system
Given the following post, respond as if you're commenting on Reddit:
human
What is the most fundamental definition of energy?

If I think about it, it seems that energy is like time, in that we all experience it, yet nailing down exactly what it is isn't so easy.
Thoughts?
gpt
It can be derived from Noether's theorem.  "Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law." - en.wikipedia.org/wiki/Noether's_theorem

"For illustration, if a physical system behaves the same regardless of how it is oriented in space, its Lagrangian is rotationally symmetric; from this symmetry, Noether's theorem shows the angular momentum of the system must be conserved. The physical system itself need not be symmetric; a jagged asteroid tumbling in space conserves angular momentum despite its asymmetry – it is the laws of motion that are symmetric. As another example, if a physical experiment has the same outcome regardless of place or time (having the same outcome, say, somewhere in Asia on a Tuesday or in America on a Wednesday), then its Lagrangian is symmetric under continuous translations in space and time; by Noether's theorem, these symmetries account for the conservation laws of linear momentum and energy within this system, respectively."

tl;dr Because the laws of physics are constant with time, due to Noether's theorem, there exists a corresponding conservation.  We define this conservation law to be the conservation of Energy.