Top quark mass, Higgs mass, and supersymmetry

The difficulties of both standard model and its minimal super-symmetric version are getting worse as the experimental data are getting more precise.

1. Situation in the standard model

The most recent situation in the standard model is discussed in the posting New Top Quark Mass? in Peter Woit's blog. Top quark mass is the source of problems. According to the posting, the latest combined CDF/D0 result is: m_t = 174.3 +/- 3.4 GeV. The previous result using Run I data of m_t = 178.0 +/- 4.3 GeV. In the standard model, the new top quark mass implies a value for the Higgs mass of 94 +54/-35 Gev. The problem is that a considerable portion of this range is excluded by the LEP result that the Higgs mass must be above 114 GeV.

2. Situation in the minimal super-symmetric version of standard model

The situation in the minimal super-symmetric version of the standard model (MSSM) discussed in the posting Fine-Tuned in Jacques Distler's blog is not brighter. MSSM predicts a relation between the masses of Z⁰, Higgs, top and stop. The lowest order prediction relates Z⁰ masses and is violated already now. Loop corrections predict that Higgs mass depends logarithmically on the mass ratio of top and stop. This can save the situation provided stop mass is high enough. The recent mass for top implies that stop mass must be above 850 GeV. This does not look natural. A further problem is that the quadratic term in Higgs potential contains a contribution which is proportional to the mass squared of stop so that the large value of stop mass forces fine tuning: the level of tuning is 1 per cent for the recent data.

3. Situation in TGD

Elementary particle physics bloggers do not seem to be too worried about the situation. Peter Woit sees this as a diplomatic gesture: why speak publicly about unpleasant things just when 100 years has passed from the miraculous year when Einstein published his articles revolutionizing the physics. Personally I would speak about a deep crisis. I hope that this could be forgiven: 27 years of total devotion has led a new beautiful theory eagerly waiting for the moment when the attitudes are ripe for it to replace the old and sick standard model. Since Peter Woit made it absolutely clear that the discussion about alternative scenarios replacing standard model and possibly allowing to understand elementary particles masses will not be tolerated in his blog, I can only make comments about the situation here.

• p-adic thermodynamics for super-conformal algebra allows to understand elementary particle mass scales and also masses in one per cent precision. p-Adic mass calculations are discussed in the five chapters comprising the second part of p-Adic TGD. Number theoretical existence conditions, super-conformal symmetry, and p-adic length scale hypothesis fix the mass spectrum. Only the integers characterizing p-adic length scales of elementary particles remain free parameters but due to the exponential sensitivity of the p-adic mass scale to the value of this integer, the choices are highly unique and comes from the freedom to choose CKM matrix. CKM matrix can be fixed by number theoretical constraints by using minimal input (Cabibbo angle and CP breaking parameter).
• The basic deviation from the standard model is that the dominating contribution to fermion masses comes from p-adic thermodynamics rather than from the coupling to Higgs. Hence the coupling of Higgs to fermions can be much weaker than in standard model. Hence the rate for Higgs production can be by a factor 1/100 slower than predicted by standard model. This could explain why Higgs has not been detected if it exists. The question whether TGD really predicts Higgs is not yet settled. Group theoretical considerations favor its existence and one can imagine a candidate for Higgs.
• The model predicts the existence of p-adically scaled up versions of elementary particles. The real surprise was that these scaled up variants allow to replace Gell-Mann mass formula for the masses of low lying hadrons. The model explains some forgotten anomalies such as Aleph anomaly and suggests that the strange bumps in the measured mass distribution of top quark correspond to the scaled up variants of lighter quarks.
• TGD predicts super-conformal invariance but this symmetry does not imply space-time super-symmetry. The generators of global super-symmetries generated by covariantly constant right handed neutrino simply vanish identically. Super-conformal symmetries are genuine symmetries but change particle masses. The new exotic particles correspond to colored excitations and do not give rise to long range forces.
• TGD suggests also the existence of a scaled up variant of hadron physics corresponding to Mersenne prime M₈₉ characterizing also intermediate gauge boson. The mysterious Centauro events appearing above cosmic ray energies of about 10⁶ GeV provide support for M₈₉ hadron physics.
  • Centauros are estimated to involve a production of a "fireball" of mass of 180+/- 60 GeV. By a direct scaling the mass of the proton of M₈₉ physics would be 481 GeV and one might wonder whether the fireball could result in the collision of a relativistic M₈₉ baryon with an ordinary nucleon inducing M₈₉--> M₁₀₇ phase transition producing extremely dense phase of ordinary quark-gluon matter decaying via "color glass condensate" to ordinary hadrons.
  • Color glass condensate would correspond to a state of conformally confined quarks and gluons Bose-Einstein condensed at highly tangled color magnetic string in Hagedorn temperature. This condensate would represent a particular instance of dark matter behaving in many respects like blackhole but which Planck length replaced with hadronic length scale. The evaporation this hadronic blackhole would predict isotropic spectrum for the decay products consistent with the experimental findings. The photons emitted from the system would be BE condensates of "dark photons" decaying to ordinary photons: this could explain why photons expected from the decays of neutral pions are not detected. The formation of a hadronic black hole explains also the puzzling RHIC findings discussed previously in this blog.

