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There are three radii associated with the electron: The Bohr radius, Compton radius and Classical radius. These radii have never been associated with any physical electron geometry. A possible toroidal geometry is presented here, with connections to the Boltzmann constant and the Cosmic Microwave Background temperature., pdf export from a Maple document

The size and shape of a single photon is a property of photon shown in the collision of the photon with charged particles. Applying scattering theory and classical electrodynamics is the most reliable way to solve this problem. The main intention of this paper is to reveal the electromagnetic structure of a single photon. It establishes the formulas for the Poynting vector (energy flow vector) and the energy density. Applying the new explanation of Compton wavelength creates the probability formula for the Compton effect when a photon collides with an electron. The research discovers that the electromagnetic field of a single linearly polarized photon confines to a membrane-like cuboid, while the electromagnetic field of a single circularly polarized photon confines to a membrane-like shell of a hollow cylinder.

The Standard Model of particle physics requires nine lepton and quark masses as inputs, but does not incorporate neutrino masses required by neutrino oscillation observations. This analysis addresses these problems, explaining Standard Model particle masses by describing fundamental particles as solutions of Einstein’s equations, with radii 1/4 their Compton wavelength and half of any charge on rotating particles located on the surface at each end of the axis of rotation. The analysis relates quark and lepton masses to electron charge and mass, and identifies neutrino masses consistent with neutrino oscillation observations.

Previously, we proposed an empirical equation describing the relationship between the gravitational force and the temperature of the cosmic microwave background (CMB). After evaluating our equation, we discovered many empirical equations describing the electromagnetic force in terms of the CMB, including equations for the Rydberg constant, the Bohr radius, the Compton wavelength, the classical electron radius, the Hartree energy, the Coulomb’s law with distance, and the ratio between the gravitational force and electric force. The background theory is not yet complete. However, we can justify why the discovered empirical equations should not be coincidence.

We state and explain the total rate at which a charged non-rotating black hole emits charged particles, taking into account both Hawking radiation and Schwinger pair production simultaneously. We give concrete formulae for this emission rate in certain limits, with the greatest simplification occurring when the black hole is much larger than the particle's Compton wavelength. We provide an interpretation of the result in terms of a tunnelling process, both through the black hole horizon and the surrounding electric field, and comment on how suppression due to tunnelling modifies the emission spectrum., 27 pages, 4 figures

The main goal of the present work is a unitary approach of the physical origin of the corrections to the magnetic moment of free and bound electron. Based on this approach, estimations of lowest order corrections were easily obtained. In the non-relativistic limit, the Dirac electron appears as a distribution of charge and current extended over a region of linear dimension of the order of Compton wavelength, which generates its magnetic moment. The e.m. mass (self-energy) of electron outside this region does not participate to this internal dynamics, and consequently does not contribute to the mass term in the formula of the magnetic moment. This is the physical origin of the small increase of the magnetic moment of free electron compared to the value given by Dirac equation. We give arguments that this physical interpretation is self-consistent with the QED approach. The bound electron being localized, it has kinetic energy which means a mass increase from a relativistic point of view, which determines a magnetic moment decrease (relativistic Breit correction). On the other hand, the e.m. mass of electron decreases at the formation of the bound state due to coulomb interaction with the nucleus. We estimated this e.m. mass decrease of bound electron only in its internal dynamics region, and from it the corresponding increase of the magnetic moment (QED correction). The corrections to the mass value are at the origin of the lowest order corrections to the magnetic moment of free and bound electron.

The particle physics Standard Model involves three charge 0 neutrinos, three charge e leptons, three charge (2/3)e quarks, and three charge −(1/3)e quarks, where e is electron charge. However, the Standard Model cannot explain why there are three generations of particles in each charge state and makes no predictions relating to quark and lepton masses. This analysis, treating Standard Model particles as spheres with radii 1/4 the particle Compton wavelength, explains three, and only three fermions are in each charge state and relates first generation quark masses to the electron mass.

A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects such as electrons. A superfluid vacuum formed the base to describe the basic vortex structure and properties of the electron, whereas various formulations derived from hydrodynamic laws described the electron vortex circumference, radius, angular velocity and angular frequency, angular momentum (spin) and magnetic momentum. A vortex electron fully explained the associations between momentum and wave, and hydrodynamic laws were essential in deriving the energy and angular frequency of the electron. In general, an electron traveling in space possesses internal and external motions. To derive the angular frequency of its internal motion, the Compton wavelength was used to represent the length of one cycle of the internal motion that is equal to the circumference of the electron vortex. The angular frequency of the electron vortex was calculated to obtain the same value according to Planck’s theory. A traveling vortex electron has internal and external motions that create a three-dimensional helix trajectory. The magnitude of the instantaneous velocity of the electron is the resultant of its internal and external velocities, being equal to the internal velocity reduced by the Lorentz factor (whose essence is presented in a detailed formulation). The wavelength of the helix trajectory represents the distance traveled by a particle along its axis during one period of revolution around the axis, resulting in the same de Broglie wavelength that corresponds to the helix pitch of the helix. Mathematical formulations were presented to demonstrate the relation between the energy of the vortex and its angular frequency and de Broglie’s wavelength; furthermore, Compton’s and de Broglie’s wavelengths were also differentiated.

