Text: The Physics of Negative Mass Tachyons Referenced Terms and Names Tachyons, antigravity, FTL, superluminal, faster than light, faster-than-light, quarks, gluons, mesons, spin, charm, relativity, neutrinos, photons, electrons, protons, neutrons, pions, muons, leptons, hadrons, Bohr Magnetons, nucleus, chromodynamics, hyperluminal, quasar, Planck, Einstein, de Broglie, Schroedinger, Heisenberg, Dirac, Kepler, Ptolemy, Ptolemaic Abstract o This web page provides a summary derivation of the first and only theoretical tachyon model to agree with experiment. No other tachyon model, to date, has produced agreement with experiment. It is a unified model that produces agreement with experiment for the electron, the proton, the neutron, the light nuclei, and the mesons. o The data that is used to verify this model is well known from the standard physics literature, especially the Review of Particle Physics, published by the Particle Data Group of the American Physical Society. No source that is controversial or possibly bogus is used. This model is, in short, a reinterpretation of existing particle data that is accepted by and used by the physics community. o All attempts have been made to make the presentation as simple as possible so that even someone with a relatively modest background in physics can carry out the calculations with a simple hand calculator. Hence, it is shown just how simple basic subatomic physics can be if presented properly. o The model is a Bohr-like revolving particle model that utilizes a negative mass tachyon in conjunction with a revolving, but very tiney, charged point particle. The tachyon, being unable to drop below the speed of light, causes the positive mass charged particle to revolve in a relatively large orbit, thus generating a magnetic moment while maintaining agreement with experiment in that the charged particle for the electron is know to be extremely small. o Specifically, the heavier positive mass muon captures a negative mass tachyon to form an electron. The muon, in turn, consists of a positive mass pion and another negative mass tachyon. The radii of the revolving electron and the muon are determined from the cutoff energies of the well known mu -> e and the rare, direct pi -> e conversions curves. These radii determine the magnetic moments of the electron and the muon. The resulting magnetic moments are found to be the well known Bohr magnetons, identically. That is, the magnetic moments are These values are well known to agree with experiment. By requiring that the electron's charged particle have integral multiples of its de Broglie wavelength, its magnetic moment is improved to within 39 ppm of experiment. (Quantum electrodynamical corrections do much better in terms of accuracy, but there is nothing obvious to preclude its use as a correction factor for this model.) o The residual energies of the conversions are 20 eV and 123 KeV for the electron and muon conversions, respectively, somewhat larger in magnitude than the experimentally estimated masses of their respective neutrinos, but more than enough to account for the neutrinos' masses. o Based on this, it would be expected that colliding electrons and positrons would produce at least muons, pions, and gamma rays. This agrees with observation. All of this, of course, makes the pion the mother particle of the lepton family. This is quite at odds with the standard particle model. And while indirect evidence has generally been interpreted to mean that the pion is a spin 0 particle, the implication here is that the pion has a magnetic moment, albeit extremely small. o Similarly, a proton consists of a heavier sigma hyperon that has combined with another negative mass tachyon. Converse to the electron/muon model, the magnetic moment of the proton is used to determine its dimensions. These dimensions agree to within 3% of the with the experimental dimensions that are determined from both high and low energy scattering data. o By adding a revolving pion-tachyon combination to the center of the proton, we form a neutron. The ground state energy of the pion is 4076 MeV, and its excitation energies are found to be E = 4075/n2 , where n ranges from 1 - 9. As shown below, the first order transitions of this bound pion, an analog of the Bohr model's Lyman series, produce the "charmed" psi mesons within 5 % of the experimental values. The second order transitions, an analog of the Bohr model's Balmer series, produce the eta through the ao(980) mesons generally to within 4 %. Theses energies are also produced by colliding electrons and positrons, so that one must conclude that the unbound pion itself resonates. Again, there is no relationship between this model and the standard model. o Note that a negative mass particle is inherently an antigravity particle. o And while this model agrees quite well with experiment, there is no relationship whatsoever between it and the generally accepted standard particle model. This model is described in more detail in a book, The Physics of Tachyons, and in the published papers provided at the end of this web page. o As can be seen, comparing this extremely simple particle model to the extremely complex standard particle model is like comparing the extremely simple Kepler planetary model to the complex Ptolemaic planetary model that was prevalent in the middle ages. And while both particle models may agree with experiment, there is no comparison beyond that. There are no quarks, gluons, or strings here, just as there were no epicycles in the Kepler model. And here, mesons are not classified according to strangeness, or flavor. This model is even politically correct in that there is no reference to chromodynamics, or