In school, kids learn about different types of energy. They learn about solar energy and wind energy, nuclear energy and chemical energy, electrical energy and mechanical energy, and potential energy and kinetic energy. They learn that energy is conserved, that it can never be created or destroyed, but only change form. They learn that energy makes things happen, that you can use energy to do work, that energy is different from matter.
Some, between good teaching and good students, manage to impose order on the jumble of concepts and terms. Others end up envisioning the whole story a bit like Pokemon, with different types of some shared “stuff”.
Energy isn’t “stuff”, though. So what is it? What relates all these different types of things?
Energy is something which is conserved.
The mathematician Emmy Noether showed that, when the laws of physics are symmetrical, they come with a conserved quantity. For example, because the laws of the physics are the same from place to place, momentum is conserved. Similarly, because the laws of physics are the same from one time to another, Noether’s theorem states that there must be some quantity related to time, some number we can calculate, that is conserved, even as other things change. We call that number energy.
If energy is that simple, why are there all those types?
Energy is a number we can calculate. It’s a number we can calculate for different things. If you have a detailed description of how something in physics works, you can use that description to calculate that thing’s energy. In school, you memorize formulas like 
Because of this, you shouldn’t think of energy as a substance, or a fuel. Energy is something we can do: we physicists, and we students of physics. We can take a physical system, and see what about it ought to be conserved. Energy is an action, a calculation, a conceptual tool that can be used to make predictions.
Most things are, in the end.
4 gravitons 
ah, Energy ! in Phys 101 I learned the steps : first comes Force, then Mass, then Mass with a Speed and finally Mass with an Acceleration, which is ‘force’ again, and, weirdly, Mass with speed-squared (oh, that is, like, force * distance) as Energy.
Only, in Phys 102 we start over again, but not ab initio. Force isn’t real, at best it’s the gradient of a potential, speed is still distance over time, but whose distance and whose time is up for discussion. And the mass thinghy, well, euh, E²=p²c²+m²(c²)² , no?
I don’t know if, or at what level, QFT defines its concepts afresh. Or does it build up a circular reasoning by modifying and extending the kitchen-garden concepts of Phys 101 without improving the solidity of its foundations?
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For energy, you’re really looking not for QFT, but for something earlier: advanced classical mechanics, that late undergrad/early grad class with all the Lagrangians and Hamiltonians. QFT then builds on that foundation.
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