virtue of theoretician nowadays and it is easy to apply methods instead of conceptualization and attacking those nasty real world problems, which have been around for decades and to which even the most refined methodology does not bite. As a result huge quantities of "literature" read by no one is produced.

I know that the following is politically very uncorrect to say this aloud but since I have nothing to lose, I will do it. The basic difference to the situation at the golden era of theoretical physics is that the field is full of mediocrits without real gift and passion. They dictate the standards of the field with the consequence that the people capable and willing to devote themselves to slow time consuming conceptualization have no chances in the competition for academic positions. The survivors are methodologists, people completely uncritically using the same conceptual framework as was used already at the times of Dirac and confusing problem solving with computation. These people could do valuable work in a situation when the field is in healthy condition with a lot of routine things to do but not just now.

To continue in the politically uncorrect mode: an effective but cruel manner to resolve the situation could be a considerable reduction of the funding of this part of theoretical physics so that only the really brilliant and strongly motivated people would continue (even without funding) and people with less gift and passion could find jobs providing challenges more appropriate to them. This would also reduce the gigantic flow of trash papers to which significant works by non-names are drowned, and would help to get rid of the situation in which only the works of names receive attention irrespective of their quality.

The fatal step

In the environment favoring application of recipe instead of thinking, many fatal steps have been made during the last thirty years after standard model. From TGD point view it is easy to identify the sequence of these most fatal steps: most of them were visible already 26 years ago. The first wrong step of course the most fatal one and was the acceptance of the standard model group structure as such. The identification of quark color as a spinlike quantum number: this is where the troubles began.

In TGD framework color corresponds to color partial waves -not spinlike quantum number-, and this simple observation leads in few minutes to a one page explanation of all the known elementary particle quantum numbers. Imagine what a joy it has been to work from the beginning with a theory allowing a tight interaction between real world and the attempts to mathematize the theory. I can safely say that every real progress in the theory has involved input from experiment (anomalies being also of extreme importance) and that all purely formal theoretical developments without this connection have been failures. I am sad that the people in string hegemony have not had the experience of seeing that the theory really works and solves its problems instead of creating new ones all the time. This kind of experience gives incredible motivation and without it I could not continue to work seven days a week as unemployed and without academic human rights.

After this first wrong step the rest is sad history leading unavoidably to landscape, brane world scenarios, and anthropic principle as the last stray of hope. There is of course nothing bad in anthrophic reasoning as such: theoretical physics is a big seesaw puzzle in which all kinds of consistency conditions are well-come. Taking anthropic principle as a basic pillar of the theory is however non-sense.

Why?

I have asked many times which is the ultimate reason for the recent situation and developed several explanations. Perhaps the most convincing explanation is the extremely narrow conceptual scope of recent day theoretical physics due to uncritical acceptance of the reductionistic dogma. Although the word "consciousness" has ceased to be a taboo in neuroscience, it continues to be such in just those circles who are supposed to develop the most fundamental theories about existence. Historians of physics will work hardly to understand why people with brains of Witten were not able to not to see how unbalanced their approach was and therefore doomed to fail from the beginning.

Personally I am convinced that the only manner to make real progress is to develop a quantum theory of consciousness. Just the realization of what the problems are, gives a fresh bird's eye of view to the crisis in theoretical physics. The quantum theory of consciousness (there are still people believing that classical mechanics is enough for understanding consciousness!) should provide a model for life and its evolution and a general vision about the hierarchy of life forms and identify our position in this hierarchy. One outcome of this theory should be an explanation for why the universe seems to be tailored for us. Is this due a quantum evolution of consciousness replacing the universe with a new one quantum jump by quantum jump and what are its mechanisms? This approach is a diametrical opposite for raising ourselves and the life as we know it to a corner stone of theoretical framework.

I have followed my own teachings. My documented work consist of 7 online books about quantum TGD and 8 online books about TGD inspired theory of consciousness and of quantum biology at my homepage. I can safely say that TGD is excellent candidate for "it" (I know that saying this provides excellent material for crackpot labelling activities but this does not matter). Colleagues can waste as many decades as they wish to develop even funnier brane world scenarios but sooner or later they must return to the roots and end up with TGD.