color! Ernst L. Wall Istituto per la Ricercia de Base Monteroduni, Italy Email - ewall@shore.net (Note: Comments are solicited.) To see the broad spectrum of Monteroduni Research, see preliminary web by clicking here. Last Updated on March 12, 1997 by Ernst L. Wall The Definition of a Tachyon Tachyons are particles whose velocity exceeds the velocity of light. While many believe that the existence of particles with hyperluminal (superluminal) velocities (FTL, or Faster-Than-Light velocities) is precluded by relativity, this is not the case if the particle is created with a velocity already exceeding the velocity of light. What relativity precludes, within the boundaries of our present technologies, is the acceleration of a subluminal particle to hyperluminal velocities. What is also not precluded is the possibility that technology might someday be developed that will permit the relativistic limitations to be overcome, and hyperluminal velocities to be achieved by subluminal objects. The most well known tachyon model uses an imaginary mass. As interesting as that model is, mathematically speaking, an imaginary mass has no physical meaning. As a result, that model has, as yet, produced no agreement with experiment. That model and its mathematics is discussed extensively in an excellent review by Recami and Mignani in Rivista Del Nuovo Cimento 4, 209, (1974). A Brief Comment on Units of Mass and Units For those with minimal experience with subatomic particles, a few comments should be made on the mass terminology used here. For example, the mass of an electron is 9.1093896 x 10-28 grams. But this is a little clumsy for human beings to deal with on a daily basis, especially verbally. It is easier to express the mass in terms of electron volts, which for the electron is 0.511 MeV, where MeV is an abreviation for million electron volts. Further, the early particle accelerators, such as the Van der Graaf generator and the Cocroft-Walton machine used high voltages to accelerate the particles, and an electron volt is the amount of work done when a charged particle moves through a potential of one volt. Hence, it was natural to express the energy in terms of the voltage with which the particle was accelerated. The equivalent mass energy relationship is obtained from the Einstein relationship, namely E=mc2. To calculate E, we use the particle mass in grams along with the speed of light which is c= 2.99792458 x 1010 cm/sec. The resulting energy, E, is in ergs. However, from electrodynamics we know that one erg is equivalent to 6.24150636 x 1011 eV, where eV is the abreviation for electron volts. Hence, the calculation is quite simple, so the reader should have a try at it with his hand calculator. Particle Mass (gms) Mass-Energy (MeV) Magnetic Moment (Ergs/gauss) electron 9.1093896x10-28 0.51099906 9.2847701x10-21 proton 1.6726231x10-24 938.27231 1.4106076x10-24 neutron 1.6748286x10-24 939.56563 9.6623707x10-24 muon 1.8835327x10-25 105.658387e-24 4.4904514x10-23 pion 2.488018x10-25 139.5675 4.3x10-24 (No, it's not zero, spin 0 or not.) Deuteron 3.3435860x10-24 1875.61339 4.3307375x10-24 In addition, the following constants will be needed: Constant's Name Symbol Value Unit Speed of light c 2.99792458x1010 cm/sec Elementary Charge e 4.80320680x10-10 statcoulombs* Elementary Charge e 1.60217733x10-19 coulombs Planck's Constant h 6.6260755x10-27 erg-sec Planck's Constant/2pi h_bar 1.05457266x10-27 erg-sec Nuclear and subatomic dimensions are usually expressed in fm, which can stand for Fermis, which is10-13 centimeters, or femtometers, which is 10-15 meters. (Obviously the same length, but different units.) The Meson Model Because of its extreme simplicity and its excellent fit to the experimental meson data, we will present the meson portion of the model prior to the actual derivation of the overall model. The first meson to be physically observed was the muon, and some 10 years later, the pion. Still later, other mesons were observed in various high energy particle collisions as interaction energies, or even as free particles. These resulted typically from pion-proton collisions, K meson-proton collisions, or electron-positron collisions. Some of the earlier and more spectacular observations were made inside hydrogen bubble chambers. Typically, these reactions produce pions as by products, although K mesons and other mesons are also produced. From the standpoint of this model, all mesons arise from a resonating pion, whose internal binding energy is 4076 MeV. But what is so interesting is that the pion (again from the standpoint of this model) is the mother particle of the muon and the electron, so that one would expect that electron-positron collisions must produce at least pions, muons, and gamma rays, as well as the other meson energies. The most obvious would be the psi resonances. In fact, some of them were originally published in a table of excitation energies in a tachyon-hadron paper (see references below), but their significance was overlooked at the time. These internal pion excitation levels are given by Em(n) = 4076/n2, where the index, n, ranges from 1 through 9. To obtain the various meson energies, you may use the above equation as follows: 1. First, calculate the 9 levels of Em using the values 1 - 9 for n. These are shown in the energy level and transition energy diagram, below. The first three levels of Em correspond to the energy levels of the psi(4415), the phi(1020), and the K- mesons to within - 8 % to +8 %. The next two levels correspond to resonances that arise from a K- proton collision and a pi- proton collison, these resonances having energies of 280 MeV and 156 MeV, with agreements of -9.3 % and -4.3 %, respectively. These latter resonances two will be discussed in more detail in an upcoming revision of The Physics of Tachyons. 