What is energy?

Energy is one of the more fundamental concepts of both classical and modern physics.  But just what is energy?  That’s an excellent question, with a lot more to it than you’d think. 

Every time you look at it, you learn something new.  Let’s see if I can surprise you. (intro music) Energy is easier to recognize than define. 

You know it when you see it, like a speeding racecar, a taut bow, and- this may be the most energetic thing known to man- a group of four year olds who have been fed espresso and a bag full of gummy bears. Scientists try to make the definition a bit more precise, and say that energy is the capacity for doing work.  That doesn’t help most people, as physicists use the word work in a technical way.

Colloquially, I think that you might call energy a property of things in motion, or something that could, in principle, cause something to move.  There are many different kinds of energy, for example: potential, kinetic, thermal, electrical, chemical, and nuclear, to name a few. The big categories are kinetic and potential.

Kinetic energy is the energy of motion, be it translational, which is a fancy word for, you know- moving, or things like vibration or rotation.  The first kind of kinetic energy you learn about is translational energy.  If you have an object of mass m, with a velocity v, then the translational kinetic energy is one half m v squared. 

By the way, a future video will explore that equation in much more detail. Potential energy is stored energy.  It's usually created when an object is moved against a force, like stretching a spring, or lifting an object against gravity.   

It’s called potential energy, because while the object isn’t moving, it will if you let it go.  Potential energy generally depends on the strength of the force and how far you move an object in the force field. The most familiar form of potential energy is gravitational. 

If you lift an object and drop it, it moves downward.  Lift it higher, which means move it longer distances against the force, it gets more potential energy.  And, of course, that means when it hits the floor, it's moving faster than if you only lifted it a little bit.

We think of energy as being a concept that originated with Newton, but it didn’t start with him.  He thought the important thing to describe motion was what we now call momentum, which is just equal to mass times velocity.  On the other hand, a contemporary and rival by the name of Gottfried Wilhelm Leibniz championed something closer to what we now know as energy.

He thought the quantity that mattered was mass times velocity squared. The reasons for the two positions were largely philosophical and it took a French intellectual by the name of Émilie du Châtelet to sort it all out.  By dropping steel balls into a bed of soft clay, she found that the depth that the balls penetrated depended on the height from which she dropped them and the square of the velocity at which they hit the ground.

She also proposed the idea that energy was conserved and worked out the formula for gravitational potential energy.  Some have considered her work as the time where the importance of energy began to be appreciated and formalized. No one individual can be credited with developing the idea of energy in all its forms. 

It took decades to work it all out and included input from famous physics names like Carnot, Joule, Bernoulli, Boltzmann, Maxwell, and many others. In the modern world, we can think of kinetic energy as things that move – like translate, rotate, and vibrate – and potential energy, being when an object is moved against a force. That force arises from some sort of field interacting with some kind of charge. 

Examples include an electric field and charge, or gravity and mass.  In cases like those, if you release objects, they will begin to move and this will transform that potential energy into kinetic energy. Now just why energy is such a big deal was originally pretty mysterious and it only became clear when German mathematician Emmy Noether realized something enormously profound about the universe. 

She realized that conservation laws were a consequence of symmetries in the laws of nature.  If the laws of nature were unchanging over time – and I mean the deeply fundamental laws of nature – then energy would be conserved – that is to say unchanging. She also showed that if the laws didn’t change with location, then momentum would be conserved. 

But that’s a topic for another time.  And I made an entire video about Emmy Noether, which you can watch if you’re interested.  I put a link to it in the description below.

So, I’ve told you the physicist’s definition of energy and I gave you a rough definition of what kinetic and potential energy are, and I ended up telling you why energy is conserved.  Is that it?  Are we done?

Well, not yet.  For one thing, so far what I’ve talked about are objects with mass.  It’s not only massive objects that can have energy. 

Massless photons also carry energy.  Photons are moving ripples in electromagnetic fields, so moving fields have to be added to the list of objects with energy. And, of course, Einstein showed that mass and energy were equivalent and mutable, and you can change one into the other and back again. 

That doesn’t make much sense from a classical point of view- after all, a stationary and massive object in outer space, far from all gravitational fields, has mass, but it isn’t moving.  So, in my example, it has neither kinetic, nor potential, energy, but it does have mass.  If mass is energy, then something isn’t making sense, since energy is present without kinetic or potential energy being present.

The situation is resolved when you look deeply into the fundamental nature of mass.  When you do that, you find that ordinary mass is located in the mass of protons and neutrons and, when you look into where their mass comes from, it comes from the motion and forces governing nearly massless objects inside protons and neutrons.  Indeed, the nuclei that make up each and every one of us are tiny vortices- subatomic tempests- of moving and nearly massless particles, held under strong forces. 

I made an entire video that goes into this and, again, the link is in the description. If mass is just energy swirling in a single location, with the swirling energy not moving- basically a stationary tornado, then we’re back to the definition of kinetic and potential energy.  That swirling thing isn’t a perfect description, but it’s a reasonable mental image and good enough to get a rough idea.

And that’s almost the entire story.  Energy is motion and forces, and it is unchanging, sloshing into this form and that.  It’s somewhat analogous to how the atoms of the universe change form- like how dirt becomes grass becomes a cow becomes a person which becomes dust, and the cycle renews.

There is one final twist to the whole thing. While energy is often said to be conserved because of Noether’s insights about symmetries of the laws of nature, energy conservation isn’t 100% true.  The universe is expanding, and it is filled with a field of constant energy density. 

Constant density and expanding volume mean that the energy of that form – which is called dark energy, by the way – that energy is increasing.  In an expanding universe, energy isn’t conserved. Furthermore, when you talk about the fact that distant galaxies look redder than they should because of the expansion of space, that has a consequence. 

You see, the amount of energy carried by light depends on the color of light and redder light has lower energy.  Thus, it appears that photons of light from distant galaxies have less energy than they did when it was emitted.  This implies that in cosmological situations, with a changing shape of space time, energy is also not conserved.

And this is a universal truth.  In general relativity, in which the size and geometry of space and time are changing, energy isn’t necessarily conserved.  You see, Noether’s insight relied on the mathematics of unchanging space and time. 

Release that condition, and Emmy’s mathematics no longer applies. The lack of conservation of energy in general relativity is a complicated one- probably worth a video or two on its own.  However, that’s not the topic of this video. 

I put a link to a website that talks about it if you’re interested.  Be warned- it can be quite technical. So, at the deepest known level of reality, what is energy? 

It is forcefields and objects that interact with them.  That’s potential energy.  Kinetic energy is the motion of the fields- and remember that mass is mostly moving fields- that stationary tornado thing.

Kinetic and potential energy of all kinds slosh back and forth into one another in an endless dance, changing identity, but never changing the amount, forced to be the same by the mathematical structure of the laws of motion.  That is, unless you’re talking about the universe as a whole, and there, energy conservation is a more complicated thing, requiring that you revisit the meaning of the words energy and conserved. From one point of view, energy is terribly complicated, while from another, it is breathtakingly simple. 

It’s a delightful and dizzying topic, with layers upon layers, and one that is always fascinating. Okay, so that was an incredible topic, with many different levels of complexity.  If you enjoyed the video, please like, subscribe and share. 

And keep on thinking about energy, which is one of the deepest and most fundamental topics of modern physics.  And that’s saying a lot because, as you know, physics is everything.