Wednesday, December 17, 2008

Antimatter as dark matter?

Intuitively the scaling of Planck constant scales up quantum lengths, in particular the size of causal diamond CD defined as intersection of future and past directd lightcones. This looks trivial but one one must describe precisely what is involved to check internal consistency and also to understand how to model the quantum phase transitions changing Planck constant. It turns out that the back of the Big Book along with CDs is analogous to Josephson junction which in presence of dissipation leads to the separation of charges to different pages. This might relate to the generation of matter antimatter asymmetry of the visible matter.

The first manner to understand the situation is to consider CD with a fixed range of M4 coordinates. The scaling up of the covariant Kähler metric of CD by r2=(hbar/hbar0)2 scales up the size of CD by r. Another manner to see the situation is by scaling up the linear M4 coordinates by r for the larger CD so that M4 metric becomes same for both CDs. The smaller CD is glued to the larger one isometrically together along (M2ÇCD) Ì CD anywhere in the interior of the larger CD. What happens is non-trivial for the following reasons.

  1. The singular coverings and factor spaces are different and M4 scaling is not a symmetry of the Kähler action so that the preferred extrema in the two cases do not relate by a simple scaling. The interpretation is in terms of the coding of the radiative corrections in powers of hbar to the shape of the preferred extremals. This becomes clear from the representation of Kähler action in which M4 coordinates have the same range for two CDs but M4 metric differs by r2 factor.

  2. In common M4 coordinates the M4 gauge part Aa of CP2 Kähler potential for the larger CD differs by a factor 1/r from that for the smaller CD. This guarantees the invariance of four-momentum assignable to Chern-Simons action in the phase transition changing hbar. The resulting discontinuity of Aa at M2 is analogous to a static voltage difference between the two CDs and M2 could be seen as an analog of Josephson junction. In absence of dissipation (expected in quantum criticality) the Kähler voltage could generate oscillatory fermion, em, and Z0 Josephson currents between the two CDs. Since Kähler gauge potential couples to quarks and leptons with opposite signs the current would be in opposite directions for quarks and leptons as well as for matter and antimatter. In presence of dissipation the currents would be ohmic and could force quarks and leptons and matter and antimatter to different pages of the Big Book and quarks inside hadrons would have nonstandard value of Planck constant.

  3. The discontinuities of Au and Af allow to assign electric and magnetic Kähler point charges QKe/m with M1 Ì M2 and having sign opposite to those assignable with dCD×CP2. It should be possible to identify physically M2, the line E1 representing quantization axis of angular momentum, and the position of QK.

For details and background see the updated chapter Quantum Hall effect and Hierarchy of Planck Constants of "Physics in Many-Sheeted Space-time".

Tuesday, December 16, 2008

Is dark matter anyonic?

For year or two ago I proposed an explanation of FQHE, anyons, and fractionization of quantum numbers in terms of hierarchy of Planck constants realized as a generalization of the imbedding space H=M4×CP2 to a book like structure. The book like structure applies separately to CP2 and to causal diamonds (CD Ì M4) defined as intersections of future and past directed light-cones. The pages of the Big Book correspond to singular coverings and factor spaces of CD (CP2) glued along 2-D subspace of CD (CP2) and are labeled by the values of Planck constants assignable to CD and CP2 and appearing in Lie algebra commutation relations. The observed Planck constant hbar, whose square defines the scale of M4 metric corresponds to the ratio of these Planck constants. The key observation is that fractional filling factor results if hbar is scaled up by a rational number.

In the new chapter Quantum Hall effect and Hierarchy of Planck Constants of "p-Adic Length Scale Hypothesis and Hierarchy of Planck Constants" I discussed this idea in more detail. The outcome is a rather detailed view about anyons on one hand, and about the Kähler structure of the generalized imbedding space on the other hand.

In previous postings and in the chapter Quantum Astrophysics of "Physics in Many-Sheeted Space-time" consider the idea that dark matter is in anyonic phase in astrophysical scales. Among other things this leads to an explanation for both the successes and partial failures of Bohr orbitogy in astrophysical length scales. In the following I briefly sum up some key points of the vision that anyonization and associated charged fractionization are universal aspects of dark matter identified as quantum coherent phases with large value of Planck constant.