2. Next, subtract each resulting value of Em from the first value (for n = 1), and you will have the first order transitions, or the "charmed" psi mesons to within -1.3 % to +4.7 %. (The Bohr atom's analog is the Lyman series.) These transitions are shown in the transition diagram above, and the values are plotted in the graph below along with the corresponding experimental values where the index is the value of the energy level, n, that is differenced with the value for n=1. 3. Finally, subtract each subsequent value from the second value (for n = 2), and you will have the second order transitions, These produce the seven light mesons, i.e., the eta through the ao(980). The agreement with experiment ranges from 0.5 % to -2.3 %, except for the omega(783), which is within +9.5 % of experiment. (The Bohr atom's analog is the Balmer series.) These are shown in the graph, below, along with their corresponding experimental values, where the index is the value n that is subtracted from the value n = 2. These transitions, i.e., the transitions between the level for n = 1 and the lower levels correspond to the "charmed" psi mesons. The second order transitions, the transtions between the n= 2 level and the lower levels correspond to the lighter mesons from the eta through the a0(980). 4. THE READER IS INVITED TO TRY THIS WITH A SIMPLE HAND CALCULATOR. To reiterate, it is not necessary to understand quarks, gluons, etc, to achieve this systematic agreement with experiment. Nor is reference to strangeness flavor, or color needed. The Binary Mesons Because the many mesons studied here arise from relatively large energies that produce two or more pions, we must consider that at least some of these collision should produce energy levels that are the sum of two energy levels. Since the energies can be a combination of any two levels, we combine all possible energies of the lighter mesons (the second order transitions, above) and obtain binary energy levels of the electron-positron collisions. These binary levels are graphically shown below along with their corresponding experimental values. Here, the index n arbitrarily picks up from the value n = 9 in the graph above. Both the experimental energy levels and the summed values of the light mesons are arranged in ascending numerical order and plotted. None of the experimental mesons are named here simply because there are too many of them. They are shown in detail in The Physics of Tachyons. The agreement with experiment ranges from -16 % to + 12 %. While this might appear to be only crude agreement between experiment and theory, it should be noted that no attempt was made to compensate for any binding energies between the positive and negative excited pions. Further, many of these mesons were not discovered at the time this model was originally developed, so that this model predicted more binary mesons than were know at the time. There are, however, a number of mesons above the binary set that it does not explain. These are also shown here. No attempt has been made at to account for them at this time, although it is likely that they arise as excitations from an even more massive particle than the pion. Note that the first 19 binary mesons have a scalloped shape that a reflection of the parabolic shape of the light mesons energy curve. The experimental values, while somewhat crude, seem to correspond to this scalloped shape. The first 20 levels are shown below in more detail to illustrate this shape. There is no other model that produces as many mesons as this, especially when you add the binary mesons, as described below. A Brief Comment on Magnetic Moment The origin of the magnetic moment of particles, , is the heart of this model, so that a brief discussion of it is warranted before proceeding to the actual derivation of the magnetic moments of the electron and the muon. In the simplest case, a wire loop with an electrical current flowing through it causes a magnetic field to be generated along its axis. A measure of the amount of torque that the loop would be subjected to when placed in a magnetic field is called the magnetic moment. It is calculated by multiplying the area of the loop by the current flowing through the wire. That is, = I x A ergs/gauss, where A is the area and I is the current. The current I is normally given by I = ne where n is the number of charges passing a point in the wire, and e is the charge per particle. For current as we normally use it, e = 1.602`7733x10-19 coulombs. However, in order to have a magnetic moment that is correct for the cgs system of units, we must use e = 4.8032068010-10 statcoulombs, and then that must be divided by the speed of light. I.e., I = ne/c. The amount of torque on the loop is the T = Bcos dyne-cm, where is the angle between the axis of the magnetic moment and the direction of the magnetic field, B. Insofar as its application to particles is concerned, the proton, electron, neutron, and the nuclei all have magnetic moments. The fact that the electron has a half-integral value of spin prevents any two electrons in an atoms from occupying the same energy/angular momentum. This fact causes the various atoms to combine chemically in the way that they do, thus making our world the way it is. That is, without tachyons, there would be no particle spin, and so we would not exist. (Note that, here, I am not making a distinction between spin as a quantum mechanical term and magnetic moment as a physical phenomena in this simple discussion. This may enrage quantum mechanics, but is for them to worry about their blood pressure.)

See Also:

Source: