To Foundations of Classical Electrodynamics

E. G. Bessonov

Home/Archive/arXiv

arXiv · physics/9708002

To Foundations of Classical Electrodynamics

E. G. Bessonov

View original source ↗Read source document ↗Export metadata ↓

Abstract

In the present work foundations of the law of the energy conservation and the introduction of particles in the classical electrodynamics are discussed. We pay attention to a logic error which takes place at an interpretation of the Poynting's theorem as the law of conservation of energy. It was shown that the laws of conservation of energy and momentum of the system of electromagnetic fields and charged particles does not follow from the equations of electrodynamics and the violation of these laws is displayed at the energy change of particles. Particular examples are considered which make it possible to restrict a possible kind of fields of a non-electromagnetic origin. We hope that this work will permit to produce a more comprehensive analysis and to stimulate the next step to the development of the foundations of the classical and quantum electrodynamics.

Explore related subjects

physics.class-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

E. G. Bessonov. 1997-08-21. To Foundations of Classical Electrodynamics. https://arxiv.org/abs/physics/9708002

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Unifying pendulum-like dynamical regimes via complex time

We present an alternative derivation of exact solutions for pendulum-like systems across all dynamical regimes using a standard technique in an undergraduate mathematical physics course: the Cauchy residue theorem, entirely independent from the traditional Jacobi elliptic functions. The solutions are exact in both the time and frequency domains, providing continuous trajectories and precise frequency decompositions. Pendulum-like dynamics is a foundational model across many areas of physics, underlying systems ranging from classical nonlinear oscillators to superconducting qubits and cold-atom tunneling platforms. While its time-domain solutions are well-known in terms of Jacobi elliptic functions, its obscured frequency-domain solutions have led a large body of theoretical and experimental work to develop and apply approximate methods when studying its spectral behavior. We discover that all regimes arise from a single spectral kernel, with parity selection distinguishing the periodic motions and the separatrix representing their discrete-to-continuum limit. Regime changes thus correspond to symmetry-driven reorganizations in frequency space rather than changes in the underlying spectral structure, with the stopping trajectory representing the continuum limit. By completely bypassing the traditional Jacobi elliptic functions, and relying on the symmetrical structure of the complex time plane, the derivation shows that the symmetrical spectral structure is not merely an algebraic artifacts of elliptic integrals, but fundamentally connected to the dynamical symmetries of the system. The derivation presented here not only serves as a powerful pedagogical exercise for this long-standing physics problem, but also reveals a highly symmetrical spectral organization in nonlinear dynamics.

physics.class-ph↗

arXiv2026

Spectral taxonomy for quartic systems: fundamental clock, parity, and continuum

A symmetric quartic potential is a physics model with expansive applications, ranging from broadband energy harvesters, quantum tunneling in molecules and the early universe, to torque-free spacecraft rotation. Its rich dynamics have been traditionally classified into regimes and expressed as disjointed time-domain solutions. Here we build a taxonomy for this broad class of motions and discover that their regimes exhibit a symmetrical spectral structure: they share a fundamental clock, obey parity selection, and dissolve into the separatrix through a discrete-to-continuum transition. Applied to the famous Dzhanibekov effect where a rotating body periodically undergoes rapid 180-degree flips in its attitude, the taxonomy reveals its spectral anatomy. The three principal-axis rotations share a common clock while occupying distinct parity channels, with stable-axis branches exchanging DC bias across the separatrix. We discuss a case study where the three spectral pillars: clock, parity, and continuum, survive the Wick rotation from real-time into imaginary-time kinematics.

physics.class-ph↗

arXiv2026

From Symmetry and Continuity to the Lorentz Transformation

We derive the Lorentz transformation from spacetime symmetries and continuity, without assuming the invariance of the speed of light. Spacetime homogeneity yields an additive coordinate map; continuity along four linearly independent inertial worldlines, together with additivity, establishes linearity throughout spacetime. Spatial isotropy and the assumed continuous local one-parameter group structure of collinear boosts yield velocity reciprocity and determine a generalized Lorentz-type family parameterized by $κ$. The velocity law and the empirical identification of its invariant speed with the coordinate speed of light in vacuum select the Lorentzian branch, fixing $κ=-1/c^2$ and recovering the Lorentz transformation.

physics.class-ph↗