Charge fractionization is a fundamental piece of quantum TGD and should be extremely general phenomenon and the basic characteristic of dark matter known to contribute 95 per cent to the matter of Universe.

  1. In TGD framework scaling hbar = mhbar0 implies the scaling of the unit of angular momentum for m-fold covering of CD only if the many particle state is Zm singlet. Zm singletness for many particle states allows of course non-singletness for single particle states. For factor spaces of CD the scaling hbar® hbar/m is compensated by the scaling l® ml for Lz=lhbar guaranteing invariance under rotations by multiples of 2p/m. Again one can pose the invariance condition on many-particle states but not to individual particles so that genuine physical effect is in question.

  2. There is analogy with Z3-singletness holding true for many quark states and one cannot completely exclude the possibility that quarks are actually fractionally charged leptons with m=3-covering of CP2 reducing the value of Planck constant so that quarks would be anyonic dark matter with smaller Planck constant and the impossibility to observe quarks directly would reduce to the impossibility for them to exist at our space-time sheet. Confinement would in this picture relate to the fractionization requiring that the 2-surface associated with quark must surround the tip of CD. Whether this option really works remains an open question. In any case, TGD anyons are quite generally confined around the tip of CD.

  3. Quite generally, one expects that dark matter and its anyonic forms emerge in situations where the density of plasma like state of matter is very high so that N-fold cover of CD reduces the density of matter by 1/N factor at given sheet of covering and thus also the repulsive Coulomb energy. Plasma state resulting in QHE is one examples of this. The interiors of neutron stars and black hole like structures are extreme examples of this, and I have proposed that black holes are dark matter with a gigantic value of gravitational Planck constant implying that black hole entropy -which is proportional to 1/hbar - is of same order of magnitude as the entropy assignable to the spin of elementary particle. The confinement of matter inside black hole could have interpretation in terms of macroscopic anyonic 2-surfaces containing the topologically condensed elementary particles. This conforms with the TGD inspired model for the final state of star inspiring the conjecture that even ordinary stars could posses onion like structure with thin layers with radii given by p-adic length scale hypothesis.

    The idea about hierarchy of Planck constants was inspired by the finding that planetary orbits can be regarded as Bohr orbits : the explanation was that visible matter has condensed around dark matter at spherical cells or tubular structures around planetary orbits. This led to the proposal that planetary system has formed through this kind of condensation process around spherical shells or flux tubes surrounding planetary orbits and containing dark matter.

    The question why dark matter would concentrate around flux tubes surrounding planetary orbits was not answered. The answer could be that dark matter is anyonic matter at partonic 2-surfaces whose light-like orbits define the basic geometric objects of quantum TGD. These partonic 2-surfaces could contain a central spherical anyonic 2-surface connected by radial flux tubes to flux tubes surrounding the orbits of planets and other massive objects of solar system to form connected anyonic surfaces analogous to elementary particles.

    If factor spaces appear in M4 degrees of freedom, they give rise to Zn Ì Ga symmetries. In astrophysical systems the large value of hbar necessarily requires a large value of na for CD coverings as the considerations of - in particular the model for graviton dark graviton emission and detection - forces to conclude. The same conclusion follows also from the absence of evidence for exact orbifold type symmetries in M4 degrees of freedom for dark matter in astrophysical scales.

  4. The model of DNA as topological quantum computer assumes that DNA nucleotides are connected by magnetic flux tubes to the lipids of the cell membrane. In this case, p-adically scaled down u and d quarks and their antiquarks are assumed to be associated with the ends of the flux tubes and provide a representation of DNA nucleotides. Quantum Hall states would be associated with partonic 2-surfaces assignable to the lipid layers of the cell and nuclear membranes and also endoplasmic reticulum filling the cell interior and making it macroscopic quantum system and explaining also its stability. The entire system formed in this manner would be single extremely complex anyonic surface and the coherent behavior of living system would result from the fusion of anyonic 2-surfaces associated with cells to larger anyonic surfaces giving rise to organs and organisms and maybe even larger macroscopically quantum coherent connected systems.

    In living matter one must consider the possibility that small values of na correspond to factor spaces of CD (consider as example aromatic cycles with Zn symmetry with n = 5 or n = 6 appearing in the key molecules of life). Large hbar would require CP2 factor spaces with a large value of nb so that the integers characterizing the charges of anyonic particles would be shifted by a large integer. This is not in accordance with naive ideas about stability. One can also argue that various anomalous effects such as IQHE with n equal to an integer multiple of nb would have been observed in living matter.

