Particle masses from a Calabi-Yau Authors: S.L. Glashow Comments: 89 pages (sorry) Report-no: BU-4/2005Sheldon Glashow was one of the few who for two decades ago did his best to warn for what might happen when all intellectual resources are forced to work with single idea, which has no empirical support. Now the worst has happened. Just for fun and knowing that I had nothing to lose, also I told for twenty years ago in my application to a research post in the Institute of Theoretical Physics of Helsinki University, what the failures of string theory are, and I was correct and for obvious reasons. I am now waiting that my colleagues come to tap me on shoulder, to praise my far-sightedness, and apologize;-)! Back to business. I continued to work with the claimed properties ORMEs and irrespective of whether ORMEs are fraud or not, I have now a beautiful model for what happens in the phase transition increasing the value of hbar and leading to the formation of conformally confined blocks of protons and electrons. Conservation laws and Uncertainty Principle give decisive constraints on the model for this phase transition. The crucial new observation is that the phase transition to dark matter can occur at the level of protons and electrons and thus would increase their Compton lengths by a factor hbar_s/hbar.We identify the unique Calabi-Yau background that leads to a realistic heterotic Standard Model at low energies. A dual G2 compactification of M-theory and a Calabi-Yau four-fold compactification of F-theory is constructed. A self-mirror discrete symmetry protects the stability of the proton, stabilizes all moduli, and implies realistic neutrino mass matrices, in agreement with our recent results. In order to avoid abstract rubbish, we calculate the masses of elementary quarks and leptons. After including first 7 loops, worldsheet instantons and D3-brane instantons, the muon/electron mass ratio turns out to be approximately 206.76826535236246, for example. The low-energy electroweak theory by Glashow et al. with three fundamental Higgs bosons is a trivial consequence of the model. The lightest supersymmetric particle is predicted to be a neutralino at 200.504 GeV. There have been 63.8 e-foldings of inflation. We speculate that the backgrounds without the Glashow self-mirror discrete symmetry are exponentially suppressed in the Hartle-Hawking state, and our vacuum is therefore a unique SUSY-breaking four-dimensional cosmology that arises from string theory. Finally, we argue that our discoveries make string theory safe. Permanently safe. We also write down the most general bootstrap conditions for string/M-theory, and show that the two-dimensional worldsheet conformal field theories and the AdS/CFT models represent two large classes of solutions of our conditions.

### Input from conservation laws

The conservation of angular momentum and energy-momentum pose strong conditions on what can happen when Planck constant increases.*1. Angular momentum quantization*hbar_s becomes a new unit of angular momentum. Unless the system possesses a vanishing angular momentum, something analogous to a spontaneous magnetization must happen with magnetized region becoming basic unit. If Hudson's claim about high rotational states of nuclei is true, this mechanism might explain them. Of course, the large unit of angular momentum is a very precise experimental signature.

*2. Scaling of Compton length and time*Energy and momentum conservation and Uncertainty Principle imply that Compton length and Compton time must increase by a factor hbar_s/hbar . In particular, the space-time sheets defining the Compton lengths of particles increase in size by this factor. In the case of atomic nucleus the generalization of the basic formula would give r= hbar_s/hbar =Z^2alpha/v0, v_0= 4.6*10^{-4}. v_0 is proportional the ratio of Planck length and CP_2 length in TGD Universe. For Z=46 (Pd) the formula would give r =about 3.36*10^4 so that proton Compton length would become roughly 10^{-11} meters. This size scale is smaller than atomic size of order 10^{-10} meters which would explain why the phase transition does not occur under the usual circumstances. For Z=79 (Gold) one has r=about 9.9*10^{4} so that (and rather remarkably!) Compton length achieves atomic size. In the phase transition protonic space-time sheets would fuse together to form a larger join along boundaries condensate. There is a direct analogy with the transition to super-conductivity or super-fluidity believed to involve the increase of the non-relativistic wavelength lambda= hbar/p defined by the three-momentum p so that the volumes defined by this wavelength overlap for the neighboring particles. This could in turn increase the net charge of the conformally confined sub-systems and hence also the parameter hbar_{s} so that Compton length would increase further. A kind of cascade like process could occur. Nuclear protons would de-localize whereas neutrons would remain localized to a nuclear volume. One could speak of conduction particles or even super-conducting particles, where particle could refer to proton, nucleus, or block of nuclei. If the p-adic prime characterizing the resulting Compton space-time sheet is larger than the space-time sheets (flux tubes?) carrying Earth's gravitational field, only the gravitational mass of neutrons would respond to it.

