What is an energy regime?

What exactly is energy?

• This question has bothered me ever since elementary school. In a physical sense, what exactly is energy? I've always been taught it's the "ability to perform work", but that's quite abstract. Meanwhile, we talk about physical things having certain amounts of energy, releasing energy, absorbing energy, and transferring energy. Are we really saying that these particles are releasing an ability, absorbing an ability, and transferring an ability? It all seems too abstract to be measured so specifically and concretely. Other than that definition, I've heard many people say, "we really don't know what energy is". If that's true, does that mean energy is the physical equivalent of the mathematical complex number--we don't know what it represents, but we can use it and manipulate it to get results that make sense? The more I think about it, the more I feel like "energy" could be described as "the sensitivity of an object to the influence of force carriers". As in, the more energy you have, the less likely you are to be affected by a force. Is that at all an accurate--or even sensible--statement? I guess what I'm really asking is, "What is energy? Do we, as a species, even know?"

• Answer:

  The problem is that in elementary school, you don't have the necessary tools to understand it. It is indeed an abstract concept, but an immensely useful one. It all starts when you look at mechanics and the equations of motion and so on. In theoretical mechanics, you soon find that in a given situation, certain quantities are conserved: Momentum, Energy, Angular Momentum are, in many cases, conserved. This makes calculations very easy. Energy is in this framework just the quantity that is conserved when the system is time-independent. I would disagree that we don't know what energy is. It's just that you cannot put it in everyday language. It's a dynamic quantity that measures how much work you have to put into a system to make it so: How much work do you need to make something so fast, or how much work do you need to carry something up that high, or how much work do you need to charge a capacitor to this charge at that voltage etc. etc. In theoretical mechanics, the motion of a system is described by the Hamiltonian function, which then turns out to be just another way to write down the energy, so basically, energy is the function that determines a system's overall motion. In quantum mechanics, energy is the expectation value of the Hamiltonian operator. So I'd say physicists have a pretty clear definition of energy.