TGD diary

Quantum p-adic deformations of space-time surfaces as a representation of finite measurement resolution?

2012-01-26T00:50:00.000-08:00

A mathematically - and also physically - fascinating question is whether one could use quantum arithmetics as a tool to build quantum deformations of partonic 2-surfaces or even of space-time surfaces and how could one achieve this. These quantum space-times would be commutative and therefore not like non-commutative geometries assigned with quantum groups. Perhaps one could see them as commutative semiclassical counterparts of non-commutative quantum geometries just as the commutative quantum groups (see this) could be seen commutative counterparts of quantum groups.

As one tries to develop a new mathematical notion and interpret it, one tends to forget the motivations for the notion. It is however extremely important to remember why the new notion is needed.

In the case of quantum arithmetics Shnoll effect is one excellent experimental motivation. The understanding of canonical identification and realization of number theoretical universality are also good motivations coming already from p-adic mass calculations. A further motivation comes from a need to solve a mathematical problem: canonical identification for ordinary p-adic numbers does not commute with symmetries.
There are also good e motivations for p-adic numbers? p-Adic numbers and quantum phases can be assigned to finite measurement resolution in length measurement and in angle measurement. This with a good reason since finite measurement resolution means the loss of ordering of points of real axis in short scales and this is certainly one outcome of a finite measurement resolution. This is also assumed to relate to the fact that cognition organizes the world to objects defined by clumps of matter and with the lumps ordering of points does not matter.
Why quantum deformations of partonic 2-surfaces (or more ambitiously: space-time surfaces) would be needed? Could they represent convenient representatives for partonic 2-surfaces (space-time surfaces) within finite measurement resolution?
1. If this is accepted there is not compelling need to assume that this kind of space-time surfaces are preferred extremals of Kähler action.
2. The notion of quantum arithmetics and the interpretation of p-adic topology in terms of finite measurement resolution however suggest that they might obey field equations in preferred coordinates but not in the real differentiable structure but in what might be called quantum p-adic differentiable structure associated with prime p.
3. Canonical identification would map these quantum p-adic partonic (space-time surfaces) to their real counterparts in a unique a continuous manner and the image would be real space-time surface in finite measurement resolution. It would be continuous but not differentiable and would not of course satisfy field equations for Kähler action anymore. What is nice is that the inverse of the canonical identification which is two-valued for finite number of pinary digits would not be needed in the correspondence.
4. This description might be relevant also to quantum field theories (QFTs). One usually assumes that minima obey partial differential equations although the local interactions in QFTs are highly singular so that the quantum average field configuration might not even possess differentiable structure in the ordinary sense! Therefore quantum p-adicity might be more appropriate for the minima of effective action.
The conclusion would be that commutative quantum deformations of space-time surfaces indeed have a useful function in TGD Universe.

Consider now in more detail the identification of the quantum deformations of space-time surfaces.

Rationals are in the intersection of real and p-adic number fields and the representation of numbers as rationals r=m/n is the essence of quantum arithmetics. This means that m and n are expanded to series in powers of p and coefficients of the powers of p which are smaller than p are replaced by the quantum counterparts. They are quantum quantum counterparts of integers smaller than p. This restriction is essential for the uniqueness of the map assigning to a give rational quantum rationals.
One must get also quantum p-adics and the idea is simple: if the pinary expansions of m and n in positive powers of p are allowed o become infinite, one obtains a continuum very much analogous to that of ordinary p-adic integers with exactly the same arithmetics. This continuum can be mapped to reals by canonical identification. The possibility to work with numbers which are formally rationals is utmost importance for achieving the correct map to reals. It is possible to use the counterparts of ordinary pinary expansions in p-adic arithmetics.
One can defined quantum p-adic derivatives and the rules are familiar to anyone. Quantum p-adic variants of field equations for Kähler action make sense.
1. One can take a solution of p-adic field equations and by the commutativity of the map r=m/n→ r_q=m_q/n_q and of arithmetic operations replace p-adic rationals with their quantum counterparts in the expressions of quantum p-adic imbedding space coordinates h^k in terms of space-time coordinates x^α.
2. After this one can map the quantum p-adic surface to a continuous real surface by using the replacement p→ 1/p for every quantum rational. This space-time surface does not anymore satisfy the field equations since canonical identification is not even differentiable. This surface - or rather its quantum p-adic pre-image - would represent a space-time surface within measurement resolution. One can however map the induced metric and induced gauge fields to their real counterparts using canonical identification to get something which is continuous but non-differentiable.
This construction works nicely if in the preferred coordinates for imbedding space and partonic (space-time) surface itself the imbedding space coordinates are rational functions of space-time coordinates with rational coefficients of polynomials (also Taylor and Laurent series with rational coefficients could be considered as limits). This kind of assumption is very restrictive but in accordance with the fact that the measurement resolution is finite and that the representative for the space-time surface in finite measurement resolution is to some extent a convention. The use of rational coefficients for the polynomials involved implies that for polynomials of finite degree WCW reduces to a discrete set so that finite measurement resolution has been indeed realized quite concretely!

Consider now how the notion of finite measurement resolution allows to circumvent the objections against the construction.

Manifest GCI is lost because the expression for space-time coordinates as quantum rationals is not general coordinate invariant notion unless one restricts the consideration to rational maps and because the real counterpart of the quantum p-adic space-time surface depends on the choice of coordinates. The condition that the space-time surface is represented in terms of rational functions is a strong constraint but not enough to fix the choice of coordinates. Rational maps of both imbedding space and space-time produce new coordinates similar to these provided the coefficients are rational.
Different choices for imbedding space and space-time surface lead to different quantum p-adic space-time surface and its real counterpart. This is an outcome of finite measurement resolution. Since one cannot order the space-time points below the measurement resolution, one cannot fix uniquely the space-time surface nor uniquely fix the coordinates used. This implies the loss of manifest general coordinate invariance and also the non-uniqueness of quantum real space-time surface. The choice of coordinates is analogous to gauge choice and quantum real space-time surface preserves the information about the gauge.

For background see chapter Quantum Arithmetics of "Physics as Generalized Number Theory".

The anatomy of quantum jump in zero energy ontology

2012-01-26T00:18:00.000-08:00

The understanding of the anatomy of quantum jump identified as a moment of consciousness in the framework of Zero energy ontology (ZEO) is gradually getting more detailed and the following is the summary of the recent understanding. The general vision about quantum jump in zero energy ontology generalizes the ordinary auantum measurement theory bringing in also the selection of maximal set of mutually commuting set of observables. Also the connection with the breaking of time reversal invariance at the level of zero energy states as a necessary condition for the non-triviality of U-matrix is new.

Quantum jump begins with unitary process U described by unitary matrix assigning to a given zero energy state a quantum superposition of zero energy states. This would represent the creative aspect of quantum jump - generation of superposition of alternatives.
The next step is a cascade of state function reductions proceeding from long to short scales. It starts from some CD and proceeds downwards to sub-CDs to their sub-CDs to ...... At a given step it induces a measurement of the quantum numbers of either positive or negative energy part of the quantum state. This step would represent the measurement aspect of quantum jump - selection among alternatives.
The basic variational principle is Negentropy Maximization Principle(NMP) stating that the reduction of entanglement entropy in given quantum jump between two subsystems of CD assigned to sub-CDs is maximal. Mathematically NMP is very similar to the second law although states just the opposite but for individual quantum system rather than ensemble. NMP actually implies second law at the level of ensembles as a trivial consequence of the fact that the outcome of quantum jump is not deterministic.
For ordinary definition of entanglement entropy this leads to a pure state resulting in the measurement of the density matrix assignable to the pair of CDs. For hyper-finite factors of type II₁ (HFFs) state function reduction cannot give rise to a pure state and in this case one can speak about quantum states defined modulo finite measurement resolution and the notion of quantum spinor emerges naturally. One can assign a number theoretic entanglement entropy to entanglement characterized by rational (or even algebraic) entanglement probabilities and this entropy can be negative. Negentropic entanglement can be stable and even more negentropic entanglement can be generated in the state function reduction cascade.

The irreversibility is realized as a property of zero energy states (for ordinary positive energy ontology it is realized at the level of dynamics) and is necessary in order to obtain non-trivial U-matrix. State function reduction should involve several parts. First of all it should select the density matrix or rather its Hermitian square root. After this choice it should lead to a state which prepared either at the upper or lower boundary of CD but not both since this would be in conflict with the counterpart for the determinism of quantum time evolution.

Generalization of S-matrix

ZEO forces the generalization of S-matrix with a triplet formed by U-matrix, M-matrix, and S-matrix. The basic vision is that quantum theory is at mathematical level a complex square roots of thermodynamics. What happens in quantum jump was already discussed.

U-matrix as has its rows M-matrices , which are matrices between positive and negative energy parts of the zero energy state and correspond to the ordinary S-matrix. M-matrix is a product of a hermitian square root - call it H - of density matrix ρ and universal S-matrix S commuting with H: [S,H]=0. There is infinite number of different Hermitian square roots H_i of density matrices which are assumed to define orthogonal matrices with respect to the inner product defined by the trace: Tr(H_iH_j)=0. Also the columns of U-matrix are orthogonal. One can interpret square roots of the density matrices as a Lie algebra acting as symmetries of the S-matrix.
One can consider generalization of M-matrices so that they would be analogous to the elements of Kac-Moody algebra. These M-matrices would involve all powers of S.
1. The orthogonality with respect to the inner product defined by < A| B> = Tr(AB) requires the conditions Tr(H₁H₂Sⁿ)=0 for n≠ 0 and H_i are Hermitian matrices appearing as square root of density matrix. H₁H₂ is hermitian if the commutator [H₁,H₂] vanishes. It would be natural to assign n:th power of S to the CD for which the scale is n times the CP₂ scale.
2. Trace - possibly quantum trace for hyper-finite factors of type II₁) is the analog of integration and the formula would be a non-commutative analog of the identity ∈t_S¹ exp(inφ) dφ=0 and pose an additional condition to the algebra of M-matrices. Since H=H₁H₂ commutes with S-matrix the trace can be expressed as the sum
  ∑_i,jh_is_j(i)= ∑_i,j h_i(j)s_j
  of products of correspondence eigenvalues and the simplest condition is that one has either ∑_j s_j(i)=0 for each i or ∑_i h_i(j)=0 for each j.
3. It might be that one must restrict M matrices to a Cartan algebra for a given U-matrix and also this choice would be a process analogous to state function reduction. Since density matrix becomes an observable in TGD Universe, this choice could be seen as a direct counterpart for the choice of a maximal number of commuting observables which would be now hermitian square roots of density matrices. Therefore ZEO gives good hopes of reducing basic quantum measurement theory to infinite-dimensional Lie-algebra.

Unitary process and choice of the density matrix

Consider first unitary process followed by the choice of the density matrix.

There are two natural state basis for zero energy states. The states of these state basis are prepared at the upper or lower boundary of CD respectively and correspond to various M-matrices M_K⁺ and M_L^-. U-process is simply a change of state basis meaning a representation of the zero energy state M_K^+/- in zero energy basis M_K^-/+ followed by a state preparation to zero energy state M^+/-_K with the state at second end fixed in turn followed by a reduction to M_L^-/+ to its time reverse, which is of same type as the initial zero energy state.
The state function reduction to a given M-matrix M_K^+/- produces a state for the state is superposition of states which are prepared at either lower or upper boundary of CD. It does not yet produce a prepared state on the ordinary sense since it only selects the density matrix.
The matrix elements of U-matrix are obtained by acting with the representation of identity matrix in the space of zero energy states as
I= ∑_K | K⁺> < K⁺|
on the zero energy state | K^-> (the action on | K⁺> is trivial!) and gives
U⁺_KL= Tr(M⁺_KM⁺_L) .
In the similar manner one has
U^-_KL=(U^+†)_KL= Tr(M^-_LM^-_K) = (U⁺_LK)^* .
These matrices are Hermitian conjugates of each other as matrices between states labelled by positive or negative energy states. The interpretation is that two unitary processes are possible and are time reversals of each other. The unitary process produces a new state only if its time arrow is different from that for the initial state. The probabilities for transitions |K₊> → |K_-> are given by
p_mn= |Tr(M_K⁺ M_L⁺)|².

State function preparation

Consider next the counterpart of the ordinary state preparation process.

The ordinary state function process can act either at the upper or lower boundary of CD and its action is thus on positive or negative energy part of the zero energy state. At the lower boundary of CD this process selects one particular prepared states. At the upper boundary it selects one particular final state of the scattering process.
Restrict for definiteness the consideration to the lower boundary of CD. Denote also M_K by M. At the lower boundary of CD the selection of prepared state - that is preparation process- means the reduction
∑_m⁺n^-M^+/-_m⁺n^-| m⁺> | n^-> → ∑_n^-M^+/-_m⁺n^-| m⁺> | n^-> .
The reduction probability is given by
p_{m= ∑_n^- | M_m⁺n^-|² = ρ_m⁺m⁺ .}
For this state the lower boundary carries a prepared state with the quantum numbers of state | m₊> . For density matrix which is unit matrix (this option giving pure state might not be possible) one has p_m=1.

State function reduction process

The process which is the analog of measuring the final state of the scattering process is also needed and would mean state function reduction at the upper end of CD - to state | n^-> now.

It is impossible to reduce to arbitrary state | m₊> | n_-> and the reduction must at the upper end of CD must mean a loss of preparation at the lower end of CD so that one would have kind of time flip-flop!
The reduction probability for the process
| m₊ >== ∑_n^-M_m⁺n^-| m⁺> | n^-> → n_->= ∑_m⁺M_m⁺n^-| m⁺> | n^->
would be
p_{mn =| M_mn|² .}
This is just what one would expect. The final outcome would be therefore a state of type | n^-> and - this is very important- of the same type as the state from which the process began so that the next process is also of type U⁺ and one can say that a definite arrow of time prevails.
Both the preparation and reduction process involves also a cascade of state function reductions leading to a choice of state basis corresponding to eigenstates of density matrices between subsystems.

Can the arrow of geometric time change?

A highly interesting question is what happens if the first state preparation leading to a state | K⁺> is followed by a U-process of type U^- rather than by the state function reduction process |K⁺> → |L^->. Does this mean that the arrow of geometric time changes? Could this change of the arrow of geometric time take place in living matter? Could processes like molecular self assembly be entropy producing processes but with non-standard arrow of geometric time? Or are they processes in which negentropy increases by the fusion of negentropic parts to larger ones? Could the variability relate to sleep-awake cycle and to the fact that during dreams we are often in our childhood and youth. Old people are often said to return to their childhood. Could this have more than a metaphoric meaning? Could biological death mean return to childhood at the level of conscious experience? I have explained the recent views about the arrow of time here .

For background see new chapter Construction of Quantum Theory: More About Matrices of "Towards M-matrix" .

How it went?

2012-01-24T23:39:00.000-08:00

Mark McWilliams requested some kind of summary about the development of TGD, and I decided to write an article about the the history of TGD. I could not avoid telling also about turning points of my personal life since my work and life are to high extent one and the same thing.

I have tried to represent the development chronologically but I must confess that I have forgotten precise dates so that the chronology is not exact. Very probably I have also forgotten many important ideas and many side tracks which led nowhere. Indeed, the study of the tables of contents of books and old blog postings and What's New articles at the homepage forces me to wonder how I can forget something so totally.

The article should help a novice to get an overall view about the basic ideas of TGD are their evolution during these 34 years. To myself a real surprise was to see how many deep ideas have emerged after 2005: one can really speak about a burst of new ideas. Most of them relate to the evolution of the mathematical aspects of TGD and to their physical interpretation but also the experimental input from LHC, Fermilab, and elsewhere has played a decisive role in stimulating ideas about the interpretation of the theory.

Unavoidably the emphasis is on the latest ideas and there is of course the risk that some of them are not here to stay. Even during writing process some ideas developed into more concrete form. A good example is the vision about what happens in quantum jump and what the unitarity of U-matrix really means, how M-matrices generalize to form Kac-Moody type algebra, and how the notion of quantum jump in zero energy ontology (ZEO) reproduces the basic aspects of quantum measurement theory. Also a slight generalization of quantum arithmetics suggested itself during the preparation of the article.

I gave to the article a title which is easy to guess: "Evolution of TGD". It can be found at my homepage which is now living at webhotel with address http://tgdtheory.com/.

Note: The links of old postings to my homepage do not work anymore. Apologies. To get to the link work one can replace "http://tgd.wippiespace.com/" with "http://tgdtheory.com/", and if this does not work, with "http://tgdtheory.com/public_html/".

Does 2-adic quantum arithmetics explain p-adic length scale hypothesis?

2012-01-19T02:22:00.000-08:00

For p=2 quantum arithmetics looks singular at the first glance. This is actually not the case since odd quantum integers are equal to their ordinary counterparts in this case. This applies also to powers of two interpreted as 2-adic integers. The real counterparts of these are mapped to their inverses in canonical identification.

Clearly, odd 2-adic quantum quantum rationals are very special mathematically since they correspond to ordinary rationals. It is fair to call them "classical" rationals. This special role might relate to the fact that primes near powers of 2 are physically preferred. CDs with n=2^k would be in a unique position number theoretically. This would conform with the original - and as such wrong - hypothesis that only these time scales are possible for CDs. The preferred role of powers of two supports also p-adic length scale hypothesis.

The discussion of the role of quantum arithmetics in the construction of generalized Feynman diagrams allows to understand how for a quantum arithmetics based on particular prime p particle mass squared - equal to conformal weight in suitable mass units - divisible by p appears as an effective propagator pole for large values of p. In p-adic mass calculations real mass squared is obtained by canonical identification from the p-adic one. The construction of generalized Feynman diagrams allows to understand this strange sounding rule as a direct implication of the number theoretical universality realized in terms of quantum arithmetics.

Witten about mass gap

2012-01-18T23:20:00.000-08:00

Witten has a nice talk about mass gap problem in 3-D (mostly) and 4-D gauge theories demonstrating how enormous his understanding and knowledge about mathematical physics is. Both Peter Woit and Kea have commented it.

In 3-D case the coupling strength g² has the dimension of inverse length and therefore it would not be surprising if mass gap would emerge. Witten argues that by adding to the theory a Chern-Simons term the theory could reduce in long length scales to non-trivial topological QFT at the IR limit. This would be also a nice manner to resolve the IR difficulties of 3-D gauge theories. Could one imagine effective reduction to topological QFT in long length scales also in 4-D case as a solution to IR divergences?

In D=4 the situation is much more difficult since the gauge coupling is dimensionless. My un-educated is opinion is that the proper question is whether the theory actually exists mathematically and my equally un-educated guess is that it does not - unless one brings in the mass scale somehow by hand. The standard Muenchausen trick to bring the scales in perturbation theory is via UV and IR cutoffs. This is going outside what one means with gauge theory strictly mathematically. In order to make progress, one must bring in the new physics and mathematics. A rigorous mathematical formulation of 4-D gauge theory is not enough: it simply does not exist since something very important is missing.

TGD view about the mass gap problem

TGD is one proposal for what this new physics and mathematics could be. I do not try to re-explain in any detail what this new physics and mathematics might be since I have done this explaining for 6 years in this blog. The basic statement is however that the fundamental UV length scale must be present explicitly in the definition of the theory and must have concrete geometric interpretation rather than being a dimensional number like string tension. In TGD framework it corresponds to the "radius" of CP₂, which is fixed from simple symmetry arguments as the only possible choice. This scale is not an outcome of some conceptually highly questionable procedure like spontaneous compactification, which has paralyzed theoretical physics for more than two decades and led to the landscape problem and the proposal to bring anthropic principle to physics - something extremely uninviting for anyone who has spent few minutes by trying to understand what one can say about consciousness as a physicist and mathematician.

To my rebellionary view the mathematics of standard gauge theories is not enough.

Quite a far reaching generalization is needed besides the replacement of the recent view about space-time with the identification of space-times as 4-surfaces.
The usual positive energy ontology having its roots in Newtonian mechanics based on absolute time (Hamiltonian approach especially) must be replaced with zero energy ontology which is natural in the relativistic context.
A further generalization is number theoretical universality requiring that the physics in different number fields must be unified to single coherent whole.
In some of the latest postings I have explained how the number theoretical universality would be realized in terms of quantum arithmetics - something also missing from ordinary gauge theory but for the existence of which there exist indications (quantum groups, inclusions of hyper-finite factors, and Shnoll effect on experimental side). In particular, the size scales of CDs coming as powers of 2 correspond to p=2 quantum arithmetics, which is very special in the sense that for odd integers it is just the ordinary arithmetics. For other primes p the corresponding p-adic length scale is in preferred position since the states with mass squared proportional to p as almost massless states giving an almost pole to the propagator which is given in terms of M² momentum. I dare to hope that these observations finally answer the question why p-adic primes near powers of two are favored physically.

Further comments about mass gap

I cannot avoid the temptation to represent some further comments related to how the mass gap - or rather a hierarchy of mass gaps defined by p-adic mass scales in turn expressible in terms of p-adic prime and the fundamental mass scale defined by CP₂ mass - emerges in TGD.

One of the surprises of zero energy ontology was that that all - including those associated with virtual particles - braid strands carrying fermion numbers are on massless on mass shell states with possibly negative sign of energy so that wormhole contact can have space-like virtual net momentum. This leads to extremely powerful restrictions of loops integrals and guarantees finiteness and with certain additional natural assumptions deriving from ZEO the number of contributing diagrams is finite (discussed in recent postings: see this and this), and therefore guarantees algebraic universality (sum of infinite number of rationals (rational functions) need not be rational (rational function)!).
Quite recently I have learned finally to accept that for generalized Feynman diagrams the presence of preferred M²⊂M⁴ having interpretation in terms of quantization axis of energy and spin is unavoidable (see for instance this). Of course, also propagators for on mass shell massless states are literally infinite unless one restricts the momentum in propagator to its M² projection. There is integral over different choices of M² so that Poincare invariance is not lost. Also number theoretic vision forces M² with an interpretation as commutative subspace of complexified octonions. The last posting about Very Special Relativity and TGD gave one additional justification M².
Witten talks about 3-D gauge theories with emphasis on Chern-Simons term and the idea that in long length scales one obtains a non-trivial topological QFT for non-trivial mass gap. In TGD framework effective 2-dimensionality - or strong form of holography - follows from strong form of General Coordinate Invariance and for preferred extremals of Kähler action the action reduces to Chern-Simons terms if weak form of electric-magnetic duality holds true at the space-like 3-D surfaces at the ends of space-time sheet and at wormhole throats.
The special features of light-like 3-surfaces and boundaries of CDs is that they allow an extension of 2-D conformal invariance by their metric 2-dimensionality: this actually raises 4-D space-time and 4-D Minkowski space in completely unique position mathematically. An extremely simple and profound discovery, whose communication has turned out to be impossible- I think that even my cat is able to understand its significance-: what is wrong with these bright-minded colleagues in their academies;-)? An interesting question raised by Witten's talk is whether also TGD as almost topological TGD in some sense reduces to topological QFT at long length scales for given p-adic length scale. Exponential decrease of correlation function as function of distance might imply this but what happens on light-like boundaries of CDs?
There are also open questions. For instance, should one assign different M² to each sub-CD of CD or to each propagator line connecting the 3-vertices? One can be even more general and also consider a local choices of M² defined by an integrable distribution of M^{2⊂ M⁴ defining the analog of string world sheet.}

The special role of M²⊂M⁴ in relation to mass gap

The special role of M²⊂M⁴ in the construction of generalized Feynman diagrams deserves additional comments.

What is remarkable that gauge conditions generalize in the sense that it is M² momentum that appears in gauge conditions so that also the third polarization for gauge bosons creeps into the spectrum and even photon, gluons, and gravitons would receive small mass given in terms of IR cutoff given by the largest causal diamond in the hierarchy of causal diamonds defining the experimental range of length scales about which experimentalist can gain information. This is of course extremely natural from the view point of experimentalist.
Physical particles are bound states of massless states with parallel M² momenta assigned with the wormhole throats of the same wormhole contact. Also this bring in the overall important IR cutoff - and thus mass gap - not present in gauge theories. UV cutoff given by the size of the smallest CD gives UV cutoff. As already mentioned, there is no breaking of Poincare invariance.
The highly non-trivial question is how the p-adic mass calculations can be consistent with the massless of braid strands. How can wormhole throat satisfy stringy mass formula if it is massless? One of the latest realizations is that that it is not the full M⁴mass squared but the longitudinal M² mass squared, which is quantized by the stringy mass formula! The modified Dirac equation indeed strongly suggests that M² momenta have integer valued components. I could not however decide whether only hyper-complex primes should be accepted: it now seems that integers coming as multiple of given hyper-complex integer, whose modulus square is prime, must be allowed. Particles would get longitudinal mass squared by p-adic thermodynamics and this mass would be the observed mass. Mass gap again but only in longitudinal degrees of freedom
There is also experimental support for the necessity of introducing M². In QCD one characterizes partons with M² momentum and this again brings to gauge theory as a purely mathematical construct - something which really is not there! The great experimental question is whether Higgs exists or not. In TGD Higgs mechanism is replaced by a microscopic mechanism based on p-adic thermodynamics and identification of the mass squared as longitudinal mass squared (in Lorentz invariance manner since one averages over different M²:s). The natural prediction is that instead of Higgs there is entire M⁸⁹ hadron physics to be discovered. If Higgs really is there as some bloggers have already revealed to us;-), profound re-interpretation of TGD is necessary.

New physics in non-perturbative sector

Asymptotically free gauge theories can handle the UV divergences by using renormalization group approach bringing in a scale analogous to QCD Lambda. Lambda defines the IR scale identified as the length scale associated with hadronization and confinement. One gets rid of UV scale altogether (but not from the mathematically tedious and ugly procedures removing UV infinities). In perturbative gauge theories IR remains however a source of difficulties since one really does not know how to calculate anything since the proposed expression for IR scale is non-analytic function of coupling constant strength (expressible in terms of exp(-8π²ℏ/g²), I hope I remember correctly). Also twistor approach is plagued by IR divergences. These difficulties are of course the reason for arranging a conference about mass gap problem! I do not however believe that the mass gap is a mathematical problem within the framework of 4-D gauge theories. One must go outside the system.

In TGD framework magnetic flux tubes are the concrete classical space-time correlate for non-perturbative aspects of quantum theory and appear in all applications from primordial cosmology to biology to elementary particle physics. They are not present in gauge theories. They are obtained as deformations of what I call cosmic strings, which are Cartesian products of string world sheets in M² with 2-D complex sub-manifolds of CP². In this case one cannot anymore speak about space-time as a small deformation of Minkowski space. The quantized size scale of the complex sub-manifolds brings in the scale via string tension. Wormhole contacts themselves are magnetic monopoles and thus homologically non-trivial surfaces of CP₂ with quantized area so that again the fundamental mass scale creeps in. Note that the Kähler action for the magnetic flux tubes and also for deformations CP₂ vacuum extremals contains a power of exp(-8π²ℏ/g²) giving rise to non-analyticity in g. In gauge theories classical action for instantons would give rise kind of factor.

Note: The address of my homepage has changed and the links to my homepage from the earlier postings will fail. The cure of the problem is the replacement of tgd.wippiespace or tgdq.wippiespace in the address with tgdtheory.

Very Special relativity and preferred role of M2 for generalized Feynman graphs

2012-01-17T23:44:00.000-08:00

The preferred role of M² in the construction of generalized Feynman diagrams could be used as a criticism. Poincare invariance is lost. The first answer to the criticism is that one integrates of the choices of M² so that Poincare invariance is lost. One can however defend this assumption also from different view point. Actually Glashow and Cohen did this in their Very Special Relativity proposal! While scanning old files, I found an old text about Very Special Relativity of Glashow and Cohen, and realized that it relates very closely to the special role of M² in the construction of generalized Feynman diagrams. There is article Very Special Relativity and TGD at my homepage but for some reason the text has disappeared from the book that contained it. I add the article more or less as such here.

Configuration space ("world of classical worlds", WCW) decomposes into a union of sub-configuration spaces associated with future and past light-cones and these in turn decompose to sub-sub-configuration spaces characterized by selection of quantization axes of spin and color quantum numbers. At this level Poincare and even Lorentz group are reduced. The possibility that this kind of breaking might be directly relevant for physics is discussed below.

One might think that Poincare symmetry is something thoroughly understood but the Very Special Relativity proposed by nobelist Sheldon Glashow and Andrew Cohen suggests that this might belief might be wrong. Glashow and Cohen propose that instead of Poincare group, call it P, some subgroup of P might be physically more relevant than the whole P. To not lose four-momentum one must assume that this group is obtained as a semi-direct product of some subgroup of Lorentz group with translations. The smallest subgroup, call it L₂, is a 2-dimensional Abelian group generated by K_x+J_y and K_y-J_x. Here K refers to Lorentz boosts and J to rotations. This group leaves invariant light-like momentum in z direction. By adding J_z acting in L₂ like rotations in plane, one obtains L₃, the maximal subgroup leaving invariant light-like momentum in z direction. By adding also K_z one obtains the scalings of light-like momentum or equivalently, the isotropy group L₄ of a light-like ray.

The reasons why Glashow and Cohen regard these groups so interesting are following.

All kinematical tests of Lorentz invariance are consistent with the reduction of Lorentz invariance to these symmetries.
The representations of group L₃ are one-dimensional in both massive and massless case (the latter is familiar from massless representations of Poincare group where particle states are characterized by helicity). The mass is invariant only under the smaller group. This might allow to have left-handed massive neutrinos as well as massive fermions with spin dependent mass.
The requirement of CP invariance extends all these reduced symmetry groups to the full Poincare group. The observed very small breaking of CP symmetry might correlate with a small breaking of Lorentz symmetry. Matter antimatter asymmetry might relate to the reduced Lorentz invariance.

The idea is highly interesting from TGD point of view. The groups L₃ and L₄ indeed play a very prominent role in TGD.

The full Lorentz invariance is obtained in TGD only at the level of the entire configuration space ("world of classical worlds", WCW) which is union over sub-configuration spaces associated with what I call causal diamonds (see this). These sub-configuration spaces decompose further into a union of sub-sub-configuration spaces for which a choice of quantization axes of spin reflects itself at the level of generalized geometry of the imbedding space (quantum classical correspondence requires that the choice of quantization axes has imbedding space and space-time correlates) (see this). The construction of the geometry for these sub-worlds of classical worlds reduces to light-cone boundary so that the little group L₃ leaving a given point of light-cone boundary invariant is in a special role in TGD framework.
The selection of a preferred light-like momentum direction at light-cone boundary corresponds to the selection of quantization axis for angular momentum playing a key role in TGD view about hierarchy of Planck constants associated with a hierarchy of Jones inclusions implying a breaking of Lorentz invariance induced by the selection of quantization axis. The number theoretic vision about quantum TGD implies a selection of two preferred axes corresponding to time-like and space-like direction corresponding to real and preferred imaginary unit for hyper-octonions (see this). In both cases L₄ emerges naturally.
The TGD based identification of Kac-Moody symmetries as local isometries of the imbedding space acting on 3-D light-like orbits of partonic 2-surfaces involves a selection of a preferred light-like direction and thus the selection of L₄.
Also the so called massless extremals representing a precisely targeted propagation of patterns of classical gauge fields with light velocity along typically cylindrical tubes without a change in the shape involve L₄. A very general solution ansatz to classical field equations involves a local decomposition of M⁴ to longitudinal and transversal spaces and selection of a light-like direction (see this).
The parton model of hadrons assumes a preferred longitudinal direction of momentum and mass squared decomposes naturally to longitudinal and transversal mass squared. Also p-adic mass calculations rely heavily on this picture and thermodynamics mass squared might be regarded as a longitudinal mass squared (see this). In TGD framework right handed covariantly constant neutrino generates a super-symmetry in CP₂ degrees of freedom and it might be better to regard left-handed neutrino mass as a longitudinal mass.

This list justifies my own hunch that Glashow and Cohen might have discovered something very important.

Reader interested in background can consult to the article Algebraic braids, sub-manifold braid theory, and generalized Feynman diagrams and the new chapter Generalized Feynman Diagrams as Generalized Braids of "Towards M-Matrix".

MY HOMEPAGE ADDRESS CHANGES!!

2012-01-17T17:48:00.000-08:00

I accidentally learned that the host providing the computer storage finishes all this kind of activity. Accidentally because the finnish enterprises behind Wippie - Saunalahti and Elisa - had decided to do the whole thing in complete secrecy and had cut both phone and email connections related to wippie-space.

In trying to contact the only response was that your password is wrong. Many extremely frustrated and irritated people in web told about this. The big bosses have however calculated that the people practically losing their how life work in this manner are a minority which they need not care of.

It was extremely difficult to find what is happening and what I should do. It turned out that I cannot use the old addresses.

The old web addresses

tgd.wippiespace. com

and

tgdq.wippiespace.com

will be replaced by

tgdtheory.com.

For some time I will disappear from web just as I did for three years ago when Helsinki University decided to get rid of my web presence and also managed quite well.

I will do best to update the web addresses appearing in the books and articles in home page and also in viXra.org but this will take time. Apologies. The new web page should be at use within few days.

Any concrete ideas to help in the situation are welcome!! In particular, there should be manners to communicate search engines about the change of the address.

Number theoretical universality and quantum arithmetics, renormalization, and relation of TGD to N=4 SYM

2012-01-15T22:34:00.000-08:00

In the previous posting I already discussed the proposal for how twistorial construction could generalize to apply to generalized Feynman diagrams in TGD framework. During last days I have made a further progress in understanding of the number theoretical aspects of the proposed construction.

In particular, I finally have simple and general justification for the hypothesis that length scales coming as powers of two and p-adic length scales associated p-adic primes near powers of 2 are very special. The explanation is extremely simple: quantum arithmetics is characterized by prime p and for p=2 all odd quantum integers are identical with ordinary integers so that only powers of two mapped to their inverses distinguish 2-adic quantum arithematics from the ordinary one.

I have also corrected some erratic statements in the view about coupling constant evolutiont and compared the approach to that of N=4 SYM developed by Nima Arkani Hamed and others. Therefore this posting contains some material overlapping with the previous posting.

Number theoretical universality

The construction of the amplitudes should be number theoretically universal meaning that amplitudes should make sense also in p-adic number fields or perhaps in adelic sense in the tensor product of p-adic numbers fields. Quantum arithmetics is characterized by p-adic prime and canonical identification mapping p-adic amplitudes to real amplitudes is expected to make number theoretical universality possible.

