What's new inPhysics in ManySheeted SpaceTimeNote: Newest contributions are at the top! 
Year 2006 
About the interpretation of the parameter v_{0}The formula for the gravitational Planck constant contains the parameter v_{0}/c=2^{11}. This velocity defines the rotation velocities of distant stars around galaxies. The presence of a parameter with dimensions of velocity should carry some important information about the geometry of dark matter spacetime sheets. Velocity like parameters appear also in other contexts. There is evidence for the Tifft's quantization of cosmic redshifts in multiples of v_{0}/c=2.68× 10^{5}/3: also other units of quantization have been proposed but they are multiples of v_{0} (see this). The strange behavior of graphene includes high conductivity with conduction electrons behaving like massless p"../articles/ with light velocity replaced with v_{0}/c=1/300. The TGD inspired model explains the high conductivity as being due to the Planck constant h(M^{4})= 6h_{0} increasing the delocalization length scale of electron pairs associated with hexagonal rings of monoatomic graphene layer by a factor 6 and thus making possible overlap of electron orbitals. This explains also the anomalous conductivity of DNA containing 5 and 6cycles (same reference).
1. Is dark matter warped? The reduced light velocity could be due to the warping of the spacetime sheet associated with dark electrons. TGD predicts besides gravitational redshift a nongravitational redshift due to the warping of spacetime sheets possible because spacetime is 4surface rather than abstract 4manifold. A simple example of everyday life is the warping of a paper sheet: it bends but is not stretched, which means that the induced metric remains flat although one of its components scales (distance becomes longer around direction of bending). For instance, empty Minkowski space represented canonically as a surface of M^{4}× CP_{2} with constant CP_{2} coordinates can become periodically warped in time direction because of the bending in CP_{2} direction. As a consequence, the distance in time direction shortens and effective lightvelocity decreases when determined from the comparison of the time taken for signal to propagate from A to B along warped spacetime sheet with propagation time along a nonwarped spacetime sheet. The simplest warped imbedding defined by the map M^{4}→ S^{1}, S^{1} a geodesic circle of CP_{2}. Let the angle coordinate of S^{1} depend linearly on time: Φ= ω t. g_{tt}} component of metric becomes 1R^{2}ω^{2} so that the light velocity is reduced to v_{0}/c=(1R^{2}ω^{2})^{1/2}. No gravitational field is present. The fact that M^{4} Planck constant n_{a}h_{0} defines the scaling factor n_{a}^{2} of CP_{2} metric could explain why dark matter resides around strongly warped imbeddings of M^{4}. The quantization of the scaling factor of CP_{2} by R^{2}→ n_{a}^{2}R^{2} implies that the initial small warping in the time direction given by g_{tt}=1ε, ε=R^{2}ω^{2}, will be amplified to g_{tt}= 1n_{a}^{2}ε if ω is not affected in the transition to dark matter phase. n_{a}=6 in the case of graphene would give 1x≈ 1 1/36 so that only a one per cent reduction of light velocity is enough to explain the strong reduction of light velocity for dark matter.
2. Is c/v_{0} quantized in terms of ruler and compass rationals? The known cases suggests that c/v_{0} is always a rational number expressible as a ratio of integers associated with npolygons constructible using only ruler and compass.
3. Tifft's quantization and cosmic quantum coherence An explanation for Tifft's quantization in terms of Jones inclusions could be that the subgroup G of Lorentz group defining the inclusion consists of boosts defined by multiples η= nη_{0} of the hyperbolic angle η_{0}≈ v_{0}/c. This would give v/c= sinh(nη_{0})≈ nv_{0}/c. Thus the dark matter systems around which visible matter is condensed would be exact copies of each other in cosmic length scales since G would be an exact symmetry. The property of being an exact copy applies of course only in single level in the dark matter hierarchy. This would mean a delocalization of elementary p"../articles/ in cosmological length scales made possible by the huge values of Planck constant. A precise cosmic analog for the delocalization of electron pairs in benzene ring would be in question. Why then η_{0} should be quantized as ruler and compass rationals? In the case of Planck constants the quantum phases q=exp(imπ/n_{F}) are number theoretically simple for n_{F} a ruler and compass integer. If the boost exp(η) is represented as a unitary phase exp(imη) at the level of discretely delocalized dark matter wave functions, the quantization η_{0}= n/n_{F} would give rise to number theoretically simple phases. Note that this quantization is more general than η_{0}= n_{F,1}/n_{F,2}. For more details see the chapter TGD and AstroPhysics.