Newtonian gravity is modified here via Mach's inertia principle (inertia fully governed by universe) and it is generalized to gravitationally quantum bound systems, resulting scale invariant fully relational dynamics (mere ordering upon actual objects), answering to rotation curves and velocity dispersions of the galaxies and clusters (large scale quantum bound systems), successful in all dimensions and scales from particle to the universe. Against the Milgrom’s theory, no fundamental acceleration to separate the physical systems to the low and large accelerations, on the contrary the Newtonian regime of HSB galaxies sourced by natural inertia constancy there. All phenomenological paradigms are argued here via Machian modified gravity generalized to quantum gravity, especially Milgrom empirical paradigms and even we have resolved the mystery of missing dark matter in newly discovered Ultra Diffuse Galaxies (UDGs) for potential hollow in host galaxy generated by sub quantum bound system of the globular clusters. Also we see that the strong nuclear force (Yukawa force) is in reality, the enhanced gravity for limitation of the gravitational potential because finite-range of the Compton wavelength of hadronic gravity-carriers in the nucleuses, reasoning to resolve ultimately, one of the biggest questions in the physics, that is, so called the fine structure constant and answering to mysterious saturation features of the nuclear forces and we have resolved also the mystery of the proton stability, reasonable as a quantum micro black hole and the exact calculation of the universe matter. Tully-Fisher and Fabor-Jackson relations and Fish's and Freeman's laws of the constant central gravitational potential and universalization of Baryonic Fish's law are next paradigms argued here. We don’t play with mathematical functions to set them with empirical results and we don’t simulate the models but the Newton's empirical gravity is returned to its fundamental face logically.

K. Suto has recently pointed out an interesting relativistic extension of Rydberg’s formula. Here we also discuss Rydberg’s formula, and offer additional evidence on how one can easily see that it is non-relativistic and therefore a good approximation, at best, when . We also extend the Suto formula to hold for any atom and examine the formula in detail.

Based on a model of fermions which implies a model of photons, a model of the neutron is constructed by merging two photons of equal energy propagating in opposite directions. The fermion model is outlined, and the merging of two photons is described in detail. The radius of the neutron obtained in this way is Rn = 0.84008… fm. This value is four times the reduced Compton wavelength of the neutron. Assuming the same model for the proton, one obtains a value of Rp = 0.84123… fm, which agrees with the most recent experimental value for the charge radius of the proton within the given limits of error. The neutral charge of the neutron is reproduced, and the positive charge of the proton follows within the model, if the proton is formed via the anti-neutron by losing one electron. S = ±ħ/2, and zero dipole moment, is also reproduced for proton and neutron. Further, a value of the magnetic moment of the neutron of μ= &minus2.00μN (μN: nuclear magnetic moment), and of the proton of μ = 2.666… μN is predicted. The deviation by ca. 5% from the recommended respective values of (&minus1.9130μn), and (2.793μn) is ascribed to the (g-2)-anomaly. Finally, the relation of the model with the established description of the nucleons in terms of three quarks bound by gluons is shortly discussed.

In a recent paper, we [1] discussed that Suto [2] has pointed out an interesting relativistic extension of Rydberg’s formula. In that paper, we had slightly misunderstood Suto’s approach, something we will comment on further here. The relativistic Suto formula is actually derived from a theory where the standard relativistic momentum relation is changed. The relativistic Rydberg formula we presented and mistakenly thought was the same as Suto’s formula is, on the other hand, derived to be fully consistent with the standard relativistic energy-momentum relation. Here we will point out the differences between the formulas and correct some errors in our previous paper. The paper should give deeper and better intuition about the Rydberg formula and what it represents.

The controlled motion of a body in a central gravitational field without mass flow is considered. The possibility of moving the body in the radial direction from the center of attraction due to changes in the kinetic moment relative to the center of mass of the body is shown. A scheme for moving the body using a system of flywheels located in the same plane in near-circular orbits with different heights is proposed. The use of the spin of elementary particles is considered as flywheels. It is proved that using the spin of elementary particles with a Compton wavelength exceeding the distance to the attracting center is energetically more profitable than using the momentum of these particles to move the body. The calculation of motion using hypothetical particles (gravitons) is presented. A hypothesis has been put forward about the radiation of bodies during accelerated motion, which finds indirect confirmation in stellar dynamics and in an experiment with the fall of two bodies in a vacuum. The results can be used in experiments to search for elementary particles with low energy, explain cosmic phenomena and to develop transport objects on new physical principles.

Here we will assume that there is a Planck length [1] limit on the maximum length contraction that is related to the reduced Compton wavelength. Our focus will be on the maximum velocity of subatomic particles, which of a moving particle as measured from the laboratory frame (“rest” frame) cannot be shorter than the Planck length as measured with Einstein-Poincare synchronized clocks.