    A more attractive option is that both CD and CP2 are replaced with singular coverings. Spin and charge fractionization takes place but the effects are small if both na, nb, and na/nb are large. An interesting possibility is that the ends of the flux tubes assumed to connect DNA nucleotides to lipids of various membranes carry instead of u, d and their anti-quarks fractionally charged electrons and neutrinos and their anti-particles having nb=3 and large value of na. Systems such as snowflakes could correspond to large hbar zoom ups of molecular systems having subgroup of rotation group as a symmetry group in the standard sense of the word.

    The model of graviton de-coherence constructed in allows to conclude that the fractionization of Planck constant has interpretation as a transition to chaos in the sense that fundamental frequencies are replaced with its sub-harmonics corresponding to the divisor of hbar/hbar0 = r/s. The more digits are needed to represent r/s, the higher the complexity of the system. Period doubling bifurcations leading to chaos represent a special case of this. Living matter is indeed a system at the boundary of chaos (or rather, complexity) and order and larger values of nb would give rise to the complexity having as a signature weak charge and spin fractionization effects.

  5. Coverings alone are enough to produce rational number valued spectrum for hbar, and one must keep in mind that the applications of theory do not allow to decide whether only singular factor spaces are really needed.

For details see the new chapter Quantum Hall effect and Hierarchy of Planck Constants of "p-Adic Length Scale Hypothesis and Hierarchy of Planck Constants".

Sunday, December 14, 2008

Revised vision about quantum astrophysics

I 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.

  1. Key element is the notion of partonic 2-surface, which for large values of Planck constant can have astrophysical size. This surface contains dark matter in anyonic many particle state if it surrounds the tip of so called causal diamond (the intersection of future and past directed light-cones). Also flux tubes surrounding the orbits of planets and other astrophysical objects containing dark matter would be connected by radial flux tubes to central anyonic 2-surface so that the entire system would be anyonic and quantum coherent in astrophysical scale. Visible matter is condensed around these dark matter structures.

  2. Since space-times are 4-surfaces in H=M4×CP2 (or rather, its generalization to a book like structure), gravitational Bohr rules can be formulated in a manner which is general coordinate invariant and Lorentz invariant.

  3. The value of the parameter v0 appearing in gravitational Planck constant varies and this leads to a weakened form of Equivalence Principle stating that v0 is same for given connected anyonic 2-surface, which can have very complex topology. In the case of solar system inner planets would be connected to an anyonic surface assignable to Sun and outer planets with different value of v0 to an anyonic surface assignable to Sun and inner planets as a whole. If one accepts ruler-and-compass hypothesis for allowed values of Planck constant very powerful predictions follow.

This general conceptual framework is applied to build simple models in some concrete examples.

  1. Concerning Bohr orbitology in astrophysical length scales, the basic observation is that in the case of a straight cosmic string creating a gravitational potential of form v12/r Bohr quantization does not pose any conditions on the radii of the circular orbits so that a continuous mass distribution is possible. This situation is obviously exceptional. If one however accepts the TGD based vision that the very early cosmology was cosmic string dominated and that elementary particles were generated in the decay of cosmic strings, this situation might have prevailed at very early times. If so, the differentiation of a continuous density of ordinary matter to form the observed astrophysical structures would correspond to an approach to a stationary situation governed by Bohr rules for dark matter and in the first approximation one could neglect the intermediate stages.

  2. This general picture is applied by considering some simple models for astrophysical systems involving planar structures. There are several universal predictions. Velocity spectrum is universal and only the Bohr radii depend on the choice of mass distribution. The inclusion of cosmic string implies that the system associated with the central mass is finite. Quite generally dark parts of astrophysical objects have shell like structure like atoms as do also ring like structures.

  3. p-Adic length scale hypothesis provides a manner to obtain a realistic model for the central objects meaning a structure consisting of shells coming as half octaves of the basic radius: this obviously relates to Titius-Bode law. Also a simple model for planetary rings is obtained. Bohr orbits do not follow cosmic expansion which is obtained only in the average sense if phase transitions reducing the value of basic parameter v0 occur at preferred values of cosmic time. This explains why v0 has different values and also the decomposition of planetary system to outer and inner planets with different values of v0.