Orbital radii of exoplanets and Bohr quantization of planetary orbitsOrbital radii of exoplanets save as a test for the Bohr quantization of planetary orbits. Hundreds of them are already known and in tables (Masses and Orbital Characteristics of Extrasolar Planets using stellar masses derived from Hipparcos, metalicity, and stellar evolution) basic data for for 136 exoplanets are listed. The tables also provide references and links to sources giving data about the stars, in particular star mass M using solar mass M_{S} as a unit. Hence one can test the formula for the orbital radii given by the expression r/r_{E}= (n^{2}/5^{2}) ×(M/M_{S})× X , X= (n_{1}/n_{2})^{2}, n_{i}=2^{ki}× ∏_{si}F_{si} , F_{si} in the set {3,5,17,257, 2^{16}+1} . Here a given Fermat prime F_{si} can appear only once. It turns out that the simplest option assuming X=1 fails badly for some planets: the resulting deviations of of order 20 per cent typically but in the worst cases the predicted radius is by factor of ≈ .5 too small. The values of X used in the fit correspond to X having values in {(2/3)^{2}, (3/4)^{2}, (4/5)^{2}, (5/6)^{2}, (15/17)^{2}, (15/16)^{2}, (16/17)^{2}} ≈ {.44, .56,.64,.69,.78, .88,.89} and their inverses. The tables summarizing the resulting fit using both X=1 and X giving optimal fit are here. The deviations are typically few per cent and one must also take into account the fact that the masses of stars are deduced theoretically using the spectral data from star models. I am not able to form an opinion about the real error bars related to the masses. The Appendix of the chapter TGD and Astrophysics contains more details.

Dark matter based model for Pioneer and flyby anomaliesThis has been very enjoyable period for dark matter afficionado. During last month I have had an opportunity to apply TGD based vision about dark matter to about five existing or completely new anomalies. Just yesterday I learned about the new findings related to Pioneer and flyby anomalies which challenge the standard theory of gravitation. I have proposed earlier a model for Pioneer anomaly resulting as a byproduct of an explanation of another anomaly which can be understood if cosmic expansion is compensated by a radial contraction of solar system in local RobertsonWalker coordinates. The recent findings reported here allow to sharpen the model suggesting a universal primordial mass density associated with the solar system. The facts about flyby anomaly lead to a model in which anomalous energy gain of the spacecraft in Earthcraft rest system results when it passes through a spherical layer of dark matter containing Earth's orbit (this is of course too stringent model). These structures are predicted by the model explaining the Bohr quantization of planetary orbits to served as templates for the condensation of visible matter around them. 1. Explanation of Pioneer anomaly in terms of dark matter I have proposed an explanation of Pioneer anomaly as a prediction of a model explaining the claimed radial acceleration of planets which is such that it compensates the cosmological expansion of planetary system. The correct prediction is that the anomalous acceleration is given by Hubble constant. The precise mechanism allowing to achieve this was not proposed. A possible mechanism is based the presence of dark matter increasing the effective solar mass. Since acceleration anomaly is constant, a dark matter density behaving like ρ_{d} = (3/4π)(H/Gr), where H is Hubble constant giving M(r) propto r^{2}, is required. For instance, at the radius R_{J} of Jupiter the dark mass would be about (δa/a) M_{S}≈ 1.3× 10^{4}M_{S} and would become comparable to M_{S} at about 100R_{J}=520 AU. Note that the standard theory for the formation of planetary system assumes a solar nebula of radius of order 100AU having 23 solar masses. For Pluto at distance of 38 AU the dark mass would be about one per cent of solar mass. This model would suggest that planetary systems are formed around dark matter system with a universal mass density. For this option dark matter could perhaps be seen as taking care of the contraction compensating for the cosmic expansion by using a suitable dark matter distribution. Here the possibility that the acceleration anomaly for Pioneer 10 (11) emerged only after the encounter with Jupiter (Saturn) is raised. The model explaining Hubble constant as being due to a radial contraction