Pardon me if this is the wrong section for this question, but "energy" seemed like a topic that could fit in almost any category on this site.

Either way, I'm sure many people on here have seen this quote by Feynman:

Is Feynman correct about this? Because the way Feynman puts this, it makes it sound as if energy - while having tremendous use as an abstract concept, in formulas that can can make very useful predictions, etc - is fundamentally mysterious.

Feynman was speaking provocatively. He liked to do that. I think he was simply alluding to the mystery of quantum physics.

Energy is not that mysterious at the macroscopic level. Energy is a defined quantity. It is defined that way because it is useful. It is useful, generally, because it is a quantity that is conserved in interactions (at least those involving gravitational and electro-magnetic forces). As such, it helps us to analyse interactions. Energy is the ability to do work. Work is done by applying a force over a distance.

I don't think Feynman had any difficulty with macroscopic energy but perhaps he did. In a fundamental sense, we don't really understand what inertia is. If we don't understand inertia, then we don't really understand force. If we don't understand force, we don't understand energy in that sense.

Things are very different at very small distances, however. That is where energy becomes mysterious. This appears to be what Feynman is referring to. The quantity that we define as energy is not continuous at the very small level. We don't really understand why that is. It just is the way things are. We can calculate permitted energies of various particles or configurations of particles. We can do the math. We just lack a fundamental understanding of "why".

Right, which seems to be what Feynman is saying (and what he says in the paragraph preceding the quote): He's happy to treat energy as an abstract concept used to work out calculations and make predictions and so on, a conserved quantity in a calculation. It has utility as that concept. But then Feynman seems to draw a distinction between that abstract concept, and (for lack of a better way to put it) "what energy really is." That's what surprised me. And if that's really the case - say, that there are certain things we understand primarily as calculations and formulas, but we're not clear on the reality behind those formulas - that's okay. I just wanted to make sure I was reading Feynman right, and if he was correct on this topic.

Energy is not an obvious tangible quantity. It was not recognized as important until well after Newton (although there was some recognition that the quantity mv^2 had significance - it was called the vis-viva).

But energy is not an entirely abstract quantity either (such as entropy). It is somewhat tangible. The amount of damage a bullet does, for example, is proportional to its energy. Same with a car collision: the damage is proportional to the masses of the colliding cars and to the square of their relative speed. We also associate "energy" with heat. The amount of heat we feel (mass x temperature change) is proportional to the amount of energy expended in creating that increase in heat.

The mystery is not so much in why energy is conserved or what it is signifies physically at the macroscopic level (although, since it is based on inertia, it is still somewhat mysterious). The real mystery is why it behaves the way it does at the quantum level.

Feynman begs the question: what does it mean to understand something? Understanding is always incomplete. Understanding is the result of reducing phenomena to fewer and fewer things that we don't understand - ie to fewer a priori principles or facts that we simply have to accept. If we can create a macroscopic model, we may say we "understand" something. But it just means that we understand it in terms of macroscopic phenomena that we simply accept. No macroscopic model works for quantum mechanics. It is just too weird. So we have to base predictions on a set of abstract mathematical rules rather than tangible (macroscopic) phenomena.

So whether Feynman was saying we don't understand quantum mechanics because we don't have a macroscopic model for it or whether he was saying that quantum mechanics is based on a set of rules that do not seem to have a simpler way of being expressed, he was quite right. There is no simpler model for quantum mechanics - at the present time. If the rules were to become simpler, it would not mean that we would completely understand the quantum world. It would just mean that we would understand it better.

I think that is about all you can take from Feynman's quote.

Energy is slippery it has so many forms and can move from one form to another. From kinetic to potential. From macroscopic kinetic to microscopic kinetic. From particle anti-particle annihilation to ? to different particle anti-particle. From photon and ground state atom to excited state atom.