What is Energy? Like, seriously, what is it? Here's a question that's been on my mind for quite some time now.
What the actual hell is energy?
Like, seriously. I understand real-life is nothing like fiction where characters and machines can shape energy into tangible spheres, beams and various other forms, but I honestly can't take the notion that energy is merely a property of a physical system seriously anymore given everything I've learnt about it.
Ok, ok... first of all, energy can change forms... no, hold on... energy can EXIST in multiple forms. Light, thermal, kinetic, sound/vibrational, electromagnetic/radiant, etc. The ability to change forms, you know, TRANSFORM feels like something a physical thing that doesn't just exist as a property of a system has the ability to do. Hell, matter has the ability to do just that, and matter, like it or not, is an actual thing that we can define and see.
Speaking of seeing things, light. It's something we can see with our eyes (like matter) and it can exist in the form of a particle called a photon, and let me tell you these little buggers can do some pretty crazy stuff. What kind of crazy stuff though? Well laser beams (which are made of photons of light) have the ability to defect matter to the point that it either ruptures, ignites or both, and objects such as crystals and mirrors have the ability to reflect those beams in the opposite direction they were pointed at. Even crazier than this however is a photon's ability to move, like, actually straight up apply motion to matter by transferring their momentum to them.
Let me repeat that. Photons, which are LITERALLY made of energy and have no mass whatsoever, have the ability to apply force to physical objects and cause them to move. Solar sails use the momentum from the Sun's rays to achieve a speed of 18,600 miles per second (or 67,100,000 mph if you wanna get technical). Yes, the amount of energy we're dealing with here is unreasonable by the standards of our planet's various nuclear plants and wind turbines, but the point still stands. Light shouldn't be able to move anything like this unless light itself was also a 'thing'.
And finally, just to top it all off we have Einstein's famous E = MC² equation, which gave rise to the notion that matter (or I guess mass in this case) and energy were one and the same and could be transformed into each other. Now, we already have tons of examples of this formula working in one direction in the form of combustion, nuclear explosions, nuclear fission and nuclear fusion, but we've also seen scientists achieve the opposite affect and turn energy in the form of photons into matter and antimatter particles via a particle collider. The Big Bang also created matter out of energy, and we even have evidence of this in the form of the Cosmic Microwave Background.
So energy can exist in multiple forms, physically interact with matter as if it were something tangible, can be turned directly into matter and vice-versa and some forms of energy like light, sound and heat can be perceived by the naked eye (ok, that's a lie. Only light can actually be visibly seen by the human eye, the other two require special technology). If energy really can't be considered a 'thing' the same way that matter is often considered a 'thing', why does it have any of these properties? Why can I clearly feel and see its effects on the world around me? What actually is energy?
 A: Here is the most intuitive explanation of energy that I have come across myself:
Energy is "stored" motion.
Energy is a term invented for things that might in the future exert forces on objects and thus move them (possibly microscopically such as in the case of heat, thermal energy and the notion of temperature).
When you lift a book to the shelf, then there's no real-life difference in the state of the book. Still, the book has a new ability: it can fall down and hit something (causing momentum transfer and make that something move). That fact is termed energy. In this case gravitational potential energy. Don't think of energy as something tangible or concrete that you should be able to see. It is just a term used for forces waiting to be exerted, for motion that might be initiated.
A: This answer expands on the answer by contributor Steeven.
I start with the case of a gas in some cannister, we'll make that a cilinder with a piston.
The gas has a particular temperature, which means the molecules of the gas have a particular average velocity.
For the purpose of this thought demonstration: let the cilinder/piston be such that there is no exchange of heat between the gas and the cilinder/piston. (For instance, you can have a temperature probe inside the cilinder, and when the gas heats up you use heaters such that the temperature of the cilinder matches the temperature of the gas.)
As we know, gas has elastic properties.
When you compress the gas you are doing work upon the gas, increasing the temperature and density.
When you ease off on the compressive force the direction of work being done reverses, and the expansion of the gas is doing work, moving the piston.
The pressure that a gas exerts on the walls of whatever is containing the gas arises from molecules colliding with the walls.
When you are doing work upon the gas, compressing it, you are storing elastic potential energy in the gas by increasing the quantity of motion of the gas.

Of course, the question is then: is the above example a fluke, or is this an instance of something structural?
Let me consider the case of elastic deformation of a solid. Let me consider the example of a metal strip that is designed to allow storing elastic potential energy, such as the strips of metal that are used to construct leaf springs.
Atoms have a proper size where the atom is in the lowest possible energy state. When a metal undergoes elastic deformation the atoms of the metal lattice hardly move with respect to each other; the atoms are deformed at the atomic level. (If the atoms do slide with respect to each other the result is plastic deformation, which is permanent. Elastic deformation is when the material bounces back when you release it.)
A deformed atom is in a higher energy state than the the lowest possible state. Some of the energy of that higher state is in the form of faster motion of the electrons of the atom. To my understanding the majority of the additional energy is in electromagnetic field effects.

A research programme that would seek to describe potential energy as a state of motion would then seek to describe electromagnetic field effects as involving some state of motion.
For instance, the act of separating a positive and a negative charge from each other would then be described as a process that generates a state of motion in some mediator of electromagnetic interaction. This state of motion would then be described as having a tendency to accelerate charged particles in the direction of where the opposite charge is. The lowest quantity of motion state is then one where there is no charge separation.
I don't know whether such a scheme of 'potential energy as a state of motion' can be turned into a consistent theory, but I find it an interesting thought.