This is achieved if the amplitudes should be expressible in terms of quantum rationals and rational functions having quantum rationals as coefficients of powers of the arguments. This would be achieved by simply mapping ordinary rationals to quantum rationals if they appear as coefficients of polynomials appearing in rational functions.

Quantum rationals are characterized by p-adic prime p and p-adic momentum with mass squared interpreted as p-adic integer appears in the propagator. If M² mass squared is proportional to this p-adic prime p, propagator behaves as 1/P²∝ 1/p, which means that one has pole like contribution for these on mass shell longitudinal masses. p-Adic mass calculations indeed give mass squared proportional to p. The real counterpart of propagator in canonical identification is proportional to p. This would select the all CD characterized by n divisible by p as analogs of propagator poles. Note that the infrared singularity is moved and the largest p-adic prime appearing as divisor of integer characterizing the largest CD indeed serves as a physical IR cufoff.

It would seem that one must allow different p-adic primes in the generalized Feynman diagram since physical particles are in general characterized by different p-adic primes. This would require the analog of tensor product for different quantum rationals analogous to adeles. These numbers would be mapped to real (or complex) numbers by canonical identification.

How to get only finite number of diagrams in a given IR and UV resolution?

In gauge theory one obtains infinite number of diagrams. In zero energy ontology the overall important additional constraint comes from on mass shell conditions at internal lines and external lines and from the requirement that the M² momentum squared is quantized for super-conformal representation in terms of stringy mass squared spectrum.

This condition alone does not however imply that the number of diagrams is finite. If forward scattering diagram is non-vanishing also scattering without on mass shell massive conditions on final state lines is possible. One can construct diagrams representing a repeated n→ n scattering and combining these amplitudes with non-forward scattering amplitude one obtains infinite number of scattering diagrams with fixed initial and final states. Number theoretic universality however requires that the number of the contributing diagrams must be finite unless some analytic miracles happens.

The finite number of diagrams could be achieved if one gives for the vision about CDs within CDs a more concrete metric meaning. In spirit of Uncertainty Principle, the size scale of the CD defined by the temporal distance between its tips could correspond to the inverse of the momentum scale defined as its inverse. A further condition would be that the sub-CDs and their Lorentz boosts are indeed within the CD and do not overlap. Obviously the number of diagrams representing repeated n-n scattering forward scattering is finite if these assumptions are made. This would also suggest a scale hierarchy in powers of 2 for CDs: the reason is that given CD with scale T=nT(CP₂) can contain two non-overlapping sub-CDs with the same rest frame only if sub-CD has size scale smaller than nT_CP₂/2. This applies also to the Lorentz boosts of the sub-CDs.

Amplitudes would be constructed by labeling the CDs by integer n defining its size scale. p-Adicity suggests that the factorization of n to primes must be important and if n=p condition holds true, a new resonant like contribution appears corresponding to p-adic diagrams involving propagator.

Should one allow all M² momenta in the loops in all scales or should one restrict the M² momenta to have a particular mass squared scale determined somehow by the size of CD involved? If this kind of constraint is posed it must be posed in mathematically elegant manner and it is not clear how to to this.

Is this kind of constraint really necessary? Quantum arithmetics for the length scale characterized by p-adic prime p would make M² mass squared values divisible by p to almost poles of the propagators, and this might be enough to effectively select the particular p and corresponding momentum scale and CD scale. Consider only the Mersenne prime M₁₂₇=2¹²⁷-1 as a concrete example.

How to realize the number theoretic universality?

One should be able to realized the p-adicity in some elegant manner. One must certainly allow different p-adic primes in the same diagram and here adelic structure seems unavoidable as tensor product of amplitudes in different p-adic number fields or rather - their quantum arithmetic counterparts characterized by a preferred prime p and mapped to reals by the substitution p→ 1/p. What does this demand?

One must be able to glue amplitudes in different p-adic number fields together so that the lines in some case must have dual interpretation as lines of two p-adic number fields. It also seems that one must be able to assign p-adic prime and quantum arithmetics characterized by a given prime p to to a given propagator line. This prime is probably not arbitrarily and it will be found that it should not be larger than the largest prime dividing n characterizing the CD considered.
Should one assign p-adic prime to a given vertex?
1. Suppose first that bare 3-vertices reduce to algebraic numbers containing no rational factors. This would guarantee that they are same in both real and p-adic sense. Propagators would be however quantum rationals and depend on p and have almost pole when the integer valued mass squared is proportional to p.
2. The radiative corrections to the vertex would involve propagators and this suggests that they bring in the dependence on p giving rise to p-adic coupling constant evolution for the real counterparts of the amplitudes obtained by canonical identification.
  1. Should also vertices obey p-adic quantum arithmetics for some p? What about a vertex in which particles characterized by different p-adic primes enter? Which prime defines the vertex or should the vertex somehow be multi-p p-adic? It seems that vertex cannot contain any prime as such although it could depend on incoming p-adic primes in algebraic or transcendental manner.
  2. Could the radiative corrections sum up to algebraic number depending on the incoming p-adic primes? Or are the corrections transcendental as ordinary perturbation theory suggests and involve powers of π and logarithm of mass squared and basically logarithms of some primes requiring infinite-dimensional transcendental extension of p-adic numbers? If radiative corrections depend only on the logarithms of these primes p-adic coupling constant evolution would be obtained. The requirement that radiative vertex corrections vanish does not look physically plausible.
3. Only CDs corresponding to integers m< n would be possible as sub-CDs. A geometrically attractive possibility is that CD characterized by integer n allows only propagator lines which correspond to prime factors of integers not larger than the largest prime dividing n in their quantum arithmetics. Bare vertices in turn could contain only primes larger than the maximal prime dividing n. This would simplify the situation considerably- This could give rise to coupling constant evolution even in the case that the radiative corrections are vanishing since the rational factors possibly present in vertices would drop away as n would increase.
4. Integers n=2^k give rise to an objection. They would allow only 2-adic propagators and vertices containing no powers of 2. For p=2 the quantum arithmetics reduces to ordinary arithmetics and ordinary rationals correspond to p=2 apart from the fact that powers of 2 mapped to their inverses in the canonical identification. This is not a problem and might relate to the fact that primes near powers of 2 are physically preferred. Indeed, the CDs with n=2^k would be in a unique position number theoretically. This would conform with the original - and as such wrong - hypothesis that only these time scales are possible for CDs. The preferred role of powers of two supports also p-adic length scale hypothesis.

These observations give rather strong clues concerning the construction of the amplitudes. Consider a CD with time scale characterized by integer n.

For given CD all sub-CDs with m<n are allowed and all p-adicities corresponding to the primes appearing as prime factors of given m are possible. m=2^k are in a preferred position since p=2 quantum rationals not containing 2 reduce to ordinary rationals.
The geometric condition that sub-CDs and their boosts remain inside CD and do not overlap together with momentum conservation and on-mass-shell conditions on internal lines implies that only a finite number of generalized Feynman diagrams are possible for given CD. This is essential for number theoretical universality. To each sub-CD one must assign its moduli spaces including its not-too-large boosts. Also the planes M² associated with sub-CDs should be regarded as independent and one should integrate over their moduli.
The construction of amplitudes with a given resolution would be a process involving a finite number of steps. The notion of renormalization group evolution suggests a generalization as a change of the amplitude induced by adding CDs with size smaller than smallest CDs and their boosts in a given resolution.
It is not clear whether increase of the upper length scale interpreted as IR cutoff makes sense in the similar manner although physical intuition would encourage this expectation.

How to understand renormalization flow in twistor context?

In twistor context the notion of mass renormalization is not straightforward since everything is massless. In TGD framework p-adic mass scale hypothesis suggests a solution to the problem.

At the fundamental level all elementary particles are massless and only their composites forming physical particles are massive.
M² mass squared is given by p-adic mass calculations and should correspond to the mass squared of the physical particle. There are contributions from magnetic flux tubes and in the case of baryons this contribution dominates.
p-Adic physics discretizes coupling constant flow. Once the p-adic length scale of the particle is fixed its M² momentum squared is fixed and massless takes care of the rest.

Consider now how renormalization flow would emerge in this picture. At the level of generalized Feynman diagrams the change of the IR (UV) resolution scale means that the maximal size of the CDs involve increases (the minimal size of the sides decreases).

Concerning the question what CD scales should be allowed, the situation is not completely clear.

The most general assumption allows integer multiples of CP₂ scale and would guarantee that the products of hermitian matrices and powers of S-matrix commuting with them define Kac-Moody type algebra assignable to M-matrices. If one uses in renormalization group evolution equation CDs corresponding to integer multiples of CP₂ length scale, the equation would become a difference equation for integer valued variable.
p-Adicity would suggest that the scales of CDs come as prime multiples of CP₂ scale. The proposed realization of p-adicity indeed puts CDs characterized by p-adic primes p in a special position since they correspond to the emergence of a vertex corresponding to p-adic prime p which depends on p in the sense that the radiative corrections to 3-vertex can give it a dependence on log(p). This requires infinite-D transcendental extension of p-adic numbers.
As far as coupling constant evolution in strict sense is considered, a natural looking choice is evolution of vertices as a function of p-adic primes of the particles arriving to the vertex since radiative corresponds are expected to depend on their logarithms.
p-Adic length scale hypothesis would allow only p-adic length scales near powers of two. There are excellent reasons to expect that these scales are selected by a kind of evolutionary process favoring those scales for CDs for which particles are maximally stable. The fact that quantum arithmetics for p=2 reduces to ordinary arithmetics when quantum integers do not contain 2 raises with size scales coming as powers of 2 in a special position and also supports p-adic length scale hypothesis.

Renormalization group equations are based on studying what happens in an infinitesimal reduction of UV resolution scale would mean. Now the change cannot be infinitesimal but must correspond to a change in the scale of CD by one unit defined by CP₂ size scale.

The decrease of UV cutoff means addition of new details represented as bare 3-vertices represented by truncated triangle having size below the earlier length scale resolution. The addition can be done inside the original CD and inside any sub-CD would be in question taking care that the details remain inside CD. The hope is that this addition of details allows a recursive definition. Typically addition would involve attaching two sub-CDs to propagator line or two propagator lines and connecting them with propagator. The vertex in question would correspond to a p-adic prime dividing the integer characterizing the sub-CDs. Also the increase of the shortest length scale makes sense and means just the deletion of the corresponding sub-CDs. Note that also the positions of sub-CDs inside CD manner since the number of allowed boosts depends on the position. This would mean an additional complication.
The increase of IR cutoff length means that the size of the largest CD increases. The physical interpretation would be in terms of the time scale in which one observes the process. If this time scale is too long, the process is not visible. For instances, the study of strong interactions between quarks requires short enough scale for CD. At long scales one only observes hadrons and in even longer scales atomic nuclei and atoms.
One could also allow the UV scale to depend on the particle. This scale should correspond to the p-adic mass scales assignable to the stable particle. In hadron physics this kind of renormalization is standard operation.

Comparison with N=4 SYM

The ultimate hope is to formulate all these ideas using precise formulas. This goal is still far away but one can make trials. Let us first compare the above proposal to the formalism in N=4 SYM.

In the construction of twistorial amplitudes the 4-D loop integrals are interpreted as residue integrals in complexified momentum space and reduces to residues around the poles. This is analogous to using "on mass shell states" defined by this poles. In TGD framework the situation is different since one explicitly assigns massless on-mass-shell fermions to braid strands and allows the sign of the energy to be both positive and negative.
Twistor formalism and description of momentum and helicity in terms of the twistor (λ,μ) certainly makes sense for any spin. The well-known complications relate to the necessity to use complex twistors for M⁴ signature: this would correspond to complexified space-time or momentum space. Also region momenta and associated momentum twistors are the TGD counterparts so that the basic building bricks for defining the analogs of twistorial amplitudes exist.

An important special feature is that the gauge potential is replaced with its N=4 super version.

This has some non-generic implications. In particular gluon helicity -1 is obtained from 1 ground state by "adding" four spartners with helicity +1/2 each. This interpretation of the two helicities of a massless particle is not possible in N<4 theories nor in TGD and the question is whether this is something deep or not remains open.
In TGD framework it is natural to interpret all fermion modes associated with partonic 2-surface (and corresponding light-like 3-surfaces) as generators of super-symmetry and fermions are fundamental objects instead of helicity +1 gauge bosons. Right-handed neutrino has special role since it has no electroweak or color interactions and generates SUSY for which breaking is smallest.
The N=2 SUSY generated by right-handed neutrino and antineutrino is broken since the propagator for states containing three fermion braid strands at the same wormhole throat behaves like 1/p³: this is already an anyon-like state. The least broken SUSY is N=1 SUSY with spartners of fermions being spin zero states. The proposal is that one could construct scattering amplitudes by using a generalize chiral super-field associated with N equal to the number of spinor modes acting on ground state that has vanishing helicity. For N=4 it has helicity +1. This would suggest that the analogs of twistorial amplitudes exist and could even have very similar formulas in terms of twistor variables.
The all-loop integrand for scattering amplitudes in planar N=4 SYM relies of BCFW formula allowing to sew two n-particle three amplitudes together using single analog of propagator line christened as BCFW bridge. Denote by Yn,k,l n-particle amplitudes with k positive helicity gluons and l loops. One can glue Y_{n_L,k_L,l_L} and Y_{n_R,k_R,l_R} by using BCFW bridge and add "entangled " removal of two external lines of Y(n+2,k+1,l-1) amplitude with n= n_L+n_R-2,k=k_L+k_R,l=l_L+l_R to get Y_n,k,l amplitude recursively by starting from just two amplitudes defining the 3-vertices. The procedure involves only residue integral over the Gl(k,n) for a quantity which is Yangian invariant. The question is whether one could apply this procedure by replacing N=4 SUSY with SUSY in TGD sense and generalizing the fundamental three particle vertices appropriately by requiring that they are Yangian invariants?
One can also make good guesses for the BCFW bridge and entangled removal. By looking the structure of the amplitudes obtained by the procedure from 3-amplitudes, one learns that one obtains tree diagrams for which some external lines are connected to give loop. The simplest situation would be that BCFW bridge corresponds to M² fermion propagator for a given braid strand and entangled removal corresponds to a short cut of two external lines to internal loop line. One would have just ordinary Feynman graphs but vertices connected with Yangian invariants (not that there is sum over loop corrections). It should be easy to kill this conjecture.

Proposal for a twistorial description of generalized Feynman graphs

2012-01-14T05:09:00.000-08:00

Listening of the lectures of Nima Arkani-Hamed is always an inspiring experience and so also at this time. The first recorded lectures was mostly about the basic "philosophical" ideas behind the approach and the second lecture continued discussion of the key points about twistor kinematics which I should already have in my backbone but do not. The lectures stimulated again the feeling that the generalized Feynman diagrammatics has all the needed elements to allow a twistorial description. It should be possible t to interpret the diagrams as the analogs of twistorial diagrams.

A couple of new ideas emerged as a result of concentrate effort to build bridge to the twistorial approach.

Generalized Feynman diagrams involve only massless states at wormhole throats so that twistorial description makes sense for the kinematical variables. One should identify the counterparts of the lines and vertices of the twistor diagrams constructed from planar polygons and counterparts of the region momenta.
M²⊂ M⁴ appears as a central element of TGD based Feynman diagrammatics and M² projection of the four momentum appears in propagator and also in the modified Dirac equation. I realized that p-adic mass calculations must give the thermal expectation value of the M² mass squared. Since the throats are massless this means that the transversal momentum squared equal to CP₂ contribution plus conformal weight contribution to mass squared.
It is not too surprising that a very beautiful interpretation in terms of the analogs of twistorial diagrams becomes possible. The idea is to interpret wormhole contacts as pairs of lines of twistor diagrams carrying on mass shell momenta. In this manner triangles with truncated apexes with double line representing the wormhole throats become the basic objects in generalized Feynman diagrammatics. The somewhat mysterious region momenta of twistor approach correspond to momentum exchanges at the wormhole contacts defining the vertices. A reasonable expectation is that the Yangian invariants used to construct the amplitudes of N=4 SUSY can be used as basic building bricks also now.
Renormalization group is not understood in the usual twistor approach and p-adic considerations and quantization of the size of causal diamond (CD) suggests that the old proposal about discretization of coupling constant evolution to p-adic length scale evolution makes sense. A very concrete realization of the evolution indeed suggest itself and would mean the replacement of each triangle with the quantum superposition of amplitudes associated with triangles with smaller size scale and contained with the original triangle characterized by the size scale of corresponding CD containing it. In fact the incoming and outgoing particles of of vertex could be located at the light-like boundaries of CD.
The approach should be also number theoretically universal and this suggests that the amplitudes should be expressible in terms of quantum rationals and rational functions having quantum rationals as coefficients of powers of the arguments. Quantum rationals are characterized by p-adic prime p and p-adic momentum with mass squared interpreted as p-adic integer appears in the propagator. This means that the propagator proportional to 1/P² is proportional to 1/p when mass squared is divisible by p, which means that one has pole like contribution. The real counterpart of propagator in canonical identification is proportional to p. This would select the all CD characterized by n divisible by p as analogs of poles.

What generalized Feynman diagrams could be?

Let us first list briefly what these generalized Feynman diagrams emerge and what they should be.

Zero energy ontology and the closely related notion of causal diamond (CD are absolutely essential for the whole approach. U-matrix between zero energy states is unitary but does not correspond to the S-matrix. Rather, U-matrix has as its orthonormal rows M-matrices which are "complex" square roots of density matrices representable as a product of a Hermitian square root of density matrix and unitary and universal S-matrix commuting with it so that the Lie algebra of these Hermitian matrices acts as symmetries of S-matrix. One can allow all M-matrices obtained by allowing integer powers of S-matrix and obtains the analog of Kac-Moody algebra. The powers of S correspond to CD with temporal distance between its tips coming as integer multiple of CP₂ size scale. The goal is to construct M-matrices and these could be non-unitary because of the presence of the hermitian square root of density matrix.
If is assumed that M-matrix elements can be constructed in terms of generalized Feynman diagrams. What generalized Feynman diagrams strictly speaking are is left open. The basic properties of generalized Feynman diagrams - in particular the property that only massless on mass shell states but with both signs of energy appear- however suggest strongly that they are much more like twistor diagrams and that twistorial method used to sum up Feynman diagrams apply.

The lines of the generalized Feynman diagrams

Generalized Feynman diagrams are constructed using solely diagrams containing on mass shell massless particles in both external and internal lines. Massless-ness could mean also massless-ness in M⁴× CP₂ sense, and p-adic thermodynamics indeed suggests that this is true in some sense.

For massless-ness in M⁴× CP₂ sense the standard twistor description should fail for massive excitations having mass scale of order 10⁴ Planck masses. At external lines massless states form massive on mass shell particles. In the following this possible difficulty will be neglected. Stringy picture suggests that this problem cannot be fatal.
Second possibility is that massless states form composites which in the case of fermions have the mass spectrum determined by CP₂ Dirac operator and and that that physical states correspond to states of super-conformal representations with ground states weight determined by the sum of vacuum conformal weight and the contribution of CP₂ mass squared. In this case, one would have massless-ness in M⁴ sense but composite would be massless in M⁴× CP₂ sense. In this case twistorial description would work.
The third and the most attractive option is based on the fact that its is M² momentum that appears in the propagators. The picture behind p-adic mass calculations is string picture inspired by hadronic string model and in hadron physics one can assign M² to longitudinal parts of the parton momenta.
One can therefore consider the possibility that M² momentum square obeys p-adic thermodynamics. M² momentum appears also in the solutions of the modified Dirac equation so that this identification looks physically very natural. M² momentum characterizes naturally also massless extremals (topological light rays) and is in this case massless. Therefore throats could be massless but M² momentum identifiable as the physical momentum would be predicted by p-adic thermodynamics and its p-adic norm could correspond to the scale of CD.
Mathematically this option is certainly the most attractive one and it might be also physically acceptable since integration over moduli characterizing M² is performed to get the full amplitude so that there is no breaking of Poincare invariance.

There are also other complications.

Massless wormhole throats carry magnetic charges bind to form magnetically neutral composite particles consisting of wormholes connected by magnetic flux tubes. The wormhole throat at the other end of the wormhole carries opposite magnetic charge and neutrino pair canceling the electro-weak isospin of the physical particle. This complication is completely analogous to the appearance of the color magnetic flux tubes in TGD description of hadrons and will be neglected for a moment.
Free fermions correspond to single wormhole throats and the ground state is massless for them. Topologically condensed fermions carry mass and the ground states has developed mass by p-adic thermodynamics. Above considerations suggests that the correct interpretation of p-adic thermal mass squared is as M² mass squared and that the free fermions are still massless! Bosons are always pairs of wormhole throats. It is convenient to denote bosons and topologically condensed fermions by a pair of parallel lines very close to each other and free fermion by single line.
Each wormhole throat carries a braid and braid strands are carriers of four-momentum.
1. The four momenta are parallel and only the M² projection of the momentum appears in the fermionic propagator. To obtain Lorentz invariance one must integrate over boosts of M² and this corresponds to integrating over the moduli space of causal diamond (CD) inside which the generalized Feynman diagrams reside.
2. Each line gives rise to a propagator. The sign of the energy for the wormhole throat can be negative so that one obtains also space-like momentum exchanges.
3. It is not quite clear whether one can allow also purely bosonic braid strands. The dependence of the over all propagator factor on longitudinal momentum is 1/p²ⁿ so that throats carrying 1 or 2 fermionic strands (or single purely bosonic strand) are in preferred position and braid strand numbers larger than 2 give rise to something different than ordinary elementary particle. It is probably not an accident that quantum phases q=exp(i2π/n) give rise to bosonic and fermionic statistics for n=1,2 and to braid statistics for n>2. States with n≥ 3 are expected to be anyonic. This also reduces the large super symmetry generated by fermionic oscillator operators at the partonic 2-surfaces effectively to N=1 SUSY.

In the following It will be assume that all braid strands appearing in the lines are massless and have parallel four-momenta and that M² momentum squared is given by p-adic thermodynamics and actually mass squared vanishes. It is also assumed that M² momenta of the throats of the wormhole throats are paralleI in accordance with the classical idea that wormhole throats move in parallel. It is convenient to denote graphically the wormhole throat by a pair of parallel lines very close to each other.

Vertices

The following proposal for vertices neglects the fact that physical elementary particles are constructed from wormhole throat pairs connected by magnetic flux tubes. It is however easy to generalizes the proposal to that case.

Conservation of momentum holds in each vertex but only for the total momentum assignable to the wormhole contact rather than for each throat. The latter condition would force all partons to have parallel massless four-momenta and the S-matrix would be more or less trivial. Conservation of four-momentum, the massless on mass shell conditions for 4-momenta of wormhole throatas and on mass shell conditions M² momentum squared given by stringy mass squared spectrum are extremely powerful and it is quite possible that one obtains in a given resolution defined by the largest and smallest causal diamonds finite number of diagrams.
I have already earlier developed argments strongly suggesting that that only three-vertices are fundamental kenociteallb/elvafu. The three vertex at the level of wormhole throats means gluing of the ends of the generalized line along 2-D partonic two surface defining their ends so that diagrams are generalization of Feynman diagrams rather than 4-D generalizations of string diagrams so that a generalization of a a trouser diagram does not describe particle decay). The vertex can be BFF or BBB vertex or a variant of this kind of vertex obtained by replacing some B:s and F:s with their super-partners obtained by adding right handed neutrino or antineutrino on the wormhole throat carrying fermion number. Massless on mass shell conditions hold true for wormhole throats in internal lines but they are not on mass shell as a massive particles like external lines.
What happens in the vertex is momentum exchange between different wormhole throats regarded as braids with strands carrying parallel momenta. This momentum exchange in general corresponds to a non-vanishing mass squared and can be graphically described as a line connecting two vertices of a triangle defined by the particles emerging into the vertex. To each vertex of the triangle either massless fermion line or pair of lines describing topologically condensed fermion or boson enters. The lines connecting the vertices of the triangle carry the analogs of region momenta kenociteallb/Yangian, which are in general massive but the differences of two adjacent region momenta are massless. The outcome is nothing but the analog of the twistor diagram. 3- vertices are fundamental and one would obtain only 3-gons and the Feynman graph would be a collection of 3-gons such that from each line emerges an internal or external line.
A more detailed graphical description utilizes double lines. For FFB vertices with free fermions one would have 4-gon containing a pair of vertices very near to each other corresponding to the outgoing boson wormhole decribed by double line. This is obtained by truncating the bosonic vertex of 3-gon and attaching bosonic double line to it. For topologically condensed fermions and BBB vertex one would have 6-gon obtained by truncating all apices of a 3-gon.

Some comments about the diagrammatics is in order.

On mass shell conditions and momentum conservation conditions are extremely powerful so that one has excellent reasons to expect that in a given resolution defined by the largest and smallest CD involves the number of contributing diagrams is finite.
The resulting diagrams are very much like twistor diagrams in N=4 D=4 SYM for which also three-vertex and its conjugate are the fundamental building bricks from which tree amplitudes are constructed: from tree amplitudes one in turn obtains loop amplitudes by using the recursion formulas. Since all momenta are massless, one can indeed use twistor formalism. For topologically condensed fermions one just forms all possible diagrams consisting of 6-gons for which the truncated apices are connected by double lines and takes care that n lines are taken to be incoming lines.
The lines can cross, and this corresponds to the analog of non-planar diagram. I have proposed a knot-theoretic description of this situation based on the generalized braiding matrix appearing in integrable QFTs defined in M². By using a representation for the braiding operation which can be used to eliminate the crossings of the lines one could transform all diagrams to planar diagrams for which one could apply existing construction recipe.
The basic conjecture is that the basic building bricks are Yangian invariants. Not only for the conformal group of M⁴ but also for the super-conformal algebra should have an extension to Yangian. This Yangian should be related to the symmetry algebra generated by the M-matrices and analogous to Kac-Moody algebra. For this Yangian points as vertices of the momentum polygon are replaced with partonic 2-surfaces.

Generalization of the diagrammatics to apply to the physical particles

The previous discussion has neglected the fact that the physical particles are not wormhole contacts. Topologically condensed elementary fermions and bosons indeed correspond to magnetic flux pairs at different space-time sheets with wormhole contacts at the ends. How could one describe this situation in terms of the generalization Feynman diagrams?

The natural guess is that one just puts two copies of diagrams above each other so that the triangles are replaced with small cylinders with cross section given by the triangle and the edges of this triangular cylinder representing magnetic flux tubes. It is natural to allow momentum exchanges also at the other end of the cylinder: for ordinary elementary particle these ends carry only neutrino pairs so that the contribution to interactions is screening at small momenta. Also momentum exchanges long the direction of the cylinder should be allowed and would correspond to the non-perturbative low energy degrees of freedom in the case of hadrons. This momentum exchange assignable to flux tube would be between the truncated triangle rather than separately along the three vertical edges of the triangular cylinder.

Number theoretical universality and quantum arithmetics

The approach should be also number theoretically universal meaning that amplitudes should make sense also in p-adic number fields. Quantum arithmetics is characterized by p-adic prime and canonical identification mapping p-adic amplitudes to real amplitudes is expected to make the universality possible.

This is achieved if the amplitudes should be expressible in terms of quantum rationals and rational functions having quantum rationals as coefficients of powers of the arguments. This would be achieve by simply mapping ordinary rationals to quantum rationals if they appear as coefficients of polynomials appearing in rational functions.

Quantum rationals are characterized by p-adic prime p and p-adic momentum with mass squared interpreted as p-adic integer appears in the propagator. If M² mass square is proportional to this p-adic prime p, propagator behaves as 1/P²∝ 1/p, which means that one has pole like contribution for these on mass shell longitudinal masses. p-Adic mass calculations indeed give mass squared proportional to p. The real counterpart of propagator in canonical identification is proportional to p. This would select the all CD characterized by n divisible by p as analogs of poles.

How to understand renormalization flow in twistor context?

In twistor contex the notion of mass renormalization is not straightforward since everything is massless. In TGD framework p-adic mass scale hypothesis suggests a solution to the problem.

At the fundamental level all elementary particles are massless and only their composites forming physical particles are massive.
M² mass squared is given by p-adic mass calculations and should correspond to the mass squared of the physical particle. There are contributions from magnetic flux tubes and in the case of baryons this contribution dominates.
p-Adic physics discretizes coupling constant flow. Once the p-adic length scale of the particle is fixed its M² momentum squared is fixed and massless takes care of the rest.

Concerning the question what CD scales should be allowed, the situation is not completely clear.

The most general assumption allows integer multiples and would guarantee that the products of hermitian matrices and powers of S-matrix commuting with them define Kac-Moody type algebra assignable to M-matrices. If one uses in renormalization group evolution equation CDs corresponding to integer multiples of CP₂ length scale, the equation would become a difference equation for integer valued variable.
p-Adicity would suggest that the scales of CDs come as prime multiples of CP₂ scale.
p-Adic length scale hypothesis would allow only p-adic length scales near powers of two. There are excellent reasons to expect that these scales are selected by a kind of evolutionary process favoring those scales for CDs for which particles are maximally stable.

The decrease of UV cutoff means that the vertex amplitudes associated with smallest truncated 3-polygons in the diagram are replaced with the sum of all amplitudes in which smaller polygons down to the cutoff size and having 3-external legs appear. The change of the total amplitude in this replacements define renormalization group equation. Conservation of four-momentum and on mass shell conditions suggest that only finite number of terms are allowed.
The increase of UV cutoff means that the size of the largest CD increases. The physical interpretation would be in terms of the time scale in which one observes the process. If this time scale is too long, the process is not visible. For instances, the study of strong interactions between quarks requires short enough scale for CD. At long scales one only observes hadrons and in even longer scales atomic nuclei and atoms.
One tends to think that the diagrams are imbedded in M² allowing identification as 2-plane in Minkowski space-time. This in turn would suggest that the step increasing UV resolution corresponds of replacement of triangles with graphs consisting of smaller triangles contained by them and having no intersections. This interpretation is attractive but might not be needed. Essential conditions are momentum conservation and on mass shell conditions.
One could also allow the UV scale to depend on the particle. This scale should correspond to the p-adic mass scales assignable to the stable particle. In hadron physics this kind of renormalization is standard operation.

Standing waves in TGD

2012-01-13T04:19:00.000-08:00

Four-wave mechanism is one of the basic mechanism encountered in laser physics. It is not obvious what the description of four-wave mechanism is at the basic level in TGD framework. In Maxwellian approach one introduces non-linear F⁴ term in the Lagrangian: here F is the electromagnetic field strength. This approach must be replaced by something else in TGD level if one wants a microscopic description.

To end up with this description by making first the question how to understand amplitude modulation. Even this is not enough. One must ask what is the first principle description for the linear superposition of fields in TGD framework. I have described this description in the earlier posting. The basis idea is that superposition does not occur for fields: only for their quantal effects. Some of the implications are discussed here, here, and here.

Also the phenomena of amplitude modulation and four-wave interaction would be effects appearing as quantal reactions of charged particles to the presence of space-time sheets carrying fields. They need not be present for the induced gauge fields. One might perhaps even say that these effects appear only at the level of conscious perception involving quantum jumps but not at the level of classical fields. This would be a direct evidence for the quantal character of conscious experience.

The summation of effects of em fields can induce amplitude modulation. If charged particles have topological sum contacts to the two space-time sheets carrying classical fields with different frequencies, the rate for quantum jumps is proportional to the modulus squared for the sum of the forces caused by these fields, and one obtains amplitude modulation visible as different and sum of the frequencies involved. In the case of massless extremals the sum and difference of frequencies appear only if MEs corresponding to opposite directions of 3-momentum are present. This leads to an effect that would be regarded as being caused by a standing electromagnetic wave. MEs correspond to waves propagating in single direction for a given sign of frequency, and in TGD framework it is highly implausible that standing waves could be realized as classical gauge fields. Probably I have not been the only child who has experienced standing wave in a rope as mysterious and somehow otherworldly phenomenon.

Similar description applies to four-wave mechanism. Four space-time sheets can give rise to the sums of four frequencies appearing with both signs in the sum and the temporally constant effect is obtained when the sum of the frequencies vanishes.

Quantum view about metabolism

2012-01-11T20:29:00.000-08:00

After the writing of the first version of the chapter discussing quantum view about metabolism for about decade ago several new ideas have emerged. Since 2007 the evidence that photosynthesis involves quantum coherence in electronic degrees of freedom in the cell scale has been accumulating: this discovery is in blatant conflict with the predictions of standard quantum theory but conforms nicely with one of the oldest TGD based proposal that living matter is high T_c electronic super-conductor and with the identification of dark matter as phases with large value of Planck constant.

Both the new ideas and the new experimental results motivated rewriting of the chapter. Below is a brief summary about the new ideas that have emerged during last years, and questions raised by them, and how they affect the quantum model of metabolism at the basic level. Especially interesting new result is a concrete and testable proposal for how living matter acts as a high T superconductor bound to have practical implications. This proposal allows also to understand the basic aspects of bio-chemistry (why the number of valence bonds per molecule is maximized). Also a unification of three different views about high living matter manages to be macroscopic quantum system emerges. This unification is only one example of amazing convergence of the basic ideas of TGD that has taken place during the last years.

1. Three different views about living matter as a macroscopic quantum system

There are three different views about how living system manages to be a macroscopic quantum system.

The first vision is based on various kinds of super-conductivities. Electronic super-conductivity is assigned with the cell membrane and plays a key role in the model of cell membrane as a Josephson junction. Furthermore, the effects of ELF em fields on vertebrate brain (see this) suggest that biologically important ions form macroscopic quantum states and cyclotron Bose-Einstein condensates of bosonic ions have been suggested. The TGD based view about atomic nuclei (see this) predicts exotic nuclei chemically equivalent with ordinary ones but being bosons rather than fermions. Also these exotic ions could also form cyclotron Bose-Einstein condensates. Large value of Planck constant would guarantee that cycloctron energies proportional to hbar are above thermal energy.
A more precise view about hierarchy of Planck constants as an implication of the enormous vacuum degeneracy of Kähler action has emerged (see this). According to this view non-standard values of Planck constant are only effective.
As the idea about the hierarchy of Planck constants emerged, I proposed that favored values of Planck constant could comes are powers of 2¹¹. This was just a first guess inspired partially by the observation that the mass ratio of proton and electron is 940/.5= 1880 ∼ 2¹¹. I managed to find indications supporting this hierarchy and also this chapter contains traces of this idea. I became later skeptic but one could actually imagine a mechanism implying this kind of hierarchy. Dark protons with say r=hbar/hbar₀= 1836=4× 3³× × 17 would correspond to approximately same Compton length as ordinary electrons. It is natural to assign this value of hbar also to electrons and this gives Compton length 44.6 Angstroms not far from the p-adic length scale L(149)≈ 50 Angstroms assigned with the lipid layer of cell membrane. The condition that dark proton corresponds to this Compton length gives r= 1836²: the electron Compton length comes now 8.1 μm, which corresponds to cell size scale. One could continue the resulting hierarchy of Planck constants indefinitely.
The notion of negentropic entanglement making sense for rational and even algebraic entanglement probabilities has emerged as a possible characterizer of living matter emerged (see this). Quantum arithmetics allows to generalize the notion of rational so that p-adic real correspondence mediated by canonical identification is fixed uniquely and is both continuous and respects symmetries. One implication is an explanation for Shnoll effect , which could be important also in living matter.

