<p>Special relativistic particle mechanics is based upon Newton’s second law that the applied force is balanced by the rate of change of momentum. Schrödinger’s quantum wave theory makes use of differential operators rather than variables to describe quantities such as energy and momentum, and leading to a wave equation that successfully describes the physics at the atomic scale. Both theories are equally successful in their region of applicability, and the challenge posed here is to formulate a model that might incorporate both and thereby improve our understanding as to why these extremes might be so effective. We describe in simple terms how such a mathematical model might be developed, and we use vectors and vector differential identities to show that under certain conditions both energy and momentum are governed by the wave equation. The resulting theory admits a force expression exactly mirroring the Lorentz force formula of electromagnetism. Comparison of the two formulae suggests that Newtonian mechanics as the rate of change of momentum corresponds to the electric field while the new element of the proposed theory is that which corresponds to the magnetic field. Accordingly, we might infer that existing special relativistic particle mechanics, which is essentially Newton’s second law, has a status which is equivalent to the theory of electromagnetism without the phenomenon of magnetism. It remains to be established that the omission of “magnetic mechanics" from conventional mechanical accounting is responsible for dark energy and dark matter phenomena.</p>