Text: The Proton Model The proton consists of a sigma hyperon and still another negative mass tachyon. However, the sigma hyperon -> proton conversion has no curve with a clearly defined cutoff energy such as there is for the electron and the muon. Therefore, an inverse approach must be used for the proton. Using the above configuration and the magnetic moment of the proton ( muP = 1.4106076 x 10-23 ergs/gauss ) in Eq. 24, we find that the charged particle's orbital radius, rc , is 0.58736077 fm.The masses of the proton and sigma hyperon are 938.27231 MeV and 1189.37 MeV, respectively. The result is that their mass ratio is RP =1.2676, and the mass of the tachyon is -251.10 MeV. Using these values in Eq. 15, the radius of the tachyon's orbit is found to be 2.782 fm. High energy and low energy scattering experiments indicate that these radii agree with experiment to within 3 %. The Neutron Model Adding a similarly orbiting, but smaller negatively charged pion with its tachyon to the center of the proton, and we have a neutron. That is to say, it is a coaxial model with the orbits sharing the same orbital plane and revolving in the same direction. Subtracting the magnetic moment of the neutron ( muN = 9.6623707 x 10-24 ergs/gauss ) from that of the proton, we find that the orbiting pion's magnetic moment is mupi = 0.4443705 x 10-23 ergs/gauss. (Note, incidentally, that this value is within 2.5 % of the magnetic moment of the deuteron.) Using this value in Eq. 24 to calculate the radius of the orbiting pion's charged particle, we find it to be 0.18503077 fm. High energy scattering experiments have verified this value. Equating the pion's de Broglie wavelength to the circumference of its orbit, its energy level is found to be 4076 MeV. Its excited levels are found to be Em = 4076/n2 MeV, with values of the index, n, ranging from 1 through 9. This accounts for energy levels of the meson model previously shown. The first of these resonances to be discovered was a neutron resonance and was called the J particle by S. Ting. Then, the same resonance was found in ep collisions by B. Richter. Hence, it appears that the meson family consists of various states of the pion, both within the neutron and in the electron. The Light Nuclei Now consider the attraction of neutrons and protons to form a deuteron. If a proton approaches a neutron, its sigma hyperon will attract the neutron's pion, thus axially deforming the neutron and causing it to behave as a deformable dipole. While the sigma hyperons electrostatically repel one other, they are both attracted to the pion, thus causing this model to be somewhat similar to the Yukawa model. This produces a highly nonlinear attractive force, so that an experimental evaluation of the force would cause it to appear to have no relationship to simple electrostatic forces. The spacing of the sigma hyperons is 1.323 fm, and their magnetic energies are 0.2276 MeV each. Using these, the sum of the calculated electrostatic and magnetostatic binding energies is 2.381 MeV, as compared with the measured deuteron's binding energy of 2.2246 MeV, a 7.0 % difference. Similarly, crude calculated values for the binding energy of tritium is 28.3 % less than the experimental value, and for the helium-three binding energy is 43 % less than the experimental value. This is discussed in detail in The Physics of Tachyons. These values are not precise because they are based on crude estimates rather than carefully integrated algorithms. However, in spite of the lack of precision, an argument can be made that these light nuclei could be at least partially bound by electromagnetic forces, and not totally by a separate nuclear force. It is likely that with more careful calculations, better agreement will be obtained. But if these large errors are disturbing, it should be noted that a perusal of the Physical Review will reveal many models with errors of 50 %, or worse, in those cases where the authors have the nerve to make a comparison with experiment. In many cases, they conveniently ignore that little matter of comparison with experiment, but the mathematical elegance can be impressive, even if it is useless. The calculated magnetic moment of deuterium is within 2.5 % of experiment, the calculated magnetic moment of helium-three is within 1.7 % of experiment, and the magnetic moment of tritium is within 3.5 % of experiment. "Space Warps" And for those who might ask, there is no "space warp" of any kind involved in this model, nor any similarity to anything mentioned in Star Trek outside of the word "tachyon". But of course, the demonstration of the existence of tachyons might well suggest the possibility of someday breaking the light speed barrier. Obviously, that