Empathic reader probably guesses that sometimes I must feel myself quite frustrated while wittnessing the deepening crisis in theoretical particle physics. hep-th has become a symbol of the situation. In ancient times it contained preprints about high energy particle physics, nowadays it contains only M-theory stuff having nothing to do with elementary particle physics or physics of any other kind. The fact that the discussion about alternatives is openly discouraged and censored does not make me feel better.

Is the transformation of ordinary matter to dark matter possible in macroscopic length scales?

Even the possibility to transform ordinary matter to dark matter molecular length scales would have dramatic implications. For instance, it would give substantial support for the vision that the magnetic body of the Earth's magnetic field serves as a circuitry allowing the transfer of bio-molecules in the length scale of magnetosphere (see here).

The finding that rotating magnetic systems generate magnetic walls and the hypothesis that these walls carry dark matter provide good clues about how to achieve this kind of phase transition. The model for plasmoids as primitive life-forms involving rotating magnetic fields relies on this finding. Plasmoids themselves might be able to transform to dark matter. Shoulders discovered the existence of micron sized negatively charged clusters containing about 10¹¹ electrons and about 10⁶ ions which he reports to be able to transform to a invisible form as reported in the book of Moray B. King.

The possibility to perform this transformation for macroscopic objects would have even more dramatic implications since the objects in dark matter phase would pass through ordinary solids without any difficulty. The first implications that come in mind relate to technology (manipulation of properties of condensed matter from interior), to medicine (many-sheeted surgical operations), and research of large condensed matter systems (say the study of Earth's interior).

1. Are macroscopic visible-to-dark phase transitions possible?

One can wonder whether visible-to-dark phase transition could occur also spontaneously in macroscopic length scales. There is indeed quite a lot of documented evidence.

• Hutchison effect involves a catastrophic fracture of metal samples when posed to a radiation. Also physical objects of different composition were reported to become inexplicably embedded in each other once these objects were radiated. For a couple of years I discussed a model for this effect here. The phase transition involved with this model was not identified as ordinary-to-dark matter transformation but the basic many-sheeted mechanism inducing the temporary transparency is essentially the same.
• The appearance of human made artifacts in places where they should not occur is this kind of effect. There are a lot of reports for this kind of artifacts (see this, this , and this). These reports can of course be claimed to be just folklore. On the other hand, many of these artifacts are in museums and precise reports about where they were found exist. There are also reports about this kind of objects in journals like Scientific American. Hence one must consider seriously the possibility that the stories about artifacts in wrong place are real. Creationists have used these artifacts as an objection against Darwinian view about evolution and as a support that the actual age of universe is not more than what Bible tells. This kind of explanation is very difficult to take seriously by anyone with basic knowledge about science. T. Twietmeyer has proposed that a transformation of the ordinary matter to a form in which it can pass ordinary matter is involved with these phenomena.

Man-made objects are reported to appear in so old archeological layers that even our species did not yet exist. The ages of the artifacts discussed in previous references , if really the same as that of environment, vary from 50.000 years up to 300 million years. Artifacts have been found inside rock, inside geods which are small spherical stones with hollow interiors lined with crystals, and inside coal. Examples of artifacts found are an object which seems to be a candlestick holder, "coin", nails, screw, an object which resembles spark plug, a strange cube like object made of iron, metal nodules, gold chain, iron pot, brass bell, etc... Tornadoes are reported to induce transfer of human made artifacts to places where they should not exist. A piece of field straw penetrating through a window pane without breaking it has been reported. According to second report, a rubber tire which was not cut appeared after tornado surrounding a telephone pole that had a wooden crossbar and power lines on top. This kind of topological impossibilities would be a clear-cut signature of the ordinary-to-dark phase transition. Tornadoes are indeed basic examples of primitive living systems involving rotating magnetic and Z⁰ magnetic fields and thus generating magnetic walls or more general rotating flux quanta containing dark matter.

2. TGD based explanation for artifacts in wrong places

The TGD based mechanism explaining the findings would be the transformation of the artifact to dark matter phase (its mass would not be changed appreciably) and subsequent free fall in the gravitational field of Earth in the case that the object still feeds its gravitational flux to the space-time sheet carrying Earth's gravitational field. The object would quite literally be swallowed by Earth. For a vanishing initial velocity the time t spent in the dark matter phase would relate the depth h at which the object falls freely as t=(2h/g)^1/2, g≈ 10 m/s². From the typical depths at which the objects are found, one can conclude that the time spent in dark matter phase is measured in seconds. A possible explanation is that the rotation period of magnetic field creating the dark matter phase is usually not longer than this.

