General Formulation and Basic Equations

In this chapter we present the proposed reformulation of Newton’s second law and a number of general results relating to this extension. Since the origin and motivation for the proposed model emanate from both the particle-wave duality of de Broglie and Maxwell’s formulation of electromagnetism, in the following two sections, we mention some of their considerable achievements. These two sections provide some of the background motivation leading to the model developed here. In the subsequent section, we show that a straightforward analysis of the integrated rate-of-working equation indicates four distinct states of matter. In five sections thereafter, we progressively state the proposed extension of Newton’s second law and then develop a number of general outcomes relating to this proposal, including an important identity for the spatial physical force. In addition, assuming the existence of either a work done function or if the external forces are generated from an applied external potential, then in either case a conservation of energy statement applies. In either of these cases or if we assume the Einstein energy-mass variation with velocity, then Newton’s second law as the total rate of change of momentum emerges from the proposed reformulation.