This raises several questions.

How high T_c super conductivity based on dark electron pairs and negentropic entanglement relate?
Could it be that electron pairs in valence bonds are the carriers of negentropic entanglement and that they generate the magnetic flux tubes as parts of their magnetic bodies and in this manner space-time correlates for macroscopic quantum coherence? This makes sense only if the valence electron pairs in living matter have spin 1. The Cooper pairs of high T_c super-conductors are ineed known to have spin 1 (see this). If this view is correct, biological evolution would favor the maximization of covalent electron pairs and this indeed seems to be the case (carbohydrates, fundamental biomolecules, phosphates having as many as 8 valence bonds!) .
Why large hbar would make possible negentropic entanglement or even force it? Is there some purely number theoretic reason for this? For instance, could the p-adic prime p characterizing quantum arithmetics divide the integer n characterizing the Planck constant or could prime valued integers n be favored?

2. Genetic code and dark nucleon states

New realization of the genetic code in terms of dark proton sequences identified as dark nucleons was discovered (see this and this).

The states of dark proton are in natural one-one correspondence with DNA, RNA, tRNA, and amino-acids and vertebrate genetic code is realized in a natural manner. Dark nucleons realized DNA codons as entangled quark triplets. The effective chemical formula H_1.5O for water in atto-second time scale supports this view (see this). How the notion of dark nucleon relates to negentropic entanglement of electrons? Could dark electron pairs and dark nucleons correspond to the same value of Planck constant? Could both dark protons and dark electrons play a key role in metabolism.
The simplest guess is that DNA strands are accompanied by dark nuclei with one dark proton per DNA nucleotide. The resulting positive charged would stabilize the system by partially neutralizing the negative charge density due to the phosphorylation (2 negative charges per nucleotide). Dark proton sequences could be associated also with other important bio-polymers. If the spins of the dark protons are parallel the dipole magnetic fields give rise to flux tubes connecting the protons and one can assign to the large hbar protons a macroscopically quantum coherent phase.
The natural guess would be that dark nucleus realization of the genetic code induces the biological realization as evolution assigns to dark nucleon sequences DNA, RNA, and aminoacid sequences with 1-1 correlation between dark nucleon state and basic unit of the sequence. The dark realization of genetic code suggest a totally new view about biological evolution as a process, which is analogous to R&D in high tech industry rather than being completely random (see this). The candidates for new genes could be tested at dark matter level and in the case that they work they would be transcribed to their chemical equivalents.

3. New ideas related to metabolism

Also new ideas related to metabolism have emerged at the same time when evidence for quantal aspects of photosynthesis has been emerging (see this, this, this, and this).

Negentropic entanglement leads also to the idea about energy metabolism and negentropy transfer as different sides of the same coin. The model for DNA as topological in turn suggest that ADP → ATP and its reverse can be interpreted as a standardized reconnection process re-organizing connections between distant molecules connected by magnetic flux tubes by the relay defined by ATP molecule. Metabolic energy would - or at least could - go to the re-organization of the flux tube connections and therefore of the negentropic quantum entanglement. The question is how to fuse this vision with the hypothesis about metabolic currencies as differences of zero point kinetic energies for space-time sheets.
The radiation from Sun defines the fundamental metabolic currency. Solar radiation cannot be said to negentropic since negentropic entanglement is a 2-particle property. Solar photons could possess a large value of hbar or - more plausibly - suffer at the magnetic body of the living system a phase transition increasing the value of hbar. Could the absorption of large hbar photons arriving from Sun or from magnetic body by electrons generate spin 1 valence electron pairs pairs or provide the metabolic energy needed to re-arrange the flux tube connections between distant molecules by ADP+P_i → ATP process?

4. DNA as a topological quantum computer vision

The vision about DNA as topological quantum computer (see this) has turned out to be very general allowing to imagine several concrete realizations. The essential element is the coding of DNA nucleotides and one can imagine several options.

The original proposal for the realization of DNA as topological quantum computer is based on the representation of DNA nucleotides A, T, C, G as quarks u, d and their antiquarks and requires scaled up version of QCD (see this). This idea looks rather outlandish but could be justified by the strange findings of mathematician Barbara Shipman about honeybee dance (see this) and also by the p-adic length scale hierarchy and the hierarchy of Planck constants suggesting scaled variants of QCD like physics also in the length scale range relevant to the living cell.
The question whether one could one use spin 1 triplet and spin 0 singlet of dark electron pair instead of quarks and their antiquarks to represent codons, is rather obvious. The problem is that S= 0 state for electron pair however gives rise to vanishing dipole field so that flux tube structure would not be possible. The generation of flux tube structure along which supra currents can flow is however an essential element of the proposed mechanism of super-conductivity.
DNA as topological quantum computer hypothesis lead to the hypothesis that it is O= :s to which one must assign the flux tube pair responsible for the representation of the genetic code. Why O= would be in special role? And why should one have a pair of flux tubes? Could this relate to the coding of nucleotides by electron pairs? If there are two parallel flux tubes, one obtains tensor product 3× 3= 5+3+1 of electron triplets at the ends of the flux tubes. Could it be that A,T,C, and G are represented in terms of 3 and 1 and that the breaking of rotational invariance implies mixing of singlet and S_z=0 state of triplet so that nucleotides and their conjugates could correspond to the resulting two pairs related by reflection.
ATP→ ADP+P_i would correspond to the reconnection of the flux tubes of the flux tube pair with hydrogen bonds associated with two water molecules. The flux tubes would split and end to water molecules containing valence electron pair so the negentropic entanglement might not be totally lost. The reverse process would create flux tube connection labelled by the spin state equivalent of A,T,C, or G.

5. Pessimistic generalization of the second law of thermodynamics

The possibility of negentropic entanglement raises the question about the fate of the second law of thermodynamics. The proposal for a generalization of the second law of thermodynamics (see this) based on the most pessimistic vision is that entropy indeed increases also when negentropic entanglement is generated in state function reduction. If the generation of negentropic entanglement is accompanied by a compensating entropic entanglement, how it is generated? Or is the maximally pessimistic generalization really necessary? Is it implied automatically in time scales longer than the characteristic time scale associated with the causal diamonds serving as the basic correlates for conscious selves. One must apply ensemble description in these time scales: does the non-determinism of quantum jump imply second law at the level of ensemble automatically. If this argument is correct, second law would cease to hold in time scales than that characterizing the relevant CD. One might be able to anwer these quesetion by trying to understand the situation in the case of metabolism.

During writing I realized that the old chapter must be split to two pieces. The chapter of "Biosystems as Conscious Holograms" contains the updated material.

Is it really a Higgs?

2012-01-10T19:43:00.000-08:00

Peter Woit tells in This Week's rumour that CMS has found that the signal for what could be Higgs in gamma-gamma decay channel is two times higher than it should be. The optimistic interpretation is that both ATLAS and CMS have been a little bit lucky. But can we believe this? Statistics has been improving: how it is possible that also CMS is getting "lucky"!

If the good luck continues, one is forced to challenge the idea that the signal represents standard model Higgs. SUSY Higgs cannot help since standard SUSY itself is in deep difficulties experimentally. We cannot forget that there are also Higgs like signals at higher masses but these were "forgotten" in the midst of the Higgs hysteria - at least by bloggers who seem to suffer from rather short span of long term memory. Some of us even experienced a sudden conversion from a phanatic no-fairiest to an equally phanatic believer-in-Higgs;-).

In the zero energy ontology of TGD Higgs is not needed at all. A scaled up variant of ordinary hadron physics characterized by Mersenne prime M₈₉ is however "almost-predicted" (better to be cautious!) with mass scale 512 higher than that for ordinary hadron physics. This hadron physics can be said to replace Higgs.

The mesons of this hadron physics should be detected first at LHC. In particular, M₈₉ pion and spion (obtained by replacing quark and antiquark of pion with squark and antiquark) should be there if TGD SUSY is realized in the simplest possible manner meaning the same p-adic mass scale for both quarks and squarks. The few year old discovery of exotic satellite states of ordinary pion supports this radically new view about SUSY as also the mysterious X and Y mesons which in many respects look like charmonium states but are not charmonium states. I have told about all this in the earlier postings. Here is the most recent one.

The generalization of partially conserved axial current hypothesis (PCAC) allows to predict various decay rates and leads to very similar expressions for the decay rates of M₈₉ pseudoscalar mesons as standard model for those of Higgs. Higgs vacuum expectation is replaced with the decay constant f_π of pion-like (more generally meson-like) state which in sigma model corresponds to the vacuum expectation of sigma field. Sigma model is however not necessary except as a phenomenological description in which sigma field expectation would characterize the contribution of the classical color magnetic fields to the mass of M₈₉ baryons. Quark masses would follow from p-adic thermodynamics providing a microscopic description for particle massivation: also the need for this description has been forgotten by the main stream bloggers.

In particular, spion would have 1.5 times higher gamma-gamma decay rate if one extrapolates directly the PCAC for ordinary pion by the simplest possible scaling argument. Could it be that the Higgs candidate is actually spion and pion and other mesons are also there waiting to be discovered? This is the question.

My guess is that within year Higgs hypothesis is dead and one must begin serious work in trying to resolve the problems visible already now.

Tachyonic explanation of neutrino superluminality killed

2012-01-05T18:45:00.000-08:00

New Scientist reported about the sad fate of the tachyonic explanation of neutrino superluminality. The argument is extremely simple.

You start by assuming that a tachyon having negative mass squared: m(ν)²<0 and assume that super-luminal velocity is in question. The point is that you know the value of the superluminal velocity v(1+ε)c, ε≈ 10^-5. You can calculate the energy of the neutrino as
E= |m(ν)|[-1+ v²/(v²-1)]^1/2,
|m(ν)|=(-m(ν)²)^1/2 is the absolute value of formally imaginary neutrino mass.
In good approximation you can write
E= |m(ν)|[-1+ (2ε^-1/2]^1/2 ≈|m(ν)| (2ε)^-1/2.
The order of magnitude of |m(ν)| is not far from one eV - this irrespective of whether neutrino is tachyonic or not. Therefore the energy of neutrino is very small: not larger than keV. This is in a grave contradiction whith what is known: the energy is measured using GeV as a natural unit so that there is discrepancy of 6 orders of magnitude at least. One can also apply energy conservation to the decay of pion to muon and neutrino and this implies that muon has gigantic energy: another contradiction.

What is amusing that this simple kinematic fact was not noticed from beginning. In any case, this finding kills all tachyonic models of neutrino super-luminality assuming energy conservation, and gives additional support for the TGD based explanation in terms of maximal signal velocity, which depends on pair of points of space-time sheet connected by signal and space-time sheet itself characterizing also particular kind of particle.

Even better, one can understand also the jitter in the spectrum of the arrival times which has width of about 50 ns in terms of an effect caused fluctuations in gravitational fields to the maximal signal velocity expressible in terms of the induced metric. The jitter could have interpretation in terms of gravitational waves inducing fluctuation of the maximal signal velocity c_#, which in static approximation equals to c_#=c(1+Φ_gr)^1/2, where Φ_gr is gravitational potential.

Suprisingly, effectively super-luminal neutrinos would make possible gravitational wave detector! The gravitational waves would be however gravitational waves in TGD sense having fractal structure since they would correspond to bursts of gravitons resulting from the decays of large hbar gravitons emitted primarily rather than to a continuous flow (see this). The ordinary detection criteria very probably exclude this kind of bursts as noise. The measurements of Witte attempting to detect absolute motion indeed observed this kind of motion identifiable as a motion of Earth with respect to the rest frame of galaxy but superposed with fractal fluctuations proposed to have interpretation in terms of gravitational turbulence - gravitational waves.

For details see the earlier posting, the little article Could the measurements trying to detect absolute motion of Earth allow to test sub-manifold gravity? or the chapter TGD and GRT of "Physics in Many-Sheeted Space-time".

The basic objection against TGD

2012-01-01T22:06:00.000-08:00

The basic objection against TGD is that induced metrics for space-time surfaces in M⁴× CP₂ form an extremely limited set in the space of all space-time metrics appearing in the path integral formulation of General Relativity. Even special metrics like the metric of a rotating black hole fail to be imbeddable as an induced metric. For instance, one can argue that TGD cannot reproduce the post-Newtonian approximation to General Relativity since it involves linear superposition of gravitational fields of massive objects. As a matter fact, Holger B. Nielsen- one of the very few colleagues who has shown interest in my work - made this objection for at least two decades ago in some conference and I remember vividly the discussion in which I tried to defend TGD with my poor English.

The objection generalizes also to induced gauge fields expressible solely in terms of CP₂ coordinates and their gradients. This argument is not so strong as one might think first since in standard model only classical electromagnetic field plays an important role.

Any electromagnetic gauge potential has in principle a local imbedding in some region. Preferred extremal property poses strong additional constraints and the linear superposition of massless modes possible in Maxwell's electrodynamics is not possible.
There are also global constraints leading to topological quantization playing a central role in the interpretation of TGD and leads to the notions of field body and magnetic body having non-trivial application even in non-perturbative hadron physics. For a very large class of preferred extremals space-time sheets decompose into regions having interpretation as geometric counterparts for massless quanta characterized by local polarization and momentum directions. Therefore it seems that TGD space-time is very quantal. Is it possible to obtain from TGD what we have used to call classical physics at all?

The imbeddability constraint has actually highly desirable implications in cosmology. The enormously tight constraints from imbeddability imply that imbeddable Robertson-Walker cosmologies with infinite duration are sub-critical so that the most pressing problem of General Relativity disappears. Critical and over-critical cosmologies are unique apart from a parameter characterizing their duration and critical cosmology replaces both inflationary cosmology and cosmology characterized by accelerating expansion. In inflationary theories the situation is just the opposite of this: one ends up with fine tuning of inflaton potential in order to obtain recent day cosmology.

Despite these and many other nice implications of the induced field concept and of sub-manifold gravity the basic question remains. Is the imbeddability condition too strong physically? What about linear superposition of fields which is exact for Maxwell's electrodynamics in vacuum and a good approximation central also in gauge theories. Can one obtain linear superposition in some sense?

Linear superposition for small deformations of gauge fields makes sense also in TGD but for space-time sheets the field variables would be the deformations of CP₂ coordinates which are scalar fields. One could use preferred complex coordinates determined about SU(3) rotation to do perturbation theory but the idea about perturbations of metric and gauge fields would be lost. This does not look promising. Could linear superposition for fields be replaced with something more general but physically equivalent?
This is indeed possible. The basic observation is utterly simple: what we know is that the effects of gauge fields superpose. The assumption that fields superpose is un-necessary! This is a highly non-trivial lesson in what operationalism means for theoreticians tending to take these kind of considerations as mere "philosphy".
The hypothesis is that the superposition of effects of gauge fields occurs when the M⁴ projections of space-time sheets carrying gauge and gravitational fields intersect so that the sheets are extremely near to each other and can touch each other ( CP₂ size is the relevant scale).

A more detailed formulation goes as follows.

One can introduce common M⁴ coordinates for the space-time sheets. A test particle (or real particle) is identifiable as a wormhole contact and is therefore pointlike in excellent approximation. In the intersection region for M⁴ projections of space-time sheets the particle forms topological sum contacts with all the space-time sheets for which M⁴ projections intersect.
The test particle experiences the sum of various gauge potentials of space-time sheets involved. For Maxwellian gauge fields linear superposition is obtained. For non-Abelian gauge fields gauge fields contain interaction terms between gauge potentials associated with different space-time sheets. Also the quantum generalization is obvious. The sum of the fields induces quantum transitions for states of individual space time sheets in some sense stationary in their internal gauge potentials.
The linear superposition applies also in the case of gravitation. The induced metric for each space-time sheet can be expressed as a sum of Minkowski metric and CP₂ part having interpretation as gravitational field. The natural hypothesis that in the above kind of situation the effective metric is sum of Minkowski metric with the sum of the CP₂ contributions from various sheets. The effective metric for the system is well-defined and one can calculate a curvature tensor for it among other things and it contains naturally the interaction terms between different space-time sheets. At the Newtonian limit one obtains linear superposition of gravitational potentials. One can also postulate that test particles moving along geodesics in the effective metric. These geodesics are not geodesics in the metrics of the space-time sheets.
This picture makes it possible to interpret classical physics as the physics based on effective gauge and gravitational fields and applying in the regions where there are many space-time sheets which M⁴ intersections are non-empty. The loss of quantum coherence would be due to the effective superposition of very many modes having random phases.

The effective superposition of the CP₂ parts of the induced metrics gives rise to an effective metric which is not in general imbeddable to M⁴× CP₂. Therefore many-sheeted space-time makes possible a rather wide repertoire of 4-metrics realized as effective metrics as one might have expected and the basic objection can be circumvented In asymptotic regions where one can expect single sheetedness, only a rather narrow repertoire of "archetypal" field patterns of gauge fields and gravitational fields defined by topological field quanta is possible.

The skeptic can argue that this still need not make possible the imbedding of a rotating black hole metric as induced metric in any physically natural manner. This might be the case but need of course not be a catastrophe. We do not really know whether rotating blackhole metric is realized in Nature. I have indeed proposed that TGD predicts new physics new physics in rotating systems. Unfortunately, gravity probe B could not check whether this new physics is there since it was located at equator where the new effects vanish.

For background and more details see either the article Could the measurements trying to detect absolute motion of Earth allow to test sub-manifold gravity? or the chapter TGD and GRT of "Physics in Many-Sheeted Space-time".

Could the measurements trying to detect absolute motion of Earth allow to test sub-manifold gravity?

2012-01-01T03:54:00.000-08:00

The history of the modern measurements of absolute motion has a long - more than century beginning from Michelson-Morley 1887. The reader can find in web a list of important publications giving an overall view about what has happened. The earliest measurements assumed aether hypothesis. Cahill identifies the velocity as a velocity with respect to some preferred rest frame and uses relativistic kinematics although he misleadingly uses the terms absolute velocity and aether. The preferred frame could galaxy, or the system defining rest system in cosmology. It would be easy to dismiss this kind of experiments as attempts to return to the days before Einstein but this is not the case. It might be possible to gain unexpected information by this kind of measurements. Already the analysis of CMB spectrum demonstrated that Earth is not at rest in the Robertson-Walker coordinate system used to analysis CMB data and similar motion with respect to galaxy is quite possible and might serve as a rich source of information also in GRT based theory.

In TGD framework the situation is especially interesting.

Sub-manifold gravity predicts that the effective light-velocity measured in terms of M⁴ time taken for a light signal to propagate from point A to B depends on space-time sheet, on points A and B, in particular the distance between A and B. The maximal signal velocity determined in terms of light-like geodesics has this dependence because light-like geodesics for the space-time surface are in general not light-like geodesics for M⁴ but light-like like curves. The maximal signal velocity is in general smaller than its absolute maximum obtained light-like geodesics of M⁴, depends on particle, and could be larger than for photon space-time sheets. This might explain neutrino super-luminality (see this).
Space-time sheets move with respect to larger space-time sheets and it makes sense to speak about the motion of solar system space-time sheet with respect to galactic space-time sheet and this velocity is in principle measurable. Maximal signal velocity can be defined operationally in terms of time needed to travel from point A to B using Minkowski coordinates of the imbedding space as preferred coordinates. It depends on pair of points involved: basically on the direction on and spatial distance along effectively light-like geodesic defined by the sum of the perturbations of the induced metric for the space-time sheets involved. The question is whether one could say something interesting about various experiments carried out to measure the absolute motion interpreted in terms of velocity of space-time sheet with respect to say galactic space-time-sheet.

Also in Special Relativity the motion relative to the rest system of a larger system is a natural notion. In General Relativistic framework situation should be the same but the mathematical description of the situation is somewhat problematic since Minkowski coordinates are not global due to the loss of Poincare invariance as a global symmetry. In practice one must however introduce linear Minkowski coordinates and this makes sense only if one interprets the general relativistic space-time as a perturbation of Minkowski space. This background dependence is in conflict with general coordinate invariance. For sub-manifold gravity the situation is different.

Could the measurements performed already by Michelson-Morley and followers could provide support for the sub-manifold gravity? This might indeed be the case as the purpose of the following arguments demonstrate. The basic results of this analysis are following.

The basic formulas for interferometer experiments using relativistic kinematics instead of Galilean one are same as the predictions of Cahill using different basic assumptions, and allow to conclude that already the data of Mickelson and Morley show the motion of Earth -not with respect to aether- but with galactic rest system.
The only difference is the appearance of the maximal signal velocity c_# for space-time sheet to which various gravitational fields contribute. In the static approximation sum of gravitational potentials contributes to c_#.
This allows to utilize the results of Cahill, who has carried out a re-analysis of experiments trying to detect what he calls absolute motion using these formulas. Cahill has also replicated the crucial experiments of Witte.
The value of the velocity as well as its direction can be determined and the results from various experiments are consistent with each other. The travel time data demonstrate a periodicity due to the rotation of Earth and motion with respect a preferred frame identifiable as a galactic rest frame. The tell-tale signature is the periodicity of sidereal day instead of exact 24 hour periodicity. The travel time for photons shows fluctuations which might be interpreted in terms of gravitational waves having fractal patterns. TGD view about gravitons would suggest that the emission takes place -not as a continuous stream- but in burst-wise manner producing fractal fluctuation spectrum. These fluctuations could show themselves as a jitter also in the neutrino travel times discovered by Opera collaboration.

One must answer several questions before one can make predictions.

The reduction of light velocity in the case that there are many space-time sheets whose M⁴ projections intersect, is described using common M⁴ coordinates for the space-time sheets. The induced metric for given space-time sheet is the sum of flat M⁴ metric and CP₂ contribution identified as classical gravitational field. The hypothesis is that in good approximation a linear superposition for the effects of the gravitational fields holds true in the sense that a test particle having wormhole throat contacts to these space-time sheets experiences the sum of the gravitational fields of various sheets. Similar description holds for induced gauge fields.
From this one can identify the reduced light velocity in the static situation as c_#=(g_tt)^1/2. In a more realistic necessary non-local treatment one calculates the effective light-velocity by assuming that the orbit of massless state n geometric optics approximation is light-like geodesic for the sum of the metric perturbations: this line is not a light-like geodesic of any of the space-time sheets.
In the general the effective metric defined in this manner is not imbeddable as induced metric. This description of linear super-position allows to circumvent the basic objection against TGD, which is that induced metric and gauge fields are extremely strongly correlated since they are expressible in terms of CP₂ coordinates and their gradients and that the variety of metrics representable as induced metrics is extremely restricted. Same of course applies to gauge fields. This resuls is extremely important and would deserve a separate blog posting.
How the reduced light-velocity c_# relates to the reduced light-velocity in medium which is usually described by introducing the notions of free and polarization charges and magnetization and magnetization currents. In the simple situation when polarization tensor is scalar, refractive index n characterizes the reduction of the light velocity: V=c_#/n. Since the reduction of maximal signal velocity due to sub-manifold is purely gravitational and its reduction in medium has an electromagnetic origin, one can argue that the two notions have nothing to do with each other. Hence c_# should be treated as a local concept possibly depending on direction of motion by taking the limit when light-like geodesic with respect to effective metric becomes infinitesimally short. This dependence can be deduced by comparing light-like geodesics emanating from a point and calculating the maximal signal velocity as a function of direction angles of the light-like geodesic and the spatial distance along it.
What happens to the boundary conditions between different media deduced from the structural equations of classical electrodynamics and Maxwell equations? For instance, does the refraction of light take place also when c_# changes? It might of course be that c_# changes only in astrophysical scales - maybe at the surfaces of astrophysical objects - and stays constant at the boundaries between two media in laboratory scale but nevertheless this issue should be understood. The safest guess is that at the level of kinematic local Lorentz invariance still holds true so that the tangential wave vectors identifiable in terms of massless momentum components are conserved at boundaries and one obtains law of refraction also now.
In TGD Universe space-time sheets can move with respect to each other and the larger space-time sheet defines the analog of absolute reference frame in this kind of situation. Also in cosmology one can assign to CMB radiation a specific frame and Earth indeed moves with respect to it rather than being at rest in the global Robertson-Walker coordinate system. For Earth solar system is one such frame. Galactic rest system is second such preferred reference frame. To both one can assign linear Minkowski coordinates, which play a special physical. The obvious question is whether this kind of motion could be detected and whether the measurements carried out to detect absolute motion could allow to deduce this kind of velocity with respect to galactic rest system.
The question is how photons in medium behave when this kind of motion is present. Assume that the medium is characterized by refractive index n so that one has V= c_#/n and that space-time sheet moves with respect to larger one by velocity v characterized by direction angles and magnitude. Here c_#<c₀ is the maximal signal velocity at the space-time sheet. For definiteness assume that the larger space-time sheet corresponds to galaxy.
1. In the measurements of light velocity the light propagates in medium with velocity V<c_#<c₀, and the question is how to describe this mathematically. In his experiments Michelson assumed summation of velocities based on Galilean invariance. This is of course wrong and Special Relativity suggests summation of velocities according to the relativistic formula:
  V →V₁(v,u) == [V+ vu]/[1+ u(Vv/c_#²)] ,
  V= c_#/n , u=cos(θ) .
  Here θ is the direction of the light signal with respect to the velocity v. This formula might be justified in TGD framework: also photon has very small but non-vanishing mass and summation formula for velocities can be applied. This demands the assumption of local Lorentz invariance made routinely in General Relativity. Also it requires that the complex process of repeated absorption and emission of photons is described by a propagation of photon with the reduced velocity.
2. This predicts two effects which might be seen in the experiments trying to measure absolute velocity and its direction. Both solar and galactic gravitational field and also its perturbations - even gravitational waves- can affect the signal velocity via fluctuations in c_# deduced from the superposition of the perturbative contributions of CP₂ to the effective induced metric. Second effect is due to the change of the propagation time. This change depends on the propagation direction. Note however that also c_# in general has the directional dependence and only in the situation when the components g_ti vanish, this dependence is trivial. In the Newtonian approximation the assumption g_ti≈ 0 is made and corresponds to the description of the situation in terms of gravitational potential.

For background and more details see either the article Could the measurements trying to detect absolute motion of Earth allow to test sub-manifold gravity? or the chapter TGD and GRT.

The TGD based interpretation of the God helmet experiments

2011-12-28T21:30:00.000-08:00

In the previous posting I described the God helmet experiments of Persinger briefly and Persinger's own interpretation of the results. Anyone interested to understand what neurotheology is about should listen the inspiring talk God and the Brain - The Persinger 'God Helmet', The Brain, and visions of God by Todd Murphy.

In this posting I will discuss the TGD inspired interpretation of the results of Persinger's experiments. To put it in very concise manner: whereas Persinger interprets right brain as "visitor" explaining sense of presence experiences and even meeting of God, I identify the "visitor" of the visitor experiences as the personal magnetic body or in the case of enlightment experiences as the emergence of a new layer to its fractal structure. Magnetic body would be also responsible for the third person aspect of conscious experience, which means that we tend to see ourselves from bird's eye perspective. Magnetic bodies make as social animals, and are responsible for the cultural evolution and explain why we differ so much from our cousins although the genomes differ so little.

1. Frequency modulation as a "code of consciousness"

Maxwell's electrodynamics would suggest that a superposition of endogenous and external magnetic fields takes place in God helmet experimens and is partially responsible for the effects. This is clear from the fact that quite spesific magnetic stimulation is used (signals derived from EEG during the second stage). In TGD framework one should be able to interpret this.

In TGD Universe endogenous magnetic fields could form a fractal hierarchy: flux quanta inside flux quanta. Several critical values of magnetic field expected. Flux quanta could be flux tubes or sheets (DNA strands could be traversed by flux sheets and one could have hierarchy of genomes making possible collective gene expression at various levels).
There is a hierarchy of Planck constants so that one can assign to the cell membrane potential a Josephson frequency proportional to 1/hbar and to cyclotron frequencies photon energy proportional to hbar.
The code for the communications from biological body to various levels of the magnetic body relies on the modulation of the Josephson frequencies assignable to the cell membrane. Assuming that the value of Planck constant is integer multiple of its standard value these frequencies span an enormous range. In the case of EEG the Planck constant is of order 10¹³ in order to for photons with the energy of visible photon to have frequency about 10 Hz. Since Josephson frequency is proportional to the membrane potential, the modulations of the membrane potential induce modulations of Josephson frequency so that the signal sent to the magnetic body is modulated and this frequency modulation must define the "code of consciousness".
The frequencies involved with these communications are sums of harmonics of Josephson frequency and cyclotron frequency and also cyclotron frequencies can be modulated by modulating magnetic fields. The simplest possibility is that the external magnetic field induces modulation of the magnetic field. This modulation is small since the field strength is of order .01 Gauss and by a factor 1/20 smaller than the endogenous magnetic field B_end=.2 Gauss suggested by the effects of ELF em fields on vertebrate brain. Of course also other field values are expected to be present.

2. The basic philosophy behind the TGD based model

The basic philosophy behind the TGD based explanation of God helmet experiences differs in many respects from that behind the model of Persinger and Murphys. Therefore it is good to describe this philosophy first.

In the normal social consciousness based strongly on verbal communications the left brain self dominates and social interactions actually split the left brain self from right brain self so that right brain self remains a silent companion unable to express itself except throught intuitions. This raises some questions.
Could just the need to communicate the experience verbally automatically project "me" to left brain me and cut if from "right brain self" so that only the memories of left brain self are communicated. What would happen if the subject person would communicate with external world by singing? Often persons who have lost their ability to speak and comprehend spoken language can communicate by singing. Would the the projection occur to left brain self and could the memories be different?
Persinger and Murphy seem to assume that right brain is God from the perspective of the left brain. Magnetic body is responsible for the third person aspect of consciousness and also for the ability to see the dying biological body from the bird's eye perspective during OBEs accompanying also NDEs, which accordingy to Murphy could be quite real. There is indeed evidence that a subject person unable to move from bed has been able to see objects which she should not have been able to see. If magnetic body is real it could also receive extra-sensory information.
Could the magnetic body of right brain or of the entire brain be in some sense the God from the view point of the brain? The TGD based interpretation for the vision of Jaynes about bicameral consiousness as a predecessor of modern consciousness would conform with this. The God of old testament would be the personal magnetic body which would not have yet become a highly integrated part of self and could be experienced as an outsider. Jaynes also proposes that the consciousness of schizophrenic is much like bicameral consciousness.
It is not necessary to assume that the right amygdala is specialized to produce negatively colored motions and left amygdala positive emotions. Same applies also to the proposed roles of right and left hippocampi. In fact, according to Wikipedia article about lateralization of brain function depression is linked with hyperactive right hemisphere and selective involvement in "processing negative emotions, pessimistic thoughts and unconstructive thinking styles". A relatively hypoactive left hemisphere is said to be "specifically involved in processing pleasurable experiences" and "relatively more involved in decision-making processes". One can interpret this in many manners. The hyper-activity of right hemisphere could tend to cut its connection with its magnetic body and cause a depressive mood.
Intense nerve pulse activity could cause this if nerve pulse generation breaks coherence of the EEG oscillation due to the oscillating membrane potentials inducing generation of signals to the magnetic body. The reduced neural activity of left hemisphere would mean a better connection to the magnetic flux tube and positive emotional coloring.
Note that this picture conforms with spiritual practices which teach that the manner to achieve piece of mind and bliss is to stop thinking, which indeed means reduce neural activity and more stable connection to the magnetic body. If one takes this conceptualization seriously, one could conclude that the modern hectic society tends to split the connections to the personal magnetic bodies. Since they represent higher levels in the hierarchy of conscious entities, this would lead to a loss of spirituality and also social regression if magnetic bodies are responsible for social structures and cultural evolution.
For about 26 years ago I had also a long-lasting "enlightment" experience - actually two of them. The general structure of these experiences fits with thde proposed general format. The first experience began with the experience of getting in contact with what I spontaneously called Great Mind. I started to make all kinds of questions which I imagined of writing to a monitor that I saw in front of me. Later I realized that the writing was not necessary. I also understood that our communication was severaly estricted by the fact that my language did not yet have words for to express the messages of this Great Mind so that the messages contained a lot of "blancos".
I had an experience of profound understanding but did not know what I understood. I also felt that everything around me has extremely deep meaning. One of the first questions I did was "How long I will live?". From the humorous reply expressed as an endless rapid running of a counter containing a long sequence of digits I understood that there is no death. I also asked "Am I alone in this Universe?". The reply was enigmatic "You are a God!".
Later it somehow became clear that this God like entity was actually in some sense me. A possible interpretation could be that a new higher layer to the hierarchy of layers of my personal magnetic body had emerged as this God like creature became a part of my personal magnetic body. Much later I realized that this paradoxical realization was the analog for Brahman=Atman identity of Eastern philosophies.

Consider now the more technical assumptions.

One can assume that right and left brain selves can entangle to form a single self and that magnetic flux tubes between brain hemispheres closely associated with the connecting nerve bundles serve as a correlate for this entanglement. In TGD framework the notion of negentropic entanglement makes sense and means entanglement entropy defined number theoretically is negative rather than being positive as usually. Negentropy Maximization Principle for quantum jumps guarantees the stability of negentropic entanglement. Entanglement probabilities must be rational or at most algebraic numbers or negentropic entanglement.
The basic mechanism would be reconnection of magnetic flux tubes. Typically two parallel connecting flux tubes would touch each other and reconnect to form U-shaped flux tubes representing flux tubes beginning and returning to left (right magnetic body). What is the role of the external magnetic field in this process? Could the closed flux tubes of the external magnetic fields reconnect with those connecting the right hemisphere to left hemisphere. Suppose that magnetic flux tubes indeed serve as geometric correlates for attention interpreted as negentropic entanglement.
Could one say that the magnet creating chirp signal catches the attention of the right brain magnetic body directed to the right hemisphere? Could the splitting of the connection to the magnetic body create the negative emotions. It is enough that the magnet- magnetic body entanglement becomes entropic to destroy the entanglement in state function reduction if one believes in NMP and perhaps this occurs.
One an ask whether this kind of mechanism could explain also the effects of strong (or order 1 Tesla) fields on brain in transcranial magnetic stimulation or is the standard explanation in terms of eddy currents inducing nerve pulse patterns enough to explain the effects.