Dark matter hierarchy corresponds to a hierarchy of quantum critical systems in modular degrees of freedom

Dark matter hierarchy corresponds to a hierarchy of conformal symmetries Z_n of partonic 2-surfaces with genus g≥ 1 such that factors of n define subgroups of conformal symmetries of Z_n. By the decomposition Z_n=∏_p|n Z_p, where p|n tells that p divides n, this hierarchy corresponds to an hierarchy of increasingly quantum critical systems in modular degrees of freedom. For a given prime p one has a sub-hierarchy Z_p, Z_p²=Z_p× Z_p, etc... such that the moduli at n+1:th level are contained by n:th level. In the similar manner the moduli of Z_n are sub-moduli for each prime factor of n. This mapping of integers to quantum critical systems conforms nicely with the general vision that biological evolution corresponds to the increase of quantum criticality as Planck constant increases.

The group of conformal symmetries could be also non-commutative discrete group having Z_n as a subgroup. This inspires a very shortlived conjecture that only the discrete subgroups of SU(2) allowed by Jones inclusions are possible as conformal symmetries of Riemann surfaces having g≥ 1. Besides Z_n one could have tedrahedral and icosahedral groups plus cyclic group Z_2n with reflection added but not Z_2n+1 nor the symmetry group of cube. The conjecture is wrong. Consider the orbit of the subgroup of rotational group on standard sphere of E³, put a handle at one of the orbits such that it is invariant under rotations around the axis going through the point, and apply the elements of subgroup. You obtain Riemann surface having the subgroup as its isometries. Hence all subgroups of SU(2) can act as conformal symmetries.

The number theoretically simple ruler-and-compass integers having as factors only first powers of Fermat primes and power of 2 would define a physically preferred sub-hierarchy of quantum criticality for which subsequent levels would correspond to powers of 2: a connection with p-adic length scale hypothesis suggests itself.

Spherical topology is exceptional since in this case the space of conformal moduli is trivial and conformal symmetries correspond to the entire SL(2,C). This would suggest that only the fermions of lowest generation corresponding to the spherical topology are maximally quantum critical. This brings in mind Jones inclusions for which the defining subgroup equals to SU(2) and Jones index equals to M/N =4. In this case all discrete subgroups of SU(2) label the inclusions. These inclusions would correspond to fiber space CP₂→ CP₂/U(2) consisting of geodesic spheres of CP₂. In this case the discrete subgroup might correspond to a selection of a subgroup of SU(2)subset SU(3) acting non-trivially on the geodesic sphere. Cosmic strings X²× Y² subset M⁴×CP₂ having geodesic spheres of CP₂ as their ends could correspond to this phase dominating the very early cosmology.

For more details see the revised chapter Construction of Quantum Theory: Symmetries of "Towards S-matrix" or the chapter Construction of Elementary Particle Vacuum Functionals of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy.

TGD allows only three fermion families!

Writing a comment to Kea's posting revealed a connection with my much earlier work with elementary particle vacuum functionals, where theta functions θ_[a,b](z,Ω) with characteristic [a,b] for Riemann surface of genus g as functions of z and Teichmueller parameters Ω are the basic building blocks of modular invariant vacuum functionals defined in the finite-dimensional moduli space whose points characterize the conformal equivalence class of the induced metric of the partonic 2-surface. Obviously, kind of spinorial variants of theta functions are in question with g+g spinor indices for genus g.

The case of Hurwitz thetas corresponds to g=1 Riemann surface (torus) so that a and b are g=1-component vectors having values 0 or 1/2 and Hurwitz zeta corresponds to θ_[0,1/2]. The four Jacobi theta functions listed in Wikipedia must correspond to these thetas for torus. The values for a and b are 0 and 1 for them but this must be a mere convention.