*3. Objection*There is an objection against the proposed picture. Nuclei possess large em and Z^0 charges. If the naive criterion Z^2\alpha >1 is correct, the transition should occur already for Z>Z_0=11, which corresponds to Mg. Why doesn't the phase transition occur for ordinary nuclei and delocalize their em charges to a volume of size of order L= r\times L, L ordinary nuclear size, r=hbar_s/hbar? a) The manner to circumvent this paradox might be simple. The precise criterion for the occurrence of the phase transition is that the perturbation series in powers of Z^2\alpha fails to converge. Z^2\alpha=1 is just a naive guess for when this occurs. b) Also the assumption that nucleons always form single join along boundaries condensate inside nucleus is too naive. Rather, several clusters of protons and neutrons are expected to be present as TGD inspired model for nucleus indeed assumes. In fact, the non-occurrence of this transition for ordinary nuclei would give an upper bound for the size of this kind of clusters in terms of Z and A-Z. Even the strange sounding claim of Hudson about high spin states of nuclei might make sense. The formation of high rotational states means that nucleus behaves a single coherent whole. Therefore join along boundaries condensates of size of entire nucleus are more probable for high spin states. A conceivable possibility is that also in RHIC experiments with colliding Gold nuclei this kind of phase transition occurs so that there might after all be a connection with the esoteric claims of Hudson.

### Connection with cold fusion

The basic prediction of TGD is a hierarchy of fractally scaled variants of non-asymptotically free QCD like theories and that color dynamics is fundamental even for our sensory qualia (visual colors identified as increments of color quantum numbers in quantum jump). The model for ORMEs suggest that exotic protons obey QCD like theory in the size scale of atom. If this identification is correct, QCD like dynamics might be studied some day experimentally in atomic or even macroscopic length scales of order cell size and there would be no need for ultra expensive accelerators! The fact that Palladium is one of the "mono-atomic" elements used also in cold fusion experiments as a target material obviously puts bells ringing.*1. What makes possible cold fusion?*I have proposed that cold fusion might be based on Trojan horse mechanism in which incoming and target nuclei feed their em gauge fluxes to different space-time sheets so that electromagnetic Coulomb wall disappears. If part of Palladium nuclei are "partially dark", this is achieved. Similar mechanism might be required also in the case of classical Z^0 force, and one cannot exclude the possibility that also blobs of neutrons can spend some time in dark matter states. Note however that the claim of Hudson about 4/9 reduction of weight does not support this directly. Another mechanism could be the de-localization of protons to a larger volume than nuclear volume induced by the increase of hbar. This means that reaction environment differs dramatically from that appearing in the usual nuclear reactions and the standard objections against cold fusion would not apply anymore.

*2. Objections against cold fusion*The following arguments are from an excellent review article by Storms. a) Coulomb wall requires an application of higher energy. Now electromagnetic Coulomb wall disappears. In TGD framework classical Z^0 force defines a second candidate for a Coulomb wall but according to the model for neutrino screening discussed in the screening is highly local and could overcome the problem. Of course, one must re-evaluate earlier models in light of the possibility that also neutrons might delocalized in some length scale. b) If a nuclear reaction should occur, the immediate release of energy can not be communicated to the lattice in the time available. In the recent case the time scale is however multiplied by the factor r=hbar_s/hbar and the situation obviously changes. c) When such an energy is released under normal conditions, energetic particles are emitted along with various kinds of radiation, only a few of which are seen by various CANR (Chemically Assisted Nuclear Reactions) studies. In addition, gamma emission must accompany helium, and production of neutrons and tritium, in equal amounts, must result from any fusion reaction. None of these conditions is observed during the claimed CANR effect, no matter how carefully or how often they have been sought. The large value of hbar implying a small value of fine structure constant would explain the small gamma emission rate. If only protons form the quantum coherent state then fusion reactions do not involve neutrons and this could explain the anomalously low production of neutrons and tritium. c) The claimed nuclear transmutation reactions (reported to occur also in living matter) are very difficult to understand in standard nuclear physics framework. The model allows them since protons of different nuclei can re-arrange in many different manners when the dark matter state decays back to normal. d) Many attempts to calculate fusion rates based on conventional models fail to support the claimed rates within PdD (Palladium-Deuterium). The atoms are simply too far apart. This objection also fails for obvious reasons.