3. The model for God helmet experiences

Consider now a the general TGD inspired model explaining God helmet experiences.

The magnetic chirp during the first stage tends to decouple the right hemisphere from its magnetic body and possibly also from the magnetic body of left brain. This alone creates the negatively colored emotions- kind of feeling of being abandoned by God. This could be also general mechanism of depression and the manner to cure depression would be re-establishment of this connection.
At quantum level the cutting of the magnetic connection would mean the desctruction of entanglement between parts of the two brain hemispheres or between part of right hemisphere and its magnetic body temporarily. This would lead to the splitting of self to right and left brain sub-selves or the loss of the right hemisphere magnetic body entanglement.
If one is ready to take seriously the notion of number theoretic entropy, the minimum condition would be that the magnetic chirp causes the entanglement probabilities become non-rational or even non-algebraic numbers so that the number theoretic entropy does not make sense. Ordinary entanglement entropy is always non-negative and state function reduction reduces the entanglement and self splits to two.
During the second stage the simultaneous activation of both hemispheres by artificial neuronal signals derived from the EEG of amygdala and hippocampus would fuse both hemispheres to single coherent unit so that the mental images of the right hemisphere would contribute to the conscious experience. The coherence could increase from what it is during ordinary wake-up consciousness dominated by verbal communications. "Being nearer to God" alone could give rise to highly positived colored emotions and to a direct experience of seeing the God/light being/magnetic body and explain the experience of meaningfulness and deep understanding without being able to express what one understands. This inability could be simply to the lack of appropriate language. There is no need to assign this experience to the right hippocampus.

For background and pdf version of the text see the new chapter TGD Based View about Classical Fields in Relation to Consciousness Theory and Quantum Biology of "TGD and EEG".

Persinger's work with God helmet

2011-12-28T21:25:00.000-08:00

Anyone - atheist or believer - wanting to learn about Persinger's work and the basic insights of neuro-theology should listen the extremely inspiring talk God and the Brain - The Persinger 'God Helmet', The Brain, and visions of God by Todd Murphy. Persinger's work (for refereces to the articles by Persinger and collaborators see the Wikipedia article about God helmet) suggests that the temporal pattern of the modulation of magnetic field strength (FM would be in question for slow variations) is important. We do not however know the "code". Also the strength of the magnetic field can be important. Note that the effects of very weak ELF em fields on vertebrate brain take place in amplitude windows.

The modulation of magnetic field would probably induce FM of cyclotron frequencies. The model for hearing suggests this kind of modulation as a manner to represents the frequencies of the sound wave. Also phase information is very important: time reversed speech sounds very different as normal speech but has the same power spectrum. Modulations would be slow in the time scales defined by the audible frequency range. .1 seconds would represent lower limit for the variation rate of modulation. Audible frequencies above 20 Hz.

1. God helmet

God helmet or Koren helmet named after its inventor is the device used by Persinger and collaborators to study the effects of magnetic field on consciousness. Transcranial magnetic stimulation is not in question: TCMS uses fields of order Tesla whereas Persinger uses magnetic fields with strength of order .01 Gauss. This is 2 per cent of the nominal value of Earth's magnetic field. There is a coil above both temporal lobes and the active coil rotates counterclockwise.

At the first stage the coil above right temporal lobe rotates counterclockwise. A chirp sequence is used. Chirp means use of an oscillating magnetic field with maximum amplitude about 1 microTesla with oscillation frequency going gradually down. The interpretation is that right-brain self is activated and dominates conscious experiences. The experiences have negative emotional coloring and sometimes the subject person has even fearful experiences.
At second stage both coils rotate counterclockwise. The signal is derived from amygdala and hippocampal EEG. Faraday cage is used to eliminate external electromagnetic perturbations and also sensory deprivation is necessary (subject person is blind-folded and in an acoustic chamber). Earth's magnetic field is present, which might have relevance and is indeed used in experiments related to the hypothesis that the variations in Earth's magnetic field affect consciousness.
A burst of left brain activity is reported to take place during second stage. Also visitor experience is reported to occur during this period. This can mean meeting of God/light being, of angels, of deceased or of group of "beings", or just sense the presence of some conscious entity. A strong sense of meaning can accompany the experience. 80 per cent of subjec persons experience at least the sense of presence.

2. Persinger's experiments and cyclotron frequencies

A more quantitative description of the God helmet experiment assuming that cyclotron frequencies are essential goes as follows.

The field strength used by Persinger is of the order .01 Gauss and very weak and different from B_end=.2 Gauss which is .4B_E with B_E=.5 Gauss the nominal value of the Earth's magnetic field. Cyclotron frequencies are by a factor of order 1/20 smaller than for B_end. This gives .75 Hz for Ca⁺⁺.
From this it is clear that the changes of cyclotron frequencies would be small in static external field in Persinger's experiments and could be treated as a small perturbation. External magnetic field could superpose with B_end=.2 Gauss and affect cyclotron states and induce transitions between them. This would induce effects on EEG visible as frequency modulations. It seems that the period for the oscillation of B must be longer than cyclotron period for this picture to make sense.
One expects a fractal hierarchy of field strengths for endogenous magnetic fields and B≈ .01 Gauss could correspond to higher levels of consciousness so that cyclotron frequencies for these fields would be important. In this case the external magnetic field would not be a small perturbation. The cyclotron frequencies of DNA strand carrying charge density of 2 elementary charges per nucleotide from the phosphates depend only weakly on the length of DNA strand and are about 1 Hz in B_end. Could the cyclotron radiation from cyclotron states associated with the external magnetic field induce interaction with DNA cyclotron states in field B_end=.2 Gauss?
Consider next the time scales. The stimulation of right brain lasts during the first stage last about half an hour. There are however many lacking bits of data.
1. In what range are the values of the rotation frequency for the magnetic field? ELf frequencies are used. If EEG frequencies are in question the rotation should be slower what the lowest EEG frequency involved and below 1 turn per second.
2. The rotated magnetic field is time dependent. Chirp sequences are used to stimulate temporal lobe. What is the duration of single chirp and the frequency range covered during chirp? A good guess is that the frequency range is that of EEG. The natural expectation is that the duration of chirp is much longer than the periods in the frequency range considered. This would mean that one scan entire frequency range and that it makes sense to say that the changes of frequency during chirp is slow as compared to the instantaneous frequency.
3. EEG signals from left amygdala or hippocampus are used to stimulate both temporal lobes during the second stage. This means that their natural frequency scale should be in the range 1-100 Hz. These time scales would be shorter than the time scale of order 1 second assignal to Ca⁺⁺. This suggests that small aplitude modulation of the cyclotron frequencies in EEG range is in question. The signals sent to the magnetic body would be determined by this modulation and at least in the second stage this modification would carry information.

3. Persinger's explanation

Persinger's own explanation for the findings relies on what might be called neurotheology.

The basic claim of Persinger is that the experiences in question are produced by brain so that meeting of God would not be real. Todd Murphy emphasizesthat it is actually impossible to conclude anything about the existence or non-existence of God on basis of these experiments. He however claims that evolution would have developed for brain the ability to produce visions of God which often accompany near death experiences and make it easier to accept the unavoidablity of the biological death. The reader can decide whether these two statements are consistent or not.
The general idea is that both right and left amygdala, which are the most sensitive parts of the brain because the membrane potential is nearest to the threshold for nerve pulse generation. The right hippocampus is assumed to be responsible for non-verbal, "silent" thinking and left brain hemisphere to verbal thinking. This general picture is used by Todd Murphy to understand the conscious experiences accompanying death process about which near death experiences give a information. The experiences generated by God helmet during the first stage would be akin to the fearful emotions associated with near death experiences (NDE). The experiences during the second stage bring in mind the spiritual experiences accompanying death process and having strong positive emotional coloring.
Persinger and Murphy propose that left amygdala is specialized to produce positive emotions (happiness, bliss, and even experience of encountering God or almost synonymously light being). Right amygdala would be specialized to produce negative emotions (such as fear and horror) and one can assign with it also depressive mood. This is not a generally accepted theory. If one accepts it, the natural question is whether right amygdala could serve as a kind of entropic dump pit and left amygdala as as a highly negentropic structure. The empirical data does not force the poor right amygdala to be a whole-daily sufferer.

Consider now the explanation of the experiences induced by God helmet. The lecture by Todd Murphy helps considerably in attempts to understand the gist of the explanation and also helsp to see its problematic aspects.

The selves of right and left brain fuse in some sense to form single self normally. The nerve bundles connecting the brain hemispheres allowing communications between them are essential for this integration. Right brain self is assumed to be sub-ordinate for left brain self. Magnetic pulses during the first period decompose self to two pieces: one could call them right and left self.
During the first stage the mental images from the right brain self become dominating and fearful experiences are due to the fact that right brain amygdala, which is specialized to produce negative emotions, is hyper-active. This phase is believed to break the connection between left and right brain hemispheres. The anecdotal evidence by Todd Murphy suggests a correlation between non-verbal mood of consciousness and negative emotions. One must be however very cautious because extreme fear and horror alone might make impossible not only verbal communication but any coherent action.
During the second stage both left and right brain are stimulated and expected contribute to the mental images of self when the connection between the hemispheres is intact. If I have understood correctly, the proposal is that the splitting of self to separate selves induced during the first phase is present almost permanently during the second phase and that left brain self dominates.
The temporary "intrusion" of the right hemisphere self to the consciousness of left brain self would give rise to visitor experience. Intrusions would mean occasional re-establishment of the connection between hemispheres. One can question the assumption that God experience and the sensed presence represent instances of the same basic experience due to the intrusion. One could also argue that sensed presence is a signal for the breakdown of the connection and is created by the realization that there is also another self using the same biological body.
The model of Todd Murphy for near death experiences would be that right amygdala can give rise to extremely frightening experiences but that the flow of the information to left amygdala transforms this experience to its emotional opposite. The right hippocampus suggested to be responsible for "silent" thinking would be responsible to the experiences of deep meaningfulness and of understanding. To my opinion this picture is too complex and involves too many ad hoc assumptions.

Somehow my personal feeling is that this model is not quite correct. For instance, I do not understand the meaning "intrusion"? This could be of course be just my misunderstanding. Also the hypothesis about the specialization of left and right amygdala looks strange. In the next posting I will describe the TGD inspired interpretation of Persinger's findings.

For background and pdf version of the text see the new chapter TGD Based View about Classical Fields in Relation to Consciousness Theory and Quantum Biology of "TGD and EEG".

TGD based view about classical fields, consciousness theory, and quantum biology

2011-12-28T03:50:00.000-08:00

In TGD Universe gauge fields are replaced with topological field quanta. Examples are topological light rays, magnetic/electric flux tubes and sheets, and flux quanta carrying both magnetic and electric fields. Flux quanta form a fractal hierarchy in the sense that there are flux quanta inside flux quanta. It is natural to assume quantization of Kähler magnetic flux. Braiding and reconnection are the basic topological operations for flux quanta.

The basic question is how the basic notions assigned with the classical gauge and gravitational fields understood in standard sense generalize in TGD framework.

Superposition and interference of the classical fields is very natural in Maxwell electrodynamics and certainly experimentally verified phenomena. Also the notion of hologram relies crucially on the notion of interference. How can one describe the effects explained in terms of superposition of fields in a situation in which the theory is extremely non-linear and all classical gauge fields are expressible in terms of CP₂ coordinates and their gradients? It is also rather clear that the preferred extremals for Kähler action decompose to space-time regions representing space-time correlates for quanta. The superposition of classical fields in Maxwellian sense is impossible.
How can one cope with this situation? The answer is based on simple observation: only the effects of the classical fields superpose. There is no need for the fields to superpose. Together with the notion of many-sheeted space-time this leads to elegant description of interference effects without any need to assume that linearization is a good approximation.
Topological quantization brings in also braiding and reconnection of magnetic flux tubes as basic operations for classical fields. These operations for flux tubes have also Maxwellian counterparts at the level of field lines. Braiding and reconnection are in a central role in TGD Universe and especially so in in TGD inspired theory of consciousness and quantum biology. The challenge is to build a coherent overall phenomenological view about the role of topologically quantized classical fields in biology and neuroscience. For instance, one can ask what is the precise formulation for the notion of conscious hologram and whether magnetic flux tubes could serve as correlates of entanglement (or at least negentropic entanglement suggested by the number theoretic vision and identified as a basic signature of living matter).
Topological quantization and the notion of magnetic body are especially important in TGD inspired model of EEG. The attempt to understand the findings of Persinger from the study of what is known as God helmet leads to a considerable progress in the understanding the possible role of topologically quantized classical fields in biology and neuro-science.

I do not bother to type more and instead give a link to the article TGD based view about classical fields, consciousness theory, and quantum biology.

About the notion of conscious hologram

2011-12-27T01:02:00.000-08:00

In earlier posting Comparison of Maxwellian and TGD views about classical gauge fields I compared Maxwellian and TGD based notions of classical fields. The comparison was restricted to the linear superposition of fields which in TGD framework is restricted to linear superposition of effects of classical fields: the space-time sheets representing classical fields are indeed separate and it is enough that their M⁴ projections intersect. Summation of effects means at classical level summation of forces caused by them due to the fact that particles have topological sum contacts to both space-time sheets. The notion of hologram relies crucially on the superposition of fields and this this forces to reformulate the notion of hologram in TGD framework.

In TGD inspired theory of consciousness the idea about living system as a conscious hologram is central. It is of course far from clear what this notion means. Since the notions of interference and superposition of fields are crucial for the description of the ordinary hologram, the proposed general description for the TGD counterpart for the superposition of fields is a natural starting point for the more precise formulation of the notion of conscious hologram. In the following only the notion of conscious hologram is discussed. Also the formulation of the notion of ordinary hologram in TGD framework is an interesting challenge.

Consider ordinary hologram first. Reference wave and reflected wave interfere and produce an interference pattern to which the substrate of the hologram reacts so that its absorption coefficient is affected. When the substrate is illuminated with the conjugate of the reference wave, the original reflected wave is generated. The modification of the absorption coefficient is assumed to be proportional to the modulus squared fro the sum of the reflected and reference waves. This implies that the wave reflected from the hologram is in good approximation identical with the original reflected wave.
Conscious hologram would be dynamical rather than static. It would be also quantal: the quantum transitions of particles in the fields defined by the hologram would be responsible for the realization of the interference pattern as a conscious experience. The previous considerations actually leave only this option since the interference of classical fields does not happen. Reference wave and reflected wave correspond now to any field configurations. The charged particles having wormhole contacts to the space-time sheets representing the field configurations experience the sum of the fields involved, and this induces quantum jumps between the quantum states associated with the situation in which only the reference wave is present.
This would induce a conscious experience representing an interference pattern. The reference wave can also correspond to a flux tube of magnetic body carrying a static magnetic field and defining cyclotron states as stationary state. External time dependent magnetic field can replace reflected wave and induces cyclotron transitions. Also radiation fields represented by MEs can represent the reference wave and reflected wave.
If there is need for the "reading" of the hologram it would correspond to the addition of a space-time sheet carrying fields which in good approximation have opposite sign and same magnitude as those in the sheet representing reference wave so that the effect on the charged particles reduces to that of the "reflected wave". This step might be un-necessary since already the formation of hologram would give rise to a conscious experience. The conscious holograms created when the hologram is created and when the conjugate of the reference wave is added give rise to two different conscious representations. This might have something to do with holistic and reductionistic views about the same situation.
One can imagine several realizations for the conscious hologram. It seems that the realization at the macroscopic level is essentially four-dimensional. By quantum holography it would reduce at microscopic level to a hologram realized at the 3-D light-like surfaces defining the surfaces at which the signature of induce metric changes (generalized Feynman diagrams having also macroscopic size - anyons or space-like 3-surfaces at the ends of space-time sheets at the two light-like boundaries of CD. Strong form of holography implied by the strong form of general coordinate invariance requires that holograms correspond to collections of partonic 2-surfaces in given measurement resolution. This could be understood in the sense that the charged particles defining the substrate can be described mathematically in terms of the ends of the corresponding light-like 3-surfaces at the ends of CDs. The cyclotron transitions could be thought of as occurring for particles represent as partonic 2-surfaces topologically condensed at several space-time sheets.

One can imagine several applications in TGD inspired quantum biology.

One can develop a model for how certain aspects of sensory experience could be understood in terms of interference patterns for signals sent from the biological body to the magnetic body. The information about the relative position of the magnetic body and biological body would be coded by the interference patterns giving rise to conscious sensory percepts. This information would represent geometric qualia giving information about distances and angles basically. There would be a magnetic flux tube representing the analog of the reference wave and magnetic flux tube carrying the analog of reflected wavel which could represent the effect of neural activity. When the signal changes with time, cyclotron transitions are induced and conscious percept is generated. In principle it there is no need not compensate for the reference wave although also this is possible.
The natural first guess is that EEG rhythms (and those for its fractal generalization) represent reference waves and that the frequencies in question are either harmonics of cyclotron frequencies or linear combinations of these and Josephson frequency assignable to cell membrane (and possibly its harmonics). The modulation of membrane potential (membrane is regarded as a super-conductor) would induce modulations of Josephson frequency and if large enough would generate nerve pulses. These modulations would define the counterpart of the reflected wave. The flux tubes representing unperturbed magnetic field would represent reference waves.
For instance, the motion of the biological body changes the signal at the space-time sheets carrying the signal and this generates cyclotron transitions giving rise to a conscious experience. Perhaps the sensation of having a body is based in this mechanism. The signals could emerge from directly from cells: it could be that this sensation corresponds to lower level selves rather than us. Second option is that nerve pulses to brain induce the signals sent to the our magnetic body.
The motion of biological body relative to biological body generates virtual sensory experience which could be responsible for the illusions like train illusion and the unpleasant sensory experience about falling down from cliff by just imagining it. OBEs could be also due to the virtual sensory experiences of the magnetic body. One interesting illusion results when one swims long time in windy sea. When one returns to the shore one has rather long lasting experience of being in sea. Magnetic body gradually learns to compensate the motion of sea so that the perception of the wavy motion is reduced. At the shore this compensation mechanism however continues to work. This mechanism represents an example of adaptation and could be a very general mechanism. Since also magnetic body uses metabolic energy, this mechanism could have justification in terms of metabolic economy.
Also thinking as internal, silent speech might be assigned with magnetic body and would represent those aspects of the sensory experience of ordinary speech which involve the quantum jumps at magnetic body- the associated geometric qualia- but not the primary sensory percept. This speech would be internal speech since there would be no real sound signal or virtual sound signal from brain to cochlea.
Conscious hologram would make possible to represent phase information. This information is especially important for hearing. The mere power spectrum is not enough since it is same for speech and its time reversal. Cochlea performs an analysis of sounds to frequencies. It it is not easy to imagine how this process could preserve the phase information associated with the Fourier components. It is believed that both right and left cochlea are needed to abstact the phase difference between the signals arriving to right and left ear allowing to deduce the direction of the source neural mechanisms for this has been proposed but these mechanism are not enough in case of speech. Could there exists a separate holistic representation in which sound wave as a whole generates a single signal interfering with the reference wave at the magnetic body and in this manner represents as a conscious experience the phase?
Also the control and reference signals from the magnetic body to biological body could create time dependent interference patterns giving rise to neural response initiating motor actions and other responses. Basically the quantum interference should reduce the magnitude of membrane resting potentials so that nerve pulses would be generated and give rise to motor action. Similar mechanism would be at work at the level of sensory receptors - at least retina. The generation of nerve pulses would mean kind of emergency situation at the neuronal level. Frequency modulation of Josephson radiation would be the normal situation.

For background see the chapter General View About Physics in Many-Sheeted Space-Time : Part I.

The latest Matrix model hype

2011-12-23T20:56:00.000-08:00

Peter Woit told in his "This Week's Hype" series about a press release titled The mechanism that explains why our universe was born with 3 dimensions: a 40-year-old puzzle of superstring theory solved by supercomputer. Peter Woid gives a long citation of the hype and also discusses the background. I encountered a New Scientist article about this hype already few weeks ago and got so irritated that almost decided to write a blog posting but managed to calm down myself.

The challenge of a theoretician working with higher dimensions is to explain why our world seems to be 4-dimensional. No explanation for this fact has emerged in super string models: Kaluza-Klein approach led to Calabi-Yau's but led to the landscape catastrophe. Also 3-dimensional branes have been proposed to be in special role. The recent "solution" of the problem is actually rewarming of an old Kaluza-Klein spirited proposal. The idea is that somehow the symmetry-group of 10-dimensional space would reduce to SO(3) and this could be interpreted as isometries of 3-D Euclidian space. What the Japanese group has done are lattice calculations for what they call Matrix model, which is one of the extremely fuzzy variants of M-theory. It is suggested to provide nothing less than a non-perturbative formulation of M-theory.

In TGD framework the explanation for both the dimension 8 of imbedding space and the dimension D=4 of its Minkowski space factor and the dimension D=4 of space-time surface images from symmetry considerations. The world of classical worlds (space-time surfaces identified as preferred extremals of Kähler action) has Kähler geometry only if it has infinite-D isometry group. The conformal symmetries of the light-like 3-surfaces defining the surfaces at which the induce metric changes its signature and at the same time also generalized Feynman graphs extend the ordinary 2-D conformal symmetries and one obtains infinite-D isometr group. This is possible only for 4-D space-time surfaces. Also the light-cone boundary of light-cone of 4-D Minkowski space has extended conformal symmetries so that 4-D Minkowski space is unique.

There are also other reasons- in particular those related to the dimensions of classical number fields selecting these dimensions and M⁴× CP₂. It is of course useless to tell this to the colleagues: they refuse to listen to a pariah and prefer to contine beating their intelligent heads on the wall. The weird activities with Matrix represent only one example of this acticity.

The derivation of Matrix model

I decided to check what Matrix model means -if anything- and found an article by Tom Banks and some others about Matrix model. It is Christmas Eve so that I want to put it mildly: my feelings were mixed. There are long sequences of hand waving arguments before one ends up with what is christened as Matrix model.

One begins with M-theory and considers branes, which as such are very questionable objects physically. One suddenly decides that 0-branes representing point-like particles are fundamental rather than strings which would be analogous to 1-branes. All higher dimensional branes would be constructed from 0-branes. This would mean return to old days when particles where point-like. But do let this to disturb you. It is good to change the liturgy sometimes.
After this one puts an infinite number of 0-branes- point like particles- on top of each other at same point of 10-D space-time. Like putting infinite-number of point like particles on top of each other. Stay calm and trust the M-theoretician. He knows. Then M-theoretician tells that AdS-correspondence says that the 10 coordinates assignable to the the points form actually matrices in SU(N)×U(1) at the limit of infinite N so that the 10 coordinates have become 10 non-commutating matrix valued coordinates. If you have difficulties swallowing this remember that everyone learns that you are an imbecille with an intelligence quotient of amoeba if you say this aloud.
The AdS/CFT approach relies on the physical idea that the particles at different branes defined U(1) factors of gauge group. If the branes in the stack carry fermionic single particle states states one can indeed construct from them generators of SU(N)×U(1). This idea does not look non-sense to me: for finite number of N it might indeed give rise to a dynamical gauge group having interpretation as gauge symmetry allowing to describe finite measurement resolution in TGD framework. This however gives rise to gauge potentials with non-commutative gauge group, not non-commutative coordinates of 10-D space-time. This is a little problem- actually not so little - but let us trust M-theoreticians and identify vector potentials with 10-D space-time coordinates.
M-theoretician decides that the dynamics of everything is dictated by Yang-Mills Hamiltonian restricted to the world line of the stack of 0-branes. It should be possible to replace Yang-Mills Hamiltonian with corresponding Lagrangian and I shall indeed do this in the sequel to see what results.

This is the theory of everything in non-perturbative formulation! Certainly simple as will be found but to me- a crackpot with intelligence quotient of amoeba - this looks complete non-sense physically. The Japanese research group responsible for the hype has taken all this seriously and decided to do computer simulations. The value of N is replaced with a finite value for approximation purposes. One decides that Kaluza-Klein compactification to 4-D space-time takes places if symmetry breaking takes place reducing SO(9) as rotational symmetries to SO(3). The claim is that numerical calculations show that this happens.

Classical Lagrangian Matrix model

Just for fun I decided to check what YM Lagrangian in 1-D time-line would give.

The field equations express the vanishing of non-Abelian gauge currents. Gauge condition is naturally A₀=0 corresponding to vanishing of the time component of gauge potential. There would be no time in this Universe but let us not bet worried. One can write YM equations and they state the vanishing of YM currents: J^α=0.
J⁰=0 can be solved exactly and the solutions says that the other components of the potential are like the coordinates of a free particles A_i= x_i(0)+v_i(0) t. Particle interpretation happens to make sense except that time is constant.
Classically the conditions Jⁱ=[A_j,[A_i,A^j]]=0 give for matrix conditions on initial values of x_i(0) and v_i(0). Four conditions for each component corresponding to powers tⁿ, n=0,1,2,3. These equations are symmetric under the exchange of positions and momenta- kind of duality. Classically they represent infinite number of polynomial equations of third order in variables x_i(0) and p_i(0) restricting the motion to an algebraic surface in infinite-D space of 9-vectors with matrix valued components. The polynomials are homogenous so that scalings of initial values are symmetries.
An interesting ansatz consist of restricting the vector potentials to subgroup of U(∞). One obtains infinite hierarchy of solutions for which the motion of pseudo particle takes place in finite-dimensional subgroup U(n) or its subgroup. As a special case on also obtains solutions which correspond to Cartesian products ∏ U(n_i). The interpretation as N-particle solutions is attractive. For Cartesian powers of U(1):s the constraints are identically satisfied. For Cartesian powers of SU(2) one obtains what looks like particles in 3-space with coefficients of Lie-algebra generators of SO(3) interpreted as coordinates of 3-space.

Quantum variant of Lagrangian Matrix model

The classical solvability apart from constraints suggests that also the quantized variant of the theory is solvable.

Let us assume that wave functions are in the space defined by initial values x_i(0). The standard commutation relations for the matrix elements of A_i and p_i= dA_i/dt= p_i(0) reduce to those for x_i(0) and p_i(0). The matrix elements of these matrices are just like the position and momentum coordinates for free particle in Euclidian space. The conditions Jⁱ=0 reduces to four sets of equations corresponding to powers n=0,1,2,3 of t. n=0 gives infinite number of third order polynomial equations for initial values of x_i(0). n=1 gives second order partial differential equations linear in x_i(0). n=2 gives gives first order partial differential equations quadratic in x_i(0). n=3 gives infinite numer of third order partial differential equations in p_i(0).
Also in the quantum one has the hierarchy of solutions assignable to subgroups of U(∞) and their Cartesian products. If one wants something like emergent 3-space I would assign it to wave functions corresponding to the Cartesian powers of SU(2). I would try to show that the constraints favor this kind of solutions and that for higher dimensions of SU(N) or its subgroups the number of conditions is too large. I would also ask whether the fact that SU(2) Lie-algebra is in some sense the building brick of higher dimensional Lie algebras as the general form of the presentation of Lie algebras demonstrates could somehow mean that also more complex solutions are perturbations of those for Cartesian powers of SU(2). These questions are useful but it turns out that another 3-D Lie algebra- Heisenberg algebra- seems to be more interesting as effective gauge algebra.

The case of SU(2)

Are the resulting quantum equations sensible? For simplicity one can consider solutions restricted to SU(2) subgroup in the sense that the subgroup of U(∞) is N:th Cartesian power of SU(2) with interpretation in terms of N-particle state.

There are 3× 9=27 coordinates x_i(0). There are 3× 9 equations for n=0. The naive conclusion consistent with the scaling invariance and counting the number of conditions is that the only solution is x_i(0)=0.
This conclusion is too hasty. One can have solutions for which x_i is restricted to 1-D subspace of E⁹. In this case the conditions expressible in terms of 3-D cross product are identically satisfied since cross products vanish. In this case the situation is indeed 3-dimensional and one can say that solution describes a pointlike free particle moving in 3-D space defined by the SU(2) Lie algebra valued preferred coordinate of E⁹. I have failed to to find more general solutions to the conditions.
One can also consider wave functions restricted to 1-dimensional sub-manifolds of E⁹. Constraint conditions are identifically satisfied since the operators corresponding to n=1,2,3 vanish identically. The dimension of the higher dimensional space place no role since everything depends on the 3-D cross product characterizing quaternions and making SU(2) as a gauge group unique. The overall wave function would be restricted to a 2-D plane M² of M¹⁰. Amusingly, in TGD framework preferred planes M² of M⁴ play a key role.

The effectively one-dimensional solutions exist for any matrix algebra since gauge field vanishes identically and therefore also gauge current. Hence SU(2) is not in special position.

Effectively 3-dimensional solution ansatz based on Heisenberg algebra

One obtains effectively 3-dimensional solution ansatz by restricting the consideration to 3-D subspace of E⁹.

Using the notation [x_i(0) =A_i the solution ansatz reads is of form (A₁, A₂, t[A₁,A₂])
Here t is arbitrary real parameter. n=0 contributions to the gauge currents vanish if one has
[A₁,[A₁,A₂]]=0
[A₂,[A₁,A₂]]=0.
This implies that the algebra generated by A_i is a matrix representation of Heisenberg algebra and the Lie algebra of gauge group is replaced by non-compact Heisenberg group. Finite-dimensional representations of this algebra are non-unitary but infinite-dimensional representations can be unitary.
For n=3 the equations are also identically satisfied by the Heisenberg algebra property.
The equations for n=1 and n=2 one obtains conditions on the wave function. Heisenberg algebra characterizes harmonic oscillator and for the vacuum state the condition that annihilation operator creates vacuum can be regarded as the analog of this conditions. On physical grounds one expects something like harmonic oscillator wave functions. Could one apply the analog of standard quantization meaning that the wave functions depend only on single coordinate -say that associated with x₁(0).
A possibility that comes into mind is that action of the differential operators representing momentum p₁(0) is given by
p₁(0)Ψ= kx₁(0) Ψ
so that the conditions on Ψ reduce to those for n=0 and are identically satisfied by Heisenberg algebra property.
This kind of condition is also analogous to a covariant constancy condition and makes sense for single coordinate. The value of the parameter k characterizes the width harmonic oscillator Gaussian (scale of energy spectrum for harmonic oscillator).
What is interesting is that one would have something analogous to what happens in TGD. The solution would be 3-dimensional and its time evolution would span a 4-D subspace. Uncertainy Principle for Heisenberg algebra would allow the wave function depend on single coordinate and one would effectively have 2-dimensional plane.
Whether it makes sense to generalize the solution ansatz so that the linear 3-D subspaces of E⁹ are replaced with more general 3-D sub-manifolds is not clear.

A more general solution ansatz is obtained by considering the Cartesian powers of 3-D Heisenberg algebra. One obtains also solutions for which Q_i= A_i, i=1,...,4 and P_i=A_i, i=5,...,8 commute the identity matrix in the generalization of Heisenberg algebra generated by the phase space coordinates Q_i and P_i. Again unitary representations are infinite-dimensional. In this case the harmonic oscillator wave function would be effectively 4-dimensional.

Could N=∞ limit for gauge theory interpreted in terms of generalized Heisenberg algebra

Could one think of D=4 gauge theory at the limit when the dimension N of gauge group approaches infinity. Just for Christmas fun let us assume that it is literally infinite and apply the idea that the gauge potentials form a 3-D Heisenberg algebra.

Assume A₀=0 as a gauge condition. Assume also Heisenberg algebra
[A₁,A₂]= m A³
with other commutators vanishing. This condition makes sense for Hermitian fields strength in an infinite-D representation of Heisenberg algebra using infinite-D unitary gauge group. The new element is the interpretation of gauge potentials as generators of local Lie-algebra representable as Hermitian objects in infinite-D unitary gauge algebra.
Consider first the vanishing of J⁰. The expression of the electric field strength reduce by gauge condition to F_0i = -∂_tA_i and is identical to that of Abelian gauge field theory.
What about the equations stating the vanishing of Jⁱ? In this case the Heisenberg algebra guarantees the vanishing of the trilinear terms in the currents. The gauge field strengths F₁₃ and F₂₃ reduce also to their Abelian expressions. F₁₂= ∂₂A₁ -∂₁A₂+mA₃. Field equations stating the vanishing of J³ are Maxwellian. In J¹=0 ( J²=0) the term m∂₂A³ (-m∂₁A³) appears as effective source term so that the field serves as a linear sources for itself.
Again one might apply the analogy with harmonic oscillator and argue that the wave functions in the space of field configurations can depend only on single component of gauge potential- say A₁. The interpretation would be in terms of polarization direction. The special role of A₃ corresponds to the direction of 3-momentum in gauge theory.
Also now Cartesian powers of Heisenberg algebra are possible and one obtains the analogs of many-particle states with varying directions of polarizations. One can assign to the solution also a preferred plane of M² defined by time axes and the preferred component of gauge potential. With a good will one might say that M² is analogous to string world sheet. One can ask whether symplectic transformations in E² could give rise to more general solutions with a local polarizaion direction.

What would be non-trivial is that the field equations would linearize completely by using Heisenberg algebra ansatz and the otherwise difficult-to-treat local non-linearity would reduce to well-understod local Lie algebra commutations.

Conclusions

What can one conclude from this exercise?

A rather general solution ansatz is expressible as a product solution corresponding to N:th Cartesian power of U(1). For U(1) factors the solutions can be said to be 9-dimensional since there are no constraints on the 9 coordinates x_i(0). Another solution -even more trivial - solution ansatz reduces to 1-dimensional sub-space of E⁹ and has vanishing gauge field strength for any gauge algebra. Constraint equations are trivially satisfied.
A genuinely 3-dimensional solution ansatz is obtained if one allows the gauge potentials to generate 3-D Heisenberg algebra. If the matrix algebra is infinite-dimensional, sub-algebra of U(&infty;), the matrices in question can be made unitary. Solution ansatz seems to work if one performs standard quantization in Heisenberg algebra so that wave functions depend on single coordinate x_i only. This solution ansatz generalizes by replacing the Heisenberg group with its Cartesian power.
The idea that 3-D space somehow emerges from Matrix theory is based on the reduction of isotropy group from SO(9) ⊂ SO(1,9) to SO(3). One might perhaps say that for the Heisenberg ansatz 3-dimensionality is obtained in this sense. Heisenberg group acts as gauge group. When the Cartesian power of Heisenberg group, the solution could be seen as describing free particles moving in 3-D space.
The Lagrangian variant of the Matrix model is a nice toy model but to my opinion has very little to do with physics.