TGD Universe is quantum critical and quantum criticality corresponds very naturally to what has been identified as the transition region to quantum chaos.

  1. The basic formulation of quantum TGD is consistent with what has been learned from the properties of quantum chaotic systems and quantum chaotic scattering. Wave functions are concentrated around Bohr orbits in the limit of quantum chaos, which is just what dark matter picture assumes.

  2. The model for the emission and detection of dark gravitons allows to conclude that the transition to chaos via generation of sub-harmonics of fundamental frequency spoiling the original exact periodicity corresponds to a sequence of phase transitions in which Planck constant transforms from integer to a rational number whose denominator increases as chaos is approached. This gives a precise characterization for the phase transitions leading to quantum chaos in general.

  3. In this framework the chaotic motion of astrophysical object becomes the counterpart of quantum chaotic scattering and the description in terms of classical chaos is predicted to fail. By Equivalence Principle the value of the mass of the object does not matter at all so that the motion of sufficiently light objects in solar system might be understandable only as quantum chaotic scattering. The motion of gravitationally unbound comets and rings of Saturn and Jupiter and the collisions of galactic structures known to exhibit the presence of cart-wheel like structures define possible applications.

The description of gravitational radiation provides a stringent test for the idea about dark matter hierarchy with arbitrary large values of Planck constants. In accordance with quantum classical correspondence, one can take the consistency with classical formulas as a constraint allowing to deduce information about how dark gravitons interact with ordinary matter. The standard facts about gravitational radiation are discussed first and then TGD based view about the situation is sketched.

For details and background see the updated chapter Quantum Astrophysics of "Physics in Many-Sheeted Space-time".

Thursday, December 11, 2008

New URL for my homepage

Note: The URL of my home page has changed to http://tgd.wippiespace.com/public_html/index.html. Few weeks after the discovery of CDF anomaly and after I had informed in physics blogs that TGD predicted the new physics explaining this anomaly as well as a long list of other anomalies already 1990 (the article is published in International Journal of Theoretical Physics) Helsinki University informed me that the old URL is not available after 10.12. With the help of some friendly souls the date was changed to 31.12. Otherwise TGD had disappeared from the web totally since for some reason they are unable to redirect visitors to the new URL after the page has been removed! Please update the link since the older link does not work next year.

About dark matter and CDF anomaly

Tommaso Dorigo told in his posting about the talk of Nima-Arkadi Haed relating to dark matter and CDF anomaly. Nima and others are beginning to realize what I realized for 3 years ago. Dark matter is not not just some neutral extremely weakly interacting particle but there are a lot of them and they can be also charged.

This is still rather ugly idea since it forces to introduce additional gauge group having standard model gauge groups as subgroup. In TGD framework the hierarchy of Planck constants realized in terms of book like structure of generalized 8-D imbedding space containing space-times as 4-surfaces realizes this much more elegantly since darkness is relative: all matter at pages different from the page of us is dark from our perspective since local interaction vertices are not possible. Gauge group is just the universal standard model gauge group having purely number theoretical interpretation.

I glue my reseponse to Tommaso Dorigo's blog also here.

Amusing, just this is what I have been talking for years but in much more elegant form and in much more detail with applications ranging from quantum Hall effect to astrophysics to cosmology to quantum biology.

Much of honor goes to Laurent Nottale who noticed that inner and outer planetary orbits can be seen as Bohr orbits with a gigantic value of Planck constant. The TGD explanation is in terms of condensation of visible matter around 2-D surfaces defining anyonic systems consisting of dark matter with very large Planck constant and therefore in macroscopically quantum coherent phase. This would be the basic mechanism for the formation of planetary systems (see my blog).

This finding and various biological anomalies led to the generalization of 8-D imbedding space of TGD having a book like structure with pages labeled by different values of Planck constant (this is oversimplification), and containing space-times as 4-surfaces. Typically the light-like 3-surfaces - the basic objects of TGD Universe- are at one particular page but tunneling is possible by leakage through the back of the book.

We would live at one particular page and the matter at other pages would be dark relative to us. It can be just ordinary particles if stability conditions allow this (anyonic phase is highly suggestive). There are no local interaction vertices between particles belonging to different pages. This explains darkness.

