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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. The retarded integrals, in particular, turn out not to represent proper solutions of the inhomogeneous wave equations.

Traditionally the outcome of Michelson's interference experiment has been interpreted as evidence against the existence of a luminiferous medium called ?ether?. Einstein, however, emphasized in 1920 that an ether must exist in spite of Michelson's null result. In this paper it is shown that a medium theory ? be it for light or for sound ? actually predicts the observed null result. Michelson expected a gradual fringe shift when his apparatus was turned in the ?ether wind?. Such a phase change would, however, require a temporary frequency change in one of the interferometer arms. Since wind does not alter the frequency in the interferometer, a phase shift cannot occur either.

If more than two systems are moving relatively to each other, the Lorentz Transformation leads to inconsistencies which do not occur when the Galilei Transformation is adopted.

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 Poincar? in 1906. Einstein probably picked it up from Voigt directly.

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.

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.

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.

By investigating the motion of a point charge in an electrostatic and in a magnetostatic field, it is shown that the relativistic transformation of electromagnetic fields leads to ambiguous results. The necessity for developing an `electrodynamics for moving matter' is emphasized.

The frequency shifts predicted by the 'relativistic' Doppler effect are derived in the photon picture of light. It turns out that, in general, the results do not depend exclusively on the relative velocity between observer and light source. In this respect, the relativistic Doppler effect is not distinct from the classical one, where the shifts are also different depending on whether the source or the observer moves. The 'relativistic' formulae for these two cases have been confirmed by experiment and are described in many textbooks. It was, however, not recognized that they are at variance with Einstein's relativity principle extended to electromagnetic waves.

In his famous paper of 1905 Einstein postulated that the velocity of light be constant in all inertial systems. Measurements with increasing accuracy confirmed the justification of this conjecture, so that today we have in fact replaced the normal meter by the cesium second and nine numbers. A physicist measuring the velocity of light, who would come up with a result different from the nine legal numbers, would just have used an illegal system of units.

In his General Theory of Relativity (GRT) Einstein conceded that the velocity of light may depend on the gravitational potential which would explain the deflection of light passing heavy masses. In order to verify any variation of c experimentally, one would need to measure the velocity of light at different gravitational potential. This is, however, no longer possible having abolished the normal meter. It is, therefore, now custom to postulate also in GRT the constancy of c and explain the observed deflection and the longer duration of the passage of light near gravitational centers by a distorted metric of space.

There are, however, experiments carried out on earth which are much easier to interpret when we follow Einstein?s original conjecture, namely that the velocity of light depends on the gravitational potential. Curiously enough, these experiments are commonly taken as a confirmation of GRT, but this is in fact only true when we allow for a variation of the velocity of light. If not, a violation of the energy principle would be the consequence.

In this note we discuss the famous experiment by Pound and Rebka of 1960 who used the M?ssbauer effect to measure the ?apparent weight of photons?. We compare it with the ?Maryland experiment? of Alley proving that atomic clocks run faster with increasing distance from the gravitational center. Both experiments are frequently said to confirm in an ?equivalent? way a simple formula derived in GRT, but, as already hinted by Pound and Rebka, this is actually not true. We include in our comparison a simple gedanken experiment which is based on the conservation of energy and we come to the conclusion that the real experiments may be reconciled when we allow for a variation of the velocity of light.