• Macroscopic quantities of dark matter could result in catastrophic events like fractures. The potential wall hindering the formation of the fracture might be overcome by the formation of dark matter phase in the immediate vicinity of the fracture. Nuclear transmutations should occur routinely in dark matter phase and there is indeed evidence for the transmutations in living matter, in cold fusion and fracto-fusion. The long lasting emission of light from fractures (earth lights observed in the lines of seismic activity) might be identifiable as coherent beams of dark photons decaying to ordinary photons. UFOs might have interpretation as plasmoids.
• The observed difficult-to-understand properties of lightnings might find explanation if lightning track is in dark matter phase so that charged particles are in effectively super-conducting phase so that electrons can accelerate to relativistic velocities. This suggests that electric discharges in high voltage could produce dark matter (perhaps this is one function of nerve pulse). Ball lightnings might induced generation of dark matter.

To sum up, it is very easy to get scientific respect by claiming that all these reports are cooked up by swindlers and taken seriously by crackpots. I however dare hope that some ingenious experimentalist would see the trouble of finding whether TGD explanation is correct by trying to develop a method of inducing the phase transition to dark matter along the lines proposed. For more details see the the chapter Quantum Coherent Dark Matter and Bio-Systems as Macroscopic Quantum Systems).

The mystery of mono-chromatic galactic gamma rays

Lubos Motl commented about the finding of galactic gamma rays which have energies very nearly to the rest of mass of electron. There was already a couple of years ago an article Astronomers claim dark matter breakthrough in New Scientist about this same topic. See also C. Boehm, D. Hooper, J. Silk, M. Casse (2003), MeV Dark Matter: Has It Been Detected?, arXiv:astro-ph/0309686. The proposal has been that these rays originate in the decays of electrons and positrons which are nearly at rest. TGD suggests a different explanation. 1. Lepto-hadrons My personal explanation for the gamma rays is based on the explanation of much older anomaly manifesting itself in heavy ion collisions at the collising energy just above the Coulomb wall (my earliest reference seems to be A. T. Goshaw et al(1979), Phys. Rev. Lett. 43, 1065). Evidence for a pion like pseudoscalar resonance decaying to electron positron pair very nearly at rest was found. The TGD based identification of the resoance is as a pion like bound state of color octed excitations of ordinary electrons possible in TGD since color is not a spin like quantum number at fundamental level but corresponds to CP₂ partial waves. The decay of leptopion BE condensate induced by the presence of pseudoscalar "instanton density" E.B created in nuclear collisions would yield the strange decay signatures. Perhaps the basic reason for why the observed resonances have been put under the rug is that asymptotic freedom dogma excludes them: the decay widths of W and Z simply leave no room for new light particles if asmptotic freedom prevails. If this is not the case, it is possible to have entire hierarchy of physics described by QCD type theories and existing only in finite range of length and momentum transfer scales. This is indeed predicted by TGD if quantum classical correspondence is taken seriously: non-vacuum extremals (with respect to inertial but not gravitational four-momenta) necessarily carry long range classical color fields. 2. TGD counterparts of cosmic strings In TGD cosmic strings dominate the very early cosmology with mass density behaving as 1/a² (a is lightcone proper time) so that initial singularity disappears since the mass per comoving volume going to zero. These cosmic strings are of form X²×Y², X² minimal surface in M⁴ and Y² complex sub-manifold of CP₂. During cosmic expansion they gradually transform to magnetic flux tubes of increasing thickness. 3. Bose-Einstein condensates of long leptohadronic magnetic flux as a particular instance of dark matter Leptohadronic (color) magnetic flux tubes with thickness about 1/m_e are good candidates for the carriers of leptopion BE condensates. The corresponding minimal magnetic field strength would be about eB=about m_e² =about 10¹⁰ Tesla with cyclotron frequency about electron mass. Magnetic fields of magnitude about 10⁹ Tesla have been assigned with supernovae. Also cyclotron transitions in a magnetic field with strentgh about 10⁹ Tesla could give rise to photons with energies around MeV but now also the harmonics of the basic line would be observed. Leptohadrons would be only a particular case of dark matter whereas dark energy would correspond to the magnetic energy of magnetic flux tubes. A TGD based model for dark matter can be found here. Leptohadrons are discussed here, and leptopions as explanation of .511 MeV gammas are discussed here. Matti Pitkanen

New Einstein or new science community?

Lee Smolin wondered for some time ago "Why No New Einstein?" in Physics Today. Smolin analyzed the reasons for the recent dead end in fundamental physics and proposed also some concrete ways to make progress. The article stimulated vivid discussions as in Not-Even-Wrong and detailed responses as in Lubos Motl's blog.

New Einstein or new science community?