would require some advancement beyond our present technology. How to Obtain Detailed Information on the Tachyon Model The negative mass tachyon is described in various publications by Ernst L. Wall in the standard physics literature. It is also described in the 241 page book, The Physics of Tachyons, Ernst L. Wall, 1995, ISBN I-57485-001-6. It is published by the Hadronic Press, 35246 US 19 North #115, Palm Harbor, FL 34684, USA. Phone: (813) 934 - 9593. Special Price for Individuals, $30. The book is also carried by: o The International Tesla Society, PO Box 5686, Colorado Springs, CO 80931. Phone (800) 397-0137; o Quantum Books near MIT for Boston area residents, (617) 494-5042. Additional Publications by Ernst Wall o "The Role of Tachyons in Electron Spin and Muon Spin", Bulletin of the American Physical Society, 30, 729 (1985). o "The Role of Tachyons in Proton Spin", Bulletin of the American Physical Society, 30, 729 (1985). o Indirect Evidence for the Existence of Tachyons: A Unified Approach to the mu->e and the pi->mu Conversion Problem", Hadronic Journal 8, 311 (1985). o "On Tachyons and Hadrons", Hadronic Journal 9, 239 (1986). o "Unresolved Problems of the Tachyonic Models of the Electrons and the Muon", Hadronic Journal 9, 263 (1986) o "Time Cancellation Hypothesis", Bulletin of the American Physical Society, 33, 1076 (1988). o "Charm, Other Resonances, and the Tachyonic Particle Model", Bulletin of the American Physical Society, 33, 1076 (1988). o "On Pion Resonances and Mesons, Time Cancellation, and Neutral Particles", Hadronic Journal 12, 309 (1989). o "Hamming Code Error Correction for Microprocessors", Chapter 3, Microprocessor Applications Handbook, edited by D. Stout. McGraw-Hill, 1981. o "Applying the Hamming Code to Microprocessor- Based Systems", Electronics (McGraw-Hill) 52, p. 103 (1980). (Note that this was the feature (cover) article of this issue.) o "Edge Injection Currents and Their Effects on 1/f Noise in Planar Schottky Diodes", Solid State Electronics 19, p. 389 (1976). o E. D. Adams, G. C. Straty, and E. Wall. "Thermal Expansion Coefficient and Compressibility of Solid Helium-three", Physical Review Letters 15, p. 549 (1965) o E. D. Adams and E. L. Wall. "Thermal Expansion Coefficient and Compressibility of Solid Helium-three", Bulletin of the American Physical Society 10, p. 519 (1965). (Note that these were the first measurements of the PVT surface of solid helium-three.) Other Interesting Technical Web Sites The Institute for New Energy - Click Here Phil Gibb's Old Cyclotron Laboratory - Click Here (More to be added later.) APPENDIX Causality - While many physicists worry about the causality associated with the reverse time direction of tachyons, it is pointed out here that in this model, the tachyon is bound to a positive mass, charged particle in a closed system, and so the effects of causality need not be worried about, at least in the case of a first order calculation. Insofar as time travel is concerned, the random nature of atomic processes would likely preclude anyone getting younger if he achieved hyperluminal velocities. This is not to say that reverse time has no effect whatever. It might well be that there is a cancellation effect between the reverse time of the tachyon and the forward time of the charged particle, but only at the microscopic particle level. However, that possible effect has not been explored extensively, as yet. More is said about this in The Physics of Tachyons. But, consider that the Starship Enterprise, on a brief junket to the colony on Neptune, goes to warp factor 1 until it gets near Neptune, and then it drops below light speed. Have the colonists on Neptune gone backwards in time just to accommodate the Enterprise? Not likely! Have the crew members become younger? Not likely, because molecular processes will still be random processes. Precedence - This model began as an ad hoc model, and many physicists object ad hoc models. However, when it was extended to other areas than the lepton family, it produced surprisingly good results. But for those who still object, they should recall that the Kepler model was pure ad hoc, but it influenced Isaac Newton in his development of classical physics. Planck's black body radiation model was pure add hoc. Einstein described his photoelectric equation as "heuristic", i.e., one step above ad hoc. Bohr's model was ad hoc. De Broglie's thesis committee considered his thesis to be ad hoc. In fact, Einstein's recommendation was necessary in order for them to accept the thesis. Without these developments, Schroedinger's and Heisenberg's work would not have been developed, or if it had, it would have been pure ad hoc because there would have been no