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

All of matter is just energy, we look at it closer and closer, and we get to something like quantum foam or the vacuum energy.

Isn't this just a measurement of energy?
It doesn't really tell us what energy is.

So what exactly is energy?
gpt
This is a Big Question. Let me give a few different points of view, very roughly in order of historical development (but all of them are still valid today).

*Energy is a bookkeeping device.* In Newtonian mechanics, given a particular starting point and particular interactions, not every outcome is possible! It turns out to be useful to keep track of certain quantities that *don't change* over time, so they must be the same at the beginning and the end of some process. One such quantity (for appropriate interactions) is energy. If you take one-half the mass of an object times the square of its speed, and add that number up for all objects, and also add a particular quantity called 'potential energy' that depends on the locations of all the objects, that number will always remain constant. The terms you add up will change, but their total will not. In this view, energy is simply this number that stays the same and is useful for deciding what can and can't happen.

*Energy is the conserved quantity associated with time-translation symmetry.* Emmy Noether realized and proved a deep fact about those numbers that don't change in time ('conserved quantities'). They are associated with *symmetries of the laws of physics.* It sounds kind of woo-woo, but you can prove mathematically: because the laws of physics do not change over time, there is a particular number (which you can derive a formula for from the laws of physics) that is constant. That number is the same quantity, energy, from above. It works the other way, too---since we experimentally observe conservation of energy, it follows that the laws of physics are the same over time (within the precision we can measure).

Noether's version of energy generalizes nicely beyond Newtonian mechanics, so you can extend the definition of energy to electromagnetic fields (it turns out electric and magnetic fields store energy) and relativistic mechanics (from whence we get E^2 = m^(2)c^(4) + p^(2)c^(2)).

The full relativistic generalization leads nicely to the most modern view: *energy is (a certain part of) the thing that bends spacetime.* Just like we can think of electric charge as 'the thing that produces electric fields,' we can think of energy as 'the thing that bends spacetime.' More technically, energy is but one part of the stress-energy tensor, which provides the source of spacetime curvature. Indeed, in modern physics, even when ignoring the effects of gravity, you can answer the question 'how much energy is here' by asking how spacetime *would* bend if it could. Whatever stress-energy tensor you get out of the calculation will be conserved and equivalent to the first two definitions of energy. (Weirdly, this way of finding the conserved energy can be easier than finding it directly.)

The first two formulations imply that energy is just a number we calculate---a convenience---and we could do without it if we just plugged along and calculated. The third implies that energy is a real thing that has real, gravitational effects on our world. And those aren't incompatible--they're equivalent!