On the Existence of K. Meyl's Scalar Waves

摘要

In the fall of 2000, several talks were delivered by K. Meyl. These talks described his theory of so-called Tesla's scalar waves (e.g., in Meyl ["Scalar Waves..." (2000) and "Longitudinalwellen-Experiment..." (2000)], and on his Web site). In the following article, we shall mainly discussed the theoretical part of there publications, although the experimental part would deserve a detailed discussion in its own right. The scalar wave, according to Meyl, is an irrotational electric vector solution E of the homogeneous wave equation having non-vanishing sources. However, and this is Meyl's logical flaw, it is not the homogeneous wave equation but Maxwell's equations that are the actual starting point of any theory of electromagnetic waves. And, as will be seen see in Section 1, the homogeneous wave equation is valid only in vacuum and in its natural generalization, in homogeneous materials without free charges and currents, while in other cases the inhomogeneous wave equation would apply. So in Section 2, our next immediate result is that Meyl's source conditions are inconsistent with the material properties. Hence, we have to assume the vector field E to be source free. But— as will be shown further for this case—Maxwell's equations do not admit other than trivial scalar waves of the Meyl type, since only time- independent solutions are admissible. Under those conditions, the only permissible conclusion is that Meyl's scalar waves do not exist. At the end of his talks (Meyl, "Scalar Waves..." [2000] and "Longitudinalwellen-Experiment..." [2000]), Meyl makes another remarkable assertion, which we shall discuss in Section 3. Meyl claims to have generated 'vortex' solutions that propagate faster than light. But for solutions of the homogeneous wave equation, this would clearly contradict a well-known theorem of the mathematical theory of the wave equation. In addition, Meyl's proof for his claim will turn out to be a simple flaw of thinking.