nt - p h / 99 03 07 7 v 3 5 N ov 1 99 9 Motion of a relativistic particle and the vacuum ∗

A vacuum medium model is advanced. The motion of a relativistic particle in relation to its interaction with the medium is discussed. It is predicted that elementary excitations of the vacuum, called ”inertons,” should exist. The equations of the particle path in Euclidean space are derived. The motion is marked by the basic quantum mechanical relations E = hν and Mv0 = h/λ (here, λ is the amplitude of spatial oscillations of the particle along the trajectory, i.e., the interval at which the velocity of the particle is periodically altered from v0 to 0 and then from 0 to v0; ν is the frequency of these oscillations). Analysis is performed on the transition to wave mechanics where λ manifests itself as the de Broglie wavelength, and ν is the distinctive frequency of the ”particle-wave”. A prerequisite for the wave solution to be Lorentz-invariant is treated. A hypothesis for a plausible hydrodynamic description of the relativistic particle motion is covered.