  This paper models the classical diffusion of a main particle through a
heatbath by means of a pre-limit microscopic representation of its drifted
momentum and energy transfers at collision times. The collision point linear
interpolated path can be approximated by the solution to the "inscribed"
continuous stochastic differential equation using the same drift function.
Employing results from stochastic mechanics it is then shown that the combined
main particle/heatbath system does not exchange or radiate energy if the
probability distribution for the position of the main particle is derived from
Schroedinger's equation. Furthermore it is shown that the main particle
distance traveled between collisions and the mean inter-collision time must
satisfy a type of Minkowski invariant. Hence if there is a correlation between
the pre- and post-collision velocities of the main particle through a collision
point then the mean distance traveled can be related to the mean inter-particle
collision times via a Lorentz transformation. The last Section shows that this
approach can be applied to all elastic main particle/heatbath particle
collisions either via direct calculation involving modeling the collision
scattering or by altering the properties of the heatbath.
