What's new inPhysics in ManySheeted SpaceTimeNote: Newest contributions are at the top! 
Year 2008 
Anyonic view about black holes
A new element to the model of black hole comes from the vision that black hole horizon as a lightlike 3surface corresponds to a lightlike orbit of lightlike partonic 2surface. This allows two kinds of black holes. Fermion like black hole would correspond to a deformed CP_{2} type extremal which Euclidian signature of metric and topologically condensed at a spacetime sheet with a Minkowskian signature. Boson like black hole would correspond to a wormhole contact connecting two spacetime sheets with Minkowskian signature. Wormhole contact would be a piece deformed CP_{2} type extremal possessing two lightlike throats defining two black hole horizons very near to each other. It does not seem absolutely necessary to assume that the interior metric of the blackhole is realized in another spacetime sheet with Minkowskian signature. Second new element relates to the value of Planck constant. For (^{h}/_{2p})_{gr} = 4GM^{2} the Planck length L_{P}((^{h}/_{2p})) = �{(^{h}/_{2p}) G} equals to Schwartschild radius and Planck mass equals to M_{P}((^{h}/_{2p})) = �{(^{h}/_{2p})/G} = 2M. If the mass of the system is below the ordinary Planck mass: M � m_{P}((^{h}/_{2p})_{0})/2 = �{(^{h}/_{2p})_{0}/4G}, gravitational Planck constant is smaller than the ordinary Planck constant. Black hole surface contains ultra dense matter so that perturbation theory is not expected to converge for the standard value of Planck constant but do so for gravitational Planck constant. If the phase transition increasing Planck constant is a friendly gesture of Nature making perturbation theory convergent, one expects that only the black holes for which Planck constant is such that GM^{2}/4p(^{h}/_{2p}) < 1 holds true are formed. Black hole entropy being proportional to 1/(^{h}/_{2p}) is of order unity so that TGD black holes are not very entropic. If the partonic 2surface surrounds the tip of causal diamond CD, the matter at its surface is in anyonic state with fractional charges. Anyonic black hole can be seen as single gigantic elementary particle stabilized by fractional quantum numbers of the constituents preventing them from escaping from the system and transforming to ordinary visible matter. A huge number of different black holes are possible for given value of (^{h}/_{2p}) since there is infinite variety of pairs (n_{a},n_{b}) of integers giving rise to same value of (^{h}/_{2p}). One can imagine that the partonic surface is not exact sphere except for ideal black holes but contains large number of magnetic flux tubes giving rise to handles. Also a pair of spheres with different radii can be considered with surfaces of spheres connected by braided flux tubes. The braiding of these handles can represent information and one can even consider the possibility that black hole can act as a topological quantum computer. There would be no sharp difference between the dark parts of black holes and those of ordinary stars. Only the volume containing the complex flux tube structures associated with the orbits of planets and various objects around star would become very small for black hole so that the black hole might code for the topological information of the matter collapsed into it.
For details and background see the updated chapter Quantum Astrophysics. 
Revised vision about quantum astrophysicsI had deduced earlier a formula for the quantized Planck constant from the requirement that it represents algebraic homomorphism. Two options for which Planck constants were inverses of each other were possible. As usual, I chose the wrong one! The development of a detailed model for fractional quantum Hall effect fixed the choice on basis of physical arguments. The next task is to go through all applications and make the needed modifications. I started from Quantum Astrophysics. A glue below the abstract. The vision that the quantum dynamics for dark matter is behind the formation of the visible structures suggests that the formation of the astrophysical structures could be understood as a consequence of gravitational Bohr rules. The origin of these rules has remained a little bit mysterious until the discovery that the hierarchy of Planck constants relates very closely to anyons and fractionization of quantum numbers. For details and background see the updated chapter Quantum Astrophysics. 
Flyby anomaly as relativistic transverse Doppler effect?For half year ago I discussed a model for the flyby anomaly based on the hypothesis that dark matter ring around the orbit of Earth causes the effect. The model reproduced the formula deduced for the change of the velocity of the spacecraft at qualitative level, and contained single free parameter: essentially the linear density of the dark matter at the flux tube. From Lubos I learned about a new twist in the story of flyby anomaly. September twelfth 2007 JeanPaul Mbelek proposed an explanation of the flyby anomaly as a relativistic transverse Doppler effect. The model predicts also the functional dependence of the magnitude of the effect on the kinematic parameters and the prediction is consistent with the empirical findings in the example considered. Therefore the story of flyby anomaly might be finished and dark matter at the orbit of Earth could bring in only an additional effect. It is probably too much to hope for this kind of effect to be large enough if present. For background see the chapter TGD and Astrophysics.