1. Series of fractional modular groups and theta functions

The extensions of modular group to fractional modular groups obtained by replacing integers with integers shifted by multiples of 1/n suggest the existence of new kind of q-theta functions with characteristics [a,b] with a and b being g-component vectors having fractional values k/n, k=0,1...n-1. There exists also a definition of q-theta functions working for 0≤|q|<1 but not for roots of unity. The q-theta functions assigned to roots of unity would be associated with Riemann surfaces with additional Z_n conformal symmetry but not necessarily with generic Riemann surfaces and obtained by simply replacing the value range of characteristics [a,b] with the new value range in the defining formula for theta functions.

If Z_n conformal symmetry is relevant it is probably so because it would make the generalized theta functions sections in a bundle with a finite fiber having Z_n action. This hierarchy would correspond to the hierarchy of quantum groups for roots of unity and Jones inclusions and one could probably define also corresponding zeta function multiplets. These theta functions would be building blocks of the elementary particle vacuum functionals for dark variants of elementary particles invariant under fractional modular group. They would also define a hierarchy of fractal variants of number theoretic functions: it would be interesting to see what this means from the point of view of Langlands program involving ordinary modular invariance in an essential manner.

2. There are three fermions generations in TGD Universe

Generation-genus correspondence seems to predict infinite number of fermionic families and the basic idea has been that the vanishing of elementary particle vacuum functionals for hyper-elliptic Riemann surfaces with genus larger than 2 explains why the the number of light families is three. I have been refining this idea for at least 15 years now.

The observation related to this is that if fermions correspond to n=2 dark matter with Z₂ conformal symmetry as strong quantum classical correspondence suggests (see the previous posting), the number of ordinary fermion families is three without any further assumptions (for background see this).

To see this suppose that also the sectors corresponding to M⁴→M⁴/Z₂ and CP₂→ CP₂/Z₂ coverings are possible. Z₂ conformal symmetry implies that partonic Riemann surfaces are hyper-elliptic. For genera g> 2 this means that some theta functions of θ[a,b] appearing in the product of theta functions defining the vacuum functional vanish. Hence fermionic elementary particle vacuum functionals would vanish for g> 2 and only 3 fermion families would be possible for n=2 dark matter.

This results can be strengthened. The existence of space-time correlate for the fermionic 2-valuedness suggests that fermions quite generally to even values of n, so that this result would hold for all fermions. Elementary bosons (actually exotic particles belonging to Kac-Moody type representations) would correspond to odd values of n, and could possess also higher families. There is a nice argument supporting this hypothesis. n-fold discretization provided by covering associated with H corresponds to discretization for angular momentum eigenstates. Minimal discretization for 2j+1 states corresponds to n=2j+1. j=1/2 requires n=2 at least, j=1 requires n=3 at least, and so on. n=2j+1 allows spins j≤n-1/2. This very nice spin-quantum phase connection which very probably follows also from the representations of quantum SU(2).

These rules would hold only for genuinely elementary particles corresponding to single partonic component and all bosonic particles of this kind are exotics (excitations in only "vibrational" degrees of freedom of partonic 2-surface with modular invariance eliminating quite a number of them): ordinary gauge bosons correspond to fermion pairs at throats of a wormhole contact and decompose to SU(3) singlet and octet, whose states are labelled by handle-number pairs (g₁,g₂): they define new kind of heavy bosons giving rise to neutral flavor changing currents (could they be visible in LHC?). Note that gravitons necessarily correspond to pairs of fermions or gauge bosons connected by flux tubes so that they are stringy objects in this sense.

For more details see the revised chapter Construction of Quantum Theory: Symmetries of "Towards S-matrix".

Planetary Bohr orbitology and life

During afternoon walk it occurred to me that the quantization of planetary orbits could increase dramatically the probability for the existence of planets with same orbital radius and orbital period as Earth has. Since distance to the Sun determines the temperature of the planet, this might increase the portion of those planets in the Universe that support life as we identify it.

