Is energy *always* related to movement/motion? Is it always true to say that energy is force x distance?
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In physics, energy is the capability to do work. In order to do some work, an object has to be given energy. For example, a book lying on the ground is not going to move because it has no energy, but if you pick it up off the ground and then let go of it, it will fall to the ground. The processes that happened were you giving the book potential energy (by lifting it,) and then the book’s potential energy converting into kinetic energy (as it fell.)
You’re talking about kinetic energy (movement). There’s also things like thermal energy (when something gets hot or cold, like why it takes energy to boil water). Nuclear energy is released when atoms fuse or split, chemical energy is released in any chemical reactions, like when you digest food.
The thing to know about energy is it isn’t a thing like an atom is a thing. It’s just a way for scientists to track what’s possible in a system. The total amount of energy stays the same (conserved) and it puts a lid on the total amount of change that can happen. So you drop a ball and because the amount of energy puts a limit, you know it won’t bounce higher than it started. You also know that since it bounces somewhat lower you know that some other change must be happening. You can now go investigate that and find out that the ground and ball are slightly warmer than they were before so some of that went to heat.
What makes this confusing is that historically scientist developed all these different ways of tracing energy and didn’t realize until later they were all talking about the same thing so there a bunch of different names and ways of measuring what is fundamentally all the same thing.
Energy is magic. It’s the magic stuff that animates the world. It’s what makes heat literally move across space to stuff that isn’t as hot. Energy is the stuff that isn’t matter, it’s the stuff that *isn’t.* It’s the thing that makes reality tick while seemingly not existing at all. Energy interacts with us, but in these weird indirect ways. Truly, think of energy as magic, electricity absolutely included, an entire magical system like you’d find in a fantasy story but just renamed science and everyone pretends it’s just boring old bookkeeping.
As an electrician, trust me when I say that the truth of energy only becomes less clear as you study it more, and yes, I am an electric wizard.
Edit: and no, the energy in your equation is only the energy involved in that particular motion. There can still be other stagnant energy, or energy being used but for things other than motion, like heat or light.
Energy is the conserved quantity in a system associated to a time-symmetry. Basically, it’s a number that does not change regardless of how much the system is moving, bouncing around, etc (as long as another system does not interact with it).
Speeding bullets and fully charged batteries are energetic in the same way that pillows are soft and strawberries are sweet. By that, I mean that energy is better conceived of as a property that objects and systems have, rather than a sort of “stuff” or substance that systems can contain. The actual definition of energy is quite abstract and, while it may seem backwards, I’ll have to explain why energy is important before explaining what it actually is.
What makes energy as a concept interesting is that, unlike softness and sweetness, it obeys a conservation law. A conservation law is basically a guarantee that a certain property of a system, called a “conserved quantity”, will never change as long as that system does not interact with anything outside it. If two systems do interact, the values of their conserved quantities can change individually; however, any increase in one system’s values must be exactly counterbalanced by a decrease in the other so that the total change adds up to zero.
Only a handful of conserved quantities exist in the world. Energy is one; charge, momentum, and angular momentum are a few others. Sweetness is not, because a strawberry can ripen without some other strawberry somewhere else becoming less sweet. Being conserved makes a thing precious, almost like a form of currency. A system can’t just *become* energetic on its own; some other system must pay for that by giving up some of its own energy.
So, we’ve established that energy is conserved, but what makes energy *energy*, as distinct from momentum or angular momentum or any other conserved quantity?
It turns out that there is actually a reason each conserved quantity exists. There is an incredibly important mathematical result in physics called Noether’s theorem, which links conserved quantities to the idea of *symmetries*. You can think of a symmetry as a variable that the laws of physics do not “care about” when deciding the result of an experiment. For example, translational symmetry is the idea that the laws of physics are the same at all places, so the result of an experiment should not depend on *where* you conduct it. The laws of physics are also rotationally symmetric (it does not matter *which direction* your experiment faces) and time-translational symmetric (it does not matter *when* you conduct your experiment).
What Noether’s theorem says is that whenever a (certain type of) symmetry exists, you can derive a special number that does not change over time, i.e. a conserved quantity. It turns out that momentum is the name we gave to the conserved quantity that stems from the fact that the laws of physics are the same in all places. Angular momentum is the conserved quantity that stems from the fact that the laws of physics are the same in all directions. And energy is the conserved quantity that stems from the fact that the laws of physics are the same at all times.
Physics is agnostic to what energy is. I’m going to recreate [Feynman’s lecture on conservation of energy](https://www.feynmanlectures.caltech.edu/I_04.html), but I encourage you to read it in full.
At some point in the development of physics we noticed that there were certain numbers which tended to stay constant. For example, when considering objects moving through a gravitational field without friction, the values 1/2 m v^2 and m * h (mass x height), when added up over all the interacting objects, would stay the same. Not just experimentally, but the physical laws that accurately predicted the motion, predicted they would stay the same.
We called 1/2 m v^2 kinetic energy, and m * h potential energy (because, through the act of falling, it had the potential to become kinetic energy).
It seemed like temperature was an exception to this – energy could be lost in friction as heat dissipated. However, we discovered thermodynamics, and found a consistent way to assign an energy content to the temperature within objects, so that kinetic + potential + thermal (temperature) energy stayed constant.
Physics has continued on in this manner. We’ll find processes where energy disappears, and then find a new term to tack on to the sum to once again keep energy constant. There’s energy in movement, energy in gravitational and electric fields, energy in temperature (though that turned out to be movement as well), and eventually we found out that to keep everything consistent we even had to say that mass itself is a form of energy, and in the appropriate circumstances energy from the other forms could be lost into mass (or more explosively, energy in mass could be converted to the other forms).
What is energy? We don’t really have a better answer than – this number. We cannot directly interact with it, and physics has decided since Newton’s law of universal gravitation that it must simply accept that there are some parts of reality whose fundamental nature is not something humans can understand in the same way we can understand objects that we can grasp and move. Our brains are designed for macroscopic objects and contact forces. Energy is that property of systems that stays constant when exchanged with all the other forms of energy.
I think the best way to understand energy is to compare it to money. Energy is like the currency of the universe. It’s the potential to make physical stuff happen (e.g. moving or heating something), just as money is the potential to make societal stuff happen (e.g. making someone cook you a meal).
The problem most people end up grappling with is the desire to understand energy as a physical *thing* rather than an abstract quantity or property. Comparing it to money solves this mental problem.
You can have a bill worth a dollar, or a coin worth a dollar, or a check worth a dollar, or a piece of property that would be worth a dollar if you sold it, or a string of numbers in a bank’s computer system that state that you have a dollar in your account. But you can’t have a “pure dollar.” This one dollar that you own only exists to the extent that these different things have comparable *value* that can be converted back and forth.
Likewise, you can have a joule of kinetic energy, or a joule of chemical energy, or a joule of gravitational potential energy, etc. But you can’t just have a joule of “pure energy.” an object *carries* a certain type and amount of energy based on context, just as a dollar coin is worth a dollar because of a particular social context.
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