The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the approach where Maxwell equations and the Lorentz law of force are regarded as cornerstones of the theory allows gauge transformations. For this reason, the two theories are {\em not equivalent}. A simple example substantiates this conclusion. Quantum physics is linked to the variational principle and it is proved that the same result holds for it. The compatibility of this result with the gauge invariance of the Lagrangian density is explained.
The structure of electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potential is defined uniquely. Therefore, the approach where Maxwell equations and the Lorentz law of force are regarded as cornerstones of the theory is not equivalent to the one described above.
We show that invariance of the electric charge and relativistic kinematics lead to the transformation equations for electric field intensity and the magnetic induction.
A generalization of the classical electrodynamics for systems in absolute motion is presented using a possible alternative to the Lorentz transformation. The main hypothesis assumed in this work are: a) The inertial transformations relate two inertial frames: the privileged frame S and the moving frame S' with velocity v with respect to S. b) The transformation of the fields from S to the moving frame S' is given by H'=a(H - v D) and E'=a(E + v B) where a is a matrix whose elements depend of the absolute velocity of the system. c) The constitutive relations in the moving frame S' are given by …
A detailed study is made of the space-time transformation properties of intercharge forces and the associated electric and magnetic force fields, both in classical electrodynamics and in a recently developed relativistic classical electrodynamical theory. Important differences are found and serious errors are found in the traditional treatment of special-relativistic effects in classical electromagnetism. Fields associated with radiation processes are also considered and classical and quantum mechanical predictions are compared. An important, though trivial, mathematical error in the derivatio…
After having identified all the possible relationships between the electric field and the magnetic field in a given inertial reference frame we derive the transformation equations for the components of these fields. Special relativity is involved via the addition law of parallel speeds or via the Lorentz transformations for the space-time coordinates of the same event. Electricity and magnetism are involved via Gauss's and Ampere's laws. In this way we avoid the transformation equations for the Lorenz force components which are used in most derivations of the transformation equations for E and…
Gauge invariance, a core principle in electrodynamics, has two separate meanings. One concept treats the photon as the gauge particle for electrodynamics. It is based on symmetries of the Lagrangian, and requires no mention of electric or magnetic fields. The second concept depends directly on the electric and magnetic fields, and how they can be represented by potential functions that are not unique. A general proof that potentials are more fundamental than fields serves to resolve discrepancies. Physical symmetries, however, are altered by gauge transformations and strongly limit gauge freed…
Transformation equations for physical quantities that characterize plane electromagnetic wave propagation in transparent optical media are presented. The Doppler effect, and measurements performed by an observer moving with the wave are also considered. The results, not mentioned in introductory Physics textbooks, are simple to derive and could be used in undergraduate courses.
In the line of thought of Einstein's 1905 paper on relativity, I get a physical derivation of Lorentz transformation (LT) answering its main criticism and considerably enlarging the area of applications of the theory of relativity.
The transformation rules for the basic electrodynamical quantities are routinely derived from the hypothesis that the relativity principle (RP) applies for Maxwell's electrodynamics. These derivations leave open several questions: (1) Is the RP a true law of nature for electrodynamical phenomena? (2) Are, at least, the transformation rules of the fundamental electrodynamical quantities, derived from the RP, true? (3) Is the RP consistent with the laws of electrodynamics in one single inertial frame of reference? (4) Are, at least, the derived transformation rules consistent with the laws of el…
In a previous work, the meaning of the Planck constant $h = \left( e^2 / 2 α\right) \sqrt{μ_0 / ε_0}$, accomplished by solving Maxwell's electrodynamics laws with specific electric $1 / τ_C = 1 / R_q C_q$ and magnetic $1/ τ_L = R_q / L_q$ quantum rates for the ground-state dynamics, was reinterpreted. $R_q$, $C_q$ and $L_q$ are the resistance, capacitance and inductance quantum of the ground-state dynamics, respectively. Based on this quantum electromagnetic rate approach, here it is demonstrated that the intrinsic massless character that complies with Dirac quantum electrodynamics of the elec…
There are three electromagnetic integrals of motion that can be interpreted as the energy. These are the background energy, the elastic energy and the integral in the torsion field commonly referred to as the energy of the electromagnetic field. The integral in the torsion field gains the meaning of the energy insomuch as it is concerned with the mechanical energy of a charged particle.