The reason is that by Equivalence principle Bohr radius r₀= GM/v₀² does not depend on the mass of the planet. The orbital radii are given by r(n)= n²r₀ and velocities by v(n)=v₀/n, with v₀= 2^-11 the favored value of v₀. Orbital periods are given by T(n)= n³r₀/v₀. Earth corresponds to n=3. There are quite a lot of stars having mass differing not too much from the solar mass.

The mass of Earth affects the surface gravitation of the planet and is also an important factor. The radius of Earth determines also Schumann resonance near 10 Hz known to be important for living systems. f=10 Hz is the most important clock frequency in living matter and corresponds to the secondary p-adic time scale associated with Mersenne prime M₁₂₇ assignable to electron. Hence it would seem that the radius of Earth is an important factor.

Whether Bohr quantization poses constraints also on the masses of planets remains to be seen: the atom like character of planets and stars suggested by the simple models based on Bohr quantization supports this expectation (see this). The dark part of astrophysical objects would consist of shells with radii corresponding to p-adic length scales and thus coming as octaves of basic length in the simplest model. Titius-Bode law would reflect this shell structure for the primordial dark Sun which has expanded to planetary system via phase transitions decreasing the value of v₀ and in this manner guaranteing cosmic expansion of solar system in average sense.

To sum up, standardization is absolutely essential for life (consider only metabolic currency of .5 eV predicted to be universal in TGD Universe): Bohr quantization would guarantee standardization also in astrophysical scales.

Connection between Hurwitz zetas, quantum groups, and hierarchy of Planck constants?

Kea mentioned in her blog the action of modular group SL(2,Z) on Riemann Zeta induced by its action on theta function. In particular, she mentioned the action of the translation τ→ τ+1. Recall that the action of the generator τ→ -1/τ on theta function is essential in providing the functional equation for Riemann Zeta.

1. Hurwitz zetas form n-plets closed under the action of fractional modular group

I checked the formula for Riemann zeta in terms of theta function in Wikipedia and found that τ→τ+1 transforms θ(0,τ); to θ(1/2,τ). When applied to the representation of zeta in terms of θ this gives Hurwitz zeta ζ(s,z), with z=1/2. Riemann Zeta corresponds to ζ(s,n)=ζ(s,0) by the periodicity of theta with respect to first argument.

Thus ζ(s,0) and ζ(s,1/2) behave like a doublet under modular transformations. Under the subgroup of modular group obtained by replacing τ→τ+1 with τ→τ+2 Riemann Zeta forms a singlet. The functional equation for Hurwitz zeta relates ζ(1-s,1/2) to ζ(s,1/2) and ζ(s,1)=ζ(s,0) so that also now one obtains a doublet. This doublet might be the proper object to study instead of singlet if one considers full modular invariance.

Hurwitz zeta is obtained by replacing integers m with fractionals m/n in the defining sum formula for Riemann Zeta:

ζ(s,z)= ∑_m (m+z)^-s.

Obviously Riemann zeta results for z=n. The inspection of the functional equation for ζ(s, m/n), m=0,1,...,m-1, demonstrates that form n-plets under fractional modular transformations obtained by using generators τ→-1/τ and τ→τ+2/n. The latter corresponds to the unimodular matrix (a,b;c,d)= (1, 2/n;0,1). These matrices obviously form a group. Note that Riemann zeta is always one member of the multiplet containing n Hurwitz zetas.

These observations bring in mind fractionization of quantum numbers, quantum groups corresponding to the quantum phase q=exp(i2π/n), and the inclusions for hyper-finite factors of type II₁ partially characterized by these quantum phases. Fractional modular group obtained using generator τ→τ+2/n and Hurwitz zetas ζ(s,k/n) would very naturally relate to these and related structures.

2. Hurwitz zetas and TGD

I realized that these observations might have a direct application to quantum TGD.

1. In TGD framework inclusions of HFFs are directly related to the hierarchy of Planck constants involving a generalization of the notion of imbedding space obtained by gluing together copies of 8-D H=M⁴×CP₂ with a discrete bundle structure H→ H/Z_na×Z_nb together along the 4-D intersections of the associated base spaces (see this). A book like structure results and various levels of dark matter correspond to the pages of this book. One can say that elementary particles proper are maximally quantum critical and live in the 4-D intersection of these imbedding spaces whereas they field bodies are on the pages of the Big Book.