Could symplectic QFT allow to understand the fluctuations of CMB?Depending on one's attitudes, the anomalies of the fluctuation spectrum of the cosmic microwave background (CMB) can be seen as a challenge for people analyzing the experiments or that of the inflationary scenario. I do not pretend to be deeply involved with CMB but as I read about one these anomalies in Sean Carrol's blog and next day in Lubos's blog, I felt that I could spend some days by clarifying myself what is involved. What interests me whether the replacement of inflation with quantum criticality and hbar changing phase transitions could provide fresh insights about fluctuations and anomalies of CMB. In the following I try first to explain to myself what the anomalies are and after that I will consider some TGD inspired crazy (as always) ideas. My motivations to communicate are indeed strong: the consideration of the anomalies led to a generalization of the notion of conformal QFT to what might be called symplectic QFT having very natural place also in quantum TGD proper. A brief summary about my views is as follows.

From Equivalence Principle to Zero Energy OntologyThe tension between analytic and constructive approaches is present even in Einstein's own theory and was the basic stimulus leading to TGD. Equivalence Principle states that gravitational and inertial masses are identical. This statement is however rather problematic as Einstein himself was first to admit. Einstein's equations express the identity for gravitational and inertial energy momentum densities as a consequence of a variational principle. There is however no global version of this statement because one cannot define the notions of inertial and gravitational fourmomenta without adherence to perturbative approach. The hypothesis that spacetimes are 4D surfaces of a higherdimensional spacetime of form H=M^{4}×S resolves the problem: since Poincare symmetries become symmetries of H rather than spacetime itself. Inertial fourmomentum can be defined as a conserved Noether charge and also gravitational fourmomentum can be regarded as a Noether charge albeit nonconserved. Equivalence Principle can hold true only under some additional conditions. For instance, for the imbeddings of RobertsonWalker cosmologies inertial fourmomentum density vanishes unlike gravitational fourmomentum density, which for a long time remained quite a mystery. The real understanding of the situation became possible only after the introduction of what I call zero energy ontology. In zero energy ontology one replaces positive energy states with zero energy states with positive and negative energy parts of the state at the boundaries of future and past direct lightcones forming a causal diamond. All conserved quantum numbers of the positive and negative energy states are of opposite sign so that these states can be created from vacuum. Äny physical state is creatable from vacuum" becomes thus a basic principle of quantum TGD and together with the notion of quantum jump resolves several philosophical problems (What was the initial state of universe?, What are the values of conserved quantities for Universe, Is theory building completely useless if only single solution of field equations is realized?). At the level of elementary particle physics positive and negative energy parts of zero energy state are interpreted as initial and final states of a particle reaction so that quantum states become physical events. Equivalence Principle would hold true in the sense that the classical gravitational fourmomentum of the vacuum extremal whose small deformations appear as the argument of configuration space spinor field is equal to the positive energy of the positive energy part of the zero energy quantum state. Equivalence Principle is expected to hold true for elementary p"../articles/ and their composites but not for the quantum states defined around nonvacuum extremals. More precisely, the inertial fourmomentum assignable to the 3D ChernSimons action is nonvanishing only if one adds to the CP_{2} Kähler form a pure gauge part A_{a}=constant, where a denotes light cone proper time . A breaking of Poincare invariance is implied which is however compensated by the fact that configuration space corresponds to the union of configuration spaces associated with future and past directed lightcones. If the vacuum extremal is also an extremal of the curvature scalar, gravitational fourmomentum is conserved. In the case of CP_{2} type vacuum extremal gravitational stationarity transforms the M^{4} projection of the extremal from a random lightlike curve to a lightlike geodesic allowing an interpretation as incoming or outgoing on mass shell particle. General vacuum extremal corresponds to a virtual particle. At the classical level Equivalence Principle requires that the lightlike gravitational fourmomentum of CP_{2} vacuum extremal coincides with the lightlike inertial fourmomentum associated with ChernSimons action in this situation. This condition relates the value of A_{a} to gravitational constant G and CP_{2} radius R. G would thus appear as a fundamental constant and quantum criticality should dictate the ratio G/R^{2}. The topologically condensed CP_{2} type vacuum extremal necessarily creates a nonvacuum region around it and the resulting inertial fourmomentum corresponds to the gravitational fourmomentum. The strong form of Equivalence Principle would require that the classical 4momentum associated with Kähler action of allowed small deformations coincides with the conserved gravitational fourmomentum of the vacuum extremal extremizing curvature scalar: this might have a natural interpretation in terms of Bohr orbitology but is not be consistent with zero energy ontology inspired picture unless one has double sheeted structure with sheets possessing opposite energies such that double sheeted structure is approximated by single sheet with RobertsonWalker cosmology in GRT framework. The identification of gauge bosons as wormhole contacts and gravitons as pairs of wormhole contacts supports double sheeted structure with sheets possessing opposite arrows of geometric time. Near the vicinity of wormhole contacts (pieces of CP_{2} type vacuum extremals) the sheets which are originally vacuum extremals are deformed to nonvacuum extremals and carry inertial fourmomentum which should be equal to the gravitational four momentum of the vacuum extremal. For background see the chapter TGD and GRT . See also the article "Topological Geometrodynamics: an Overall View".

