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The question that motivates us to study physics is ``What makes things go?'' The answers we conceive to this question constitute the subject of dynamics. This is in contrast to the question we have primarily addressed so far, namely ``How do things go?'' As noted earlier, the latter question is about kinematics. Extensive preparation in the kinematics of waves and particles in relativistic spacetime is needed to intelligently address dynamics. This preparation is now complete.
In this chapter we first outline three different dynamical principles based respectively on pre-Newtonian, Newtonian, and quantum mechanical thinking. The last two are still in common use, and we first show that they are consistent with each other in the realm in which Newtonian and quantum mechanics overlap, i. e., in the geometrical optics limit of quantum mechanics. For simplicity, this relationship is first developed in one dimension in the non-relativistic limit. Higher dimensions require the introduction of partial derivatives, and the relativistic case will be considered later.
Only forces which are ``conservative'' in Newtonian mechanics, i. e., exhibit a potential energy, have a correspondence in the quantum mechanical world. Forces of this type receive our primary attention. Certain ancillary concepts in Newtonian mechanics such as work and power are introduced at this stage.