Personally I would not talk about the need to find a brand new Einstein but the need to become collectively conscious of new ideas, or even better, new theories, which are already there. As some one said in some blog: there is no need to socio-engineer a new Einstein, and as I would continue: the new ideas allowing to get out from the dead end express themselves unavoidably through some brain and have probably already done so. The question is about when the community becomes mature to become conscious of these ideas and ceases to think in terms of Names. TGD indeed represents a highly developed theory reproducing standard model, predicting 4-dimensionality of space-time, and making rich spectrum of testable predictions. The problem is that it is practically impossible to communicate TGD to the quantum field theory community. Not that it would require Einstein's brains to comprehend TGD but simply because of the incredible disdain of QFT community towards people who are not names. In practice this arrogance makes these people conditional autists who neither hear nor see anything without first receiving a signal telling that the main signal originates from a Name. I have repeatedly witnessed this attitude in blogs like "Not-Even-Wrong": the response is typically a cold silence or just some sheer sillinesses like "I visited your home page and found that this work has nothing to with science" (quite a feat for an occasional visitor taking into account that the amount of material is something like 6000 pages summarizing a work of 27 years). For these fellows it does not occur that this kind of dramatic claims would require something looking like a scientific argument as a justification. The second typical visitor is an anonymous arrogant who requires Peter to banish crackpots: an easy trick to receive respect based on fear without saying anything interesting or even anything demonstrating that the person has something do with physics. Probably these tricksters are not taken too seriously by professionals. What makes me sad that Peter Woit performs typically mass deletions when the discussion is becoming really interesting rather than only attacking against landscape or Templeton foundation. The last time this occurred when a really interesting discussion about the basic assumptions of general relativity was getting on wings. Peter of course has right to eliminate from his blog new ideas which he obviously strongly dislikes. Peter has obviously not considered the possibility that Not-Even-Wrong could find a place in history as a discussion forum where the censored ideas leading out of the dead end saw the day light. Not-Even-Wrong has probably alrady now carried out its mission since even Lubos Motl admits that M-theory is in a deep crisis and has become a serious criticist of M-theory. My sincere hope is that some far-sighted enough physicist with a formal authority would create a blog site dedicated to discussions about the basic problems and basic principles.

What it feels to be quantum field theorist?

The macho attitude of QFT people cannot be understood without knowing the underlying belief system which characterizes the state of consciousness they are experiencing. Already quantum field theorists regard themselves as very exceptional people, but string theorists view themselves as super geniuses. No wonder! They know the Feynman rules! If you really believe that Feynman rules catch everything that is worth of understanding in this Infinite Universe then you have right to feel being next to God. These people also hate philosophy and conceptualization because Feymman happened to hate philosophy. Their response to any attempt to raise discussion about conceptual problems of physics is a chilly silence. Again and again I find that most of QFT people have never realized that their formulas are an outcome of a process of conceptualization which has lasted centuries and must continue if any progress is to be made. There is no deep difference between Peter Woit and Lubos Motl: Peter Woit's dream is that the glorious days of QFT would return and Lubos Motl's dream is that the ultimate theory would give M-theory as a limiting case: no problems with fundamentals of quantum theory. The state of consciousness and world view of a typical quantum field theorist is obviously somehow badly lop-sided, and as I have written earlier, these people are in many aspects at the developmental level of a ten year old boy. It is however not easy to express more precisely what really has gone wrong in the personal development of these ten year old machos.

Brief digression to integral psychology

The need to have a better diagnosis about the psychological state of QFT people has become more and more compelling during these years that I have witnessed the degeneration of theoretical physics. I was happy to learn quite a lot in this respect when I read a summary of Ken Wilber's integral psychology, which is an ambitious attempt to integrate the views about consciousness given by disciplines such as neuroscience, psychology, transpersonal psychology, and the ancient wisdom of various cultures. Wilber's approach can be seen as an attempt to fuse together various views about universe corresponding to I, We, and It. "It" is the third person view of hard science: universe consists of dead matter and consciousness has no causal role in it. "I" is the subjective view given by personal conscious experience: all science of course relies on sensory experience and tries to explain its regularities but hard nosed methodologists have forgotten this for long time ago. Self expression is essential part of "I" view and art is how I view about the world is expressed. "We" view is the view of collective and includes more abstract notions like ethics and moral. Reader has probably realized that these three views relate to the categories of Truth, Beauty and Good: only truth (or rather "truth") is included in the world view of the hard nosed scientist. Wilber introduces the notions of state, developmental line, and stage. Basic states include at least the three basic realms of consciousness: wake-up, dreaming, and deep sleep. The practitioners of meditative disciplines claim that it is possible to be conscious in each of these states and the character of conscious experience differs dramatically in these states. Spiritual practices assign to these states different bodies labelled with various names such as ordinary body, subtle body, and causal body. It is possible to distinguish about 24 loosely correlated developmental lines. Examples of lines are motor skills, cognition, language skills, social skills, and various special gifts. Along these lines one can typically distinguish about 8-10 developmental stages. No one can end up to the highest super-conscious level in all of these lines but it helps considerably if one becomes conscious about those lines where the development has not even begun. Extremely intelligent person can behave like a psychopath and a saint or super mathematician can be infant in many lines related to the practical and social life. Wilber claimes that a high level of cognitive development is necessary for the progress in other lines: intelligent persons are able to admit that they are not so good in some lines and quickly realize that they can do something for the situation. Spirituality is often regarded as a separate line whereas Wilber believes that spirituality is not a line in itself but correlates with the developmental level at various lines. I have temptation to disagree. The reader can decide. Of course Wilber's view is that of phenomenologist and the ultimate theory of consciousness probably leads to a simpler view. Despite this this approach is very fruitful since it avoids the obvious shortcomings of various schools of psychology.