Objection against TGD SUSY

2011-12-22T01:16:00.000-08:00

TGD SUSY in its simplest form assumes that covariantly constant right-handed neutrino generates SUSY. The second purely TGD based element is that squarks would correspond to the same p-adic mass scale as partners.

This looks nice but there are objections.

The first objection relates to the tachyonicity needed to get rid of double degeneracy of light mesons consisting of u, d, and s quarks. Mesons and smesons consisting of squark pair mix and for large α_s the mixing is large and can indeed make second eigenvalue of the mass squared matrix negative. If so, these states disappears from spectrum. At least to me this looks however somewhat unaesthetic.
Luckily, the transformation of second pion-like state to tachyon and disappearance from spectrum is not the only possibility. After a painful search I found experimental work claiming the existence of states analogous to ordinary pion with masses 60, 80, 100, 140,.... MeV. Also nucleons have this kind of satellite states. Could it be that one of these states is spion predicted by TGD SUSY for ordinary hadrons? But what about other states? They are not spartners: what are they?
The second objection relates to the missing energy. SUSY signatures involving missing energy have not been observed at LHC. This excludes standard SUSY candidates and could do the same in the case of TGD. In TGD framework the missing energy would be eventually right handed neutrinos resulting from the decays of sfermions to fermion and sneutrino in turn decaying to neutrino and right handed neutrino. The naive argument is that shadronization would be much faster process than the decay of squarks to quarks and spartners of electro-weak gauge bosons and missing energy so that these events would not be observed. Shadrons would in turn decay to hadrons by gluino exchanges. The problem with this argument is that the weak decays of squarks producing right handed neutrinos as missing energy are still there!
This objection forces to consider the possibility that covariantly constant right handed neutrino which generates SUSY is replaced with a color octet. Color excitations of leptons of leptohadron hypothesis would be sleptons which are color octets so that SUSY for leptons would have been seen already at seventies in the case of electron. The whole picture would be nicely unified. Sleptons and squark states would contain color octet right handed neutrino the same wormhole throats as their em charge resides. In the case of squarks the tensor product 3⊗ 8=3+6bar+15 would give several colored exotics. Triplet squark would be like ordinary quark with respect to color.
Covariantly constant right-handed neutrino as such would represent pure gauge symmetry, a super-generator annihilating the physical states. Something very similar can occur in the reduction of ordinary SUSY algebra to sub-algebra familiar in string model context. By color confinement missing energy realized as a color octet right handed neutrino could not be produced and one could overcome the basic objections against SUSY by LHC.

What about the claimed anomalous trilepton events at LHC interpreted in terms of SUSY, which however breaks either the conservation of lepton or baryon number. In have proposed TGD based interpretation is in terms of decays of W to sW and sZ which in turn decay and produce the three lepton signature. Suppose that sW and sZ are color octets and that sleptons replace the color octet excitations of leptons responsible for leptohadron physics. One possible decay chain would involve the decays sW⁺→ sL⁺+νbar and sZ→ L⁺+sL^-. Color octet sleptons pair combine to form leptopion which decays to lepton pair. This decay cascade would produce missing energy as neutrino and this seems to be the case for other options too.

This view about TGD SUSY clearly represents a hybrid of the two alternative views about X and Y bosons as composites of either color excitations of quarks or of squarks and is just one possibility. The situation is not completely settled and one must keep mind open.

The reader can find details in the article Do X and Y mesons provide evidence for color excited quarks or squarks? or in the chapter New Particle Physics Predicted by TGD: Part I.

Comparison of Maxwellian and TGD views about classical gauge fields

2011-12-21T06:08:00.000-08:00

In TGD Universe gauge fields are replaced with topological field quanta. Examples are topological light rays, magnetic flux tubes and sheets, and electric flux quanta carrying both magnetic and electric fields. Flux quanta form a fractal hierarchy in the sense that there are flux quanta inside flux quanta. It is natural to assume quantization of Kähler magnetic flux. Braiding and reconnection are basic topological operations for flux quanta.

One important example is the description of non-perturbative aspects of strong interactions in terms of reconnection of color magnetic flux quanta carrying magnetic monopole fluxes. These objects are string like structures and one can indeed assign to them string world sheets. The transitions in which the thickness of flux tube increases so that flux conservation implies that part of magnetic energy is liberated unless the length of the flux quantum increases, are central in TGD inspired cosmology and astrophysics. The magnetic energy of flux quantum is interpreted as dark energy and magnetic tension as negative "pressure" causing accelerated expansion.

This picture is beautiful and extremely general but raises challenges. How to describe interference and linear superposition for classical gauge fields in terms of topologically quantized classical fields? How the interference and superposition of Maxwellian magnetic fields is realized in the situation when magnetic fields decompose to flux quanta? How to describe simple systems such as solenoidal current generating constant magnetic field using the language of flux quanta?

Superposition of fields in terms of flux quanta

The basic question concerns the elegant description of superposition of classical fields in terms of topological field quanta. What it means that magnetic fields superpose.

In Maxwell's linear theory the answer would be trivial but not now. Linear superposition holds true only inside topological light rays for signals propagating in fixed direction with light velocity and with same local polarization. The easy solution would be to say that one considers small perturbations of background space-time sheet and linearizes the theory. Linearization would apply also to induced gauge fields and metric and one would obtain linear superposition approximately. This does not look elegant. Rather, quantum classical correspondence requires the space-time counterpart for the expansion of quantum fields as sum of modes in terms of topological field quanta. Topological field quanta should not lose their identity in the superposition.
In the spirit of topological field quantization it would be nice to have topological representation for the superposition and interference without any linearization. To make progress one must return to the roots and ask how the fields are operationally defined. One has test particle and it experiences a gauge force in the field. From the acceleration of the test particle the value of field is deduced. What one observes is the superposition of gauge forces, not of gauge fields.
1. Let us just assume that we have two space-time sheets representing field configurations to be effectively superposed. Suppose that they are "on top" of each other with respect to CP₂ degrees of freedom so that their M⁴ volumes overlap. The points of the sheets representing the field values that would sum in Maxwell's theory are typically at distance of CP₂ radius of about 10⁴ Planck lengths. Wormhole contacts representing he interaction between the field configurations are formed. Hence the analog of linear superposition does not hold true exactly. For instance, amplitude modulation becomes possible. This is however not essential for the argment.
2. Test particle could be taken to be fermion which is simultaneously topologically condensed to both sheets. In other words, fermionic CP₂ type almost vacuum extremal touches both sheets and wormhole throats at which the signature of the induced metric changes is formed. Fermion experiences the sum of gauge forces from the two space-time sheets through its wormhole throats. From this one usually concludes that superposition holds true for the induced gauge fields. This assumption is however not true and is also un-necessary in the recent case. In case of topological light rays the representation of modes in given direction in terms of massless extremals makes possible to realize the analogy for the representation of quantum field as sum of modes. The representation does not depend on approximate linearity as in the case of quantum field theories and therefore removes a lot of fuzziness related to the quantum theory. In TGD framework the bosonic action is indeed extremely non-linear.
This view about linear superposition has interesting implications. In effective superposition the superposed field patterns do not lose their identity which means that the information about the sources is not lost - this is true at least mathematically. This is nothing but quantum classical correspondence: it is the decomposition of radiation into quanta which allows to conclude that the radiation arrives from a particular astrophysical object. It is also possible to have superposition of fields to zero field in Maxwellian sense but in the sense of TGD both fields patterns still exist. Linear superposition in TGD sense might allow testing using time dependent magnetic fields. In the critical situation in which the magnetic field created by AC current passes through zero, flux quanta have macroscopic size and the direction of the flux quantum changes to opposite.

Time varying magnetic fields described in terms of flux quanta

An interesting challenge to describe time dependent fields in terms of topological field quanta which are in many respects static structures (for instance, flux is constant). The magnetic fields created by time dependent currents serves as a good example from which one can generalize. In the simplest situation the magnetic field strength experiences time dependent scaling. How to describe this scaling?

Consider first the scaling of the magnetic field strength in flux tube quantization.

Intuitively it seems clear that the field decomposes into flux quanta, whose M⁴ projections can partially overlap. To get a connection to Maxwell's theory one can assume that the average field intensity is defined in terms of the flux of the magnetic field over a surface with area S. For simplicity consider constant magnetic field so tht one has B_aveS= Φ= nΦ₀, where Φ₀ is the quantized flux for a flux tube assumed to have minimum value Φ₀. Integer n is proportional to the average magnetic field B_ave. B_ave must be reasonably near to the typical local value of the magnetic field which manifest itself quantum mechanically as cyclotron frequency.
What happens in the scaling B→ B/x. If the transversal area of flux quantum is scaled up by x the flux quantum is conserved. To get the total flux correctly, the number of flux quanta must scale down: n → n/x. One indeed has (n/x)× xS= nS. This implies that the total area associated with flux quanta within total area S is preserved in the scaling.
The condition that the flux is exact integer multiple of Φ₀ would pose additional conditions leading to the quantization of magnetic flux if the total area can be regarded as fixed. This need not to be true.

Consider as the first example slowly varying magnetic field created by an alternating running in current in cylindrical solenoid. There are flux tubes inside the cylindrical solenoid and return flux tubes outside it flowing in opposite direction. Flux tubes get thicker as magnetic field weakens and shift from the interior of solenoid outside. For some value x of the time dependent scaling B→ B/x the elementary flux quantum Φ₀ reaches the radius of the solenoid. Quantum effects must become important and make possible the change of the sign of the elementary flux quantum. Perhaps quantum jump turning the flux quantum around takes place. After this the size of the flux quantum begins to decrease as the magnitude of the magnetic field increases. At the maximum value the size of the flux quantum is minimum.

This example generalizes to the magnetic field created by a linear alternating current. In this case flux quanta are cylinderical flux sheets for which magnetic field strength and thickness oscillators with time. Also in this case the maximum transversal area to the system defines a critical situation in which there is just single flux sheet in the system carrying elementary flux. This flux quantum changes its sign as the sign of the current changes.

For background see the chapter General View About Physics in Many-Sheeted Space-Time : Part I.

Comparison of M89 hadron physics and Higgs as explanation of 125 GeV bump

2011-12-15T03:33:00.000-08:00

The comments of Lubos and Andrew Oh-Willeke to blog posting about LHC data release inspired some comments on my side. These hastily typed comments were imprecise and I decided to write an improved version collecting the main points to a more organized structure. I want also to write about these topics to clarify to myself some important open issues in my own approach and I will do my best to debunk myself in the following. I will very probably make imprecise and even wrong statements. This is work in progress. Apologies.

1. The basic issues

The basic issue is whether the signal at LHC is a compelling evidence for Higgs or not. My claim is that it tells only that there is scalar or pseudo-scalar producing the signal and that under rather general assumptions this signal can be even quantitatively equivalent with the Higgs signal for the recently studied signatures.
Enthusiasts also forget that the signal cross section has features which do not favor its interpretation in terms of Higgs. Exclusion of Higgs does not mean the exclusion of signal! The clear structures around 135 and 145 GeV have not disappeared, there is a wide bump like structure in the entire region 110-150 GeV, and there is structure at both sides of 300 GeV. All these structures should disappear with increased statistics if Higgs interpretation is correct. We do not know whether this will happen and the natural question is whether one could interpret these structures by replacing Higgs paradigm with something else.
Higgs is also disfavored by profound theoretical reasons. It is just around the border of instability against the decay of vacuum. Could this criticality be a signal about the need to replace Higgs with something else? Presumably a microscopic description of particle massivation (provided by TGD already 15 years ago in terms of p-adic thermodynamics). Or are we happy with Higgs phenomenology which only reproduces instead of predicting?

2. Brief summary

The main results hitherto - preliminary of course - are following.

Various decay rates of pion like states of M₈₉ hadron physics can be estimated using the generalization of partially conserved axial vector hypothesis (PCAC) stating that the divergence of the axial vector current is proportional to pion field. The proportionality constant is f_πm_π². The divergence of axial current equals to the sum of instanton densities for electro-weak gauge fields and color gauge field plus the divergence of axial vector currents for u and d type quarks assuming that they are massive: this divergence is by Dirac equation proportional to the mass of the quark.
The contribution of more massive quarks is absent, which is quite a remarkable difference as compared to the standard model Higgs for which the decay amplitudes to massive quark pairs are the most important ones by the proportionality of Higgs-fermion coupling to quark mass. This holds true in M⁴ effective QFT picture: one can hope that it is a good approximation. It is is indeed known to work in orfdinary low energy hadron physics and p-adic fractality suggests that the same holds true for M₈₉ hadron physics .
If the generalization of hadronic sigma model involving u and d type is accepted then f_π can be identified as the negative of the vacuum expectation value of sigma field: f_π=-v. The inspection of the decay rates of Higgs in standard model and those predicted by PCAC /Iztykson-Zuber is my source) shows that their structure is identical. This strongly suggests that by replacing Higgs vacuum expectation value by a suitable multiple of sigma field vacuum expectation it might be possible to reproduce all decay rates of standard model Higgs. This would apply also at the level of amplitudes.
This kind of duality like relation would not be terribly surprising since the structure of these two models is very similar. This would allow to estimate the decay rates of pionlike state to various channels and have very similar results for the decay rates to weak gauge bosons and also to the states produced via the decay to virtual gauge boson pair decaying to quarks or leptons. The direct decays to other than u and d quark pairs do not appear in the lowest order.
Assuming X=f_π/m_π=91/140= .65 as for ordinary pion, the decay of pion-like state to gamma pair implied by PCAC is under very natural assumptions by a factor 1.54 times larger that the decay reate of Higgs. The observed signal cross section for gamma pair production by 125 GeV state is by the same factor about 1.5 higher than that predicted by the standard model! The magnitude of f_π=-v= -81.3 GeV is very near to W boson mass 80.4 GeV. f_π=-m_W would give m(π₈₉)= 123.6 GeV which is second favored value for the mass of the resonance.
This does not yet allow to shout Heureka! and claim that M₈₉ pion hypothesis beats Higgs hypothesis. The production rates for Higgs and pion like state need not be the same. If however the production by fusion of electroweak bosons and gluons dominates and is described by PCAC (action would be just then one has excellent hopes that the production rates are indeed identical. There is also associated production in which W or Z boson emitted by a scattered quark in either proton emits Higgs boson. Also this vertex would be governed by PCAC when Higgs is replaced by M₈₉.
The experimental data suggests that Higgs signal is much smaller than the predicted signal above 127 GeV but has bump like structure and at bumps larger than the effective signal from the standard model background. Also the p value telling the probability that standard model background is able to explain the signal cross section has sharp downwards peaks at two other masses about 127 GeV. TGD interpretation would be in terms of pion like states. This interpretation makes sense only if the proportionality coefficient X in f_π=-X m_π is considerably large than its value for ordinary pion and lowest pion like state given by Z= 91/140∼1.54. This reduces the various couplings of pion like state by a factor 1/X². This is of course possible but one should have a good explanation for why X increases with the mass of pseudo-scalar state.

One can clearly say that sigma model for low-lying M₈₉ replaces Higgs mechanism as an approximate QFT description in TGD framework and a duality like relation between sigma model description of the meson decay amplitudes and those of standard model Higgs is highly suggestive.

One can criticize various aspects of the TGD vision about both ordinary and M₈₉ hadron physics. This is good for the simple reason that counter arguments are the best manner to make progress if one is on the right track.

TGD SUSY is also in central role if one believes that higher pion like states are there and have an explanation in terms of SUSY. 25 GeV pion like state would be apart from mixing effects spion consisting of squark pair. The assumption is that SUSY is essentially unbroken and that mixing of the quarks implies that mass squared matrix is non-diagonal having element between meson and smeson states.
1. The first possibility is that second eigenstate is tachyonic due to very strong mixing proportional to α_s and must be excluded from the spectrum.
2. Second - aesthetically more attractive- option is that second eigenstate indeed is there and quite recently I indeed found evidence for narrow resonances with quantum numbers of pion with mass differences between states typically in the range 10-40 MeV. Some of these might be SUSY states.
The experimental evidence suggests that pion has satellites but that their number is much larger than SUSY alone predicts. but that their number is much larger than SUSY alone predicts. The bumpy structure of Higgs-like signal cross section suggests the same for M₈₉ hadron physics. There are two alternative but not mutually exclusive explanations. The color magnetic flux tubes for light quarks have length of the order of Compton length and one could assign to them a string tension and IR Regge trajectories. Another explanation would be in terms of Shnoll effect implying that probability distributions with single peak decompose to distribution with several peaks. The TGD based explanation of Shnoll effect suggests that it is universal and could take place even at the level of particle physics.
A strong objection against TGD SUSY is that there is no missing energy signal which should result from the decays of squarks to quark and spartner of W boson decaying in turn to lepton and sneutrino. This objection forces to consider a possible modification of the recent belief system. The covariantly constant right handed neutrino could act as super gauge symmetry annilating physical states. This reduction of SUSY is standard mechanism of SUSY breaking. The color octet CP₂ partial wave of right handed neutrino would generate superpartners. Color confinement would eliminate the decays producing right handed sneutrinos as missing energy. What would be nice is that leptohadrons could be interpreted in terms of color octet sleptons (dark in TGD sense)TGD SUSY would be realized in a similar manner both for leptons and quarks and would have been discovered for decades ago. This is of course a speculation and p-adic mass calculations should be carried out to check whether this proposal really works.

I do not bother to type more and encourage the reader to find the details in the article Higgs or M₈₉ hadron physics? or the chapter New Particle Physics Predicted by TGD: Part I of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".

LHC releases data about new particle but is it Higgs?

2011-12-14T03:16:00.001-08:00

The newest results about Higgs search using 4.9/fb of data were published yesterday and there are many articles in arXiv. The overall view is that there is evidence for something around 125 GeV. Whether this something is Higgs or some other particle decaying to Higgs remains to my opinion an open question. Lubos of course is strong in this faith on Higgs. Somewhat surprisingly Tommaso Dorigo seems the result as a firm evidence for Higgs. Matt Strassler is skeptic. The evidence comes basically from Higgs to γγ decays. There are some ZZ and WW events. CMS represented also data for more rare events. There are also indications about something at higher masses and the interpretation of them depends on the belief system of the blogger.

Bloggers were very active and Phil Gibbs certainly the most active one.

Phil Gibbs gave online comments and combinations of various data in his blog. In particular, Phil produced a combination of data from ATLAS, CMS, LEP, and Tevatron clearly supporting the existence of bump around 124 GeV. Also the other plots by Phil are very illustrative of the situation: for instance this.
Tommaso Dorigo commented the results. Tommaso gives many illustrations and sees the results as firm evidence for standard model Higgs and is skeptic about SUSY Higgs.
Lubos Motl has a nice -albeit over-optimistic from SUSY point of view - summary about the results and useful links to the articles by ATLAS and CMS.
I liked very much about Matt Strassler's critical comments making clear what is known and what is not known.
Also Resonaances had added comments on Higgs. And many other bloggers.

Overall view

It is good to try to summarize what has been found.

According to ATLAS the bump is at 126 GeV. Altogether gamma-gamma and ZZ events give 3.6 sigma deviation reducing to 2.3-2.5 sigma by look-elsewhere effect.
According to CMS the bump resides at 124 GeV. CMS has 2.6 sigma deviation reducing to 1.9 sigma when look- elsewhere effect is taken into account.
The positions of bumps reported by ATLAS and CMS are not quite same so that there is still room for the possibility that the bumps are artifacts.
Both collaborations publish also the results about signal for Higgs to ZZ decays. Fig 7 in ATLAS eprint reports three candidates Higss to ZZ events at 123.6 GeV, 124.3 GeV , and 124.8 GeV. CMS reports results about decays to bbbar, ττbar, WW, ZZ, γγ, combines the data from various channels, and compares signal cross sections to those predicted by standard model Higgs. There is structure around 145 GeV in some channels. There is also data about higher energies bump like structures both below and above 300 GeV. Maybe the standard model Higgs is not enough. SUSY indeed predicts several Higgs like states and M₈₉ hadron physics entire meson spectroscopy.

γγ channel

Both ATLAS and CMS have published an reprint in arXiv about Higgs to γγ signal.

The ratio of the γγ signal cross section to the cross section predicted by standard model is given together with 1 and 2 sigma bands describing the background signal without Higgs contributions.

Fig 8 ATLAS paper gives the observed and expected 95 per cent confidence level limits as a function of hypothesized Higgs boson mass.
Fig 3 of CMS paper gives bump around 124 GeV.

I wish that I could understand the strange oscillating behavior for the ratio of signal cross section to cross section for signals mimicking Higgs predicted in absence of Higgs. There are bumps around 126 GeV, 139 GeV and 146 GeV. Is this an artifact produced - say - by a discretization in the data processing. There is also a small bump around 113 GeV.

I am a statistical dilettante so that I can make an innocent and possibly stupid question: Could these bumps be something real? For standard model Higgs this is certainly not the case but what about TGD inspired view about new physics at LHC. Going to another extreme: could all bumps with 126 GeV bump included be only data processing artifacts? We do not know yet.

Also the probability p₀ that standard model without Higgs could explain the signal cross section is plotted.

Fig 7 of ATLAS paper gives observed and expected p₀ values as a function of the mass of hypothesized Higgs. Small p₀ tells that standard model without Higgs contribution requires upwards fluctuation whose probability is p₀ to explain the observed signal. There are strong downwards bumps at about 126 GeV and around 145 GeV. They are deeper than the prediction of standard model Higgs which might give rise to worries. There is also something very small at 139 GeV.
Fig 4 of CMS paper gives similar plot. Now the bumps of p₀ are around 123.5 GeV, 137 GeV, and 147.5 GeV.

If taken at face value, also these figures suggest three-bump structure. This might well be a statistical artifact but one can make questions and one fool like me can make more or them than the wise guys are able to answer. Here are two of them.

Could M₈₉ pion have higher excitations with a mass scale of 10-20 GeV? Could the pion-like state generating the signal besides ground state also excitations with excitation energy scale of order 20 GeV? Could these excitation assigned with the magnetic flux tube structures associated associated with scaled up u and d quarks.
A rough guess for the p-adic prime of scaled up u and d quark in M₈₉ hadron is k=113-18= 95 (k=113 corresponds to Gaussian Mersenne and nuclear p-adic length scale). This corresponds to the p-adic mass scale the estimate 16 GeV from electron's p-adic mass scale about .25 MeV. It however turns out that the actual mass must be by a factor two higher so that one would have 32 GeV mass scale.
Could stringy excitations with string tension determined by 32 GeV scale be in question? If so then also ordinary pion should have similar fine structure in mass spectrum with energy scale of 31 MeV assignable with u and d quarks with k=113. I have a vague memory that Tommaso Dorigo had reported something about low energy excitations of pion but I failed to find anything about this in web and concluded that I must have been hallucinating.
Shnoll effect is something which main stream colleagues certainly refuse to take seriously. In TGD framework one can develop a p-adic model for Shnoll effect which can be justified in terms of quantum arithmetics giving a first principle justification for the canonical identification playing a key role in p-adic mass calculations. The model predicts a number theoretic deformation of probability distributions characterized p-adic prime p. The modification replaces the rational valued parameters of distribution by quantum rationals. Typically a probabiity distribution with single bump decomposes to several ones and the phenomenon occurs also in nuclear physics.
Could this deformation be at work even in particle physics? If so, it could cause the splitting of single very wide resonance bump around 125 GeV to several sharper bumps. Even the bump like structure at 113 GeV could correspond to this wide resonance bump. The original resonance bump could be rather wide: something like 30-40 GeV. Very naive guess would be that the width of leptopion obeys able to decay to ordinary quarks Γ ∼ α_s(89) m(π₈₉). Already for α_s=.1 one could have a bump with width of about 15 GeV. For ordinary pion the impossibility of strong decays would not allow Shnoll effect. The splitting into sub-bumps by Shnoll effect would make this wide bump visible.

After a painful web search I managed to find an article titled Search for low-mass exotic mesonic structures: II. Attempts to understand the experimental results reporting that there is experimental support for narrow excited states of pion at masses 62, 80, 100, 140, 181, 198, 215, 227.7, and 235 MeV (authors mention that the last might be uncertain). The states at 100, 140, and 198 MeV are half octaves of the lightest state. The article fits the states to Regge trajectories but it is not possible to use single slope for all states. The mass differences vary between 10 and 40 GeV so that the scale is what one would expect from the above string argument. Also Shnoll effect might explain the existence of the bumps and if the explanations are consistent the spectrum of the pion states is dictated by number theoretical arguments to a high degree.

Combination of signals from all channels

CMS has also a preprint about the combination of signals from all decay channels of Higgs.

CMS gives also a figure combination of all CMS searches (γγ, bbbar,ττbar, WW, ZZ).
Figure 1 of CMS article shows a clear structure around 124 GeV. There is another structure around about 145 GeV. In standard model Higgs scenario the structure at 145 GeV would not be taken seriously since the cross section need to produce the bump would be much below the predicted one but if one accepts super-symmetric M₈₉ hadron physics, the situation changes. There is also structure around 325 GeV and in the range 260-285 GeV. M₈₉ hadron physics would assign these structures to vector mesons ρ and ω₈₉ and corresponding smesons consisting of squark and anti-squark.
CMS gives a plot comparing the ratio of best fit for signal cross section to the predicted cross section for Higgs to bbar, ττbar, γγ, ZZ, WW. The fit is rather satisfactory: for Higgs to γγ the signal cross section is about 1.7 times higher than predicted. One cannot deny that this can be seen as a strong support for standard model Higgs.
The original idea behind M₈₉ hadron physics was that it effectively replaces Higgs. If one takes the CMS result seriously this idea must be realized rather concretely: the predicted signal cross sections must be rather near to those predicted by standard model Higgs. The crucial tests are decay rates to fermion pairs and the possibly existing other resonances.

Higgsy character of 126 GeV bump is not proven!

Lubos has written a new post were he makes the strange assumption that if there is a signal it must be Higgs. Lubos also uses as a "proof" of Higgsyness the fit of Phil for which the gamma-gamma signal cross section at maximum equals to the prediction. This holds true because the fit forces it to hold true! For some reason Lubos "forgets" this!

By inspecting the figure more closely one finds that the observed cross section has a long tail unlike the predicted cross section. This long tail could correspond to the large width of resonance splitting into sub-bumps if Shnoll effect is present. If Higgs option is correct, this tail should disappear as statistics improves. Also the other structures which are present, should disappear.

What is of course remarkable that CMS paper shows that H→ γγ cross section is of the same order of magnitude and only about 1.7 times higher than the predicted cross section. This gives a constraint on M₈₉ hadron physics, which it of course might fail to satisfy unless the idea about replacement of Higgs with M₈₉ hadron physics is true at a rather quantitative level.

One should also keep in mind that the value of Higgs mass is at the lower bound for the range with stable Higgs vacuum. This is not a good sign. An interesting question is whether the mass for pion-like state of M₈₉ hadron physics is in some sense also minimal and what this minimality could mean physically: some kind of criticality - maybe on instance of quantum criticality of TGD Universe- but not criticality against the decay of Higgs vacuum?

To sum up, one can agree with the official statement: the situation remains open. What is nice that there very probably is a signal and from TGD point view the nice thing is that this signal is still consistent with M₈₉ hadron physics.

About latest Higgs rumors

2011-12-09T22:03:00.000-08:00

According to the latest rumors the mass of Higgs is now around 125 GeV. Lubos has in fact declared that Higgs has been aready found and sees this as a vindication for standard SUSY. It is good that Tommaso Dorigo took a stance on the Higgs issue: see the posting How wrong Lubos can be. I have noticed many times earlier the tendency of Lubos to fabulate.

According to Lubos, CMS has evidence for Higgs at 124 GeV and ATLAS at 126 GeV. From the posting of Tommaso providing a very useful glossary for those willing to understand the Tuesday seminar Lubos concludes that CMS will announce evidence for Higgs at 124.6 GeV. There is still a discrepancy in the mass values but Lubos takes the average of masses and produces also some sigma talk to convince himself that Higgs has been found.
What might have been found could be evidence that the spectrum of invariant mass for gamma pairs has a bump around 124.6 GeV in CMS and 126 GeV at ATLAS. The pairs would have been selected in such a manner that they are consistent with production mechanisms for Higgs bosons mentioned also by Tommaso. The decays of Higgs could produce gamma pairs via annihilation to a virtual W/Z/fermion pair annihilating to gamma pair. A jet pair associated with bbar is second and very characteristic signature of light Higgs decay (decays to ttbar are kinematically forbidden and decays to lighter quark pairs much slower).
Tommaso listed the dominant production mechanisms for Higgs. Vector boson fusion involves emission of W or Z boson by protonic quarks (quarks do not scatter first) followed by the fusion of the bosons to Higgs: the signature is two jets assignable to the protonic quarks. In gluon fusion parton in both protons emits gluon and gluons annihilate to ttbar pair annihilating to Higgs: there are no quark jets now since gluons are massless. In associated production the simplest situation involves the scattering of quarks belonging to protons by gluon exchange followed by the emission of W of Z boson emitting the Higgs. Direct emission of Higgs by a protonic quark is a slow process since the probability that proton could contain t-quark as a sea quark is very small.

Suppose that some evidence for a bump around 125 GeV in the invariant mass of gamma pair and/or jet pair assignable to bbar pair is reported in next Tuesday. Should I fall into despair and admit that whole TGD is crap as my wiser colleagues have patiently tried to tell me all these years? Not at all!

Evidence for gamma pairs would tell us that there might be a neutral particle with these decay signatures. Only this. TGD "almost-predicts" what I call M₈₉ hadron physics. Indications for this new branch of physics have been accumulating during this year. Neutral M₈₉ pion would have mass around 139 GeV and there has been a lot of n-sigma talk about indications for a neutral particle around this mass but now totally forgotten (the memory span of bloggers is fantastically short!). Charged π₈₉ would have mass around 144 GeV and might have something to do with CDF anomaly.
SUSY in TGD sense would allow quarks and squarks to have the same p-adic mass scale and even mass. This would predict both pion and spion which would smix with each other by gluino exchange meaning that mass squared matrix has non-diagonal component. The mass squared eigenstates would have different masses. The possibly existing mostly spion-like state at 125 GeV could correspond to the second eigen state (maybe some of us remembers that there was something around 119 GeV too).
The mixtures of M₈₉ pion and spion would decay to gamma pair just like ordinary pion does. Second decay mechanism would be the decay to uubar pair or ddbar pair producing two jets. For Higgs boson the outcome is two jets from bbar pair. This is a very strong signature distinguishing between TGD and standard model. If jet pairs formed from bbar pair are found around 125 GeV invariant mass, I must be able to invent a good explanation.
All production mechanisms involve four vertices some of which are weak and some strong. Vector boson fusion and gluon fusion could serve as production mechanisms also now. W/Z/gluon from both quarks of protons ( no gluon exchange between quarks) would annihilate to a quark/squark pair fusing to π₈₉/its spartner. Gluon fusion is the fastest mechanism (4 strong vertices). Associated production does not make sense now. It is however possible that either of the scattered quarks (gluon exchange) emits Z boson decaying to quark/squark pair fusing to π₈₉/its spartner. 2 strong and 2 weak vertices are involved as also in vector boson fusion. Quarks of protons scatter by gluon exchange and either of the scattered quarks emits gluon decaying to quark/squark pair. Second quark emits gluon and the resulting quark pair fuses to π₈₉/its spartner: gluon emission is necessary in order to obtain color singlet. 5 strong vertices are involved where as gluon fusion involves only 4 strong vertices.

How could one distinguish between Higgs hypothesis M₈₉ hadron physics hypothesis?

I mentioned already the jet pair from bbar pair in the case of Higgs and jet pairs from uubar or ddbar in the case of M₈₉ hadron physics. Already now data about bbar jets might exist.
As discussed in viXra blog, Higgs in the range 130-150 GeV would give a strong virtual ZZ signal producing four-lepton state. The decays of M₈₉ pion proceed mostly as strong decays so that ZZ states could be too rare to serve as a signal. It is however quite possible that ZZ and also WW signal is there just like gamma pair signal: the production mechanism for these signals would be very similar. Some rumors tell that ZZ signal has not been observed. Other rumors tell that there are some events for the rumored 125 might-be-Higgs. The rumored absence of ZZ and WW signals above 130 GeV would not favor Higgsy interpretation for 144 GeV bump (if it really exists) but supports the interpretation as M₈₉ pion.
The Higgs of standard model has only neutral component whereas pion and spion would have also charged components. One could search for charged partners of the mixtures of pion and spion. The decay signature analogous to gamma pair would be Wγ pair with the invariant mass of charged spion: probably the mass of charged spion would be slightly higher than that of neutral spion: few GeV is the scale of splitting from obtained from the mass splitting of ordinary pion by multiplying with the p-adic scale factor 512. Second decay would be to udbar pair or dubar pair producing two jets.
The fastest production mechanism for charged spions would necessarily involve W boson emission. The scattered quarks (gluon exchange) of colliding protons emits W annihilating to a quark/squark pair fusing to form a charged pion/spion (2 strong and 2 weak vertices). The analog of vector boson fusion would involve 4 weak vertices and be slower.

If ATLAS and CMS have concentrated their efforts solely in searching for the neutral Higgs, they will not have detected anything with these signatures. The belief on neutral Higgs means also that bbar jet pairs are sought for so that the uubar and ddbar jets would have been missed. One might hope that these groups are forced to look for signatures of charged Higgs like particles in not too remote future. In any case the important point is that ATLAS and CMS can only tell about the existence of a signal. Whether it is Higgs or something else remains open at this moment.

Unfortunately, too many bloggers have decided that if something is there, it must be Higgs. Also many theorists - for instance string theorist Gordon Kane have rushed to "predict" Higgs with mass that it should have on basis of rumors. Postdiction is not prediction but with a lot of good luck it might guarantee visit to Stockholm.

