arXiv subjects
Publications and source records attributed to Wolfgang Engelhardt.
Einstein's own demonstration of time dilation taken from his book with L. Infeld (1938) is analyzed. His ingenious circumnavigation of an apparent discrepancy between clock synchronisation and Lorentz transformation is discussed.
The Lorentz Transformation, which is considered as constitutive for the Special Relativity Theory, was invented by Voigt in 1887, adopted by Lorentz in 1904, and baptized by Poincaré in 1906. Einstein probably picked it up from Voigt directly.
Einstein's explanation of Mercury's perihelion motion has been verified by astronomical observations. His formula could also be obtained in Schwarzschild metric and was published already in 1898. Motion along a straight geodesic, however, namely, free fall into a gravitational center with vanishing angular momentum, is incorrectly described both by Einstein's and by Schwarzschild's equation of motion. A physical solution for free fall may be obtained by taking into account the dependence of mass on velocity in Newton's gravitational law as adopted in the physics of accelerators.
Both the classical and the relativistic composition law for velocities are applied to re-calculate the Sagnac Effect. The ensuing formulae for the fringe shift are found to differ already in first order of v/c. Whilst the classical formula is validated by interferometric measurements and verified by the GPS-system, this is not the case for the relativistic result.
In Maxwell's classical theory of electrodynamics the fields are frequently expressed by potentials in order to facilitate the solution of the first order system of equations. This method obscures, however, that there exists an inconsistency between Faraday's law of induction and Maxwell's flux law. As a consequence of this internal contradiction there is neither gauge invariance, nor exist unique solutions in general. It is also demonstrated that inhomogeneous wave equations cannot be solved by retarded integrals.
The interaction between charged particles through quasi-static fields must occur instantaneously; otherwise a violation of the energy principle would occur. As a consequence, the instantaneous transmission of both energy and information over macroscopic distances is feasible by using the quasi-static fields which are predicted by Maxwell's equations.
Complementing a study which was published in this journal in 2005, we present explicit calculations of fields predicted by Maxwell's equations both in Lorenz and in Coulomb gauge. Analytic expressions are obtainable, when the source of the fields is an oscillating electric dipole. As before it is found that the fields calculated by different methods are at variance. In addition, the reason for the discrepancies is revealed: The retarded integrals turn out not to satisfy the inhomogeneous wave equations which they are supposed to solve.
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's theorem. It is found, however, that the theorem fails in most practical instances. Other methods to find the potentials - as pursued in plasma physics - are examined and found to yield functions which depend on the chosen coordinate system. Thus they cannot be considered as invariant potentials from which physical forces may be derived. Practical consequences of these mathematical findings are discussed.
In an attempt to solve Maxwell's first order system of equations, starting from a given initial state, it is found that a consistent solution depending on the temporal evolution of the sources cannot be calculated. The well known retarded solutions of the second order equations, which are based on the introduction of potentials, turn out to be in disagreement with a direct solution of the first order system.
Classical plasmas in thermodynamic equilibrium should be neither para- nor diamagnetic due to the action of the Lorentz force. Magnetic confinement, however, is based on the observed diamagnetism of laboratory plasmas. The apparent paradox is investigated on the basis of the resistive magneto-hydrodynamic equations. It is found that, at least in simple plasma configurations, these equations do not permit a solution, i. e. the paradox cannot be resolved. It seems that the Lorentz force is a test-particle approximation which is not suitable to describe the interaction of moving particles in agreement with the conservation of energy.
The calculation of both resistive and ideal plasma equilibria amounts to solving a number of magnetic differential equations which are of the type $\vec {B}\cdot \nabla Φ=s$. We apply the necessary and sufficient criterion for the existence of the potential $Φ$ and find that a static equilibrium configuration of a magnetically confined plasma does not exist in axi-symmetric toroidal geometry.
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from the field equations we obtain, however, contradicting solutions. We conclude that the tacit assumption of uniqueness is not justified. The reason for this failure is traced back to the inhomogeneous wave equations which connect the propagating fields and their sources at the same time.