compensating cosmic expansion would predict that the anomalous acceleration should be observed everywhere, not only outside Saturn. The model in which universal dark matter density produces the same effect would allow the required dark matter density ρ_{d}= (3/4π)(H/Gr) be present only as a primordial density able to compensate the cosmic expansion. The formation of dark matter structures could have modified this primordial density and visible matter would have condensed around these structures so that only the region outside Jupiter would contain this density. There are also diurnal and annual variations in the acceleration anomaly (see the same article). These variations should be due to the physics of EarthSun system. I do not know whether they can be understood in terms of a temporal variation of the Doppler shift due to the spinning and orbital motion of Earth with respect to Sun. 2. Explanation of Flyby anomaly in terms of dark matter The so called flyby anomaly might relate to the Pioneer 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. For instance, if the spacecraft traverses shell structure, its kinetic energy per mass in Earth cm system changes by a constant amount not depending on the mass of the spacecraft: δE/m ≈ v_{inf,E}×δv= δV_{gr} = GδM_{eff,S}/R. Here R is the outer radius of the shell and v_{inf,E} is the magnitude of asymptotic velocity in Earth cm system. This very simple prediction should be testable. If the spacecraft arrives from the direction of Sun the energy increases. If the spacecraft returns back to the sunny side, the net anomalous energy gain vanishes. This has been observed in the case of Pioneer 11 encounter with Jupiter (see this). The mechanism would make it possible to deduce the total dark mass of, say, spherical shell of dark matter. One has δM/M_{S} ≈δv/v_{inf,E} ×(2K/V) , K= v^{2}_{inf,E}/2 , V=GM_{S}/R . For the case considered δM/M_{S}≥ 2× 10^{6} is obtained. Note that the amount of dark mass within sphere of 1 AU implied by the explanation of Pioneer anomaly would be about 6.2× 10^{6}M_{S} from Pioneer anomaly. Since the orders of magnitude are same one might consider the possibility that the primordial dark matter has concentrated in spherical shells in the case of inner planets as indeed suggested by the model for quantization of radii of planetary orbits. In the solar cm system the energy gain is not constant. Denote by v_{i,E} and v_{f,E} the initial and final velocities of the spacecraft in Earth cm. Let δv be the anomalous change of velocity in the encounter and denote by θ the angle between the asymptotic final velocity v_{f,S} of planet in solar cm. One obtains for the corrected e_{g,S} the expression e_{g,S}= (1/2)[(v_{f,E}+v_{P}+δv)^{2}(v_{i,E}+v_{P})^{2}] . This gives for the change δe_{g,S} δe_{g,S}≈(v_{f,E}+v_{P})· δv≈ v_{f,S} δv× cos(θ_{S})= v_{inf,S}δv × cos(θ_{S}). Here v_{inf,S} is the asymptotic velocity in solar cm system and in excellent approximation predicted by the theory. Using spherical shell as a model for dark matter one can write this as δe_{g,S}= v_{inf,S}/v_{inf,E} × G δM/R × cos(θ_{S}) . The proportionality of δe_{g,S} to cos(θ_{S}) should explain the variation of the anomalous energy gain. For a spherical shell δv is in the first approximation orthogonal to v_{P} since it is produced by a radial acceleration so that one has in good approximation δe_{g,S}≈v_{f,S}· δv≈ v_{f,E}· δv≈ v_{f,S}δv × cos(θ_{S})= v_{inf,E} δv× cos(θ_{E}). For Cassini and Messenger cos(θ_{S}) should be rather near to zero so that v_{inf,E} and v_{inf,S} should be nearly orthogonal to the radial vector from Sun in these cases. This provides a clear cut qualitative test for the spherical shell model. For TGD based view about astrophyscs see the chapter TGD and Astrophysics of "Physics in ManySheeted SpaceTime".

New Results in Planetary Bohr OrbitologyThe understanding of how the quantum octonionic local version of infinitedimensional Clifford algebra of 8dimensional space (the only possible local variant of this algebra) implies entire quantum and classical TGD led also to the understanding of the quantization of Planck constant. In the model for planetary orbits based on gigantic gravitational Planck constant this means powerful constraints on the number theoretic anatomy of gravitational Planck constants and therefore of planetary mass ratios. These very stringent predictions are immediately testable.