About blog etiquette

2011-12-09T01:31:00.000-08:00

For me blog is one of the very few communication channels that I have in the harsh academic world suffering of ethical and moral decline. I have no intention to serve as a popularizer of science: these kind of activities are for the retired professors who have a lot of spare time. I do my best to communicate the development of a theory which has a very high level of conceptualization. The reader willing to understand what I am really talking about must have a strong background in mathematics and physics. In absence of this background my text might look like random sequences of strange scientific sounding words. This could encourage some readers to what I would call free science- babble. This is not my purpose but I have however sometimes the unpleasant feeling that exactly this is what happens. This troubles me. Really.

My blog policy has been quite liberal. I have censored out only personal insults and have been forced to do this only a couple of times. There was also a systematic attempt to fill the blog with trash after the discovery of super-luminal neutrinos - maybe some colleague lost the health of his mind - but otherwise I have avoided blog terror.

I am not alone with my problem. In non-moderated blogs the discussions usually tend to transform to a total cacophony. Only few comments are needed before practically complete cognitive thermalization is achieved. There are too many participants who only want to demonstrate their cleverness. There are also those who just happened to enter the blog and - like dogs- want to leave some signature about their presence. Most participants probably have no intention to act as blog terrorists but as a rule they seem to forget completely what the topic was. Sometimes it seems that they do not even have idea about the notion of "topic".

Moderation is the manner to avoid this but it takes time and my personal problem is that deleting a post is for me like stealing a lollipop from a 5-year old: I always tend to think that the commentator is like an innocent 5-year old with good intentions even if he/she is talking about something not even remotely related to the contents of the posting. With a healthy dose of paranoia I might think that the sole goal of the commentator is to find the limits of the blogger's patience.

So: my personal humble request is that those who make comments would try to remember two simple instructive basic rules.

If you have nothing to say, no-one demands you to say it!
Posting is always about some topic. Why not to stay in that topic!

Thank you!

Addition (off-topic):. Sascha Vongehr has a nice posting about the latest rumor about evidence for Higgs with mass about 125 GeV. This mass is near to the mass causing the instability of Higgs vacuum. This opens up the possibility for a catastrophic cosmic event in which vacuum- carrying the energy of Higgs field - explodes releasing huge amounts of energy. This event would be analogous to the formation of bubble of radiation in inflationary scenario. This sounds strange. Is the problem with the Universe or with the theory? Usually it is with the theory. Who still remembers the mini blackholes at LHC predicted by some string theorists?

If no Higgs exists, the cosmic problem disappears and we can concentrate worrying about much smaller catastrophes like the fate of euro and the climate change. Remember also that the mass range around 125 GeV corresponds to the most difficult portion of the mass range concerning the discovery of the Higgs (decays to ZZ pairs are not possible). Around 125 GeV the exclusion of Higgs requires the hardest effort. Maybe Kea and this TGD guy will be remembered as saviors of the world from the gloomy fate in hands of nasty fairies;-).

QCD and TGD

2011-12-08T01:03:00.000-08:00

During last week I have been listening some very inspiring Harward lectures relating to QCD, jets, gauge-gravity correspondence, and quark gluon plasma. Matthew Schwartz gave a talk titled The Emergence of Jets at the Large Hadron Collider. Dam Thanh Son's talk had the title Viscosity, Quark Gluon Plasma, and String Theory. Factorization theorems of jet QCD discussed in very clear manner by Ian Stewart in this talk titled Mastering Jets: New Windows into Strong Interaction and Beyond.

These lecture several blog postings and also inspired the idea about a systematical comparison of QCD and TGD. This kind of comparisons are always very useful -at lest to myself - since they make it easier to see why the cherished beliefs- now the belief that QCD is the theory of strong interactions - might be wrong.

There are several crucial differences between QCD and TGD.

The notion of color is different in these two theories. One prediction is the possibility of lepto-hadron physics involving colored excitations of leptons.
In QCD AdS/CFT duality is hoped to allow the description of strong interactions in long scales where perturbative QCD fails. The TGD version of gauge-gravity duality is realized at space-time level and is much stronger: string-parton duality is manifest at the level of generalized Feynman diagrams.
TGD form of gauge-gravity duality suggests a stronger duality: p-adic-real duality. This duality allows to sum the perturbation theories in strong coupling regime by summing the p-adic perturbation series and mapping it to real one by canonical correspondence between p-adics and reals. This duality suggests that factorization "theorems" have a rigorous basis basis due to the fact that quantum superposition of amplitudes would be possible inside regions characterized by given p-adic prime. p-Adic length scale hypothesis suggests that p-adically scaled up variants of quarks are important for the understanding of the masses of low lying hadrons. Also scaled up versions of hadron physics are important and both Tevatron and LHC have found several indications for M₈₉ hadron physics.
Magnetic flux tubes are the key entities in TGD Universe. In hadron physics color magnetic flux tubes carrying Kähler magnetic monopole fluxes would be responsible for the non-perturbative aspects of QCD. Reconnection process for the flux tubes (or for the corresponding strings) would be responsible for the formation of jets and their hadronization. Jets could be seen as structures connected by magnetic flux tubes to form a connected structure and therefore as hadron like objects. Ideal QCD plasma would be single hadron like objects. In QCD framework quark-gluon plasma would be more naturally gas of partons.
Super-symmetry in TGD framework differs from the standard SUSY and the difficult-to-understand X and Y bosons believed to consist of charmed quark pair force to consider the possibility that they are actually smesons rather than mesons. This leads to a vision in which squarks have the same p-adic length scale as quarks but that the strong mixing between smesons and mesons makes second mass squared eigenstate tachyonic and thus unphysical. This together with the fact that shadronization is a fast process as compared to electroweak decays of squarks weak bosons and missing energy would explain the failure to observer SUSY at LHC.

I do not bother to type more and encourage the reader to find the details in the article QCD and TGD or the chapter New Particle Physics Predicted by TGD: Part I of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy".

Duff defends M-theory

2011-12-07T19:59:00.000-08:00

Michael Duff introduced first supermembranes as generalizations of superstrings in the late 1980s. It perhaps deserves to mention that I had ended up with 3-surfaces as generalizations of strings towards end of 1977 and published my thesis 1982 - much before Duff. This of course does not matter in the records since I am a a pariah in the community.

Now Duff has written a defense of M-theory. Peter Woit does excellent job in criticizing the defense and I do not have much to add. The time of superstring theory is now over and it is quite understandable that the members of the collapsing hegemony express their frustration.

As a brahmin of science Michael Duff does not forget to mention that the pariah deserve their position in the community.

Lisi has got three pages and one can wonder how he relates to the defense of string theory: that Lisi's theory has been a media fashion for 15 minutes does not provide any support for super string theory.
The basic claim of the hegemony has been for all these years that there are no known competitors for the M-theory: it is the only game in the town. Duff formulates this claim as a rhetoric question
It is really the case that there are brilliant loners out there and that there is some kind of conspiracy by the physics “establishment” to prevent their voices being heard?.
The gist of the answer is easy to guess. If there had been some competing ideas deserving to be taken seriously, he would certainly have noticed them during these 40 years.
Duff does not forget to mention that viXra is needed: it demonstrates that crackpots are crackpots. It is of course important to ridicule viXra since for pariah's like me viXra is one of the very few communication channels.
Duff of course mentions homeopathy and UFOs. It is always a good trick to make this association when one speaks of competing approaches. In particular TGD: I have indeed proposed a model of water memory for which the discoveries by the research group led by HIV nobelist Montagnier gave a strong support (see this). It is also easy to find in web a concrete visual proof for water memory by a group of science professionals. But this does not of cause matter: "homeopathy" and "water memory" are really scaring words and any-one who might have been ready to consider even the possibility of water memory is next to witch!

There is no need to tell intelligent reader that all this is standard rhetoric made possible by the ethical decline in Big Science. How on earth Duff could know anything about alternative approaches to the unification? Like other string theorists he has lived a sheltered life of a superstring professor in practically compete isolation from the dirty empirical reality - or low energy phenomenology as they would express it. The results from LHC challenging the basic assumptions of both GUTs and string theory demonstrate how far from experimental reality these people in their ivory towers have receded. Could these fellows really have used their spare time in web searching for alternative unifications and studying them keenly? Just try to imagine these respected professors in the act of intensely studying papers of alternative thinkers!

To my opinion the best thing that could happen to super string community would be a dramatic reduction of the funding. To some degree this reduction has already taken place. Only those who really believe in string theory and have really something non-trivial to say would be ready to continue without funding.

Higgs and me

2011-12-05T22:34:00.000-08:00

We have been told that a seminar to be held 13 December in CERN will represent results making possible a significant progress in Higgs research but that no answer to the question about the existence of Higgs exists will be provided. This could be the only politically correct manner to say that no Higgs has been found nor will be found. There might be however something else there as TGD indeed predicts. Therefore I feel that it is good time to clarify my own views about the Higgs issue.

My attitude to Higgs has developed from original denial to almost acceptance and back to denial. This denial has nothing to do with bets: anyone can bet that Higgs exists or does not exist. Without genuine justifications this kind of statements contain just single bit of information or disinformation.

Denying Higgs

My original attitude was a denial based on following arguments natural in sub-manifold gravity.

TGD does not allow Higgs as a scalar in 8-D sense: this state would be leptoquark: Minkowski scalars are always H-vectors and have generalized polarization.
If Higgs is there it should behave like a SO(4) vector in CP₂ tangent space with different directions analogous to polarizations. One can have 3+1 decomposition for tangent vectors of CP₂ under electro-weak SU(2) but the problem is that there is no manner to build covariants or invariants in this manner. CP₂ does not allow covariantly constant vector fields. The contractions of color isometry generators with the trace of second fundamental form would be general coordinate invariants but would give a color octet rather than complex electro-weak doublet (triplet plus singlet would results only if one identifies U(2) ⊂ SU(3) as electroweak gauge group).
The contractions of CP₂vierbein vectors with the trace of the second fundamental form would give a candidate for Higgs and its contraction with CP₂ gamma matrices appears in the Dirac equation for induced spinor fields and makes it inconsistent unless the trace of the second fundamental form and thus Higgs vanishes (minimal surface property). For non-minimal surfaces this identification would make Higgs contribution to mass square tachyonic. Thus this identification is not promising.
Higgs is not needed to give mass for fermions since p-adic thermodynamics takes care of this. There are however some problems in the understanding of gauge boson masses. Some additional sources of mass seem to be necessary: p-adic thermodynamics in its basic form would give extremely small second order contribution to the gauge boson masses since the inverse integer valued p-adic temperature cannot be larger than T=1/2. For fermions one has T=1.

For these reasons I believed for a long time that TGD does not predict Higgs. I could have promoted this as a dramatic prediction of sub-manifold gravitation.

Could Higgs exist after all?

The last five years in blogs have been endless n-sigma talk related to rumors about Higgs and also now this kind of rumors are around. As a genuine skeptic I became skeptic also about my basic belief and asked whether Higgs might exist also in TGD Universe. I had also to understand the additional contribution to the mass of gauge bosons and how gauge bosons get their additional polarization state. Maybe Higgs might be necessary to achieve this. The identification of the basic objects as wormhole throats and contacts carrying quantum numbers was a decisive step of progress. The irony was that the progress began with the idea that Higgs could correspond to wormhole contact! Only later came the realization that this makes sense also for gauge bosons.

Free fermions are in this picture wormhole throat pairs and topological condensation makes them massive. The throats formed in the topological condensation of fermions have vanishing magnetic charge. One has throat pair at both sheets but only the members of the second pair are connected by a Kähler magnetic flux tube.
Bosonic emergence means that bosons consist of bound states of massless on mass shel fermion and anti-fermion associated with wormhole throats of wormhole contacts connecting space-time sheets. Also virtual particles consist of massless on mass-shell states in ZEO. Also bosons consist of two wormhole contacts since the total monopole charge must vanish. The throat pairs at both sheets are connected by Kähler magnetic flux tubes carrying monopole magnetic flux. Neutrino pair at the second wormhole throat neutralizes weak isospin for both bosons and fermions.
Kähler magnetic flux tubes contribute to the mass of the particle stringy contribution. For elementary fermions the contribution from wormhole throat pair carrying fermion quantum numbers dominates the mass. In the case of hadrons the reconnection process for color magnetic flux tubes is responsible for non-perturbative aspects of hadron physics and making possible to understand what happens in the formation of jets and in hadronization. The physics in question involves new physics: contrary to the general belief jet QCD does not follow from QCD as QFT. Color magnetic flux tubes make themselves visible via what has become known as quark-gluon plasma. This terminology is misleading and based on wrong expectations: the attribute "strongly interacting" does not help much. In TGD Universe the ideal quark-gluon plasma in TGD is like a big hadron containing very many quarks and gluons rather than gas of partons as it would be in QCD proper.
In TGD the possibly existing Higgs 4-plet would have same quantum numbers as electro-weak gauge bosons 3+1 as SU(2) multiplets. There would be a nice 1-1 correspondence between Higgses and gauge bosons in CP₂ degrees of freedom. Only spin would be different. Sub-manifold gravity would be at work again.
Higgses could be there but gauge bosons would eat them to get longitudinal polarizations. All Higgs components would become longitudinal polarizations of Higgs boson. Also gauge bosons which are usually regarded a massless would have a small mass. Same applies to graviton and all super-partners. The assumption that all physical particles have at least small mass resolves the infrared singularities and there are excellent hopes about a beautiful realization of twistorial approach in zero energy ontology (ZEO).

The problem is that one must postulate a lot of Higgs like particles and also their super-partners. And all of them would be eaten. Why the trouble of preparing all these Higgses if all of them end up to the plate?

Return to Higgs denialism

Now I am becoming a Higgs denialist again. There is no need for Higgs in TGD and TGD does not allow any natural mechanism transforming Higgs like states to longitudinal components of gauge bosons.

In ZEO just the condition that boson has spin 1 implies that it is massive and has therefore also the third polarization. The argument is simple: if one wants the composite system of on mass shell massless fermion and antifermion to have helicity 1 one must assume that either the 3-momenta or energies have opposite sign or at least that the directions of 3-momenta are different. There is no need to assume that gauge bosons get the additional polarization state by eating Higgs. This applies to all states with spin.
The recent advances in the formulation of generalized Feynman diagrams (see this) lead to the identification of the analog of the gauge condition eliminating unphysical polarizations. This condition allows three polarizations in the case of spin 1 states. Analogous conclusion applies in the case of higher spins.
One can express the condition on polarizations more precisely. One can assign to each causal diamond (CD) a preferred sub-manifold M² (2-D Minkowski space) of M⁴ defining preferred time direction and spin quantization axis: the are many choices and these correspond to non-equivalent CDs. This 2-plane defines the analog for the plane in which Feynman graphs live and allows to realize the vision about generalized Feynman graphs as sub-manifold braids. M² corresponds in the number theoretical vision to hyper-complex numbers regarded as a 2-plane in the space of hyper-octonions.
The gauge condition p• ε=0 is modified. The modified condition says that the allowed polarization vectors are orthogonal to the projection p_M² of the momentum of boson to M²: p_M²• ε=0. Three polarization states are allowed instead of 2. All physical particles with spin are massive.

The conclusion is simple: no Higgs like states are needed! Just as I believed in the beginning. The prodigal son has returned back to his home! For reasons easy to understand, I am waiting eagerly the December 13:th. We know that 13 is the unlucky number but who will be the unlucky one? Higgs or me?

For more about Higgs see the chapter New Physics Predicted by TGD: Part I of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy". For background see also article Algebraic braids, sub-manifold braid theory, and generalized Feynman diagrams or the new chapter Generalized Feynman Diagrams as Generalized Braids of "Towards M-matrix".

Quark-gluon plasma in TGD Universe

2011-12-03T20:30:00.000-08:00

I listened an excellent talk by Dam Thanh Son in Harward Monday seminar series. The title of the talk was Viscosity, Quark Gluon Plasma, and String Theory. What the talk represents is a connection between three notions which one would not expect to have much to do with each other.

I decided to briefly summarize the basic points of Son's talk which I warmly recommend for anyone wanting to sharpen his or her mental images about quark gluon plasma.

I realized that the TGD variant of AdS/CFT correspondence based on string-parton duality allows a concrete identification of the process leading to the formation of strongly interacting quark gluon plasma.
"Strongly interacting" means that partonic 2-surfaces are connected by Kähler magnetic flux tubes making the many-hadron system single large hadron in the optimal case rather than a gas of uncorrelated partons. This allows a concrete generalization of the formula of kinetic gas theory for the viscosity.
One ends up also to a concrete interpretation for the formula for the η/s ratio in terms of TGD variant of Einsteinian gravitation and the analogs of black-hole horizons identified as partonic 2-surfaces. This gravitation is not fictive gravitation in 10-D space but real sub-manifold gravitation in 4-D space-time.
It is essential that TGD does not assume gravitational constant as a fundamental constant but as a prediction of theory depending on the p-adic length scale and the typical value of Kähler action for the lines of generalized Feynman graphs. Feeding in the notion of gravitational Planck constant, one finds beautiful interpretation for the lower limit viscosity which is smaller than the one predicted by AdS-CFT correspondence.

I do not bother to type all six pages here and instead recommend the reader to look at the article Algebraic braids, sub-manifold braid theory, and generalized Feynman diagrams or the new chapter Generalized Feynman Diagrams as Generalized Braids of "Towards M-matrix".

Duality between hadronic and partonic descriptions of hadron physics

2011-11-30T23:18:00.000-08:00

I found the talk of Matthew Schwartz titled The Emergence of Jets at the Large Hadron Collider belonging to the Monday Colloqium Series at Harward. The talk told about the history of the notion of jet and how it is applied at LHC. The notion of jet is something between perturbative and non-perturbative QCD and therefore not a precisely defined concept as one approaches small mass limit for jets.

The talk inspired some questions relating to QCD and hadron physics in general. I am of course not competent to say anything interesting about jet algorithms. Hadronization process is however not well understood in the framework of QCD and uses phenomenological fragmentation functions. The description of jet formation in turn uses phenomenological quark distribution functions. TGD leads to a rather detailed fresh ideas about what quarks, gluons, and hadrons are and stringy and QFT like descriptions emerge as excellent candidates for low and high energy descriptions of hadrons. Low energies are the weakness of QCD and one can well ask whether QCD fails as a physical theory at infrared. Could TGD do better in this respect?

Only a minor fraction of the rest energy of proton is in the form of quarks and gluons. In TGD framework these degrees of freedom would naturally correspond to color magnetic flux tubes carrying color magnetic energy and in proton-proton collisions the color magnetic energy of p-p system in cm system is gigantic. The natural question is therefore about what happens to the "color magnetic bodies" of the colliding protons and of quarks in proton-proton collision.

In the sequel I will develop a simple argument leading to a very concrete duality between two descriptions of hadron reactions manifest at the level of generalized Feynman graphs. The first description is in terms of meson exchanges and applies naturally in long scales. Second one is terms of perturbative QCD applying in short scales. The basic ingredients of the argument are the weak form of electric-magnetic duality and bosonic emergence leading to a rather concrete view about physical particles, generalized Feynman diagrams reducing to generalized braid diagrams in the framework of zero energy ontology (ZEO), and reconnection of Kähler magnetic flux tubes having interpretation in terms of string diagrams providing the mechanism of hadronization. Basically the prediction follows from the dual interpretations of generalized Feynman diagrams either as stringy diagrams (low energies) or as Feynman diagrams (high energies).

It must be emphasized that this duality is something completely new and a simple prediction of the notion of generalized Feynman diagram. The result is exact: no limits (such as large N limit) are needed.

Weak form of electric magnetic duality and bosonic emergence

The weak form of electric magnetic duality allows the identification of quark wormhole throats as Kähler magnetic monopoles with non-vanishing magnetic charges Q_m. The closely related bosonic emergence effectively eliminates the fundamental BFF vertices from the theory.

Elementary fermion corresponds to single wormhole throat with Kähler magnetic charge. In topological condensation a wormhole throat is formed and the working hypothesis is that the second throat is Kähler magnetically neutral. The throats created in topological condensation (formation of topological sum) are always homologically trivial since purely local process is in question.
In absence of topological condensation physical leptons correspond to string like objects with opposite Kähler magnetic charges at the ends. Topologically condensed lepton carries also neutralizing weak isospin carried by neutrino pair at the throats of the neutralizing wormhole contact. Wormhole contact itself carries no Kähler magnetic flux. The neutralization scale for Q_m and weak isospin could be either weak length scale for both fermions and bosons. The alternative option is Compton length quite generally - this even for fermions since it is enough that the weak isospin of weak bosons is neutralized in the weak scale. The alert reader have of course asked whether the weak isospin of fermion must be neutralized at all if this is the case. Whether this really happens is not relevant for the following arguments.
Whether a given quark is accompanied by a wormhole contact neutralizing its weak isospin is not quite clear: this need not be the case since the Compton length of weak bosons defines the range of weak interactions. Therefore one can consider the possibility that physical quarks have non-vanishing Q_m and that only hadrons have Q_m=0. Now the Kähler magnetic flux tubes would connect valence quarks. In the case of proton one would have three of them. About 31 year old proposal is that color hyper charge is proportional to Kähler magnetic charge. If so then color confinement would require Kähler magnetic confinement.
By bosonic emergence bosons correspond to wormhole contacts or pairs of them. Now wormhole throats have opposite values of Q_m but the contact itself carries vanishing Kähler magnetic flux. Fermion and anti-fermion are accompanied by neutralizing Kähler magnetic charge at the ends of their flux tubes and neutrino pair at its throats neutralizes the weak charge of the boson.

The dual interpretations of generalized Feynman diagrams in terms of hadronic and partonic reaction vertices

Generalized Feynman diagrams are defined in the framework of zero energy ontology (ZEO). Bosonic emergence eliminates fundamental BFF vertices and reduces generalized Feynman diagrams to generalized braid diagrams. This is essential for the dual interpretation of the qqg vertex as a meson emission vertex for hadron. The key idea is following.

Topologically condensed hadron - say proton- corresponds to a double sheeted structure: let us label the sheets by letters A and B. Suppose that the sheet A contains wormhole throats of quarks carrying magnetic charges. These wormhole throats are connected by magnetically neutral wormhole contact to sheet B for which wormhole throats carry vanishing magnetic charges.
What happens when hadronic quark emits a gluon is easiest to understand by considering first the annihilation of topologically non-condensed charged lepton and antilepton to photon - that is L+Lbar → γ vertex. Lepton and antilepton are accompanied by flux tubes at different space-time sheets A and B and each has single wormhole throat: one can speak of a pair of deformations of topologically condensed CP₂ type vacuum extremals as a correlate for single wormhole throat. At both ends of the flux tubes deformations of CP₂ type exremals fuse via topological sum to form a pair of photon wormhole contacts carrying no Kähler magnetic flux. The condition that the resulting structure has the size of weak gauge boson suggests that weak scale defines also the size of leptons and quarks as magnetic flux tubes. Quarks can however carry net Kähler magnetic charge (the ends of flux tube do not have opposite values of Kähler magnetic charge.
With some mental gymnastics the annihilation vertex L+Lbar → γ can be deformed to describe photon emission vertex L→ L+γ. The negative energy antilepton arrives from future and positive energy lepton from the past and they fuse to a virtual photon in the manner discussed.
qqg vertex requires further mental gymnastics but locally nothing is changed since the protonic quark emitting the gluon is connected by a color magnetic flux tube to another protonic quark in the case of incoming proton (and possibly to neutrino carrying wormhole contact with size given by the weak length scale). What happens is therefore essentially the same as above. The protonic quark has become part of gluon at space-time sheet A but has still flux tube connection to proton. Besides this there appears wormhole throat at space-time sheet B carrying quark quantum numbers: this quark would in the usual picture correspond to the quark after gluon emission and antiquark at the same space-time sheet associated with the gluon. Therefore one has proton with one quark moving away inside gluon at sheet A and a meson like entity at sheet B. The dual interpretation as the emission of meson by proton makes sense. This vertex does not correspond to the stringy vertex AB+CD→ AD+BC in which strings touch at some point of the interior and recombine but is something totally new and made possible by many-sheeted space-time. For gauge boson magnetically charge throats are at different space-time sheets, for meson they at the same space-time sheet and connected by Kähler magnetic flux tube.
Obviously the interpretation as an emission of meson like entity makes sense for any hadron like entity for which quark or antiquark emits gluon. This is what the duality of hadronic and parton descriptions would mean. Note that bosonic emergence is absolutely essential element of this duality. In QCD it is not possible to understand this duality at the level of Feynman diagrams.

Reconnection of color magnetic flux tubes

The reconnection of color magnetic flux tubes is the key mechanism of hadronization and a slow process as compared to quark gluon emission.

Reconnection vertices have interpretation in terms of stringy vertices AB+CD→ AD+BC for which interiors of strings serving as representatives of flux tubes touch. The first guess is that reconnection is responsible for the low energy dynamics of hadronic collisions.
Reconnection process takes place for both the hadronic color magnetic flux tubes and those of quarks and gluons. For ordinary hadron physics hadrons are characterized by Mersenne prime M₁₀₇. For M₈₉ hadron physics reconnection process takes place in much shorter scales for hadronic flux tubes.
Each quarks is characterized by p-adic length scales: in fact this scale characterizes the length scale of the the magnetic bodies of the quark. Therefore Reconnection at the level of the magnetic bodies of quarks take places in several time and length scales. For top quark the size scale of magnetic body is very small as is also the reconnection time scale. In the case of u and d quarks with mass in MeV range the size scale of the magnetic body would be of the order of electron Compton length. This scale assigned with quark is longer than the size scale of hadrons characterized by M₈₉. Classically this does not make sense but in quantum theory Uncertainty Principle predicts it from the smallness of the light quark masses as compared to the hadron mass. The large size of the color magnetic body of quark could explain the strange finding about the charge radius of proton.
For instance, the formation of quark gluon plasma would involve reconnection process for the magnetic bodies of colliding protons or nuclei in short time scale due to the Lorentz contraction of nuclei in the direction of the collision axis. Quark-gluon plasma would correspond to a situation in which the magnetic fluxes are distributed in such a manner that the system cannot be decomposed to hadrons anymore but acts like a single coherent unit. Therefore quark-gluon plasma in TGD sense does not correspond to the thermal quark-gluon plasma in the naive QCD sense in which there are no long range correlations.
Long range correlations and quantum coherence suggest that the viscosity to entropy ratio is low as indeed observed. The earlier arguments suggest that the preferred extremals of Kähler action have interpretation as perfect fluid flows. This means at given space-time sheet allows global time coordinate assignable to flow lines of the flow and defined by conserved isometry current defining Beltrami flow. As a matter fact, all conserved currents are predicted to define Beltrami flows. Classically perfect fluid flow implies that viscosity, which is basically due to a mixing causing the loss of Beltrami property, vanishes. Viscosity would be only due to the finite size of space-time sheets and the radiative corrections describable in terms of fractal hierarchy CDs within CDs. In quantum field theory radiative corrections indeed give rise to the absorbtive parts of the scattering amplitudes.

Hadron-parton duality and TGD as a "square root" of the statistical QCD description

The main result is that generalized Feynman diagrams have dual interpretations as QCD like diagrams describing partonic reactions and stringy diagrams describing hadronic reactions so that these matrix elements can be taken between either hadronic states or partonic states. This duality is something completely new and distinguishes between QCD and TGD.

I have proposed already earlier this kind of duality but based on group theoretical arguments inspired by what I call M⁸-M⁴× CP₂ duality and two hypothesis of the old fashioned hadron physics stating that vector currents are conserved and axial currents are partially conserved. This duality suggests that the group SO(4)= SU(2)_L× SU(2)_R assignable to weak isospin degrees of freedom takes the role of color group at long length scales and can be identified as isometries of E⁴ subset M⁸ just like SU(3) corresponds to the isometries of CP₂.

Initial and final states correspond to positive and negative energy parts of zero energy states in ZEO. These can be regarded either partonic or hadronic many particle states. The inner products between positive energy parts of partonic and hadronic state basis define the "square roots" of the parton distribution functions for hadrons. The inner products of between negative energy parts of hadronic and partonic state basis define the "square roots" of the fragmentations functions to hadrons for partons. M-matrix defining the time-like entanglement coefficients is representable as product of hermitian square root of density matrix and S-matrix is not time reversal invariant and this partially justifies the use of statistical description of partons in QCD framework using distribution functions and fragmentation functions. Decoherence in the sum over quark intermediate states for the hadronic scattering amplitudes is essential for obtaining the standard description.

For details and background see the article Algebraic braids, sub-manifold braid theory, and generalized Feynman diagrams or the new chapter Generalized Feynman Diagrams as Generalized Braids of "Towards M-matrix".

Eternal inflation and TGD

2011-11-29T05:09:00.000-08:00

The process leading to this posting was boosted by the irritation caused by the newest multiverse hype in New Scientist which was commented by Peter Woit. Also Lubos told about Brian Greene's The Fabric of Cosmos IV which is similar multiverse hype with Guth, Linde, Vilenkin, and Susskind as stars but also single voice of criticism was accepted (David Gross who could not hide his disgust).

The message of New Scientist article was that multiverse is now a generally accepted paradigm, that it follows unavoidably from modern physics and has three strong pillars: dark energy, eternal inflation, and the string model landscape. Even LHC has demonstrated its correctness by finding no evidence for the standard SUSY. That was the prediction of superstring models but then some-one realized that there had been some-one predicting that multiverse predicts no super-symmetry! As a matter fact, every single prediction inspired by super string models went wrong, there are good reasons to expect that Higgs will not be found, and standard SUSY has been excluded. Besides this an increasing amount of evidence for new physics not predicted by standard TOEs. And one should not forget neutrino super-luminality. All this shakes the foundations of both super-string theory, where GUT is believed to be the low energy limit of the theory with Higgs fields playing a key role. In inflationary scenarios Higgs like scalar fields carrying the vacuum energy give rise to radiation and therefore also ordinary matter.

The three pillars of the multiverse become catastrophic weaknesses if the Higgs paradigm fails. Vacuum energy cannot correspond to Higgs, the scalar fields driving inflation are not there, and one cannot say anything about possible low energy limits of super string theories since even the basic language describing them is lost!

Maybe I am becoming an old angry man but I must confess that this kind of hype is simply too much for me. Why colleagues who know what the real situation is do not react to this bullshit? Are they so lazy that they allow physics to degenerate into show business without bothering to do anything? Or does a culture of Omerta prevail as some participant in Peter Woit's blog suggested? Even if a man has seen a crime to take place, he is not allowed to reveal it. It he does, he suffers vendetta. I have experienced the academic equivalent of vendetta: not for this reason but for having the courage to think with my own brain. Maybe laziness is a more plausible explanation.

But I do not have any right to doom my colleagues if I am myself too lazy to do anything. My moral duty is to tell that this hype is nothing but unashamed lying. On the other hand, the digging of a heap of shit is really depressing. Is there any hope of learning anything? I refuse from spending time in superstring landscape but should I see the trouble of comparing eternal inflation with TGD?

In this mixed mood I decided to refresh my views about how TGD based cosmology differs from inflationary scenario. The pleasant surprise was that this comparison combined with new results about TGD inspired cosmology provided fresh insights to the relationship of TGD and standard approach and shows how TGD cures the lethal diseases of the eternal inflation. Very roughly: the replacement of the energy of the scalar field with magnetic energy replaces eternal inflation with a fractal quantum critical cosmology allowing to see more sharply the TGD counterpart of inflation and accelerating expansion as special cases of criticality. Hence it was not wasted time after all.

Wikipedia gives a nice overall summary inflationary cosmology and I recommend it to the non-specialist physics reader as a manner to refresh his or her memory.

1. Brief summary of the inflationary scenario

Inflationary scenario relies very heavily on rather mechanical unification recipes based on GUTs. Standard model gauge group is extended to a larger group. This symmetry group breaks down to standard model gauge group in GUT scale which happens to correspond to CP₂ size scale. Leptons and quarks are put into same multiplet of the gauge group so that enormous breaking of symmetries occurs as is clear from the ratio of top quark mass scale and neutrino mass scale. These unifiers want however a simple model allowing to calculate so that neither aesthetics nor physics does not matter. The instability of proton is one particular prediction. No decays of proton in the predicted manner have been observed but this has not troubled the gurus. As a matter fact, even Particle Data Tables tell that proton is not stable! The lobbies of GUTs are masters of their profession!

One of the key features of GUT approach is the prediction Higgs like fields. They allow to realize the symmetry breaking and describe particle massivation. Higgs like scalar fields are also the key ingredient of the inflationary scenario and inflation goes to down to drain tub if Higgs is not found at LHC. It is looking more and more probable that this is indeed the case. Inflation has endless variety of variants and each suffers from some drawback. In this kind of situation one would expect that it is better to give up but it has become a habit to say that inflation is more that a theory, it is a paradigm. When superstring models turned out to be a physical failure, they did not same thing and claimed that super string models are more like a calculus rather than mere physical theory.

1.1 The problems that inflation was proposed to solve

The basic problems that inflation was proposed to solve are magnetic monopole problem, flatness problem, and horizon problem. Cosmological principle is a formulation for the fact that cosmic microwave radiation is found to be isotropic and homogenous in an excellent approximation. There are fluctuations in CMB believed to be Gaussian and the prediction for the spectrum of these fluctuations is an important prediction of inflationary scenarios.

Consider first the horizon problem. The physical state inside horizon is not causally correlated with that outside it. If the observer today receives signals from a region of past which is much larger than horizon, he should find that the universe is not isotropic and homogenous. In particular, the temperature of the microwave radiation should fluctuate wildly. This is not the case and one should explain this.
The basic idea is that the potential energy density of the scalar field implies exponential expansion in the sense that the "radius" of the Universe increases with an exponential rate with respect to cosmological time. This kind of Universe looks locally like de-Sitter Universe. This fast expansion smooths out any inhomogenities and non-isotropies inside horizon. The Universe of the past observed by a given observer is contained within the horizon of the past so that it looks isotropic and homogenous.
GUTs predict a high density of magnetic monopoles during the primordial period as singularities of non-abelian gauge fields. Magnetic monopoles have not been however detected and one should be able to explain this. The idea is very simple. If Universe suffers an exponential expansion, the density of magnetic monopoles gets so diluted that they become effectively non-existent.
Flatness problem means that the curvature scalar of 3-space defined as a hyper-surface with constant value of cosmological time parameter (proper time in local rest system) is vanishing in an excellent approximation. de-Sitter Universe indeed predicts flat 3-space for a critical mass density. The contribution of known elementary particles to the mass density is however much below the critical mass density so that one must postulate additional forms of energy. Dark matter and dark energy fit the bill. Dark energy is very much analogous to the vacuum energy of Higgs like scalar fields in the inflationary scenario but the energy scale of dark energy is by 27 orders of magnitude smaller than that of inflation, about 10^-3 eV.