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the approach where Maxwell equations and the Lorentz law of force are regarded as cornerstones of the theory allows gauge transformations. For this reason, the two theories are not equivalent. A simple example substantiates this conclusion. Quantum physics is linked to the variational principle and it is proved that the same result holds for it. The compatibility of …
In this paper, a simple geometric structure is shown, which underlies the interaction Hamiltonian of quantum electrodynamics. Specifically, eight parts of the interaction Hamiltonian, corresponding to eight basic Feynman diagrams, are found derivable from two operators called fundamental interaction operators (FIOs), with the help of a superoperator that describes vacuum fluctuations. And, the two FIOs have the simple geometric meanings of mapping the state space of an electron-positron pair to that of a photon and the reverse.
The problems considered refer to the material equations of electric- and magnetoelectric induction. Some contradictions found in fundamental studies on classical electrodynamics have been explained. The notion magnetoelectric induction has been introduced, which permits symmetrical writing of the induction laws. It is shown that the results of the special theory of relativity can be obtained from these laws through the Galilean transformations. The permittivity and permeability of materials media are shown to be independent of frequency. The notions magnetoelectrokinetic and electromagnetopote…
Different approaches to special relativity (SR) are discussed. The first approach is an invariant approach in which physical quantities in the four-dimensional spacetime are represented by true tensors or equivalently by coordinate-based geometric quantities comprising both components and a basis. This approach we call the ''true transformations (TT) relativity.'' It is compared with the usual covariant approach, which mainly deals with the basis components of true tensors. The third approach is the usual noncovariant approach to SR in which some quantities are not tensor quantities, but rathe…
In this paper, a formulation, which is completely established on a quantum ground, is presented for basic contents of quantum electrodynamics (QED). This is done by moving away, from the fundamental level, the assumption that the spin space of bare photons should (effectively) possess the same properties as those of free photons observed experimentally. Within this formulation, bare photons with zero momentum can not be neglected when constructing the photon field; and an explicit expression for the related part of the photon field is derived. When a local gauge transformation is performed on …
In classical Maxwell electrodynamics, charged particles following deterministic trajectories are described by currents that induce fields, mediating interactions with other particles. Statistical methods are used when needed to treat complex particle and/or field configurations. In Stueckelberg-Horwitz-Piron (SHP) electrodynamics, the classical trajectories are traced out dynamically, through the evolution of a 4D spacetime event $x^μ(τ)$ as $τ$ grows monotonically. Stueckelberg proposed to formalize the distinction between coordinate time $x^0 = ct$ (measured by laboratory clocks) and chronol…
In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called v-gauge), we show that two kinds of magnetic vector potentials exist: one of them (solenoidal) can act exclusively with the velocity of light c and the other one (irrotational) with an arbitrary finite velocity $v$ (including a velocity more than c . We show also that the irrotational component of the electric field has a physical meaning and can propagate e…
The least action principle is established for the dynamics of a test particle in a dilaton-Maxwell background. These dynamics and background are invariant under the action of the dilatation transformation; explicit form of the corresponding generalization of the Lorentz force is established for the considered model. On a stationary background, we have found the integral of motion of the energy type. This integral is used to resolve the radial dynamics of test particles in a spherically symmetric electrostatic background.
The purpose of the dynamics of moving systems is to search for the mathematical model that describes the link between the resultant applied force, that is the cause, and the speed of system that is the effect. This mathematical link provides the law of motion and from Newton forward it has been specified by an differential equation. Starting from the principles of the Theory of Reference Frames it is possible to arrive at new interesting results in the study and in the analysis of dynamical systems provided with linear symmetry and central symmetry. Really the most interesting consequences are…
The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein-Gordon-Maxwell electrodynamics), spinor electrodynamics (Dirac-Maxwell electrodynamics), etc. In these models, evolution is typically described by modified Maxwell equations. In the case of scalar electrodynamics, the scalar complex wave function can be made real by a gauge transformation, the wave function can be algebraically eliminated from the equations of scalar electrodynamics, …
We sketch the foundations of classical electrodynamics, in particular the transition that took place when Einstein, in 1915, succeeded to formulate general relativity. In 1916 Einstein demonstrated that, with a choice of suitable variables for the electromagnetic field, it is possible to put Maxwell's equation into a form that is covariant under general coordinate transformations. This unfolded, by basic contributions of Kottler, Cartan, van Dantzig, Schouten & Dorgelo, Toupin & Truesdell, and Post, to what one may call {\em premetric classical electrodynamics.} This framework will be describe…
