arXiv subjects
Publications and source records attributed to E. L. Koschmieder.
Lattice theory is used to explain the rest masses of the stable mesons and baryons and their spin. From the mass of the charged pi-mesons follows the mass of the muons. From the mass of the muons follows the mass of the electron. We do not use hypothetical particles. Only photons, neutrinos and charge are needed to explain the mass of the elementary particles.
We study the consequences which the presence of an elementary electric charge in mu^(+-) and pi^(+-) has for the rest mass of mu^(+-) and pi^(+-). The addition of the electric charges e^(+-) to the massive neutral bodies of these particles does not increase the energy in the rest mass of the muon and pion, but rather decreases their energy by the binding energy of the electric charge to the neutral bodies of the muon and pion. The addition of a charge to the neutral neutrino lattices of the muon or pion changes the simple cubic lattices of the neutral particles to face-centered cubic lattices of the charged particles, which is essential for the stability of the particles.
It is shown that it follows from our model of the electron that its magnetic moment has an anomalous part if the magnetic field energy is taken into account. That means that the magnetic moment of our model of the electron is 1.0000565 times larger than the measured magnetic moment of the electron.
We determine the strength of the weak nuclear force which holds the lattices of the elementary particles together. We also determine the strength of the strong nuclear force which emanates from the sides of the nuclear lattices. The strong force is the sum of the unsaturated weak forces at the surface of the nuclear lattices. The strong force is then about ten to the power of 6 times stronger than the weak force between two lattice points.
The rest masses of the electron, the muon and of the stable mesons and baryons can be explained, within 1% accuracy, with the standing wave model, which uses only photons, neutrinos, charge and the weak nuclear force. We do not need hypothetical particles for the explanation of the masses of the electron, muon, mesons and baryons. We can also explain the charge of the electron, the spin of the electron, of the muon and of the stable baryons, without any additional assumption. We also have determined the rest masses of the electron-, muon- and tau neutrinos and found that the mass of the electron neutrino is equal to the fine structure constant times the mass of the muon neutrino.
We will show that one half of the rest mass of the electron is equal to the sum of the rest masses of electron neutrinos and that the other half of the rest mass of the electron is given by the energy in the sum of electric oscillations. With this composition we can explain the rest mass, the electric charge, the spin and the magnetic moment of the electron.
The rest masses of the stable mesons and baryons and the rest masses of their antiparticles, as well as the rest masses of the mu (+,-) and tau (+,-) leptons can be explained, within 1% accuracy, with the standing wave model, which uses only photons, neutrinos, charge and the weak nuclear force. And we can explain the spin of the stable mesons and baryons and the spin of the mu (+,-) and tau (+,-) leptons without any additional assumption. We can also determine the rest masses of the electron-, mu- and tau-neutrinos.
It is shown that the spin of pi (0), eta, Lambda, Sigma (+,-,0), Xi (-,0), Lambda-c (+), Sigma-c (0), Xi-c (0), and Omega-c (0) mesons and baryons can be explained by the sum of the angular momentum vectors and spin vectors of the electromagnetic waves which are in these particles according to the standing wave model. The spin of the pi (+,-), K (+,-,0), D (+,-,0), and D-S (+,-) mesons and of the neutron is the sum of the angular momentum vectors of the oscillations and of the spin vectors of the neutrinos and the electric charges which are in the cubic lattice of these particles. Spin 1/2 is the consequence of the superposition of two perpendicular standing waves of equal frequencies and amplitudes shifted in phase by pi/2. The spin of the antiparticles of the mesons and baryons is the same as the spin of the ordinary particles.
We have shown previously that the mass of the muon neutrino can be determined from the energy released in the decay of the pi (+-) mesons, and that the mass of the electron neutrino can be determined from the energy released in the decay of the neutron. We will now show how the mass of the tau neutrino can be determined from the decay of the D(s)(+-) mesons.
We can determine the intrinsic angular momentum of the mu-mesons from the sum of the angular momentum vectors of the lattice oscillations and the sum of the spin vectors of the neutrinos in the lattice and the spin vector of the electric charge which the mu-mesons carry. We used this neutrino lattice before to calculate the rest mass of the mu-mesons. Here we learn how the apparent discrepancy between the concept of a point particle and the finite size of a neutrino lattice is resolved. We also learn that the spin of the mu-mesons originates exclusively from the spin of the electric charge of the mu(+,-) mesons.