What goes wrong with a typical QFTheorist and is there any cure?

Wilber's scenario provides a rough map about the personal development. It also helps to understand what has gone wrong in the science community. The basic message of Wilber is that your world view directly reflects the level of consciousness you have achieved. Vulgar skeptic really believes in his weird world view: he simply has not become conscious of more subtle levels of existence. By reading the discussions in blogs one soon learns that quite too many participants can be classified, sorry to say this, as spiritual infants. These people continually insult other participants by calling them crackpots and loonies and insisting that they should be banished from the group. These people are like these hyper-Darwinistic animals fighting, feeding, and fucking in TV documents about Wild Nature that we can enjoy almost every evening. I think that the only manner to overcome the situation in basic science is a gradual transformation of the basic education which can be only brought up by a transformation of the basic values. The basic prerequisite for this is satisfied since, thanks to web, there is no need for a scientist to become an extreme specialist who cannot work without the support of the academic community and therefore must accepts all its prejucides. Believe or not, even an elementary particle physicist could become a civilized human being conscious about the possibility that there are also other branches of physics and even other human endeavors besides elementary particle physics. This more subtle variant of elementary particle physicist could become conscious about the possibility that standard model might not explain everything above intermediate boson length scale. Eventually he could discover that there is a phenomenon known as life about which recent day fundamental physics can say practically nothing really interesting. He could even realize that consciousness is an equally deep mystery for physics and directly related to the basic conceptual problems of quantum theory and that anyone who dreams of becoming the new Einstein should take it very seriously. At these subtler levels of consciousness this new variant of elementary particle physicist would realize that Curriculum Vitae is not the only measure of personal growth that even people without name might have something interesting to say. Matti Pitkanen

Is it possible to understand coupling constant evolution at space-time level?

It is not yet possible to deduce the length scale evolution of gauge coupling constants from Quantum TGD proper. Quantum classical correspondence however encourages the hope that it might be possible to achieve some understanding of the coupling constant evolution by using the classical theory. This turns out to be the case and the earlier speculative picture about gauge coupling constants associated with a given space-time sheet as RG invaraints finds support. It remains an open question whether gravitational coupling constant is RG invariant inside give space-time sheet. The discrete p-adic coupling constant evolution replacing in TGD framework the ordinary RG evolution allows also formulation at space-time level as also does the evolution of hbar associated with the phase resolution. 1. RG evolution of gauge coupling constants for single space-time sheet The renormalization group equations of gauge coupling constants g_i follow from the following idea. The basic observation is that gauge currents have vanishing covariant divergences whereas ordinary divergence does not vanish except in the Abelian case. The classical gauge currents are however proportional to 1/g_i² and if g_i² is allowed to depend on the space-time point, the divergences of currents can be made vanishing and the resulting flow equations are essentially renormalization group equations. The physical motivation for the hypothesis is that gauge charges are assumed to be conserved in perturbative QFT. The space-time dependence of coupling constants takes care of the conservation of charges. A surprisingly detailed view about RG evolution emerges.

• The UV fixed points of RG evolution correspond to CP₂ type extremals (elementary particles).
• The Abelianity of the induced Kähler field means that Kähler coupling strength is RG invariant which has indeed been the basic postulate of quantum TGD. The only possible interpretation is that the coupling constant evolution in sense of QFT:s corresponds to the discrete p-adic coupling constant evolution.
• IR fixed points correspond to space-time sheets with a 2-dimensional CP₂ projection for which the induced gauge fields are Abelian so that covariant divergence reduces to ordinary divergence. Examples are cosmic strings (, which could be also seen as UV fixed points), vacuum extremals, solutions of a sub-theory defined by M⁴\times S², S² a homologically non-trivial geodesic sphere, and "massless extremals".
• At the light-like boundaries of the space-time sheet gauge couplings are predicted to be constant by conformal invariance and by effective two-dimensionality implying Abelianity: note that the 4-dimensionality of the space-time surface is absolutely essential here.
• In fact, all known extremals of Kähler action correspond to RG fixed points since gauge currents are light-like so that coupling constants are constant at a given space-time sheet. This is consistent with the earlier hypothesis that gauge couplings are renormalization group invariants and coupling constant evolution reduces to a discrete p-adic evolution. As a consequence also Weinberg angle, being determined by a ratio of SU(2) and U(1) couplings, is predicted to be RG invariant. A natural condition fixing its value would be the requirement that the net vacuum em charge of the space-time sheet vanishes at least in good approximation. This would state that em charge is not screened like weak charges.
• When the flow determined by the gauge current is not integrable in the sense that flow lines are identifiable as coordinate curves, the situation changes. If gauge currents are divergenceless for all solutions of field equations, one can assume that gauge couplings are constant at a given space-time sheet and thus continuous also in this case. Otherwise a natural guess is that the coupling constants obtained by integrating the renormalization group equations are continuous in the relevant p-adic topology below the p-adic length scale. Thus the effective p-adic topology would emerge directly from the hydrodynamics defined by gauge currents.

2. RG evolution of gravitational and cosmological constants for single space-time sheet Similar considerations apply in the case of gravitational and cosmological constants.

• In this case the conservation of gravitational mass determines the RG equation (gravitational energy and momentum are not conserved in general).
• The assumption that coupling cosmological constant λ is proportional to 1/L_p² (L_p denotes the relevant p-adic length scale) explains the mysterious smallness of the cosmological constant and leads to a RG equation which is of the same form as in the case of gauge couplings.
• Asymptotic cosmologies for which gravitational four momentum is conserved correspond to the fixed points of coupling constant evolution now but there are much more general solutions satisfying the constraint that gravitational mass is conserved.
• It seems that gravitational constant cannot be RG invariant in the general case and that effective p-adicity can be avoided only by a smoothing out procedure replacing the mass current with its average over a four-volume 4-volume of size of order p-adic length scale.

3. p-Adic evolution of gauge couplings If RG invariance at given space-time sheet holds true, the question arises whether it is possible to understand p-adic coupling constant evolution at space-time level.

• Simple considerations lead to the idea that M⁴ scalings of the intersections of 3-surfaces defined by the intersections of space-time surfaces with light-cone boundary induce transformations of space-time surface identifiable as RG transformations. If sufficiently small they leave gauge charges invariant: this seems to be the case for known extremals which form scaling invariant families. When the scaling corresponds to a ratio p₂/p₁, p₂> p₁, bifurcation would become possible replacing p₁-adic effective topology with p₂-adic one.
• Stability considerations determine whether p₂-adic topology is actually realized and could explain why primes near powers of 2 are favored. The renormalization of coupling constant would be dictated by the requirement that Q_i/g_i² remains invariant.

4. p-Adic evolution in angular resolution and dynamical hbar For a given p-adic topology algebraic extensions of p-adic numbers define also a hierarchy ordered by the dimension of the extension and this hierarchy naturally corresponds to an increasing angular resolution so that RG flow would be associated also with it.

• A characterization of angular scalings consistent with the identification of hbar as a characterizer of the topological condensation of 3-surface X³ to a larger 3-surface Y³ is that angular scalings correspond to the transformations Φ --> rΦ, r=m/n in the case of X⁴ and Φ --> Φ in case of Y⁴ so that X³ becomes analogous to an m-fold covering of Y³. Rational coverings could also correspond to m-fold scalings for X³ and n-fold scalings for Y³.
• The formation of these stable multiple coverings could be seen as an analog for a transition in chaos via a process in which a closed Bohr orbit regarded as a particle itself becomes an orbit closing only after m turns. TGD predicts a hierarchy of higher level zero energy states representing S-matrix of lower level as entanglement coefficients. Particles identified as "tracks" of particles at orbits closing after m turns might serve as space-time correlates for this kind of states. There is a direct connection with the fractional quantum numbers, anyon physics and quantum groups.
• The simplest generalization from the p-adic length scale evolution consistent with the proposed role of Beraha numbers B_n=4cos²(π/n)is that bifurcations can occur for integer values of r=m and change the value of hbar. The interpretation would be that single 2π rotation in δ M⁴₊ corresponds to the angular resolution with respect to the angular coordinate φ of space-time surface varying in the range (0,2π) and is given by Δφ=2π/m.
• The evidence for a gigantic but finite value of "gravitational" Planck constant suggests that large values of hbar corresponding to 3<n<4 and defining a "generalized" Beraha number B_r are possible. For n=3 corresponding to the minimal resolution of Δ φ=2π/3 hbar would be infinite. This would allow to keep the formula for hbar(n) in its original form by replacing n with a rational number. This would mean that also rational values of r correspond to bifurcations in the range 3<r<4 at least. The interpretation would be that hbar is characterized besides the integer n assignable to Jones inclusion and to X³ also by integer m assignable to Y³, such m/n <3.

For more details see the chapters An Overview about the Evolution of Quantum TGD and for even more details the new chapter Is it Possible to Understand Coupling Constant Evolution at Space-Time Level? of TGD. Matti Pitkänen

Does dark matter provide a correct interpretation of long ranged classical electro-weak gauge fields?

