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It is shown that the correct expressions for momentum and kinetic energy of a particle moving at high speed were already implicit in physics going back to Maxwell. The demonstration begins with a thought experiment of Einstein by which he…

In this work, the relativistic phenomena of Lorentz contraction and time dilation are derived using a modified distance formula appropriate for discrete space. This new distance formula is different than Pythagoras's theorem but converges…

The equivalence of mass and energy is indelibly linked with relativity, both by scientists and in the popular mind. I prove that E = mc^2 by demanding momentum conservation of an object that emits two equal electromagnetic wave packets in…

In 1905, Einstein formulated his special relativity for point particles. For those particles, his Lorentz covariance and energy-momentum relation are by now firmly established. How about the hydrogen atom? It is possible to perform Lorentz…

We consider the so-called semiclassical variant of general relativity, where gravitational field is not quantized but matter is quantized, for the simplest composite quantum body - a hydrogen atom. We create a stationary electron quantum…

We present in this work a pedagogical way of quantizing the atomic orbit for the hydrogen's atom model proposed by Bohr without using his hypothesis of angular momentum quantization. In contrast to the usual treatment for the orbital…

Traditionally, the Planck constant $h$ makes its debut appearance in quantum physics textbooks in the context of the blackbody radiation law and subsequently as a fundamental ingredient of the physics of the photoelectric effect and the…

In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or…

In 1907, Einstein suggested an experiment with flying atoms for corroborating time dilation. In that paper, the flying atom was conceived as a flying clock: the reference to the Doppler effect was only indirect (the experiments by Stark to…

Recently, we have suggested some semi-quantitative Hamiltonian for an electron in a hydrogen atom in a weak gravitational field, which takes into account quantum effects of electron motion in the atom. We have shown that this Hamiltonian…

A consistent classical and quantum relativistic mechanics can be constructed if Einstein's covariant time is considered as a dynamical variable. The evolution of a system is then parametrized by a universal invariant identified with…

In this work we consider some consequences of the Bohr-Sommerfeld-Hansson (Old or quasi-classical) quantum theory of the Newtonian gravity, i.e. of the "gravitational atom". We prove that in this case (for gravitational central force and…

The existence of a maximal acceleration for massive objects was conjectured by Caianiello 30 years ago based on the Heisenberg uncertainty relations. Many consequences of this hypothesis have been studied, but until now, there has been no…

Path integral Monte Carlo approach is used to study the coupled quantum dynamics of the electron and nuclei in hydrogen molecule ion. The coupling effects are demonstrated by comparing differences in adiabatic Born--Oppenheimer and…

It is shown that all of the basic properties of the hydrogen atom can be consistently described in terms of classical electrodynamics instead of taking the electron to be a particle; we consider an electrically charged classical wave field,…

A new model of quantum mechanics, Classical Quantum Mechanics, is based on the (nearly heretical) postulate that electrons are physical objects that obey classical physical laws. Indeed, ionization energies, excitation energies etc. are…

In this paper we present for the first time a complete description of the Bohm model of the Dirac particle. This result demonstrates again that the common perception that it is not possible to construct a fully relativistic version of the…

A rigorous quantum relativistic approach has been used to calculate the relationship between the decay laws of an unstable particle seen from two inertial frames moving with respect to each other. In agreement with experiment, it is found…

Superconductors have often been described as `giant atoms'. The simplest description of atoms that heralded their quantum understanding was proposed by Bohr in 1913. The Bohr atom starts from some simple assumptions and deduces that the…

We study the orbits of two interacting particles described by a fully relativistic classical mechanical Hamiltonian. We use two sets of initial conditions. In the first set (dynamics 1) the system's center of mass is at rest. In the second…