The mystery of mini galaxies and the hierarchy of Planck constantsNew Scientist informs that a team led by Pieter van Dokkum at Yale University measured the light of distant galaxies from around 3 billion years after the big bang. They had the same mass as the Milky Way, but were 10 times smaller (The Astrophysical Journal, vol 677, p L5). Peering at younger regions of the sky shows that galaxies this size are no longer around, but it's not clear what happened to them. "This is a very puzzling result," says Simon White of the Max Planck Institute for Astrophysics in Garching, Germany. "Galaxies cannot disappear." Team member Marijn Franx of Leiden Observatory, the Netherlands, suspects they have since merged with extremely massive galaxies. The evidence of Bohr quantization of planetary orbits with a gigantic value of Planck constant led originally to the idea that Planck constant in TGD Universe has a spectrum of discrete values. The hierarchy of Planck constants leads to generalization of the imbedding space H=M^{4}×CP_{2} so that it becomes a book like structure with pages characterized partially by the value of Planck constant (see this). This generalization is not anymore ad hoc but is essential for the realization of quantum criticality and the construction of quantum TGD proper: for instance, Higgs mechanism and the manner how spacetime sheet is assigned with lightlike 3surfaces defining the fundamental dynamical objects of quantum TGD can be understood in this framework (see this ). The matters at different pages would be dark relative to each other since the p"../articles/ from different pages cannot appear in the same interaction vertex (see for instance this). The p"../articles/ at different pages can however interact via classical gauge and gravitational fields leaking between the pages via the back of the book, and by the exchange of p"../articles/ tunneling in the same manner and thus experiencing a phase transition changing Planck constant. The model for living matter and gravitational interactions suggests that the spacetime sheets containing dark matter are magnetic and gravimagnetic flux tubes (perhaps the attribute "wormhole magnetic" is more accurate characterization) (see this). These assumptions guarantee consistency with what is known about dark matter (long range classical gauge fields do not  or at least are not believed to exist) so that only the classical gravitational interaction and graviton exchanges necessarily involving hbar changing phase transition remain in astrophysical length scales. The interactions with p"../articles/ of visible matter via graviton exchanges are predicted to differ from what GTR predicts (see this): ordinary gravitons could appear as bursts corresponding to the decays of gigantic gravitons with large hbar to ordinary gravitons. These kind of bursts would be interpreted as external perturbations and would not be counted as gravitons. This framework also explains various really weird anomalies in neuroscience and biology, in particular those associated with living cell, if considerable part of biologically important ions are in phase with large Planck constant phase at what I call wormhole magnetic flux tubes (see this, this, this, and this). Consider now the mysterious disappearance of mini galaxies. The smooth cosmic expansion of standard cosmology is in TGD replaced by quantum leaps analogous to quantum transitions of atoms in which the Planck constant associated with the spacetime sheet increases by a factor which is most naturally power of 2. The expansion of dark matter forces the visible matter condensed around it to follow. There are several applications: in particular, the piecewise expansion of Earth explains those forgotten facts about the evolution of continents which Wegener's theory failed to explain. The disappearance of the mini galaxies would be due to this mechanism. From the assumption that this mechanism gives rise to the same outcome as smooth expansion within factor of two at given moment, one could estimate their recent size. If the galaxies are assumed to have roughly the size of Milky Way now, an upwards scaling would be roughly by a factor 8. This would mean that recent age of Universe would be about 24 billion years. For background see the chapter TGD and Astrophysics .