2. The integers n_a and n_b give Planck constant as hbar/hbar₀=n_a/n_b, whose most general value is rational number (I hope that Lubos forgives the presence of hbar₀: I know that I could put it equal to 1;-)). In Platonic spirit one can argue that number theoretically simple integers involving only powers of 2 and Fermat primes are favored physically. Phase transitions between different matters occur at the intersection.

3. The inclusions N subset M of HFFs relate also to quantum measurement theory with finite measurement resolution with N defining measurement resolution so that N-rays replace complex rays in the projection postulate and quantum space M/N having fractional dimension effectively replaces M.

4. The basic hypothesis is that the inverses of zeta function or of more general variants of zeta coding information about the algebraic structure of the partonic 2-surface appear in the admittedly speculative fundamental formula for the generalized eigenvalues of modified Dirac operator D (see this). This formula is consistent with the generalized eigenvalue equation for D but is not the only one that one can imagine.

5. The generalized eigen spectrum of D should code information both about the p-adic prime p characterizing particle and about quantum phases q=exp(i2π/n) assignable to the particle in M⁴ and CP₂ degrees of freedom. I understand how p-adic primes appear in the spectrum of D and therefore how coupling constant evolution emerges at the level of free field theory so that radiative corrections can vanish without the loss of coupling constant evolution (see this). The problem has been to understand how the quantum phase characterizing the sector of imbedding space could make itself visible in these formulas and therefore in quantum dynamics at the level of free spinor fields. The replacement of Riemann zeta with an n-plet of Hurwitz zetas would resolve this problem.

6. Geometrically the fractional modular invariance would naturally relate to the fact that Riemann surface (partonic 2-surface) can be seen as an n_a× n_b-fold covering of its projection to the base space of H: fractional modular transformations corresponding to n_aand n_b would relate points at different sheets of the covering of M⁴ and CP₂. This suggests that the fractionization could be a completely general phenomenon happening also for more general zeta functions.

3. What about exceptional cases n=1 and n=2?

Also n=1 and n=2 are present in the hierarchy of Hurwitz zetas (singlet and doublet). They do not correspond to allowed Jones inclusion since one has n>2 for them. What could this mean?

1. It would seem that the fractionization of modular group relates to Jones inclusions (n>2) giving rise to fractional statistics. n=2 corresponding to the full modular group Sl(2,Z) could relate to the very special role of 2-valued logic, to the degeneracy of n=2 polygon in plane, to the very special role played by 2-component spinors playing exceptional role in Riemann geometry with spinor structure, and to the canonical representation of HFFs of type II₁ as fermionic Fock space (spinors in the world of classical worlds). Note also that SU(2) defines the building block of compact non-commutative Lie groups and one can obtain Lie-algebra generators of Lie groups from n copies of SU(2) triplets and posing relations which distinguish the resulting algebra from a direct sum of SU(2) algebras.

2. Also n=2-fold coverings M⁴→ M⁴/Z₂ and CP₂ → CP₂/Z₂ seem to make sense. By quantum classical correspondence also the spin half property of imbedding space spinors should have space-time correlate. Could n=2 coverings allow to define the space-time correlates for particles having half odd integer spin or weak isospin? If so, bosons would correspond to n=1 and fermions to n=2.

For more details see the revised chapter Construction of Quantum Theory: Symmetries of "Towards S-matrix".

Time-like entanglement coefficients as a square root of density matrix?

I have been pondering the problem of understanding the conditions to be posed on the most general quantum state in zero energy ontology. I started from the identification of time-like entanglement coefficients as the unitary S-matrix working in case of hyperfinite factors of type II₁. Imbedding space degrees of freedom very naturally bring in a factor of type I so that that thermal S-matrices are very natural quantum states and obtained by replacing time parameter assignable to S-matrix with complex valued parameter. All quantum states do not however correspond to thermal states and one can wonder what might be the most general identification of the quantum state in zero energy ontology.