Particles can leak between different pages and it is even possible to photograph dark matter. This provides a possible explanation for various strange findings of Peter Gariaev about interaction of DNA with visible, IR and UV light. There is long list of other anomalies in living matter finding explanation in this framework. In living matter this kind of interactions would take place routinely in the model of quantum biology based on dark matter. One fascinating implication is phase transition changing the value of Planck constant and scaling up or down quantum scales typically proportional to hbar: this provides fundamental control mechanism of cellular biology where phase transition change the size scale occur very frequently.

About CDF anomaly and related anomalies. TGD predicts both leptons and quarks have colored excitations. Color octet excitations of leptons plus p-adic length scale hypothesis explains quantitatively CDF anomaly (predicts the mass of lightest excitation (charged tau-pion with mass mtau), the masses of the excitations proposed by CDF come as 2×mtau, 4×mtau, 8×mtau (neutral tau-pions) in accordance with the proposal of CDF group. Model also provides mechanism producing the muon jets and predicts a correct order of magnitude for the production cross section. Also very importantly, if colored excitations of leptons are present only at pages having nonstandard Planck constant, there is no contribution to intermediate boson decay widths from decays to colored leptons.

During years many other similar anomalies have been found. Electropions made themselves visible already at seventies in heavy ion collisions. About this I published two papers in International Journal of Theoretical Physics (1990,1992). Ortopositronium decay rate anomaly has interpretation in terms of electropion production. The gamma rays with energies at electron rest mass from galactic nuclei have interpretation as decay products of dark electro-pions. I have also discussed Karmen anomaly as the first evidence for colored excitations of muon. Year ago emerged evidence for mu-pion. For references see my earlier blog postings and also the material at my homepage.

This approach to dark matter differs from Nima's in three respects. It came three years earlier (as becomes clear by looking at old postings in my blog and links to the books and articles at my home page, there are also publications in CASYS proceedings). It is much more elegant since just the standard model gauge group is postulated (actually this gauge group follows as a prediction from number theoretic vision about TGD). And it implies a profound generalization of quantum theory itself.

This theory is however a crackpot theory according to the crowd opinion. Dear Anonymous, before telling me not to fill this blog with spam, tell me exactly what makes TGD a crackpot theory. If you bother to go to my home page and read you find that it cannot be the content. What it is then? I am really interested. Perhaps also some others are.

Note: The URL of my home page has changed http://tgd.wippiespace.com/public_html/index.html since few weeks after the discovery of CDF anomaly Helsinki University informed me that the old URL is not available after 10.12. With the help of some friendly souls the date was changed to 31.12. Otherwise TGD had disappeared from the web totally since for some reason they are unable to redirect visitors to the new URL after the page has been removed!

For details and background see the updated chapter Recent Status of Leptohadron Hypothesis of "p-Adic Length Scale Hypothesis and Dark Matter Hierarchy", and the article New evidence for colored leptons.

Tuesday, December 09, 2008

Quantum Hall effect and Hierarchy of Planck Constants

I have already earlier proposed the explanation of FQHE, anyons, and fractionization of quantum numbers in terms of hierarchy of Planck constants realized as a generalization of the imbedding space H=M4×CP2 to a book like structure. The book like structure applies separately to CP2 and to causal diamonds (CD Ì M4) defined as intersections of future and past directed light-cones. The pages of the Big Book correspond to singular coverings and factor spaces of CD (CP2) glued along 2-D subspace of CD (CP2) and are labeled by the values of Planck constants assignable to CD and CP2 and appearing in Lie algebra commutation relations. The observed Planck constant hbar, whose square defines the scale of M4 metric corresponds to the ratio of these Planck constants. The key observation is that fractional filling factor results if hbar is scaled up by a rational number.

In the new chapter Quantum Hall effect and Hierarchy of Planck Constants of "p-Adic Length Scale Hypothesis and Hierarchy of Planck Constants" I try to formulate more precisely this idea. The outcome is a rather detailed view about anyons on one hand, and about the Kähler structure of the generalized imbedding space on the other hand.