*3. Mechanism of cold fusion*One can deduce a more detailed model for cold fusion from observations, which are discussed systematically in the article of Storms and in the references discussed therein. a) A critical phenomenon is in question. The average D/Pd ratio must be in the interval (.85,.90). The current must be over-critical and must flow a time longer than a critical time. The effect occurs in a small fraction of samples. D at the surface of the cathode is found to be important and activity tends to concentrate in patches. The generation of fractures leads to the loss of the anomalous energy production. Even the shaking of the sample can have the same effect. The addition of even a small amount of H_2O to the electrolyte (protons to the cathode) stops the anomalous energy production. All these findings support the view that patches correspond to a macroscopic quantum phase involving delocalized nuclear protons. The added ordinary protons and fractures could serve as a seed for a phase transition leading to the ordinary phase. b) When D_2O is used as electrolyte, the process occurs when PdD acts as a cathode but does not seem to occur when it is used as anode. This suggests that the basic reaction is between the ordinary deuterium D=pn of electrolyte with the the exotic nucleus of the cathode. Denote by p_ex the exotic proton and by D_ex= np_ex exotic deuterium at the cathode. For ordinary nuclei fusions to tritium and ^3He occur with approximately identical rates. The first reaction produces neutron and ^3He via D+D--> n+ ^3He, whereas second reaction produces proton and tritium by 3H via D+D--> p+ ^3H. The prediction is that one neutron per each tritium nucleus should be produced. Tritium can be observed by its beta decay to ^3He and the ratio of neutron flux is several orders of magnitude smaller than tritium flux as found for instance by Tadahiko Misuno and his collaborators. Hence the reaction producing ^3He cannot occur significantly in cold fusion which means a conflict with the basic predictions of the standard nuclear physics. The explanation is that the proton in the target deuterium D_ex is in the exotic state with large Compton length and the production of ^3He occurs very slowly since p_ex and p correspond to different space-time sheets. Since neutrons and the proton of the D from the electrolyte are in the ordinary state, Coulomb barrier is absent and tritium production can occur. The mechanism also explains why the cold fusion producing ^3He and neutrons does not occur using water instead of heavy water. c) Also more complex reactions between D and Pd for which protons are in exotic state can occur. These can lead to the reactions transforming the nuclear charge of Pd and thus to nuclear transmutations. Also ^4He, which has been observed, can be products in reactions such as D+D_ex--> ^4He. The Z^0 Coulomb wall is not present in standard model. In TGD the situation is the same if the model for neutrino screening is correct or if the delocalization occurs also for neutrons. The reported occurrence of nuclear transmutation such as ^{23}Na+^{16}O--> ^{39}K in living matter (Kervran) allowing growing cells to regenerate elements K, Mg, Ca, or Fe, could be understood in this model too. d) Gamma rays, which should be produced in most nuclear reactions such as ^4He production to guarantee momentum conservation are not observed. The explanation is that the recoil momentum goes to the macroscopic quantum phase and eventually heats the electrolyte system. This provides obviously the mechanism by which the liberated nuclear energy is transferred to the electrolyte difficult to imagine in standard nuclear physics framework. e) The proposed reaction mechanism explains why neutrons are not produced in amounts consistent with the anomalous energy production. The addition of water to the electrolyte however induces neutron bursts. A possible mechanism is the production of neutrons in the phase transition p_ex--> p . D_ex--> p+n could occur as the proton contracts back to the ordinary size in such a manner that it misses the neutron. This however requires energy of 2.23 MeV if the rest masses of D_ex and D are same. Also D_ex+D_ex--> n+^3He could be induced by the phase transition to ordinary matter when p_ex transformed to p does not combine with its previous neutron partner to form D but recombines with D_ex to form ^3He_ex-->^3He so that a free neutron is left.

## 1 comment:

Matti,

You might like my current article today on Supersymmetrical realities

I will go further into this in time.

Hang in there.

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