For more than two decades one of the basic interpretational challenges of TGD has been to understand how the un-avoidable presence of long range classical electro-weak gauge fields can be consistent with the small parity breaking effects in atomic and nuclear length scales. Also classical color gauge fields are predicted, and I have proposed that color qualia correspond to increments of color quantum numbers. The proposed model for screening cannot banish the unpleasant feeling that the screening cannot be complete enough to eliminate large parity breaking effects in atomic length scales so that one one must keep mind open for alternatives. p-Adic length scale hypothesis suggests the possibility that both electro-weak gauge bosons and gluons can appear as effectively massless particles in several length scales and there indeed exists evidence that neutrinos appear in several scaled variants (hep-ph/0401099) (TGD based model is discussed here ).

1. Long range classical electro-weak and color fields as classical correlates of dark electro-weak bosons and gluons?

This inspires the working hypothesis that long range classical electro-weak gauge and gluon fields are correlates for light or massless dark electro-weak gauge bosons and gluons.

• In this kind of scenario ordinary quarks and leptons could be essentially identical with their standard counterparts with electro-weak charges screened in electro-weak length scale so that the problems related to the smallness of atomic parity breaking would be trivially resolved.
• In condensed matter blobs of size larger than neutrino Compton length (about 5 \mum if k=169 determines the p-adic length scale of condensed matter neutrinos) the situation could be different. Also the presence of dark matter phases with sizes and neutrino Compton lengths corresponding to the length scales L(k), k=151,157,163,167 in the range 10 nm-2.5 μm are suggested by the number theoretic considerations (these values of k correspond to so called Gaussian Mersennes). Only a fraction of the condensed matter consisting of regions of size L(k) need to be in the dark phase.
• Dark quarks and leptons would have masses essentially identical to their standard model counterparts. Only the electro-weak boson masses which are determined by a different mechanism than the dominating contribution to fermion masses (see this and this) would be small or vanishing.
• The large parity breaking effects in living matter would be due to the presence of dark nuclei and leptons. I have also proposed that super-fluidity corresponds to Z⁰ super-conductivity: it might be that also super-fluid phase corresponds to dark neutron phase.

2. Conformal confinement and large value of hbar

The basic prediction of TGD based model of dark matter as a phase with a large value of Planck constant is the scaling up of various quantal length and time scales. A simple quantitative model for condensed matter with large value of hbar predicts that hbar is by a factor ≈ 2¹¹ determined by the ratio of CP₂ length to Planck length larger than in ordinary phase meaning that the size of dark neutrons would be of order atomic size. In this kind of situation single order parameter would characterize the behavior of dark neutrinos and neutrons and the proposed model could apply as such also in this case. Dark photon many particle states behave like laser beams decaying to ordinary photons by de-coherence meaning a transformation of dark photons to ordinary ones. Also dark electro-weak bosons and gluons would be massless or have small masses determined by the p-adic length scale in question. The decay products of dark electro-weak gauge bosons would be ordinary electro-weak bosons decaying rapidly via virtual electro-weak gauge boson states to ordinary leptons. Topological light rays ("massless extremals") for which all classical gauge fields are massless are natural space-time correlates for the dark boson laser beams. In conformally confined phase phase Fermi statistics allows neutrinos to have same energy if their conformal weights are different so that a kind "fermionic Bose-Einstein condensate" would be in question. If both nuclear neutrons and neutrinos are in dark phase, it is possible to achieve a rather complete local cancellation of Z⁰ charge density.

3. Model for neutrino screening and implications for bio-chemistry

The model for neutrino screening developed in TGD and Condensed Matter was developed years before the ideas about the identification of the dark matter emerged. The generalization of the discussion to the case of dark matter option should be rather trivial and is left to the reader as well as generalization of the discussion of the effects of long range Z⁰ force on bio-chemistry. For more details see the chapter TGD and Condensed Matter of "TGD and p-Adic Numbers" and Quantum Coherent Dark Matter and Bio-Systems as Macroscopic Quantum Systems of "Genes, Memes, Qualia, and Semitrance". Matti Pitkanen

Observational evidence for classical Z0 force?

