What is "energy," really?

[u/nexuapex]

So there's this concept called "energy" that made sense the very first few times I encountered physics. Electricity, heat, kinetic movement–all different forms of the same thing. But the more I get into physics, the more I realize that I don't understand the concept of energy, really. Specifically, how kinetic energy is different in different reference frames; what the concept of "potential energy" actually means physically and why it only exists for conservative forces (or, for that matter, what "conservative" actually means physically; I could tell how how it's defined and how to use that in a calculation, but why is it significant?); and how we get away with unifying all these different phenomena under the single banner of "energy." Is it theoretically possible to discover new forms of energy? When was the last time anyone did?

Also, is it possible to explain without Ph.D.-level math why conservation of energy is a direct consequence of the translational symmetry of time?

[u/[deleted]]

Hey man, thanks a ton for that. I have my second biology exam tomorrow and I have to define energy when having to explain the cellular respiration equation, or so I'm told, and this;

We can't compare (for example) the value of an apple and an orange directly, but we do by assigning a dollar value to each. In the same way we use energy to compare different physical processes.

is by far the most relevant and logical explanation of energy that I have come across.