I am curious, to what extent can we think about energy as motion? Oftentimes, when the question is raised, ‘what is energy?’, the response is that it is some abstract invariant that is not directly measurable in the laboratory, but yields experimentally verifiable observable quantities (such as velocity).
Is it wrong to say that energy is motion? The following is my argument. All forces of nature impart an acceleration on objects with which they interact. Conservative forces, by definition, have potential functions, say, $U$, such that $\vec{F}=-\nabla U$. The work energy theorem shows that the change in this quantity over some path (work) is equal to the corresponding change in kinetic energy (over that path). Solving for $\vec{v}$, can we say that velocity is a function of potential energy? In other words, Energy is motion?
If potential energy is zero, there is no motion. If not, there is motion governed by the above equations and the relevant equations of motion.