Volume 10, Number 1, Spring 2002
WHAT ARE THE EQUATIONS OF MOTION
OF CLASSICAL PHYSICS?
Abstract. Action at a distance in Newtonian physics is
replaced by finite propagation speeds in classical physics, the
physics defined by the field theories of Maxwell and Einstein.
As a result, the differential equations of motion in Newtonian
physics are replaced in classical physics by functional differential equations, where the delay associated with the finite propagation speed (the speed of light) is taken into account. Newtonian equations of motion, with post-Newtonian corrections, are
often used to approximate the functional differential equations
of motion. Some mathematical issues related to the problem of
extracting the "correct" approximate Newtonian equations of
motion are discussed.