  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 relations basic for quantum mechanics: $E=h\nu$ and $Mv = h/
\lambda$ (here, $\lambda$ 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 $v$ to 0 and then from 0 to $v$; $\nu$ is
the frequency of these oscillations). Analysis is performed on the transition
to wave mechanics where $\lambda$ manifests itself as the de Broglie wavelength
and $\nu$ 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.