  1. Fundamental role is played by the assumption that the Kähler gauge potential of CP2 contains a gauge part with no physical implications in the context of gauge theories but contributing to physics in TGD framework since U(1) gauge transformations are representations of symplectic transformations of CP2. Also in the case of CD it makes also sense to speak about Kähler gauge potential. The gauge part codes for Planck constants of CD and CP2 and leads to the identification of anyons as states associated with partonic 2-surfaces surrounding the tip of CD and fractionization of quantum numbers. Explicit formulas relating fractionized charges to the coefficients characterizing the gauge parts of Kähler gauge potentials of CD and CP2 are proposed based on some empirical input.

  2. One important implication is that Poincare and Lorentz invariance are broken inside given CD although they remain exact symmetries at the level of the geometry of world of classical worlds (WCW). The interpretation is as a breaking of symmetries forced by the selection of quantization axis.

  3. Anyons would basically correspond to matter at 2-dimensional "partonic" surfaces of macroscopic size surrounding the tip of the light-cone boundary of CD and could be regarded as gigantic elementary particle states with very large quantum numbers and by charge fractionization confined around the tip of CD. Charge fractionization and anyons would be basic characteristic of dark matter (dark only in relative sense). Hence it is not surprising that anyons would have applications going far beyond condensed matter physics. Anyonic dark matter concentrated at 2-dimensional surfaces would play key key role in the the physics of stars and black holes, and also in the formation of planetary system via the condensation of the ordinary matter around dark matter. This assumption was the basic starting point leading to the discovery of the hierarchy of Planck constants. In living matter membrane like structures would represent a key example of anyonic systems as the model of DNA as topological quantum computer indeed assumes.

  4. One of the basic questions has been whether TGD forces the hierarchy of Planck constants realized in terms of generalized imbedding space or not. The condition that the choice of quantization axes has a geometric correlate at the imbedding space level motivated by quantum classical correspondence of course forces the hierarchy: this has been clear from the beginning. It is now clear that first principle description of anyons requires the hierarchy in TGD Universe. The hierarchy reveals also new light to the huge vacuum degeneracy of TGD and reduces it dramatically at pages for which CD corresponds to a non-trivial covering or factor space, which suggests that mathematical existence of the theory necessitates the hierarchy of Planck constants. Also the proposed manifestation of Equivalence Principle at the level of symplectic fusion algebras as a duality between descriptions relying on the symplectic structures of CD and CP2 forces the hierarchy of Planck constants.

For details see the new chapter Quantum Hall effect and Hierarchy of Planck Constants of "p-Adic Length Scale Hypothesis and Hierarchy of Planck Constants".

Monday, December 08, 2008

About top quark mass again

In his latest blog posting of Tommaso Dorigo summarizes the latest measurement of top quark mass by CDF. Top quark is experimentally in a unique position since toponium does not exist and top quark mass is that of free top. Therefore top quark mass provides a stringent test for TGD based mass calculations based on p-adic thermodynamics.
  1. The prediction for top quark mass depends on second order contributions to electron mass and top mass parameterized by numbers Yt and Yt varying in the interval [0,1). This contribution is of order one per cent. Once Ye is fixed, the CP2 size (and mass scale) is fixed completely from electron mass.
  2. The prediction for top quark mass is 167.8 GeV for Yt=Ye=0 (vanishing second order corrections) and 169.1 GeV for Yt=1 and Ye=0 (maximal possible mass for top). The prediction is reduced for Ye>0 since CP2 mass scale is reduced.
  3. The experimental estimate for mt remained for a long time somewhat higher than the prediction of TGD. The previous experimental average value was m(t)=169.1 GeV with the allowed range being [164.7, 175.5] GeV (see the blog posting of Tommaso Dorigo). The fine tuning Ye=0,Yt=1 giving 169.1 GeV is somewhat un-natural.
  4. The most recent value obtained by CDF reported in detail by Tommaso Dorigo is mt=165.1+/- 3.3+/- 3.1 GeV. This represents lower bound for the mass consistent for Ye=Yt=0. The prediction increases for Yt>0. Clearly, TGD passes the stringent test posed by the top quark mass.
For details see the chapters p-Adic Mass Calculations: Elementary Particle Masses (Table 3) and p-Adic Mass Calculations: Hadron Masses (Table 1). of "p-Adic Length Scale Hypothesis and Hierarchy of Planck Constants".