rationale for the development. Further, some would argue that Dirac's model was ad hoc because there was no a priori reason for his utilizing matrices the way he did. He himself said of it that "I was only looking for some pretty mathematics." So if anyone wishes to retain his intellectual "purity of essence" and not use ad hoc models or anything derived from them, then that person fobidden to utilize Newtonian mechanics and quantum mechanics. Light Speed Charged Particles - It is inherent in this model that the magnetic moment of particles arises from very tiny charged particles revolving in very much larger orbits at the speed of light. This allows the revolving charge to have sufficient area to generate a magnetic moment while remaining consistent with the experimental observations that the charged particle is extremely small. As will be shown, the radius of the electron's charged particle's orbital radius is 386.15933 fm, or the reduced Compton wave length for the electron. Likewise, the muon's charged particle's orbital radius is 1.8675947 fm, or its reduced Compton wavelength. The absolute maxim diameter of the charged particle, based on this model, is 0.185 fm, with no lower limit. (High energy scattering measurements indicate that its radius is actually of the order of 10-4 fm.) This is a radical departure from conventional models. These charged particles are not accelerated to these velocities, but when the particles are created, they are created with these orbital velocities, much in the same sense that tachyons are created with hyperluminal velocities. Charged Particles as Stationary Photons - These revolving systems, such as electrons, appear to behave as stationary photons, but they are bound by the laws of relativity when they move as a system. But for the extreme skeptic, recall that there is some indication that the jets ejected from quasars appear to have light speed velocities, so that there may be some prior precedent for luminal, or even superluminal, light emitting particles. (Note also that Lucas and Bergman have a particle model that does not use a point charged particle, but uses a ring charge that revolves at light speed. It does not use tachyons to maintain the system balance. See their web site at www.cormedia.com/css/info.html.) Radiating, Revolving Charged Particles - A common objection expressed about this kind of model is that revolving charged particles would be expected to radiate their energy away. However, it is to be emphasized that this is a light speed particle, and there is no a priori reason to assume that it must radiate its energy away as would be expected for sublight speed particles. But in the simplest case, consider its orbit to be a ground state orbit. (Shades of Neils Bohr! It worked for him!!) But a more specific explanation is to be found in the fact that the revolving light speed particles appear to be stationary photons. (For more on this, see Eq. 27 and the discussion following it.) But more important, the equation that describes revolving charged particles does not hold for light speed particles. It goes to infinity at these speeds. Relativity has passed every test to which it has been subjected, but it has been tested only in the subluminal domain. While it might be possible that relativity is relevant to the luminal and superluminal domain, there is no a priori reason to assume that it must be particularly relevant to these domains. This model is concerned only with luminal and hyperluminal velocities and is, therefore, not at variance with any measured aspect of relativity. Quantum mechanics has been extraordinarily accurate in its description of the atom. This model utilizes only simple quantization, and it does not attempt to arrive at a wave function for the internal structure of the particle systems. However, there is little to place it in conflict with quantum mechanics as it applies to atomic structures, although its definite structure may bother some quantum theorists. Neutrinos have been detected, so therefore, they exist. However, estimates of the of the neutrino masses via Kurie measurements give upper limits of about 10 - 20 eV, so it does seem rather strange that it could be believed that the shape of the mu-> e curve (up to 52.6 MeV) can be determined by such small, non-photonic particles. Further, it should be pointed out the residual energy from the tachyonic mu-> e conversion is 19.83 eV, and the residual energy of the pi -> mu conversion is 122.97. These numbers are within range of the respective experimental estimates of the upper limits of neutrino masses. In any case, they are not needed to account for the Bohr magneton in this model.

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