Pythagorean Metric in Particle's Relativistic Dynamics

Abstract

A new non-traditional quasi-classical description of the particle dynamics (QCDPD) is outlined. The “quasi-classical” attribute is suggested by the closeness—although not identity—to the description of a classical system, in the framework of classical dynamics. Founded on a suitable one-to-one mapping of the timelike 4-vectors of Minkowski's spacetime onto the real 4-dimension vector space, QCDPD is mathematically equivalent to the traditional description of special relativity. However, in QCDPD a new frequency fulfilling the same transformation law as the frequency of an oscillator is employed. It turns out that the special-relativity particle is, in fact, modeled as an oscillator which is essentially classical. The associated wave is a natural consequence of such a model.