New results in planetary Bohr orbitology1. Preferred values of Planck constants and ruler and compass polygons The starting point is that the scaling factor of M^{4} Planck constant is given by the integer n characterizing the quantum phase q= exp(iπ/n). The evolution in phase resolution in padic degrees of freedom corresponds to emergence of algebraic extensions allowing increasing variety of phases exp(iπ/n) expressible padically. This evolution can be assigned to the emergence of increasingly complex quantum phases and the increase of Planck constant. One expects that quantum phases q=exp(iπ/n) which are expressible using only square roots of rationals are number theoretically very special since they correspond to algebraic extensions of padic numbers involving only square roots which should emerge first and therefore systems involving these values of q should be especially abundant in Nature. These polygons are obtained by ruler and compass construction and Gauss showed that these polygons, which could be called Fermat polygons, have n_{F}= 2^{k} ∏_{s} F_{ns} sides/vertices: all Fermat primes F_{ns} in this expression must be different. The analog of the padic length scale hypothesis emerges since larger Fermat primes are near a power of 2. The known Fermat primes F_{n}=2^{2n}+1 correspond to n=0,1,2,3,4 with F_{0}=3, F_{1}=5, F_{2}=17, F_{3}=257, F_{4}=65537. It is not known whether there are higher Fermat primes. n=3,5,15multiples of padic length scales clearly distinguishable from them are also predicted and this prediction is testable in living matter. 2. Application to planetary Bohr orbitology The understanding of the quantization of Planck constants in M^{4} and CP_{2} degrees of freedom led to a considerable progress in the understanding of the Bohr orbit model of planetary orbits proposed by Nottale, whose TGD version initiated "the dark matter as macroscopic quantum phase with large Planck constant" program. Gravitational Planck constant is given by hbar_{gr}/hbar_{0}= GMm/v_{0} where an estimate for the value of v_{0} can be deduced from known masses of Sun and planets. This gives v_{0}≈ 4.6× 10^{4}. Combining this expression with the above derived expression one obtains GMm/v_{0}= n_{F}= 2^{k} ∏_{ns} F_{ns} In practice only the Fermat primes 3,5,17 appearing in this formula can be distinguished from a power of 2 so that the resulting formula is extremely predictive. Consider now tests for this prediction.
To sum up, it seems that everything is now ready for the great revolution. I would be happy to share this flood of discoveries with colleagues but all depends on what establishment decides. To my humble opinion twenty one years in a theoretical desert should be enough for even the most arrogant theorist. There is now a book of 800 A4 pages about TGD at Amazon: Topological Geometrodynamics so that it is much easier to learn what TGD is about. The reader interested in details is recommended to look at the chapter Was von Neumann Right After All? of the book "TGD: an Overview" and the chapter TGD and Astrophysics of this book. 
Higgs particle as wormhole contact and weakened form of Equivalence PrincipleQuantum classical correspondence has turned out to be the magic tool leading to the a surprisingly detailed understanding of the physics predicted by TGD. I am continuing the updating of TGD forced by the dark matter revolution and newest result relate to a more detailed understanding of particle massivation, the manner how Equivalence Principle is weakened in TGD framework, color confinement, and the variant of Higgs mechanism involved with superconductivity. The really big surprise was that Higgs particle is nothing but a wormhole contact carrying left handed weak isospin. 1. Higgs as wormhole contact, electroweak symmetry breaking, the weakening of Equivalence Principle, and color confinement The proper understanding of the concepts of gauge charges and fluxes and their gravitational counterparts in TGD spacetime has taken a lot of efforts. At the fundamental level gauge charges assignable to lightlike 3D elementary particle horizons surrounding a topologically condensed CP_{2} type extremals can be identified as the quantum numbers assignable to fermionic oscillator operators generating the state associated with horizon identifiable as a parton. Quantum classical correspondence requires that commuting classical gauge charges are quantized and this is expected to be true by the generalized Bohr orbit property of the spacetime surface. There are however nontrivial questions. Do vacuum charge densities give rise to renormalization effects or imply nonconservation so that weak charges would be screened above intermediate boson length scale? Could one assign the nonconservation of gauge fluxes to the wormhole (#) contacts, which are identifiable as pieces of CP_{2} extremals and for which electroweak gauge currents are not conserved so that weak gauge fluxes would be nonvanishing but more or less