Wave-Digital Concepts and Relativity Theory

Abstract

The wave-digital approach to numerical integration owes its advantageous behavior partly to the use of wave concepts, but mostly to the use of passivity and losslessness properties that occur naturally in physical systems. For handling such nonlinear systems, one is naturally led to certain formulations that turn out to be of fundamental physical significance, yet are violated by some basic relations in special relativity theory. By starting from classical relativistic kinematics and making some assumptions that are at least not a priori physically unreasonable, however, one is led to a modified version of relativistic dynamics that (1) is in complete accord with the formulations just mentioned, (2) yields expressions of appealing elegance (including a four-vector, thus a Lorentz-invariant, quadruplet that is of immediate physical significance and coincides with a four-vector already considered by Minkowski), and (3) is, at least at first sight, in good agreement with some reasonable analytic expectations. In this alternative approach, Newton’s second law is altered in a slightly different way than in classical relativity, and, as a consequence, Newton’s third law, which is taken over untouched in classical theory, must also be subjected to some modification. For problems concerning collisions of particles or action of fields (electromagnetic, gravitational) upon particles, the alternative approach yields exactly the same dynamic behavior as the classical theory. Corresponding experiments are thus unable to differentiate, and the same holds for some other available experimental results. This chapter builds on the same basic concepts as those that have previously been published [1] and, in some respect, expands them. On the other hand, an unnecessary additional earlier requirement that had led to an unavoidable factor 1/2 in the expression for the equivalence between mass and energy is abandoned. This way, for example, a remarkable agreement with certain results in electromagnetics is obtained. To further test the validity, the crucial issue to be considered now appears to be the kinetic energy of fast particles. A classical experiment by Bertozzi addresses this issue, but it is not yet sufficiently clear how the results obtained there should properly be interpreted in the present context. It is hoped that the present chapter can contribute to clarifying some of the issues involved, even if the conventional theory should in the end be confirmed, by accurate and unequivocal measurements, to be the one with the closet connection to reality.