Only photons are needed to explain the masses of the pi(0), eta, Lambda, Sigma(0), Xi(0), Omega(-), Lambda(c,+), Sigma(c,0), Xi(c,0), and Omega(c,0) mesons and baryons. Only neutrinos are needed to explain the mass of the pi(+-) mesons. Neutrinos and photons are needed to explain the masses of the K-mesons, the neutron and D-mesons. Surprisingly the mass of the mu-meson can also be explained by the oscillation energies and rest masses of a neutrino lattice. From the difference of the masses of the pi(+-) mesons and mu(+-) mesons follows that the rest mass of the muon-neutrino is 47.5 milli-eV. From the difference of the masses of the neutron and proton follows that the rest mass of the electron-neutrino is 0.55 milli-eV. The potential of the weak force that holds the lattices of the particles together can be determined with Born's lattice theory. From the weak force follows automatically the existence of a strong force between the sides of two lattices. The strong nuclear force is the sum of the unsaturated weak forces at the sides of each lattice and is therefore 10^6 times stronger than the weak force.
The difference of the rest masses m(pi^+-) - m(mu^+-) is nearly equal to 1/4 of the rest mass of the pi^(+-) mesons and is equal to the sum of the rest masses of the 0.7 times 10^9 muon neutrinos (respectively anti-muon neutrinos) which are in the cubic lattice of the pi^(+-) mesons according to the standing wave model. In the decay of a pi^(+) or pi^(-) meson all muon neutrinos, respectively anti-muon neutrinos, of the cubic lattice of the pi^(+-) mesons are emitted. The sum of the oscillation energies of all neutrinos in the pi^(+-) mesons is the same as the sum of the oscillation energies of the remaining neutrinos in the mu^(+-) mesons. Consequently the mass of the mu^(+-) mesons is equal to m(pi^+-) - 0.7 times 10^9 m(nu_mu) or 0.75 times m(pi^+-), within 1% in agreement with the measured ratio m(mu^+-) / m(pi^+-) = 0.757028.
We have determined theoretically the rest mass of the muon neutrino at 50 milli-eV and the rest mass of the electron neutrino at 5 meV, as well as, to 1% accuracy, the ratio of the masses of the stable elementary particles which decay by weak decays. We assume that the particles of the neutrino branch consist of a cubic, isotropic nuclear lattice, held together by the weak nuclear force. The eigenfrequencies of the lattice are calculated with Born's theory of cubic lattices. Only neutrinos are required to explain the so-called stable particles of the neutrino branch.
It is shown that the empirical rule that the masses of the stable mesons and baryons of the gamma-branch are integer multiples of the mass of the pi0 meson with a maximal deviation of 3.3% holds also for the meson and baryon resonances, regardless whether the spin of the particles is 0 or 1/2. It is also shown that the masses of the particles with weak decay are integer multiples of the mass of the charged mesons times a common factor 0.853.
The size of the stable elementary particles is investigated with the standing wave model. The particle size follows from the magnitude of the radiation pressure. It is shown that the outward directed radiation pressure is balanced by the inward directed elastic force per unit area in the cubic nuclear lattice, provided that the sidelength of the lattice is 10^(-13) cm, which agrees with the measured radius of the proton r = 0.8 \times 10^(-13) cm, within the uncertainty of the parameters.
In order to explain the empirical integer multiple rule for the stable mesons and baryons presented in the preceding paper we assume that the particles are held together in a cubic nuclear lattice. This is a novel approach to the particles, based on the fact that the range of the weak nuclear force is only a thousandth of the diameter of the nucleon, and that the crystals are the best-known macroscopic bodies held together by a microscopic force. We investigate the standing waves in a cubic nuclear lattice. From the frequency distribution of the waves follows that the masses of the $γ$-branch particles are integer multiples of $m(π^0)$. We show that each particle has automatically an antiparticle. Assuming that the energy of the oscillations is determined by Planck's formula for the energy of a linear oscillator, it turns out that the $π^0$ meson and the other members of the $γ$-branch are like cubic black bodies filled with plane, standing electromagnetic waves. Our standing wave model explains the integer multiple rule of the masses of the neutral mesons and baryons of the $γ$-branch and uses nothing else but photons. Our results justify the cubic lattice assumption.
From the well-known decays of the particles follows that the mesons and baryons consist of a $γ$-branch and a neutrino branch. From the well-known masses of the particles follows that the masses of the $γ$-branch particles are integer multiples of the mass of the $π^0$ meson, within 3%, in spite of differences in spin, isospin, strangeness and charm. The average factor in front of the integer multiples of $m(π^0)$ of the $γ$-branch particles is $1.0073 \pm 0.0184$. The masses of the $ν$-branch particles are integer multiples of the mass of the $π^\pm$ mesons, times a factor $0.86 \pm 0.02$. The existence of the integer multiple rule can be verified from the Particle Physics Summary using a calculator.