1.2 The evolution of the inflationary models

The inflationary models developed gradually more realistic.

Alan Guth was the first to realize that the decay of false (unstable) vacuum in the early universe could solve the problem posed by magnetic monopoles. What would happen would be the analog of super-cooling in thermodynamics. In super-cooling the phase transition to stable thermodynanical phase does not occur at the critical temperature and cooling leads to a generation of bubbles of the stable phase which expand with light velocity.
The unstable super-cooled phase would locally correspond to exponentially expanding de-Sitter cosmology with a non-vanishing cosmological constant and high energy density assignable to the scalar field. The exponential expansion would lead to a dilution of the magnetic monopoles and domain walls. The false vacuum corresponds to a value of Higgs field for which the symmetry is not broken but energy is far from minimum. Quantum tunneling would generate regions of true vacuum with a lower energy and expanding with a velocity of light. The natural hope would be that the energy of the false vacuum would generate radiation inducing reheating. Guth however realized that nucleation does not generate radiation. The collisions of bubbles do so but the rapid expansion masks this effect.
A very attractive idea is that the energy of the scalar field transforms to radiation and produces in this manner what we identify as matter and radiation. To realize this dream the notion of slow-roll inflation was proposed. The idea was that the bubbles were not formed at at all but that the scalar field gradually rolled down along almost flat hill. This gives rise to an exponential inflation in good approximation. At the final stage the slope of the potential would come so steep that reheating would took place and the energy of the scalar field would transform to radiation. This requires a highly artificial shape of the potential energy. There is also a fine tuning problem: the predictions depend very sensitively on the details of the potential so that strictly speaking there are no predictions anymore. Inflaton should have also a small mass and represent new kind of particle.
The tiny quantum fluctuations of the inflaton field have been identified as the seed of all structures observed in the recent Universe. These density fluctuations make them visible also as fluctuations in the temperature of the cosmic microwave background and these fluctuations have become an important field of study (WMAP).
In the hybrid model of inflation there are two scalar fields. The first one gives rise to slow-roll inflation and second one puts end to inflationary period when the first one has reached a critical value by decaying to radiation. It is of course imagine endless number of speculative variants of inflation and Wikipedia article summarizes some of them.
In eternal inflation the quantum fluctuations of the scalar field generate regions which expand faster than the surrounding regions and gradually begin to dominate. This means that there is eternal inflation meaning continual creation of Universes. This is the basic idea behind multiverse thinking. Again one must notice that scalar fields are essential: in absence of them the whole vision falls down like a card house.

The basic criticism of Penrose against inflation is that it actually requires very specific initial conditions and that the idea that the uniformity of the early Universe results from a thermalization process is somehow fundamentally wrong. Of course, the necessity to assume scalar field and a potential energy with a very weird shape whose details affect dramatically the observed Universe, has been also criticized.

2. Comparison with TGD inspired cosmology

It is good to start by asking what are the empirical facts and how TGD can explain them.

2.1 What about magnetic monopoles in TGD Universe?

Also TGD predicts magnetic monopoles. CP₂ has a non-trivial second homology and second geodesic sphere represents a non-trivial element of homology. Induced Kähler magnetic field can be a monopole field and cosmic strings are objects for which the transversal section of the string carries monopole flux. The very early cosmology is dominated by cosmic strings carrying magnetic monopole fluxes. The monopoles do not however disappear anywhere. Elementary particles themselves are string like objects carrying magnetic charges at their ends identifiable as wormhole throats at which the signature of the induced metric changes. For fermions the second end of the string carries neutrino pair neutralizing the weak isospin. Also color confinement could involve magnetic confinement. These monopoles are indeed seen: they are essential for both the screening of weak interactions and for color confinement!

2.2. The origin of cosmological principle

The isotropy and homogenity of cosmic microwave radiation is a fact as are also the fluctuations in its temperature as well as the anomalies in the fluctuation spectrum suggesting the presence of large scale structures. Inflationary scenarios predict that fluctuations correspond to those of nearly gauge invariant Gaussian random field. The observed spectral index measuring the deviation from exact scaling invariance is consistent with the predictions of inflationary scenarios.

Isotropy and homogenity reduce to what is known as cosmological principle. In general relativity one has only local Lorentz invariance as approximate symmetry. For Robertson-Walker cosmologies with sub-critical mass density one has Lorentz invariance but this is due to the assumption of cosmological principle - it is not a prediction of the theory. In inflationary scenarios the goal is to reduce cosmological principle to thermodynamics but fine tuning problem is the fatal failure of this approach.

In TGD framework cosmological principle reduces sub-manifold gravity in H=M⁴× CP₂ predicting a global Poincare invariance reducing to Lorentz invariance for the causal diamonds. This represent extremely important distinction between TGD and GRT. This is however not quite enough since it predicts that Poincare symmetries treat entire partonic 2-surfaces at the end of CD as points rather than affecting on single point of space-time. More is required and one expects that also now finite radius for horizon in very early Universe would destroy the isotropy and homogenity of 3 K radiation. The solution of the problem is simple: cosmic string dominated primordial cosmology has infinite horizon size so that arbitrarily distance regions are correlated. Also the critical cosmology, which is determined part from the parameter determining its duration by its imbeddability, has infinite horizon size. Same applies to the asymptotic cosmology for which curvature scalar is extremized.

The hierarchy of Planck constants and the fact that gravitational space-time sheets should possess gigantic Planck constant suggest a quantum solution to the problem: quantum coherence in arbitrary long length scales is present even in recent day Universe. Whether and how this two views about isotropy and homogenity are related by quantum classical correspondence, is an interesting question to ponder in more detail.

2.3 Three-space is flat

The flatness of three-space is an empirical fact and can be deduced from the spectrum of microwave radiation. Flatness does not however imply inflation, which is much stronger assumption involving the questionable scalar fields and the weird shaped potential requiring a fine tuning. The already mentioned critical cosmology is fixed about the value value of only single parameter characterizing its duration and would mean extremely powerful predictions since just the imbeddability would fix the space-time dynamics almost completely.

Exponentially expanding cosmologies with critical mass density do not allow imbedding to M⁴× CP₂. Cosmologies with critical or over-critical mass density and flat 3-space allow imbedding but the imbedding fails above some value of cosmic time. These imbeddings are very natural since the radial coordinate $r$ corresponds to the coordinate r for the Lorentz invariant a=constant hyperboloid so that cosmological principle is satisfied.

Can one imbed exponentially expanding sub-critical cosmology? This cosmology has the line element

ds² =dt²-ds₃²,

ds₃²= sinh²(t) dΩ₃²,

where ds₃² is the metric of the a=constant hyperboloid of M⁴₊.

The simplest imbedding is as vacuum extremal to M⁴× S², S² the homologically trivial geodesic sphere of CP₂. The imbedding using standard coordinates (a,r,θ,φ) of M⁴₊ and spherical coordinates (Θ,Φ) for S² is to a geodesic circle (the simplest possibility)
Φ= f(a) , Θ=π/2 .
Φ=f(a) is fixed from the condition
a = sinh(t) ,
giving
g_aa=(da/dt)²= 1/cosh²(t)
and from the condition for the g_aa as a component of induced metric tensor
g_aa= 1-R² (df/da)² =(dt/da)² = 1/cosh²(t) .
This gives
df/da=+/- 1/R × tanh(t)
giving f(a)= (cosh(t)-1)/R. Inflationary cosmology allows imbedding but this imbedding cannot have a flat 3-space and therefore cannot make sense in TGD framework.

2.4 Replacement of the inflationary cosmology with critical cosmology

In TGD framework inflationary cosmology is replaced with critical cosmology. The vacuum extremal representing critical cosmology is obtained has 2-D CP₂ projection - in the simplest situation geodesic sphere. The dependence of Φ on r and Θ on a is fixed from the condition that one obtains flat 3- metric

a²/1+r² - R²sin²(Θ)(dΦ/dr)²= a²

This gives

sin(Θ)=+/- ka , dΦ/dr=+/- (1/kR)× (r/(1+r²)^1/2 .

The imbedding fails for |ka| >1 and is unique apart from the parameter k characterizing the duration of the critical cosmology. The radius of the horizon is given by

R= &int (1/a) × [(1-R²k²)/(1-k²a²)]^1/2

and diverges. This tells that there are no horizons and therefore cosmological principle is realized. Infinite horizon radius could be seen as space-time correlate for quantum criticality implying long range correlations and allowing to realize cosmological principle. Therefore thermal realization of cosmological principle would be replaced with quantum realization in TGD framework predicting long range quantal correlations in all length scales. Obviously this realization is a in well-defined sense the diametrical opposite of the thermal realization. The dark matter hierarchy is expected to correspond to the microscopic realization of the cosmological principle generating the long range correlations.

This cosmology could describe the phase transition increasing Planck constant associated with a magnetic flux tube leading to its thickening. Magnetic flux would be conserved and the magnetic energy for the thicknened portion would be reduced via its partial transformation to radiation giving rise to ordinary and dark matter.

2.5 Fractal hierarchy of cosmologies within cosmologies

Many-sheeted space-time leads to a fractal hierarchy of cosmologies within cosmologies. The zero energy realization is in terms of causal diamonds within causal diamonds with causal diamond identified as intersection of future and past directed light-cones. The temporal distance between the tips of CD is given as an integer multiple of CP₂ time in the most general case and boosts of CDs are allowed. The are also other moduli associated with CD and discretization of the moduli parameters is strong suggestive.

Critical cosmology corresponds to negative value of "pressure" so that it also gives rise to accelerating expansion. This suggests strongly that both the inflationary period and the accelerating expansion period which is much later than inflationary period correspond to critical cosmologies differing from each other by scaling. Continuous cosmic expansion is replaced with a sequence of discrete expansion phases in which the Planck constant assignable to a magnetic flux quantum increases and implies its expansion. This liberates magnetic energy as radiation so that a continual creation of matter takes place in various scales.

This fractal hierarchy is the TGD counterpart for the eternal inflation. This fractal hierarchy implies also that the TGD counterpart of inflationary period is just a scaled up invariant of critical cosmologies within critical cosmologies. Of course, also radiation and matter dominated phases as well as asymptotic string dominated cosmology are expected to be present and correspond to cosmic evolutions within given CD.

2.6 Vacuum energy density as magnetic energy of magnetic flux tubes and accelerating expansion

TGD allows also a microscopic view about cosmology based on the vision that primordial period is dominated by cosmic strings which during cosmic evolution develop 4-D M⁴ projection meaning that the thickness of the M⁴ projection defining the thickness of the magnetic flux tube gradually increases. The magnetic tension corresponds to negative pressure and can be seen as a microscopic cause of the accelerated expansion. Magnetic energy is in turn the counterpart for the vacuum energy assigned with the inflaton field. The gravitational Planck constant assignable to the flux tubes mediating gravitational interaction nowadays is gigantic and they are thus in macroscopic quantum phase. This explains the cosmological principle at quantum level.

The phase transitions inducing the boiling of the magnetic energy to ordinary matter are possible. What happens that the flux tube suffers a phase transition increasing its radius. This however reduces the magnetic energy so that part of magnetic energy must transform to ordinary matter. This would give rise to the formation of stars and galaxies. This process is the TGD counterpart for the re-heating transforming the potential energy of inflaton to radiation. The local expansion of the magnetic flux could be described in good approximation by critical cosmology since quantum criticality is in question.

One can of course ask whether inflationary cosmology could describe the transition period and critical cosmology could correspond only to the outcome. This does not look very attractive idea since the CP₂ projections of these cosmologies have dimension D=1 and D=2 respectively.

In TGD framework the fluctuations of the cosmic microwave background correspond to mass density gradients assignable to the magnetic flux tubes. An interesting question is whether the flux tubes could reveal themselves as a fractal network of linear structures in CMB. The prediction is that galaxies are like pearls in a necklace: smaller cosmic strings around long cosmic strings. The model for the formation of stars and galaxies gives a more detailed view about this.

2.7 What is the counterpart of cosmological constant in TGD framework?

In TGD framework cosmological constant emerges, as one asks what might be the GRT limit of TGD. Space-time surface decomposes to regions with both Minkowskian and Euclidian signature of the induced metric and Euclidian regions have interpretation as counterparts of generalized Feynman graphs. Also GRT limit must allow space-time regions with Euclidian signature of metric - in particular CP₂ itself -and this requires positive cosmological constant in this regions. The action principle is naturally Maxwell-Einstein action with cosmological constant which is vanishing in Minkowskian regions and very large in Euclidian regions of space-time. Both Reissner-Nordström metric and CP₂ are solutions of field equations with deformations of CP₂ representing the GRT counterparts of Feynman graphs. The average value of the cosmological constant is very small and of correct order of magnitude since only Euclidian regions contribute to the spatial average. This picture is consistent with the microscopic picture based on the identification of the density of magnetic energy as vacuum energy since Euclidian particle like regions are created as magnetic energy transforms to radiation.

For details and background see the articles Do we really understand the solar system? and Inflation and TGD, and the chapter TGD and Astrophysics.

Nuclear physics objections against Rossi's reactor

2011-11-28T00:35:00.000-08:00

The reading of Rossi's paper and Wikipedia article led me to consider in more detail various objections against Rossi's reactor. Coulomb barrier, the lack of gamma rays, the lack of explanation for the origin of the extra energy, the lack of the expected radioactivity after fusing a proton with ⁵⁸Ni (production of neutrino and positron in beta decay of ⁵⁹Cu), the unexplained occurrence of 11 per cent iron in the spent fuel, the 10 per cent copper in the spent fuel strangely having the same isotopic ratios as natural copper, and the lack of any unstable copper isotopes in the spent fuel as if the reactor only produced stable isotopes.

Could natural isotope ratios be determined by cold fusion?

The presence of Cu in natural isotope ratios and the absence of unstable copper isotopes of course raise the question whether the copper is just added there. Also the presence of iron is strange. Could one have an alternative explanation for these strange co-incidences?

Whether unstable isotopes of Cu are present or not, depends on how fast ^ACu, A<63 decays by neutron emission: this decay is expected to be fast since it proceeds by strong interactions. I do not know enough about the detailed decay rates to be able to say anything about this.
Why the isotope ratios would be the same as for naturally occurring copper isotopes? The simplest explanation would be that the fusion cascades of two stable Ni isotopes determine the ratio of naturally occurring Cu isotopes so that cold fusion would be responsible for their production. As a matter fact, TGD based model combined with what is claimed about bio-fusion led to the proposal that stable isotopes are produced in interstellar space by cold fusion and that this process might even dominate over the production in stellar interiors. This wold solve among other things also the well-known Lithium problem. The implications of the ability to produce technologically important elements artificially at low temperatures are obvious.

Could standard nuclear physics view about cold fusion allow to overcome the objections?

Consider now whether one could answer the objections in standard nuclear physics framework as a model for cold fusion processes.

By inspecting stable nuclides one learns that there are two fusion cascades. In the first cascade the isotopes of copper would be produced in a cascade starting from with ⁵⁸Ni+n→ ⁵⁹Cu and stopping at ⁶³Cu. All isotopes ^ACu, A ∈{55,62} are unstable with lifetime shorter than one day. The second fusion cascade begins from ⁶³Ni and stops at ⁶⁵Cu.
The first cascade involves five cold fusions and 4 weak decays of Cu. Second cascade involves two cold fusions and one weak decay of Cu. The time taken by the cascade would be same if there is single slow step involved having same duration. The only candidates for the slow step would be the fusion of the stable Ni isotope with the neutron or the fusion producing the stable Cu isotope. If the fusion time is long and same irrespective of the neutron number of the stable isotope, one could understand the result. Of course, this kind of co-incidendence does not look plausible.
^A-5Fe could be produced via alpha decay ^ACu→ ^A-4Co+α followed by ^A-4Co→ ^A-5Fe +p.

Could TGD view about cold fusion allow to overcome the objections?

The claimed absence of positrons from beta decays and the absence of gamma rays are strong objections against the assumption that standard nuclear physics is enough. TGD framework it is possible to ask whether the postulated fusion cascades really occur and whether instead of it weak interactions in dark phase of nuclear matter with range of order atomic length scale are responsible for the process because weak bosons would be effectively massless below atomic length scale. For TGD inspired model of cold fusion see this and this).

The nuclear string model assumes that nucleons for nuclear strings with nucleons connected with color bonds having quark and antiquark at their ends. Color bonds could be also charged and this predicts new kind of internal structure for nuclei. Suppose that the space-time sheets mediating weak interactions between the color bonds and nucleons correspond to so large value of Planck constant that weak interaction length scale is scaled up to atomic length scale. The generalization of this hypothesis combined with the p-adic length scale hypothesis is actually standard piece of TGD inspired quantum biology (see this).
The energy scale of the excitations of color bond excitations of the exotic nuclei would be measured in keVs. One could even consider the possibility that the energy liberated in cold fusion would correspond to this energy scale. In particular, the photons emitted would be in keV range corresponding to wavelength of order atomic length sale rather than in MeV range. This would resolve gamma ray objection.
Could the fusion process ⁵⁸Ni+n actually lead to a generation of Ni nucleus ⁵⁹Ni with one additional positively charged color bond? Could the fusion cascade only generate exotic Ni nuclei with charged color bonds, which would transform to stable Cu by internal dark W boson exchange transferring the positive charge of color bond to neutron and thus transforming it to neutron? This would not produce any positrons. This cascade might dominate over the one suggested by standard nuclear physics since the rates for beta decays could be much slower than the rate for directed generation of Ni isotopes with positively charged color bonds.
In this case also the direct alpha decay of Ni with charged color bond to Fe with charged color bond decaying to ordinary Fe by positron emission can be imagined besides the proposed mechanism producing Fe.
If one assumes that this process is responsible for producing the natural isotope ratios, one could overcome the basic objections against Rossi's reactor.

The presence of em radiation in keV range would be a testable basic signature of the new nuclear physics as also effects of X-ray irradiation on measured nuclear decay and reaction rates due to the fact that color bonds are excited. As a matter fact, it is known that X-ray bursts from Sun in keV range has effects on the measured nuclear decay rates and I have proposed that the proposed exotic nuclear physics in keV range is responsible for the effect. Quite generally, the excitations of color bonds would couple nuclear physics with atomic physics and I have proposed that the anomalies of water could involve classical Z⁰ force in atomic length scales. Also the low compressibility of condensed matter phase could involve classical Z⁰ force. The possible connections with sono-luminescence and claimed sonofusion are also obvious (see this).

Cold fusion irritates again

2011-11-27T03:55:00.000-08:00

Lubos has been raging several times about the cold fusion gadget of Andrea Rossi and returned to the topic again. The claim of Rossi and physicist Fogardi is that the cold fusion reaction of H and Ni producing Cu in the presence of some "additives" (Palladium catalyst as in may cold fusion experiments gathering at its surface Ni?) .

Lubos of course "knows" before hand that the gadget cannot work: Coulomb barrier. Since Lubos is true believer in naive text book wisdom, he simply refuses to consider the possibility that the physics that we learned during student days might not be quite right. Personally I do not believe or disbelieve cold fusion: I just take it seriously as any person calling himself scientist should do. I have been developing for more than 15 years ideas about possible explanation of cold fusion in TGD framework. The most convincing idea is that large value of Planck constant associated with nuclei could be involved scaling up the range of weak interactions from 10^-17 meters to atomic size scale and also scaling up the size of nucleus to atomic size scale so that nucleus and even quarks would like constant charge densities instead of point like charge. Therefore Coulomb potential would be smoothed and the wall would become much lower (see this and this).

One must say in honor of Lubos that at this time he had detailed arguments about what goes wrong with the reactor of Rossi: this is in complete contrast with the usual arguments of skeptics which as a rule purposefully avoid saying anything about the actual content and concentrate on ridiculing the target. The reason is of course that standard skeptic is just a soldier who has got the list of targets to be destroyed and as a good soldier does his best to achieve the goal. Thinking is not what a good soldier is expected to do since the professors in the consultive board take care of this and give orders to those doing the dirty job.

As a theoretician I have learned the standard arguments used to debunk TGD: logic is circular, text is mere world salad, everything is just cheap numerology, too many self references, colleagues have not recognized my work, the work has not been published in respected journals, and so on. The additional killer arguments state that I have used certain words which are taboos and already for this reason am a complete crackpot. Examples of bad words are "water memory", "homeopathy", "cold fusion", "crop circles", "quantum biology", "quantum consciousness". There is of course no mention about the fact that I have always emphasized that I am skeptic, not a believer or disbeliever, and only make the question "What if...." and try to answer it in TGD framework. Intellectual honesty does not belong to the virtues of skeptics who are for modern science what jesuits were for the catholic church. Indeed, as Loyola said: the purpose sanctifies the deeds.

Lubos has real arguments but they suffer from strong negative emotional background coloring so that one cannot be trust the rationality of the reasoning. The core of the arguments of Lubos is following.

The water inside reactor is heated to a temperature of 100.1 C. This is slightly above 100 C defining the nominal value of the boiling point temperature at normal pressure. The problem is that if the pressure is somewhat higher, the boiling point increases and the it could happen that the no evaporation of the water takes place. If this is the case, the whole energy fed into the reactor could go to the heating of the water. The input power is indeed somewhat higher than the power needed to heat the water to this temperature without boiling so that this possibility must be taken seriously and the question is whether the water is indeed evaporated.
Comments:
1. This looks really dangerous. Rossi uses water only as a passive agent gathering the energy assumed to be produced in the fusion of hydrogen and nickel to copper. This would allow to assume that the water fed in is at lower temperature and also the water at outlet is below boiling boiling. Just by measuring the temperature at the outlet one can check whether the outgoing water has temperature higher than it would be if all input energy goes to its heating.
2. This is only one particular demonstration and it might be that there are other demonstrations in which the situation is this. As a matter fact, from an excellent video interview of Nobelist Brian Josephson one learns that there are also demonstrations in which water is only heated so that the argument of Lubos does not bite here. The gadget of Rossi is already used to heat university building. The reason why the evaporation is probably that this provides an effective manner to collect the produced energy. Also by reading the Nyteknik report one learns that the energy production is directly measured rather than being based on the assumption that evaporation occurs.
Is the water evaporated or not? This is the question posed by Lubos. The demonstration shows explicitly that there is a flow of vapor from the outlet. As Rossi explains there is some condensation. Lubos claims that the the flow of about 2 liters of vapor per second resulting from the evaporation 2 ml of water per second should produce much more dramatic visual effect. More vapor and with a faster flow velocity. Lubos claims that water just drops from the tube and part of it spontaneously evaporates. This is what Lubos wants to see and I have no doubt that he is seeing it. Strong belief can move mountains! Or at least can make possible the impression that they are indeed moving!;-).
Comments:
1. I do not see what Lubos sees but I am not able to tell how many liters of vapor per second comes out. Therefore the visual demonstration as such is not enough.
2. I wonder why Rossi has not added flow meter measuring the amount of vapor going through the tube. Second possibility is to allow the vapor condensate back to water in the tube by using heat exchanger. This would allow to calculate the energy gained without making the assumption that all that comes out is vapor. It might be that in some experiments this is done. In fact, the gadget of Rossi has been used to heat the university building but even this is not a real proof.

To sum up, Lubos in his eagerness to debunk forgets that he is concentrating on single demonstration and forgetting other demonstrations and also the published report to which his argument do not apply. I remain however skeptic (I mean real skeptic, the skepticism of Lubos and -sad to say- of quite too many skeptics- has nothing to do with a real skeptic attitude). Rossi should give information about the details of his invention and quantitative tests really measuring the heat produced should be carried out and published. Presumably the financial aspects related to the invention explain the secrecy in a situation in which patenting is difficult.

The origin of cosmic rays and cosmic rays as direct support for the hierarchy of Planck constants

2011-11-26T01:40:00.000-08:00

The origin of cosmic rays remains still one of the mysteries of astrophysics and cosmology. The recent finding of a super bubble emitting cosmic rays might cast some light in the problem.

1. What has been found?

The following is the abstract of the article published in Science.

The origin of Galactic cosmic rays is a century-long puzzle. Indirect evidence points to their acceleration by supernova shockwaves, but we know little of their escape from the shock and their evolution through the turbulent medium surrounding massive stars. Gamma rays can probe their spreading through the ambient gas and radiation fields. The Fermi Large Area Telescope (LAT) has observed the star-forming region of Cygnus X. The 1- to 100-gigaelectronvolt images reveal a 50-parsec-wide cocoon of freshly accelerated cosmic rays that flood the cavities carved by the stellar winds and ionization fronts from young stellar clusters. It provides an example to study the youth of cosmic rays in a superbubble environment before they merge into the older Galactic population. The usual thinking is that cosmic rays are not born in states with ultrahigh energies but are boosted to high energies by some mechanism. For instance, super nova explosions could accelerate them. Shock waves could serve as an acceleration mechanism. Cosmic rays could also result from the decays of heavy dark matter particles.

The story began when astronomers detected a mysterious source of cosmic rays in the direction of the constellation Cygnus X. Supernovae happen often in dense clouds of gas and dust, where stars between 10 to 50 solar masses are born and die. If supernovae are responsible for accelerating of cosmic rays, it seems that these regions could also generate cosmic rays. Cygnus X is therefore a natural candidate to study. It need not however be the source of cosmic rays since magnetic fields could deflect the cosmic rays from their original direction. Therefore Isabelle Grenier and her colleagues decided to study, not cosmic rays as such, but gamma rays created when cosmic rays interact with the matter around them since they are not deflected by magnetic fields. Fermi gamma-ray space telescope was directed toward Cygnus X. This led to a discovery of a superbubble with diameter more than 100 light years. Superbubble contains a bright regions which looks like a duck. The spectrum of these gamma rays implies that the cosmic rays are energetic and freshly accelerated so that they must be close to their sources.

The important conclusions are that cosmic rays are created in regions in which stars are born and gaint their energies by some acceleration mechanism. The standard identification for the acceleration mechanism are shock waves created by supernovas but one can imagine also other mechanisms.

2. Cosmic rays in TGD Universe?

In TGD framework one can imagine several mechanisms producing cosmic rays. According to the vision discussed already earlier, both ordinary and dark matter would be produced from dark energy identified as Kähler magnetic energy and producing as a by product cosmic rays. What causes the transformation of dark energy to matter, was not discussed earlier, but a local phase transition increasing the value of Planck constant of the magnetic flux tube could be the mechanism. A possible acceleration mechanism would be acceleration in an electric field along the magnetic flux tube. Another mechanism is super-nova explosion scaling-up rapidly the size of the closed magnetic flux tubes associated with the star by hbar increasing phase transition preserving the Kähler magnetic energy of the flux tube, and accelarating the highly energetic dark matter at the flux tubes radially: some of the particles moving along flux tubes would leak out and give rise to cosmic rays and associated gamma rays.

2.1. The mechanism transforming dark energy to dark matter and cosmic rays

Consider first the mechanism transforming dark energy to dark matter.

The recent model for the formation of stars and also galaxies is based on the identification magnetic flux tubes as carriers of mosly dark energy identified as Kähler magnetic energy giving rise to a negative "pressure" as magnetic tension and explaining the accelerated expansion of the Universe. Stars and galaxies would be born as bubbles of ordinary are generated inside magnetic flux tubes. Inside these bubbles dark energy would transform to dark and ordinary matter. Kähler nagnetic flux tubes are characterized by the value of Planck constant and for the flux tubes mediating gravitational interactions its value is gigantic. For a start of mass M its value for flux tubes mediating self-gravitation it would be hbar_gr=GM²/v₀, v₀<1 (v₀ is a parameter having interpretation as a velocity).
On possible mechanism liberating Kähler magnetic energy as cosmic rays would be the increase of the Planck constant for the magnetic flux tube occurring locally and scaling up quantal distances. Assume that the radius of the flux tube is this kind of quantum distance. Suppose that the scaling hbar→ rhbar implies that the radius of the flux tube scales up as rⁿ, n=1/2 or n=1 (n=1/2 turns out to be the sensible option). Kähler magnetic field would scale as 1/r²ⁿ. Magnetic flux would remain invariant as it should and Kähler magnetic energy would be reduced as 1/r²ⁿ. For both options Kähler magnetic energy would be liberated. The liberated Kähler magnetic energy must go somewhere and the natural assumption is that it transforms to particles giving rise to matter responsible for the formation of star.
Could these particles include also cosmic rays? This would conform with the observation that stellar nurseries could be also the birth places of cosmic rays. One must of course remember that there are many kinds of cosmic rays. For instance, this mechanism could produce ultra high energy cosmic rays having nothing to do with the cosmic rays in 1-100 GeV rays studied in the recent case.
The simplest assumption is that the thickening of the magnetic flux tubes during cosmic evolution is based on phase transitions increasing the value of Planck constant in step-wise manner. This is not a new idea and I have proposed that entire cosmic expansion at the level of space-time sheets corresponds to this kind of phase transitions. The increase of Planck constant by a factor of two is a good guess since it would increase the size scale by two. In fact, Expanding Earth hypothesis having no standard physics realization finds a beautiful realization in this framework. Also the periods of accelerating expansion could be identified as these phase transition periods.
For the values of gravitational Planck constant assignable to the space-time sheets mediating gravitational interactions, the Planck length scaling like r^1/2 would scale up to black-hole horizon radius. The proposal would imply for n=1/2 option that magnetic flux tubes having M⁴ projection with radius of order Planck length primordially would scale up to blackhole horizon radius if gravitational Planck constant has a value GM²/v₀, v₀<1, assignable to a star. Obviously this evelutionary scenario is consistent with with what is known about the relations ship between masses and radii of stars.

2.2 What is the precise mechanism transforming dark energy to matter?

What is the precise mechanism transforming the dark magnetic energy to ordinary or dark matter? This is not clear but this mechanism could produce very heavy exotic particles not yet observed in laboratory which in turn decay to very energetic ordinary hadrons giving rise to cosmic rays spectrum. I have considered a mechanism for the production of ultrahigh energy cosmic rays based on the decays of hadrons of scaled up copies of ordinary hadron physics. In this case no acceleration mechanism would be necessary. Cosmic rays lose their energy in interstellar space. If they correspond to a large value of Planck constant, situation would change and the rate of the energy loss could be very slow. The above described experimental finding about Cygnus X however suggests that acceleration takes place for the ordinary cosmic rays with relatively low energies. This of course does not exclude particle decays as the primary production mechanism of very high energy cosmic rays. In any case, dark magnetic energy transforming to matter gives rise to both stars and high energy cosmic rays in TGD based proposal.

2.3. What is the acceleration mechanism?

How cosmic rays are created by this general process giving rise to the formation of stars?

Cosmic rays could be identified as newly created matter leaking out from the system. Even in the absence of accelerating fields the particles created in the boiling of dark energy to matter, particles moving along magnetic flux tubes would move essentially like free particles whereas in orthogonal directions they would feel 1/ρ gravitational force. For large values of hbar this could explain very high energy cosmic rays. The recent findings about gamma ray spectrum however suggests that there is an acceleration involved for cosmic rays with energies 1-100 GeV.
One possible alternative acceleration mechanism relies on the motion along magnetic flux tubes deformed in such a manner that there is an electric field orthogonal to the magnetic field in such a manner that the field lines of these fields rotate around the direction of the flux tube. The simplest imbeddings of constant magnetic fields allow deformations allowing also electric field, and one can expect the existence of preferred extremals with similar structure. Electric field would induce an acceleration along the flux tube. If the flux tube corresponds to large non-standard value of Planck constant, dissipation rate would be low and the acceleration mechanism would be very effective.
Similar mechanism might even explain the observations about ultrahigh energy electrons associated with lightnings at the surface of Earth: they should not be there because the dissipation in the atmosphere should not allow free acceleration in the radial electric field of Earth.
Here one must be very cautious: the findings are based on a model in which gamma rays are generated with collising of cosmic rays with matter. If cosmic rays travel along magnetic flux tubes with a gigantic value of Planck constant, they should dissipate extremely slowly and no gamma rays would be generated. Hence the gamma rays must be produced by the collisions of cosmic rays which have leaked out from the magnetic flux tubes. If the flux tubes are closed (say associated with the star) the leakage must indeed take place if the cosmic rays are to travel to Earth.
There could be a connection with supernovae although it would not be based on shock waves. Also supernova expansion could be accompanied by a phase transition increasing the value of Planck constant. Suppose that Kähler magnetic energy is conserved in the process. This is the case if the lengths of the magnetic flow tubes r and radii by r^1/2. The closed flux tubes associated with supernova would expand and the size scale of flux tubes would increase by factor r. The fast radial scaling of the flux tubes would accelerate the dark matter at the flux tubes radially.
Cosmic rays having ordinary value of Planck constant could be created when some of the dark matter leaks out from the magnetic flux tubes as their expanding motion in radial direction accelerates or slows down. High energy dark particles moving along flux tube would leak out in the tangential direction. Gamma rays would be generated as the resulting particles interact with the environment. The energies of cosmic rays would be the outcome of acceleration process: only their leakage would be caused by it so that the mechanism differs in a decisice manner from the mechanism involving shock waves.
The energy scale of cosmic rays - let us take it to be about E=100 GeV for definiteness- gives an order of magnitude estimate for the Planck constant of dark matter at the Kähler magnetic flux tubes if one assumes that supernovae is producing the cosmic rays. Assume that electro-magnetic field equals to induced Kähler field (the space-time projection of space-time surface to CP₂ belongs homologically non-trivial geodesic sphere). Assume that E equals the cyclotron energy scale given by E_c= hbar eB/m_e in non-relativistic situation and by E_c= (hbar eB)^1/2 in relativistic situation. The situation is relativistic for both proton and electron now and at this limit the cyclotron energy scale does not depend on the mass of the charged particle at all. This means that same value of hbar produces same energy for both electron and proton.
1. The magnetic field of pulsar can be estimated from the knowledge how much the field lines are pulled together and from the conservation of magnetic flux: a rough estimate is B=10⁸ Tesla and will be used also now. This field is 2× 10¹²B_E where B_E=.5 Gauss is the nominal value of the Earth's magnetic field.
2. The cyclotron frequency of electron in Earth's magnetic field is f_c(e)=6× 10⁵ Hz in a good approximation and correspond to cyclotron energy E_c=10^-14(f_c/Hz) eV from the approximate correspondence eV↔ 10¹⁴ Hz true for E=hf. For the ordinary value of Planck constant electron's cyclotron energy would be for supernova magnetic field B_S=10⁸ Tesla equal to E_c=2× 10^-2 (f_c/Hz) eV and much below the energy scale E= 100 GeV.
3. The required scaling hbar→ r×hbar of Planck constant is obtained from the condition E_c=E giving in the case of electron one can write
  r= (E/E_c)²×(B_E/B_S) × hbar eB_E/m_e².
  The dimensionless parameter hbar eB_E/m_e²=1.2×10^-14 follows from m_e=.5 MeV. The estimate gives r∼ 2× 10¹². Values of Planck constant of this order of magnitude and even larger ones appear in TGD inspired model of brain but in this case magnetic field is Earth's magnetic field and the large thickness of the flux tube makes possible to satisfy the quantization of magnetic flux in which scaled up hbar defines the unit.
To sum up, large values of Planck constant would be absolutely essential making possible high energy cosmic rays and just the presence of high energy cosmic rays could be seen as an experimental support for the hierarchy of Planck constants. The acceleration mechanism of cosmic rays are poorly understood and TGD option predicts that there is no acceleration mechanism to search for.