random so that long range correlations would be lost? It indeed turns that one can understand the nonconservation of weak gauge fluxes in terms of wormhole contacts carrying pairs of right/left handed fermion and left/right handed antifermion having interpretation as Higgs bosons. The average nonconserved lightlike gravitational fourmomentum of wormhole contact representing Higgs boson can be identified as the inertial fourmomentum apart from the sign factor so that one can also understand particle massivation at fundamental level and a connection with padic thermodynamics based description of Higgs mechanism emerges. Also a detailed understanding about how Equivalence Principle is weakened in TGD framework emerges. Also color confinement can be understood using only quantum classical correspondence and general properties of classical color gauge field. Spin glass degeneracy allows to understand the generation of macrotemporal quantum coherence and the same mechanism allows also to understand more quantitatively color confinement by applying unitarity conditions. 2. Dark matter hierarchy and fractal copies of standard model physics The most dramatic prediction obvious from the beginning but misinterpreted for about 26 years is the presence of long ranged classical electroweak and color gauge fields in the length scale of the spacetime sheet. The only interpretation consistent with quantum classical correspondence is in terms of a hierarchy of scaled up copies of standard model physics corresponding to padic length scale hierarchy and dark matter hierarchy labelled by arbitrarily large values of dynamical quantized Planck constant. Chirality selection in the biosystems provides direct experimental evidence for this fractal hierarchy of standard model physics. 3. Wormhole contacts, superconductivity, and biology Wormhole contacts, feeding gauge fluxes from a given sheet of the 3space to a larger one, which are a necessary concomitant of the manysheeted spacetime concept. # contacts can be regarded as p"../articles/ carrying classical charges defined by the gauge fluxes but behaving as extremely tiny dipoles quantum mechanically in the case that gauge charge is conserved. # contacts must be light, which suggests that they can form BoseEinstein condensates and coherent states. The real surprise (after 27 years of TGD) was that the formation of these rather exotic macroscopic quantum phases could be identified as formation of vacuum expectation value of Higgs field for various scaled up copies of standard model physics. This kind of macroscopic quantum phases could be in a central role in the TGD inspired model for a biosystem as a macroscopic quantum system. Electromagnetically charged # contacts are also possible and would explain the massivation of photons in superconductors implying that long ranged exotic W boson exchanges play a key role in superconductivity. For more details see the chapter General Ideas about Topological Condensation and Evaporation. 
Empirical support for the padic evolution of cosmological constant?The evolution of the cosmological constant Λ is different at each spacetime sheet, and the value of Λ is determined by the padic length scale size of the spacetime sheet according to the formula Λ (k)= Λ (2)× (L(2)/L(k))^{2}, where L(k)=2^{k}L_{0}, k integer, is the padic length scale associated with prime p≈ 2^{k}. L_{0} is apart from a numerical constant CP_{2} geodesic length. Prime values of k are especially interesting. The formula is derived in the chapter TGD and Cosmology of TGD from the requirement that gravitational energy identified as the difference of inertial energies and matter and antimatter (or vice versa) is nonnegative. The result means discrete evolution of cosmological constant with jumps in which cosmological constant is reduced by a power of 2. In standard physics context piecewise constant cosmological constant would be naturally replaced by a cosmological constant behaving like 1/a^{2} as a function of cosmic time. pAdic prediction is consistent with the study of Wang and Tegmark according to which cosmological constant has not changed during the last 8 billion years: the conclusion comes from the reshifts of supernovae of type I_{a}. If padic length scales L(k)= p ≈ 2^{k}, k any positive integer, are allowed, the finding gives the lower bound T_{M} > 2^{1/2}/( 2^{1/2}1))× 8= 27.3 billion years for the recent age of the universe. Now Brad Shaefer from Lousiana University has studied the red shifts of gamma ray bursters up to a red shift z=6.3, which corresponds to a distance of 13 billion light years, and claims that the fit to the data is not consistent with the time independence of the cosmological constant. In TGD framework this would mean that a phase transition scaling down the value of the cosmological constant by a power of 2 can be located in cosmological past at a temporal distance in the range 813 billion years. For more details see the chapter Cosmic Strings.
