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A new approach to classical electrodynamics is presented, showing that it can be regarded as a particular case of the most general relativistic force field. In particular, at first it is shown that the structure of the Lorentz force comes…
The physicists of the early 20th century were unaware of two aspects which are vital to understanding some aspects of modern physics within classical theory. The two aspects are: 1) the presence of classical electromagnetic zero-point…
The confinement mechanism proposed earlier and then applied successfully to meson spectroscopy by one of the authors is interpreted in classical terms. For this aim the unique solution of the Maxwell equations, an analog of the…
The classical two-dimensional problem of non-interacting electrons scattered by short-range impurity centers in the presence of magnetic field is investigated both analytically and numerically. A strong magnetoresistance exists in such a…
A system of two initially homogeneous, physically real fields uniformly attracted to each other is considered as the simplest basis of the self-developing world structure. It is shown that the system is unstable against periodic cycles of…
The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and…
This paper aims to justify the Maxwell-Boltzmann approximation for electrons, preserving the dynamics of ions at the kinetic level. Under sufficient regularity assumption, we provide a precise scaling where the Maxwell-Boltzmann…
We establish global existence and uniqueness of the dynamics of classical electromagnetism with extended, rigid charges and fields which need not to be square integrable. We consider also a modified theory of electromagnetism where no…
Invoking Maxwell's classical equations in conjunction with expressions for the electromagnetic (EM) energy, momentum, force, and torque, we use a few simple examples to demonstrate the nature of the EM angular momentum. The energy and the…
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in vacuum is investigated within the matrix formalism. The matrix form of electrodynamics includes three real 4 \times 4 matrices. Within the…
The development of Quantum Electrodynamics (QED) is sketched from its earliest beginnings until the formulations of 1949, using the example of the divergent self-energy of the electron as a quintessential problem of the 1930's-40's. The…
The Maxwell-Lorentz theory of electrodynamics cannot readily be applied to a system of point charges: the electromagnetic field is not well-defined at the position of a point charge, an energy conservation argument is not obvious, an…
The paradox of a field of a moving locked charge (confined in a closed space) is considered and solved with the use of the integral Maxwell equations. While known formulas obtained for instantaneous fields of charges moving along straight…
There are reasons to believe that implications of a certain paradox introduced by Ginzburg and related problems have not been fully recognized. Pertinent issues remain open and unresolved. There are instances when the current widely used…
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…
In the present paper it is shown that the Maxwell theory can be finely represented in the matrix form of Dirac's equation, if the Dirac wave function is identified with the electromagnetic wave by defined way. It seems to us, that such…
The classical Euler's problem on stationary configurations of elastic rod with fixed endpoints and tangents at the endpoints is considered as a left-invariant optimal control problem on the group of motions of a two-dimensional plane…
The electromagnetic fields in Maxwell's theory satisfy linear equations in the classical vacuum. This is modified in classical non-linear electrodynamic theories. To date there has been little experimental evidence that any of these…
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged…
In this paper we study the controllability problem for a symmetric-top molecule, both for its classical and quantum rotational dynamics. The molecule is controlled through three orthogonal electric fields interacting with its electric…