Lubos Motle tells in his posting Deviations from Newton's law seen? about yet unpublished findings of a highly respected experimental group providing evidence for deviations from Newton's law at distances below 100 microns at 4 sigma level. The experimenters intend to increase the effect to 8 sigma level before publishing anything and this takes year or two. In most models gravitational force is expected to become stronger at short distances. For instance, in super string inspired models with two large dimensions for which unification of gauge and gravitational occurs in electroweak scale the gravitational 1/r² force changes to 1/r⁴ in millimeter length scale. Interestingly, 100 microns corresponds to the length scale defined by the recent value of cosmological constant. The experimenters suggest a rather wavy notion of flat graviton as an explanation for the weakening. Gravitons with wavelengths shorter than 100 microns would not exist at all. A deeper justification is lacking and to me the idea seems to be in a complete conflict with the unification program since other elementary particles have no trouble in having much smaller wave lengths. Consider now what TGD could say about the situation. One of the deviations of TGD from standard model is the prediction of classical electroweak fields resulting as projections of the CP₂ spinor connection to the space-time surface in M⁴xCP₂. Long range classical Z⁰ fields are unavoidable and I have discussed various experimental implications extensively in books about TGD. The length scale at which effects become visible corresponds to neutrino Compton length and cellular length scale about 5 micrometers (to be precise, TGD strongly suggests that neutrinos can be in several mass states so that Compton lengths in the range 10 -1000 nm are possible). In single sheeted space-time these fields would be of course a catastrophe (consider only large parity breakings) but in many-sheeted spacetime situation changes. The mysterious chirality selection in living matter could be understood in terms of the axial couplings to classical Z⁰ fields and they would play star role in bio-catalysis. Low energy neutrinos or some other particles with same electroweak quantum numbers would be needed to screen the classical Z⁰ force. The requirement that parity breaking effects are small requires that quarks feed their Z⁰ charges to space-time sheets having size about 5 microns (they correspond to p-adic prime p ≈ 2^k, k=169. I have also discussed classical Z^0 force in the context of nuclear physics here. Here I have discussed the possibility that either ordinary neutrinos, their Cooper pairs, or sneutrinos could do the screening of nuclear Z⁰ charge. The high Fermi energy in case of neutrino screening is a potential problem. Furthermore, is seems that TGD does not allow space-time supersymmetry. Dark neutrino BE condensate for which individual neutrinos would have complex conformal weights (related closely to zeros of Riemann Zeta) with entire system having real conformal weight would allow to circumvent statistics constraint and in principle would allow neutrinos to be in the same energy state. Interestingly, the Bohr radii of dark matter "super atoms" consisting of blobs of dark nuclei surrounded by dark electrons are in the range .2-.8 mm: not far from .1 mm scale defined by cosmological constant. Dark atoms and dark condensed matter I have discussed in earlier postings and the interested reader can consult the chapter Quantum Coherent Dark Matter and Bio-Systems as Macroscopic Quantum Systems. TGD view about dark matter is as a phase with a large value of hbar: in condensed matter situation the value hbar about 2¹¹ times larger than in normal condensed matter is strongly suggestive. The magnitude of this parameter is determined by the ratio of CP ₂ length scale to Planck length scale, the latter being a prediction in TGD rather than input. Classical Z⁰ force would be a natural candidate for explaining the claimed effective weakening of gravitational force and I have discussed bounds for the net density of Z⁰ charge at condensed matter space-time sheets from the requirement that Z⁰ repulsion does not exceed gravitational attraction. Matti Pitkanen

Out of Body

Out-of-body experiences (OBEs) are often understood as experience of seeing oneself from a position outside of the body. OBEs are poorly understood in the framework of neuro science and pose a challenge for the reductionistic world view. I have found these experiences especially interesting test bed for TGD inspired theory of consciousness, not least for the reason that I have quite rich personal repertoire of them. Basic differences between TGD and Maxwell's ED is topological field quantization. Magnetic fields and radiation fields decompose to field quanta which correspond to space-time sheets with outer boundary. For instance, magnetic field decomposes to flux quanta. This means that one can assign to any system a definite field identity, magnetic body. In fact a hierarchy of this kind of bodies is predicted. Typically the size of the magnetic body is much larger than of material system or biological body. In TGD framework the notion of magnetic body provides an attractive starting point in attempts to understand what OBEs and related experiences are. The basic idea is that magnetic body serves effectively as a mirror defining a third person view as a cognitive representation also in ordinary wake-up state and that during OBEs this representation becomes sensory representation. Magnetic body need not always be a personal magnetic body but could correspond to a magnetic body receiving information from several brains (collective consciousness), magnetic body of another person, or be even associated with "dead" matter. The progress in identifying dark matter as a phase of matter with large value of Planck constant making possible macroscopic quantum coherence has led to the vision about dark matter at magnetic flux quanta as quantum controller of ordinary matter in living systems. The Bose-Einstein condensates of dark photons decaying via decoherence to ordinary photons mediate interactions between ordinary and dark matter and the hypothesis is that dark photon "laser" beams from body and brain reflected at magnetic flux quanta give rise to third person aspect of consciousness which in OBEs and related experiences are realized as sensory representations. The identification of bio-photons as end products of the de-coherence of dark photon beams is natural. The model leads also to a model for dreams, hallucinations, sensory feedback from brain to sensory organs, and directed attention. Concrete models for how dark photons can give rise to experiences in various sensory modalities such as vision, hearing, olfaction, and tactile senses, are proposed. For more details see the chapter TGD Based Model for OBEs.