Relativistic mass due to a dilatant vacuum leads to a quantum reformulation of the relativistic kinetic energy

Relativistic mass change with speed is considered here as the effect of a viscous, dilatant vacuum, whose apparent viscosity is related to the Lorentz factor. Transient solid-like vacuum due to shear stress is presented as the reason why vacuum prevents the speed of massive objects from being indefinitely increased. Such a vacuum – that in a previous study allowed to exactly calculate the Pioneer anomaly, Mercury’s perihelion precession, and was shown to be compatible with stable planetary orbits – leads here to a quantum formula for the relativistic kinetic energy. A formula which distinguishes between the case of accelerated charges in a vacuum, for which a Stokes–Einstein radius comes into play, and the case of accelerated macroscopic bodies, for which the quantum potential term vanishes. In this way, incidentally, one obtains again correct results for the Pioneer 10, confirming the role of vacuum’s viscous force. This description of a quantum mechanism underlying the relativistic kinetic energy may be also helpful in constructing a theory of quantum relativity and may even tell us more about the interactions of matter with the Higgs field and the dark sector: two issues which can be themselves linked to a dilatant vacuum.

Gravitational Time Dilation Derived from Special Relativity and Newtonian Gravitational Potential

Einstein was known for often presenting "gedanken" or thought experiments (Miller, 1999). This paper is such an exercise. Time dilation in Special Relativity is based on the derived value of γ (a scalar value) (Einstein, 1905). γ will be calculated as a function of relativistic kinetic energy, allowing time dilation to become a function of relativistic kinetic energy. With the new methodology constructed, a "gedanken” experiment is considered. Can a time dilation function be derived, using Newtonian gravitational potential energy in the same manor kinetic energy was used in Special Relativity? This paper carries out the derivation and compares the results with General Relativity's Schwarzschild solution. The what if thought experiment provides a first order accuracy to GR's Schwarzschild solution.

The spinless relativistic Hulthén problem

The spinless Salpeter equation can be regarded as the eigenvalue equation of a Hamiltonian that involves the relativistic kinetic energy and therefore is, in general, a nonlocal operator. Accordingly, it is hard to find solutions of this bound-state equation by exclusively analytic means. Nevertheless, a lot of tools enables us to constrain the resulting bound-state spectra rigorously. We illustrate some of these techniques for the example of the Hulthén potential.

True dynamical tests of the weak equivalence principle for matter and anti-matter

After a brief review of the evidence for the validity of the Weak Equivalence principle for anti-matter, I show that, contrary to general belief, the near equality of the Shapiro delay for photons, neutrinos and anti-neutrinos in the galactic gravitational potential is not a true test of the WEP for their intrinsic properties and quantum numbers due to the overwhelming contribution to the gravitational mass from the relativistic kinetic energy. Then I prove the remarkable result that particles that obey the Newtonian law of dynamics automatically respect the WEP due to the firm equivalence between the law of motion and the WEP in any relativistic scenario, through gravity of all the matter in the Universe. Thus a test of the validity of Newtons's law in any force field is a true test of the WEP and provides strong direct tests of WEP for anti-particles. This result opens up an entire new insight of conceptual and practical importance for the tests of WEP.

RELATIVISTIC NON-THERMAL BREMSSTRAHLUNG RADIATION

By applying a method of virtual quanta we derive formulae for relativistic non-thermal bremsstrahlung radiation from relativistic electrons as well as from protons and heavier particles with power-law momentum distribution N(p)dp = k p-qdp. We show that emission which originates from an electron scattering on an ion, represents the most significant component of relativistic non-thermal bremsstrahlung. Radiation from an ion scattering on electron, known as inverse bremsstrahlung, is shown to be negligible in overall non-thermal bremsstrahlung emission. These results arise from theory refinement, where we introduce the dependence of relativistic kinetic energy of an incident particle, upon the energy of scattered photon. In part, it is also a consequence of a different mass of particles and relativistic effects.

CHARMONIUM SPECTRA AND DECAYS IN A SEMIRELATIVISTIC MODEL

We investigate the spectra and decays of charmonium [Formula: see text] system in a semirelativistic potential model. The Hamiltonian of our model consists of a relativistic kinetic energy term, a vector Coulomb-like potential and a scalar confining potential. From this Hamiltonian a spinless wave equation is obtained. The wave equation is then reduced to the form of a single particle Schrödinger equation. The spin dependent potentials are introduced as a perturbation. The three-dimensional harmonic oscillator wave function is employed as a trial wave function and the [Formula: see text] mass spectra is obtained by the variational method. The model parameters and the wave function that reproduce the mass spectra of the [Formula: see text] mesons are then used to investigate some of the decay properties. The results obtained are then compared with the experimental data and with the predictions of other theoretical models. We also propose possible [Formula: see text] assignments for the recently observed charmonium or charmonium-like states.