For details and background see the article Do we really understand the solar system? and the chapter TGD and Astrophysics of "Physics in Many-Sheeted Space-time".

Three year old CDF anomaly is here again!

2011-11-24T22:42:00.000-08:00

CDF anomaly - or multimuon- mystery emerged about three years ago- the preprint to arXiv.org was sent more or less at my birthday so that I regarded it with a full reason as a birthday present. The reason was that its explanation provided a further support for the existence of color octet excitations of charged leptons having the same p-adic mass scale for the lowest mass state. In this case color excited tau leptons would have been in question. For color excited electrons evidence had emerged already at seventies in heavy ion collisions. For color excited muons for a year or so before CDF anomaly.

For a series of posts about CDF anomaly by Tommaso Dorigo see this. To get handle on series of my own postings see this. For the TGD based explanation of the CDF anomaly and earlier similar anomalies see this.

This anomaly had really bad luck. This kind of new light particles are not possible in standard model: intermediate gauge boson decay widths simply leave no room for them. Average theorist of cause refuses to accept observations which are in conflict with the theory so that all these anomalies have been forgotten. As a crackpot I however respect experimental and empirical facts more than the orders of hegemony. The assumption that these particles are dark matter particles in TGD sense resolves the paradox. Being dark matter particle in TGD Universe means having a non-standard value of Planck constant coming as an integer multiple of the ordinary Planck constant. Only particles with the same value of Planck constant can appear in same vertex so that intermediate gauge boson decay widths do not pose any restrictions.

I have applied the general format of the model of CDF anomaly in several contexts (see this and this). One of the common aspects of the applications is that pion like states of leptohadron physics of scaled variant of hadron physics seem to appear in several mass scales comings as the octaves of the lowest one. Also in TGD based model for light hadrons quarks appear in several p-adic mass scales, and more precise considerations show that it is not at all clear whether also ordinary pion could have these higher octaves: their production and detection is not all easy but would provide a brilliant confirmation of p-adic length scale hypothesis.

The three year old CDF anomaly generated a lot of debate as also its slightly more than half year old brother last spring (having interpretation in terms of pion of M₈₉ hadron physics and involving very similar basic mechanism). D0 collaboration however reported that they do not see anything. Tommaso Dorigo demonstrated in his blog posting that we can indeed trust D0: it did not have any chance of observing anything!: the acceptance criteria for events made impossible to observe the anomaly. No-one was of course interested on such a minor details and CDF anomaly was safely buried in the sands of time.

By the way, a delicate change of the relevant parameters is a very effective manner to kill undesired anomalies and the people calling themselves skeptics are masters in applying this technique. One can speak of time-honored tradition here. Water memory is one of the victims of this method and no serious scientist dares say this word aloud although anyone with eyes can see concrete images taken by professional scientists and demonstrating its reality (see this). Do not believe a scientists before you know how pays for him!

To my surprise the situation changed this morning. Tommaso Dorigo reported that CDF has done a much simpler analysis and using larger sample of data. This bloody, disgusting anomaly is still there! The reader interested in details is encouraged to visit Tommaso's blog.

Hegemony is living difficult times: no sign of standard model Higgs or its counterparts in various SUSYs, no sign about standard SUSY, no sign about super-stringy new physics like mini blackholes and large extra dimensions. Just anomalies having no explanation in the theories that hegenomy is ready to consider and even worse: having an elegant explanation TGD framework. The most irritating stone in the to is the accumulating evidence for the scaled up variant of hadron physics predicted by TGD. There is also this nasty neutrino superluminality elegantly explained and almost predicted by TGD. And now this revived CDF anomaly which should have been already buried! The rope is getting tighter and tighter!

How easy it would have been to just explore this wonderful Universe with open mind?! Nature does not seem to care the least about the attempts of Big Science Bosses to tell how it should behave. But by all means my Dear Professors and Leaders of Units of Excellence: try! By beating your brilliant head against the wall sufficiently many times you might finally learn what those contemptible crackpots have learned long time ago just by using simple logic and accepting simple facts!

Algebraic braids, sub-manifold braid theory, and generalized Feynman diagrams

2011-11-20T02:10:00.000-08:00

Ulla send me a link to an article by Sam Nelson about very interesting new-to-me notion known as algebraic knots, which has initiated a revolution in knot theory. This notion was introduced 1996 by Louis Kauffmann so that it is already 15 year old concept. While reading the article I realized that this notion fits perfectly the needs of TGD and leads to a progress in attempts to articulate more precisely what generalized Feynman diagrams are.

The outcome was an article in which l summarize briefly the vision about generalized Feynman diagrams, introduce the notion of algebraic knot, and after than discuss in more detail how the notion of algebraic knot could be applied to generalized Feynman diagrams. The algebraic structrures kei, quandle, rack, and biquandle and their algebraic modifications as such are not enough. The lines of Feynman graphs are replaced by braids and in vertices braid strands redistribute. This poses several challenges: the crossing associated with braiding and crossing occurring in non-planar Feynman diagrams should be integrated to a more general notion; braids are replaced with sub-manifold braids; braids of braids ....of braids are possible; the redistribution of braid strands in vertices should be algebraized. In the following I try to abstract the basic operations which should be algebraized in the case of generalized Feynman diagrams.

One should be also able to concretely identify braids and 2-braids (string world sheets) as well as partonic 2-surfaces and I have discussed several identifications during last years. Legendrian braids turn out to be very natural candidates for braids and their duals for the partonic 2-surfaces. String world sheets in turn could correspond to the analogs of Lagrangian sub-manifolds or to minimal surfaces of space-time surface satisfying the weak form of electric-magnetic duality. The latter option turns out to be more plausible. Finite measurement resolution would be realized as symplectic invariance with respect to the subgroup of the symplectic group leaving the end points of braid strands invariant. In accordance with the general vision TGD as almost topological QFT would mean symplectic QFT. The identification of braids, partonic 2-surfaces and string world sheets - if correct - would solve quantum TGD explicitly at string world sheet level in other words in finite measurement resolution.

Irrespective of whether the algebraic knots are needed, the natural question is what generalized Feynman diagrams are. It seems that the basic building bricks can be identified so that one can write rather explicit Feynman rules already now. Of course, the rules are still far from something to be burned into the spine of the first year graduate student.

The most recent revelations about Higgs

2011-11-19T20:28:00.000-08:00

As the readers of tabloids must have already noticed, the latest combination of ATLAS and CMS searches for Higgs boson have been released and the results are practically identical with the results anticipated by Philip Gibbs. Both Jester, Peter Woit, and Tommaso Dorigo have commented the results.

There are no big surprises. Higgs is now excluded above 141 GeV. Second figure in Tommaso's blog shows the observed and predicted distribution of so called local p-value as a function of Higgs boson mass. Assuming that Higgs exists, the predicted local p-value has enormous downwards peak above 140 GeV. The observed distribution has also small downwards peak at 140 GeV here but it is not clear to me whether this really signals about the presence of a neutral particle: in TGD Universe it would be neutral M₈₉ pion with mass of 139 GeV whereas charged M₈₉ pions would have mass 144 GeV.

Here I am angry to myself because of my sloppiness: my first MATLAB estimate for M₈₉ mass performed when CDF anomaly came was based on the approximation there is no electromagnetic splitting and I scaled the mass of charged pions and got 144 GeV. I realized my error only about month or two ago. In any case, the prediction is that there should be charged companions of neutral M₈₉ pion at 144 GeV besides 139 GeV neutral M₈₉ pion.

Second downwards peak in p-value distribution is at 120 GeV. My proposal is that it corresponds to M₈₉ spion (see this). This requires some explanation. The basic assumption is that squarks and quarks have same p-adic mass scales and perhaps even identical masses and shadronization via the exchange of almost massless gluinos takes place much faster than the selectro-weak decays of squarks to quarks and electro-weak gauginos. This prevent the events with missing energy (lightest SUSY particle) predicted by standard SUSY but not observed. The missing missing energy has already led to models based on R-parity breaking requiring the non-conservation of either lepton number or baryon number. I have discussed shadronization here and will not go to further details.

A considerable mixing between pion and spion due to the large value of color coupling strength at low energies takes place and makes mass squared matrix non-diagonal. It must be diagonalized and in the case of ordinary light hadrons second mass squared eigen value is negative meaning tachyonicity. The pragmatic conclusion, which might horrify a colleague appreciating aesthetical values (I am ready to discuss about this;-)), is that the tachyonic state is absent from the spectrum and SUSY would effectively disappear for light hadrons. In the case of charmonium states mixing is weaker since α_s is weaker and both states would be non-tachyonic. The mysterious X and Y bosons would be in good approximation scharmonium states (see this).

I agree with the Jester who compares the situation to that in formed Soviet Union when secretary general has not appeared in publicity for a long time and working class and lower party officials were asking whether he is sick, unconscious, dead, and if dead how long he has been dead. My guess is that Higgs is not there and the evil particle physics hegemony might already know it but do not inform ordinary folks;-).

M₈₉ hadron physics has survived. One of the really dramatic signatures of M₈₉ would be a production of jets coming in multiples of three due to the decay of M₈₉ quarks to quark and quark pair. In the case of M₈₉ proton this would yield at least nine jets (see this). The production of M₈₉ proton pair would produce at least 18 jets: something so sensational tha it would probably revive the speculations about mini black-holes at LHC!

Nanopoulos et al (see the posting of Lubos) have taken the ultrahigh jet multiplicities seriously and proposed an explanation in terms of pair production of gluinos: the problem of model is of course the missing missing energy. 8 would be the lower bound for the jet number whereas the decay of M₈₉ proton predicts at least 9 jets. Lubos indeed speaks of nona-jets. The estimate for gluino mass by Nanopoulos et al is 518 GeV. By direct scaling the mass of M₈₉ proton is 489 GeV.

I am quite too much a theoretician with head in the clouds. Therefore I have not considered the practical implications of discovering a scaled up copy of hadron physics instead of Higgs at LHC. The recent competing two big projects for the next collider are CLIC (compact linear collider) and ILC (International Linear Collider).

The assumption motivating these projects is that Higgs (and possibly also SUSY) will be found at LHC. These colliders would allow to perform high precision measurements related to Higgs (and SUSY). For this reason one uses electron-positron collisions and the highest energy achieved in CLIC (ILC) would be 3 TeV (1 TeV) s compared to 14 TeV to be achieved at LHC. Electrons would lose their energy via brehmstrahlung if collider were circular so that linear collider is the only possible option. The mass of M₈₉ proton is predicted to be around .5 TeV. This does not exclude the study of M₈₉ hadron physics at these colliders: for instance, the annihilation to photon or Z⁰ followed by the decay to quark pair of M₈₉ hadron physics hadronizing to M₈₉ hadrons is possible.
I am of course not a professional, but it seems to me that a better choice for the next collider would be a scaled up variant of LHC with a higher collision energy for protons. This would mean starting from scratch. Sorry! I swear that I did my best to tell! I began to talk about M₈₉ hadron physics already 15 years ago but no-one wanted to listen;-)!

By adding to the soup the super-luminal neutrinos, I can say that my life as an eternally un-employed academic pariah has changed to a captivating adventure! It is wonderful to witness the encounter of theory and reality although theory is usually the one which does not survive the collision.

Are quantum states only figments of imagination?

2011-11-18T23:23:00.000-08:00

The article The quantum state cannot be interpreted statistically by Fusey, Barrett and Rudolf has created a lot of turmoil after Nature's hype for it. Lubos reacted strongly. Also Sean Carroll commented the article in so politically correct manner that it remained unclear what he was actually saying.

The starting point is the orthodox probabilistic interpretation stating that quantum states are only mathematical constructs allowing to make predictions and therefore lack a genuine ontological status. The main point of the authors is that quantum states are real and that this destroys the probabilistic interpretation. They argue that if quantum states are only probabilistic constructs one ends up with a contradiction with quantum measurement theory. I share the belief that quantum states are real but I cannot understand how this could destroy probabilistic interpretation.

The argument

I scanned through the paper and indeed found very difficult to understand how their argument could prove that probabilistic interpretation of quantum theory is wrong.

The authors assume that probabilistic interpretation of quantum theory makes possible to prepare the system in two different manners yielding two non-orthogonal states which cannot be distinguished by quantum measurements. The reason for having several preparation processes producing different states which cannot be distinguished by quantum measurements would be that the state preparation process is probabilistic. Why this should be the case I cannot understand: in fact, they use argument based on classical probability but quantum probability is not classical!
The authors assume a pair of this kind of systems giving rise to four in-distiguishable states and apply quantum measurement theory to show that one of these states is produced with vanishing probability in quantum measurement so that the states are actually distinguishable. From this reduction ad absurdum they conclude that the probabilistic interpretation is wrong.

What goes wrong with the argument?

What could go wrong with this argument? I think that the problem is that the notions used are not defined precisely and classical and quantum probabilities are confused with each other. The following questions might help to clarify what I mean.

What one means with probabilistic interpretation? The idea that probability amplitudes can be coded by classical probabilities is certainly wrong: the probabilities defined by coefficients in the quantum superposition correspond to probabilities only in the state base used and there is infinite number of them and also the phases of coefficients matter. A good example comes from classical physics: the relative phases of Fourier components in sound wave are very important for how the sound is heard, the mere intensities of Fourier components are not enough. For instance, time reversed speech has the same power spectrum as ordinary speech but sounds totally different. The authors however use a plausibility argument based on classical probability to argue that the system can be prepared to two non-orthogonal states. This destroys the already foggy argument.
What really happens in quantum measurement? What do state function reduction and state preparation really mean? Does state function reduction really occur? The authors do not bother to ponder these questions. The same can be said about any mainstream physicist who has a healthy does of opportunism in his genes. State function reduction is in a blatant conflict with the determinism of the Schrödinger equation and this alone is an excellent reason to shut up and calculate. This is also what Lubos does although "shut up" in the case of Lubos has only symbolic meaning.
If one begins to ponder what might happen in state function reduction and preparation, one soon ends up to make questions about the relationship between experienced time and the time of physicists and free will, and eventually one becomes a consciousness theorist. The price payed is life long unemployment as a pariah of academic community regarded as intellectually retarded individual by the brahmins. I can tell this on basis of personal experience.

Why I believe that quantum states are real?

Although I was not convinced by the argument of the authors, I agree with their main point that quantum states are indeed real.

In TGD Universe quantum states are as real as something can be real. Mathematically quantum states correspond to modes of WCW ("world of classical worlds") spinor fields. They are definitely not fuzzy thought constructs of theorist needed to predict probabilities (ironically enough, WCW spinor fields allow to model the Boolean cognition among other things). And the overall important point is that this in no way excludes quantum probabilistic interpretation. There is also ontological minimalism: WCW spinor fields are the fundamental objects, there is no physical reality behind them: they are the physical realities. About this aspect more in the next section.
The non-determinism of state function reduction is the stone in the shoe of the main stream physicist and the claim that quantum states represent an outcome of probabilistic imagination is an attempt to get rid of this stone or at least forget its painful presence. The idea that Schrödinger equation would temporarily cease to be true but in such a manner that various conservation laws are obeyed is of course nonsense and the manner to escape this conclusion is to give up the notion of objective reality altogether. This does not make sense physically. The alternative trick is to assume infinitude of quantum parallel realities. This does not make sense mathematically. What is the preferred basis for these parallel realities or are all basis allowed? The attempts to answer these questions make clear that the idea is absurd.

What is the anatomy of quantum jump?

What is the anatomy of quantum jump in TGD Universe?

In TGD Universe quantum quantum jump consisting of a unitary process - I call it U - followed by a state function reduction. Unitary process acts on initial prepared state by universal unitary matrix U and generates a lot of entanglement. Quantum jump as a whole replaces WCW spinor field with a new one and the laws of physics determining the modes of WCW spinor field are not given up temporarily in quantum jump. One can say that quantum jump replaces entire time evolution with a new one and this non-determinism is outside the realm of geometric time and state space. It is this non-determinism which corresponds to that associated with subjective time identified as a sequence of quantum jumps. The reduction of act of what we call free will to quantum jump is an attractive starting point of quantum consciousness theorizing.
Our view about world is created by quantum jumps between quantum states in accordance with the basic finding that conscious experience is always accompanied change (visual conscious disappears if saccadic motion is made impossible). Consciousness is between two worlds, not in the world.
There is no need to assume physical reality behind WCW spinor fields: they are the physical realities. Note however that I use plural: the idea about unique physical reality introduced in physics by Galilei must be given up. This does not require giving up the notion of objective reality completely. One only assumes hat there is infinitude of them as any physical theory indeed predicts. The key aspect of consciousness is that it makes possible to study these realities by simply staying conscious! Every quantum jump recreates the Universe and cosmic and biological and all other evolutions reduce to this endless re-creation. God as a clock smith who built the clock and forgot the whole thing after that is replaced with Divine identified as a moment of re-creation. The new ontology also liberates us from the jailhouse of materialism.
What really happens in the state function reduction? U process in general entangles the initial state with environment and creates enormously entangled universe. State function reduction proceeds for a given CD as cascade of state function reductions downwards in the the fractal hierarchy of CDs inside CDs inside... For a given subsystem the process stops when it is not anymore possible to reduce entanglement entropy by state function reduction (by Negentropy Maximization Principle). If one accepts the notion of number theoretic entropy making sense in the intersection of real and p-adic worlds, the entanglement entropy can be also negative. This kind of entanglement is stable against state function reduction and is carrier of conscious information. Hence the reduction process stops when the system is negentropic. The conjecture is that living matter resides in the intersection of real and p-adic worlds (matter and cognition) and is therefore a carrier of negentropic entanglement.

Zero energy ontology unifies state function reduction and state preparation

Zero energy ontology (ZEO) brings in additional constraints and actually unifies state function reduction and preparation.

Zero energy states are pairs of positive and negative energy states at opposite boundaries of causal diamond identified as Cartesian product of CP₂ and intersection of future and past directed light cones of M⁴. The counterparts of positive (negative) energy states in positive energy ontology are initial (final) states. In ZEO quantum jumps have fractal structure: quantum jumps occur within quantum jumps. This corresponds also to hierarchy of conscious entities: selves having sub-selves as mental images. CD is the imbedding space correlate for self.
The arrow of time is broken already the level of zero energy states and even at single particle level: in standard ontology it is broken at the level of quantum dynamics defined by state function reductions. The positive energy part (initial state) of zero energy state corresponds to a prepared state having among other things well-defined particle numbers. For non-trivial M-matrix (and S-matrix) the negative energy part of the state (final state) cannot have these properties. In state function reduction negative energy (final state) obtains these properties.
The following question shows how a genuinely new idea immediately leads to science fictive considerations. Does ZEO imply that state preparation correspond to state function reduction for positive energy part of the state (initial state) and state function reduction to the same process for the negative energy part of the state (final state)? Could these processes would be completely symmetrical? What this symmetry would imply? Can one imagine that there reduction-preparation-preparation-.... does reduction for negative-positive-negative... energy state? One would have a kind of time flip-flop: state function reduction at the other end of CD would generate non-prepared state at the other end. The arrow of time would change in each reduction.
Mystic might talk about cycle of birth and rebirth as eternal return to youth. Eternal return to youth would be nice but would make sense only if one forgets that quantum jump involves the unitary process U. if one assumes that each quantum jump involves also U, the situation changes. Some processes in living matter - say spontaneous self assembly- seem to have reversed geometric arrow of time and one might wonder whether this kind of flip-flop can occur in living matter. Here is a home exercise for the alert reader;-).

OPERA provides additional support for neutrino superluminality

2011-11-17T20:13:00.000-08:00

OPERA collaboration has just posted an eprint Measurement of the neutrino velocity with the OPERA detector in the CNGS beam providing further support for the claim that neutrinos move faster than photons. Tommaso Dorigo describes the improved measurements in this blog. I have also discussed in an earlier posting the basic new results reported in OPERA preprint (the rumor was correct at this time!). I attach the abstract of the article.

The OPERA neutrino experiment at the underground Gran Sasso Laboratory has measured the velocity of neutrinos from the CERN CNGS beam over a baseline of about 730 km with much higher accuracy than previous studies conducted with accelerator neutrinos. The measurement is based on high-statistics data taken by OPERA in the years 2009, 2010 and 2011. Dedicated upgrades of the CNGS timing system and of the OPERA detector, as well as a high precision geodesy campaign for the measurement of the neutrino baseline, allowed reaching comparable systematic and statistical accuracies. An early arrival time of CNGS muon neutrinos with respect to the one computed assuming the speed of light in vacuum of (57.8 +/- 7.8 (stat.)+8.3-5.9 (sys.)) ns was measured. This anomaly corresponds to a relative difference of the muon neutrino velocity with respect to the speed of light (v-c)/c = (2.37+/- 0.32 (stat.) (sys.)) ×10-5. The above result, obtained by comparing the time distributions of neutrino interactions and of protons hitting the CNGS target in 10.5 μs long extractions, was confirmed by a test performed using a beam with a short-bunch time-structure allowing to measure the neutrino time of flight at the single interaction level.

The new finding is that there is a jitter in arrival times: the arrival times vary within 50 ms range which corresponds to a distance about 15 m. The shortening of travel times is not however not less than 40 ns from that when neutrinos move with light velocity as the this figure that can be found from the posting of Phil Gibbs demonstrates. Is the determination of the arrival time inaccurate? Or does the neutrino velocity have values above minimum velocity larger than c?

In TGD framework this could mean that the space-time sheet along which neutrino arrives would vary from neutrino to neutrino. The simplest possibility is that its length varies and velocity is constant: this does not look totally implausible.
Also the state of neutrino inside space-time sheet could vary from neutrino to neutrino. Classical long ranged Z⁰ fields are one of the basic predictions of TGD and in the earlier posting I proposed that neutrino feels classical Z⁰ magnetic field and arrives along cyclotron orbit. This would give a discrete spectrum of arrival velocities as
v= c_#/(1+ n×hbar× Q_Z(ν)g_ZB_Z/m_ν)^1/2
with n=0,1,2,... For some value of n the velocity would become sub-luminal. If hbar is large enough, the discrete spectrum could be seen in the arrival times. This spectrum does not however look an attractive explanation for the jitter for which spectrum seems to be above minimum value rather than below maximum value.

As I have explained, TGD explanation is unique in that it requires no tachyons and thus no breaking of causality. The solution is not any ad hoc proposal to explain one particular anomaly but one of the many outcomes of a theory solving a deep conceptual problem plaguing general relativity due to the loss of Poincare invariance. TGD fuses the good aspects of special and general relativities and leads to a unification of fundamental interactions. The basically new thing is the notion sub-manifold gravity: basic principles of special and general relativities remain as such. If effective neutrino super-luminality is real - as it seems to be- it will mean to TGD what Mickelson-Morley meant for special relativity.

TGD based explanation of effective neutrino super-luminality is discussed in the article Are neutrinos super-luminal?.

P.S. There are reasons to suspect that the mightmare of any scientific dissident could be realized. US government could block websites from public and knowing the situation in Big Science it is easy to guess that scientific dissidents like me having also non-standard views about market economy would belong to the first victims. You can prevent this.

Algebraic knots and generalized Feynman diagrams

2011-11-15T20:48:00.001-08:00

Witten has been working with knots- also 2-knots - recently (for the latest popular lecture see this) and I think that his interest on these objects is not purely mathematical. Braids are central also for quantum TGD and quite recently I learned about what are called algebraic knots and braids and realized that they might provide a new mathematical building block allowing to sharpen the vision about generalized Feynman diagrams resulting as via the fusion of ordinary Feynman diagrams and braid diagrams.

This strenghens the hopes (or raises the fears?) that a collective concentrated effort could soon transform TGD from art to a mechanical calculation recipes. In the following I tell how braid theory a la TGD differs from standard braid theory, discuss briefly the notion of algebraic knots, and summarize the interpretation of generalized Feynman diagrams as a generalized braid diagrams.

How braid theory in TGD Universe differs from the standard theory?

In TGD framework knots and braids associated with preferred 3-surfaces and possibly also 2-knots and 2-braids defined by string world sheets having braids at their ends appear naturally. This because space-time dimension is D=4. Standard braid theory must be modified to sub-manifold braid theory. Braids reside at 3-surfaces with varying topologies and knot projection must be performed to a preferred 2-surface of M⁴× CP₂. To preferred Minkowski plane M² or sphere S² at light-cone boundary.

What this means from the point of view of braid theory? A typical new situation is the one in which 3-surface is locally a product of higher genus 2-surface and R so that knot strand can wind around the 2-surface: M-theorist would talk about wrapping of branes. This gives rise to what is called non-planar braid diagrams for which projection to plane produces non-standard crossings. How to cope with this kind of situation?

Algebraic knots

The answer to the question emerged as Ulla sent me a link to an article telling about algebraic knots. The introduction of the self intersection of knot - virtual crossing - besides the usual crossing below or above can be applied to non-planar braids appearing in sub-manifold braid theory. Virtual crossing combined with the algebraization of the basic moves for braids leads to completely new and very general mathematical concepts such as kei, quandle, rack, and biquandle applying also to other mathematical structures. The basic algebraic operation is a representation of the "result for x going under y". One example is group endowed with the product a*b= bⁿab^-n for n some integer. The interesting thing is that rack is aset for which the multiplication acts as automorphism. In quantum TGD completely analogous situation occurs: zero energy states define infinitesimal symmetries of S-matrix appearing as building block of M-matrices defining zero energy states.

I see bi-quandle applying to oriented knots as the most interesting structure. It is defined as operation mapping a pair of strand portions before crossing to a pair of strand portions after crossing and satisfying also set theoretic version of Yang-Baxter equation with tensor product replaced with Cartesian product. Note that Cartesian is the classical physics correlate for tensor product used to construct many particle states in quantum physics.

Why I find algebraic knots so interesting?

Why I regard algebraic knots and braids and related mathematical structures as highly interesting notions?

All generalized Feynman diagrams are reduced to sub-manifold braid diagrams at microscopic level by bosonic emergence (bosons as pairs of fermionic wormhole throats). Three-vertices appear only for entire braids and are purely topological whereas braid strands carrying quantum numbers are just re-distributed in vertices. No 3-vertices at the really microscopic level! This is an additional nail to the coffin of divergences in TGD Universe.
By projecting the braid strands of generalized Feynman diagrams to preferred plane M², one obtains a unified description of non-planar Feynman diagrams and braid diagrams (note that for Feynman diagrams the intersections have purely combinatorial origin coming from representations as 2-D diagrams: for braid diagrams intersections have different origin and non-planarity has different meaning). The necessity to choose preferred plane M² looks strange from QFT point of view but is in TGD forced by the number theoretic vision in which M² represents hyper-complex plane of sub-space of hyper-octonions which is subspace of complexified octonions. It is also forced by the condition that the choice of quantization axes has a geometric correlate both at the level of imbedding space geometry and the geometry of the "world of classical worlds".
The obvious conjecture is that Feynman amplitudes are a analogous to knot invariants constructible by gradually reducing non-planar Feynman diagrams to planar ones after which the already existing twistor theoretical machinery of N=4 SYMs would apply (for this conjecture see the earlier posting).

These ideas are not ready to press. I have just started to play with them and I cannot guarantee that the views about what is essential might not change. I am however becoming more and more convinced that quantum TGD as almost topological QFT reduces to the analog of braid theory with topological invariance replaced by symplectic invariance bringing in those aspects of physics for which the notion of length is essential.

For twistorial ideas see the chapter Yangian symmetry, twistors, and TGD of "Towards M-Matrix" and the chapter Knots and TGD of "Physics and Geometry of Infinite-Dimensional Geometry".

OPERA finds neutrinos superluminal even with 2 ns pulse spacing

2011-11-15T19:02:00.000-08:00

Lubos informs that OPERA is going to release a new public announcement in two days or so in which they will still describe faster-than-light motion of neutrinos between CERN and Central Italy even though the spacing between the pulses in the new measurements will have been reduced to just 2 nanoseconds.

2 ns spacing between the pulses implies that pulse shape and duration cannot explain the earlier OPERA result as a measurement error. Effectively one studies individual neutrinos. Pulse shape and size has provided for the main stream theorist a cheap and fast way to explain the observation out from his mindscape. Certainly this finding also kills large class of explanations for neutrino super-luminality. Of course, one must still keep mind open for some delicate measurement error. Lubos suggests that there is a systematic error in GPS system, other colleagues have not taken this option seriously.

Sooner or later colleagues might be forced to accept that there is no other alternative than admitting that special and general relativities are somehow wrong. I realized this already towards 1977;-) (and lost my job in Helsinki University within few weeks!). Sub-manifold gravity allows Poincare invariance of special relativity as an exact symmetry unlike general relativity and provides geometrization of known fundamental interactions in terms of sub-manifold geometry for H=M⁴×CP₂.

Sub-manifold gravity also leads to the notion of many-sheeted space-time meaning a revolutionary vision about space-time topology in macroscopic and even astrophysical scales. Maximal signal velocity depends on space-time sheet, has an absolute upper bound, can depend on the distance scale and particle type but not on particle energy in continuous manner, and one can build an argument why it would be higher for neutrinos than for photons. This explanation is not anything tailored to explain OPERA result but is just one particular kinematical consequence of sub-manifold gravity. As a scientist I want to not lose professional skepticism as a basic attitude, but if you do not squeal to colleagues, I can just privately reveal that TGD is it;-)!

For the details of TGD based model of effectively super-luminal neutrinos see the article Are neutrinos super-luminal?.

Anomalous direct CP breaking in D-Dbar system?

2011-11-14T20:39:00.000-08:00

Jester has a nice posting about the evidence for CP breaking in D-Dbar system found by LHCb collaboration. I warmly recommend the posting of Jester for any-one interested in details of the experiment.

The finding of LHCb

The basic object of study is the asymmetry for the decay rates of D and Dbar mesons to π⁺π^- and K⁺K^-. One could measure the difference of D and Dbar decay rates divided by their sum to get pure number -call it A_CP - in both channels separately but due to various limitations it is better to measure the difference of these asymmetries called Δ A_CP.

The analysis gives Δ A_CP=-.82+/- .21 (stat).+/- .11 (sys) per cent. The prediction of standard model is of order .01 per cent. 3.5 sigmas inspire questions about new physics due to the new heavy particles possibly appearing in the loops giving rise to the direct CP asymmetry and involving CP breaking phase of CKM matrix in an essential manner. TGD represents new particle of many kinds (squarks of M₈₉ hadron physics and their spartners for instance) but I will not try to say anything but consider to deeper aspects of direct CP breaking.

Arrow of time at single particle level as a deeper reason for direct CP breaking

We have a bad habit to get accustomed with miracles so that they do not look miracles anymore. People busily calculating loop diagrams for CP breaking containing new exotic heavy particles tend to forget the main point. Direct CP breaking - observed aeons ago for K-Kbar system - demonstrates arrow of time at single particle level and as such represents new physics. A possible deviation from standard model predictions in D-Dbar system represents just minor technical details.

Direct CP breaking means arrow of thermodynamics at single particle level: Dbar → D rate and D--→ Dbar rate are not same. The fact is that in standard physics we do not have a slightest idea about how this could happen. CKM matrix is only a parametrization.

What TGD can add is to explain what this mysterious arrow of time at single particle level could mean at the level of first principles. Zero energy ontology is the first principle now and distinguishes between standard physics and TGD.

In zero energy ontology quantum states are zero energy states (positive/negative energy part of state initial/final state in ordinary positive energy ontology). Time like entanglement coefficients define what I call M-matrix. Different M-matrices are orthogonal to each other and rows of a unitary U matrix.
M-matrix is "square root" of density matrix expressible as a hermitian square root of density matrix and unitary S-matrix. TGD is a square root of thermodynamics in well-defined sense. Thermodynamics and irreversibility enter the game at *single particle level* rather at the level of ensemble. This is new. Arrow of time means that with respect to positive energy states M-matrix involves only prepared states with well defined particle numbers etc. but not with respect to negative energy states (final states).
Irreversibility means that the rate for the transformation of D → Dbar is different from that for Dbar → D (for instance). This is just what direct CP breaking is at the level of principle.

What can one say about CKM matrix at the level of first principles?

It is a long way from the irreversibility at single particle level to the calculation of CKM matrix from the first principles, which is the real goal at deeper level. Probably for more than decade ago I worked a model for CKM matrix reducing CKM mixing to topological mixing of quarks (see this).

Number theoretical vision suggests that the elements of CKM matrix are rational or at least algebraic numbers in some simple extension of rationals.
Physically CKM mixing redues to different mixing of the topologies of quark wormhole throats carrying U and D type quarks. This is of course something totally new.
p-Adic mass calculations in turn allow to calculate p-adic mass squared for mixed quark as average of known p-adic mass squared values of non-mixed quarks. Number theoretical constraints are extremely tight since the averages divided by p-adic mass scale squared must be integers.
The principle is simple: entropies associated with mixing matrices U and D are maximized subject to these constraints. When I introduced the model I of course had no idea that this analog of second law could correspond to genuine thermodynamics (or its square root) at single quark level. The idea was that since the orbits of partonic 2-surfaces (wormhole throats) are random light-like surfaces, thermodynamics and the analog of second law could make sense. One can reproduce the observed CKM matrix but this is not a real calculation from the first principles.

Concerning the direct CP violation at the level of hadrons, the standard diagrammatic approach using CKM matrix as input probably makes sense and it is easy to imagine candidates for new heavy particles modifying standard model predictions but it is better to leave this for specialists.