Dark matter based model for Flyby anomalyThe so called flyby anomaly provides a test for any theory of gravitation, quantal or not. I have already earlier discussed a model of this anomaly based on dark matter located either at spherical shell or tube around Earth's orbit. The recent data (see this and this ) allowed to fix the model to a tube around the orbit of Earth deformed by gravimagnetic force of Earth to the direction of equatorial plane of Earth. 1. Flyby anomaly Flyby mechanism used to accelerate spacecrafts is a genuine three body effect involving Sun, planet, and the spacecraft. Planets are rotating around sun in an anticlockwise manner and when the spacecraft arrives from the right hand side, it is attracted by a planet and is deflected in an anticlockwise manner and planet gains energy as measured with respect to solar center of mass system. The energy originates from the rotational motion of the planet. If the spacecraft arrives from the left, it loses energy. What happens is analyzed the above linked article using an approximately conserved quantity known as Jacobi's integral J= e ω e_{z} · r× v. Here e is total energy per mass for the spacecraft, ω is the angular velocity of the planet, e_{z} is a unit vector normal to the planet's rotational plane, and various quantities are with respect to solar cm system. This as such is not anomalous and flyby effect is used to accelerate spacecrafts. For instance, Pioneer 11 was accelerated in the gravitational field of Jupiter to a more energetic elliptic orbit directed to Saturn ad the encounter with Saturn led to a hyperbolic orbit leading out from solar system. Consider now the anomaly. The energy of the spacecraft in planetspacecraft cm system is predicted to be conserved in the encounter. Intuitively this seems obvious since the time and length scales of the collision are so short as compared to those associated with the interaction with Sun that the gravitational field of Sun does not vary appreciably in the collision region. Surprisingly, it turned out that this conservation law does not hold true in Earth flybys. Furthermore, irrespective of whether the total energy with respect to solar cm system increases or decreases, the energy in cm system increases during flyby in the cases considered. Five Earth flybys have been studied: GalileoI, NEAR, Rosetta, Cassina, and Messenger and the article of Anderson and collaborators gives a nice quantitative summary of the findings and of the basic theoretical notions. Among other things the tables of the article give the deviation δe_{g,S} of the energy gain per mass in the solar cm system from the predicted gain. The anomalous energy gain in rest Earth cm system is δe_{E}≈ v·δv and allows to deduce the change in velocity. The general order of magnitude is δv/v≈ 10^{6} for GalileoI, NEAR and Rosetta but consistent with zero for Cassini and Messenger. For instance, for Galileo I one has v_{inf,S}= 8.949 km/s and δv_{ inf,S}= 3.92+/ .08 mm/s in solar cm system. Many explanations for the effect can be imagined but dark matter is the most obvious candidate in TGD framework. The model for the Bohr quantization of planetary orbits assumes that planets are concentrations of the visible matter around dark matter structures. These structures could be tubular structures around the orbit or a nearly spherical shell containing the orbit. The contribution of the dark matter to the gravitational potential increases the effective solar mass M_{eff,S}. This of course cannot explain the acceleration anomaly which has constant value. One can also consider dark matter rings associated with planets and perhaps even Moon's orbit is an obvious candidate now. It turns out that the tube associated with Earth's orbit and deformed by Earth's presence to equatorial plane of Earth explains qualitatively the known facts.
2. Dark matter at the orbit of Earth? The almost working model is based on dark matter on the orbit of Earth. One can estimate the change of the kinetic energy in the following manner.
Consider first some conclusions that one can make from this model.
The most recent report (see this ) provides additional information about the situation.
3. Is the tube containing the dark matter deformed locally into the equatorial plane? The previous model works qualitatively if the interaction of Earth and flux tube around Earth's orbit containing the dark matter modifies the shape of the tube locally so that the portion of the tube contributing to the anomaly lies in a good approximation in P_{E} rather than P _{O}. In this case the minimum value of the distance r_{ES} between γ _{E} and γ_{S} is maximal for the symmetric situation with θ_{i }=θ_{f} and the effect is minimal. In an asymmetric situation the minimum value of r_{ES} decreases and the size of the effect increases. Hence the model works at least qualitatively of the motion of Earth induces a moving deformation of the dark matter tube to P_{E}. With this assumption one can write ΔE in a physically rather transparent form showing that it is consistent with the basic empirical findings.
Consider now the properties of ΔE.
4. What induces the deformation? Authors suggest that the Earth's rotation is somehow involved with the effect. The first thing to notice is that the gravimagnetic field of Earth, call it B_{E}, predicted by General Relativity is quite too weak to explain the effect as a gravimagnetic force on spacecraft and fails also to explain the fact that energy increases always. GravitoLorentz force does not do any work so that the total energy is conserved and ΔE=ΔV=grad V.•Δ r holds true, where Δr is the deflection caused by the gravimagnetic field on the orbit during flyby. Since Δr is linear in v, ΔE changes sign as the velocity of spacecraft changes sign so that this option fails in several manners. Gravimagnetic force of Earth could be however involved but in a different manner.
Happy note added: The price of "../articles/ of PRL are really dirty, 25 dollars per article. Hence I decided to take the risk and put the prediction on blog without knowing whether it is correct. Today I got the article in email. The prediction for the increment of kinetic energy was correct! Champagne for that! Flyby will be for the TGD based view about dark matter what the shift of perihelion of Mercury was for General Relativity! Let us now cross our fingers and hope that it would not take too many decades for this message to diffuse through the cognitive immune system of the super string hegemony. For TGD based view about astrophysics see the chapter TGD and Astrophysics .
