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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.

gandalf61
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Spinor
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The problem is that the term energy is such a broad term, and covers such a large range of systems, that trying to come up with an intuitive definition for it like energy is motion will inevitably fail.

For example consider a stationary hydrogen atom with the electron in the $2s$ orbital. Nothing is moving here, and there is not even any (orbital) angular momentum, and yet this has energy that can be released when it transitions to the ground state. So how would you reconcile this with the energy is motion idea?

The reason we fall back to the rather arcane definition that energy is the conserved quantity associated with time shift symmetry is because it works. By all means look for more intuitive notions, but bear in mind that they will always be limited.

John Rennie
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Kinetic energy is a function of motion.

The transfer of energy will always involve motion of some sort.

Both those statements are more true and descriptive than saying "energy is motion".

It's sort of like saying "time is money" - there's a big connection between the two, but it's not precisely correct in the way you'd need it to be to consider it a philosophical or physical truth.

Señor O
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