Since density matrix formalism defines a very general formulation of quantum theory and since the quantum states in zero energy ontology are analogous to operators, the idea that time-like entanglement coefficients in some sense define a square root of density matrix is rather natural. This would give the defining conditions

ρ⁺= SS⁺ ,ρ^-= S⁺S , Tr(ρ^+/-)=1 .

ρ^+/- would define density matrix for positive/negative energy states. In the case HFFs of type II₁ one obtains unitary S-matrix and also the analogs of pure quantum states are possible for factors of type I. The numbers p⁺_m,n=|S_m,n²|/ρ⁺_m,m and p^-_m,n=|S_n,m²|/ρ^-_m,m give the counterparts of the usual scattering probabilities.

A physically well-motivated hypothesis would be that S has expression S= ρ^1/2 S₀ such that S₀ is a universal unitary S-matrix, and ρ^1/2 is square root of a state dependent density matrix. Note that in general S is not diagonalizable in the algebraic extension involved so that it is not possible to reduce the scattering to a mere phase change by a suitable choice of state basis.

What makes this kind of hypothesis aesthetically attractive is the unification of two fundamental matrices of quantum theory to single one. This unification is completely analogous to the combination of modulus squared and phase of complex number to a single complex number: complex valued Schrödinger amplitude is replaced with operator valued one.

For more details about the recent situation concerning the understanding of S-matrix see the revised chapter Construction of Quantum Theory: S-Matrix of "Towards S-matrix".

Sour grapes

A little comment about a comment by Peter Woit glued here.

No one has been able to use string theory to calculate any of the standard model parameters in terms of the others. If you don’t believe this, try and find a string theory prediction of the one still unknown SM parameter (the Higgs Mass) in terms of the others, or a string theory prediction of anything that will be seen at the LHC.

It would be huge progress if string theory (or any other theory) was able to reduce the number of free parameters in the SM, but this has not been done. Any claims otherwise are intentionally misleading.

I could more or less agree if "(or any other theory)" would not be there. One should not talk about "any other theory" when one refuses to consider the possibility that there might be any other theories than string models and LQG. This refusal manifesting itself as a censorship in Not-Even-Wrong makes Peter Woit a wrong person to say anything about these approaches. I must say that Lubos, who has been often accused of censorship, respects comments demonstrating genuine thinking even if it they do not not conform with his own beliefs. It is difficult to avoid the feeling that Peter Woit's deepest motivations have origin in his strongly negative "sour grape" attitude towards any new idea.

TGD predicts correctly the basic structure of standard model from extremely general starting point, reduces coupling constant evolution to p-adic coupling constant evolution, and makes also highly non-trivial predictions about this including relationship between color coupling strength and electro-weak U(1) coupling strength. TGD allows to reproduce physically realistic CKM matrix based on topological explanation of family replication phenomenon using very general number theoretical assumptions with minimum experimental input.

Most importantly, TGD allows to understand elementary particle masses from p-adic thermodynamics. Also Higgs contribution to particle mass can be understood in terms of thermodynamics. It would be really time for community to learn about p-adic mass calculations and if Peter Woit had a real interest in progress in physics he could have helped a lot by making his blog site an arena of genuine discussion about new ideas instead of boring endless repetition of what goes wrong in string models.

TGD also makes predictions about what might be observed in LHC: an example is p-adically scaled up copy of ordinary hadron physics (labelled by Mersenne prime M₈₉: ordinary hadron physics corresponds to M₁₀₇) meaning scaling up of mass scale about 2⁹= 512. TGD based world view forces to give up reductionistic dogma means that highly non-trivial predictions follow in all length scales: nuclear string model and quantum model of dark matter represent two examples of this kind of predictions.

The basic problem in recent theoretical physics community is that people are intellectually lazy and quite too many of them are repeating loose statements echoing what some authority said somewhere. It is also extremely easy to label someone as crackpot and this trick guarantees always a grateful audience of mediocrits.