The schoolroom textbooks told you that energy is The Capacity to do Work, and work is the transfer of energy. The words go round in circles without getting to the heart of it, and children grow into adults with no real concept of what energy is. So what is it?
We usually think of energy as being the property of a thing, something you can take away from a thing. But it isn’t like that. To illustrate what I mean, I can talk about a red balloon, a red bus, or a red red ruby. All these things have the property that we call red. A thing can be red, but you can't remove this red and hold it in the palm of your hand. You can remove the paint or the dye, and you can hold that in the palm of your hand, but you’re still holding a thing that is red. You can remove a thing from a thing, but removing a property isn’t always so easy. You can't remove the red from the dye to hold the red in the palm of your hand. Even when you imagine red, the image in your mind’s eye is a thing. You always need a thing to be red. There is no such thing as “raw red”.
The interesting thing about colour, is that buses aren’t really red. The photons of light that reflect off the paint make them look red. Only those photons aren't really red either. They only look red, because that's the way you see them. They don't have a colour, they have a frequency. They have a higher frequency when they have more energy, and they have more energy because something gave them that energy.
How do you give something some energy? Think about an old house, nestled in the countryside. It’s picturesque, worth a lot of money, and it’s built out of cob. Way back when, some medieval construction crew put some energy into shifting earth and straw to make the walls of this house. They did the same with the wood, which grew out of the earth because the trees put energy into shifting water and CO2. The guys moved stuff, because energy is all about motion. But the stuff they moved was heavy. It has mass. So we need to talk about mass and motion to talk about energy.
Let's have a little gedankenexperiment, a thought experiment. Consider a 10 kilogram cannonball, in space, travelling at 1000 metres per second. We talk about how much kinetic energy this cannonball has. We say KE=½mv² and we do the maths and get five million Joules. But what has the cannonball really got? Its mass seems real enough, I hefted it into my spaceship this morning before I took off. And its motion seems real enough too, because one false move and it’ll be smashing through my viewscreen taking my head off.
To find out more, I take a spacewalk to place a thousand sheets of cardboard in the path of my cannonball. Each sheet of cardboard exerts a small braking force, slowing the cannonball to a halt. This takes two seconds. We know that the cannonball will punch through more cardboard in the first second than in the second second, because it’s slowing down. So we reason that a cannonball travelling at 1000 m/s has more than twice the kinetic energy of one travelling at 500 m/s. We can do the arithmetic for each second, then slice the seconds up finer and finer, and we end up realising that the ½v² is the integral of all the velocities between v and 0. But what we don’t realise, is that kinetic energy is a way of describing the stopping distance for a given force applied to a given mass moving at a given velocity. You can flip it around to think about force times distance to get something moving. Or you can think in terms of damage or work. But basically that cannonball has “got” kinetic energy like it's “got” stopping distance.
It’s similar with momentum. That’s a different way of looking at mass in motion, based on force and time instead of force and distance. We look back to our cannonball and cardboard, and we know by definition that the same amount of time elapsed in the first second as in the second second. So we realise that a cannonball travelling at 1000 m/s has twice the momentum of one travelling at 500 m/s. But what we don’t realise, is that momentum is a way of describing the stopping time for a given force applied to a given mass moving at a given velocity. A cannonball has “got” momentum like it's “got” stopping time.
Now we can apply a little relativity: motion is relative. And I made a deliberate mistake when I told you about that cannonball. Because I didn’t fire the cannonball at 1000 metres a second. I dropped it off at a handy spot out near a GPS satellite, then zipped off in my spaceship in a big fat loop.
It’s me doing 1000m/s, not the cannonball. The cannonball is just sitting there in space. It hasn’t got any kinetic energy at all. I’ve got it. But wait, I don’t feel supercharged with five million Joules of energy coursing though my veins. So where is it? Where’s the kinetic energy gone? It hasn’t gone anywhere really, because all that cannonball has got, is its mass, and its motion. And that motion is relative to me. Kinetic energy and momentum are not really properties that a material object has “got”. They’re just distance-based and time-based measures associated with motion. The motion is relative, and in a way the motion has “got” the kinetic energy and the momentum.
So let’s look a little closer at motion. How do you make something move? Easy. Hit it with something else that moves. And how did you make that something else move? Where did it all start? I pitch you a baseball, you whack it with a bat, and it flies away at twenty metres per second. You made that baseball move. Now, where did the energy come from to make it move? From your muscles:
“ATP binds myosin, allowing it to release actin and be in the weak binding state (a lack of ATP makes this step impossible, resulting in the rigor state characteristic of rigor mortis). The myosin then hydrolyzes the ATP and uses the energy to move into the "cocked back" conformation. In general, evidence (predicted and in vivo) indicates that each skeletal muscle myosin head moves 10-12 nm each power stroke...”
There's more to it than that, but basically it’s all to do with binding, and bond angles. Bonds within molecules change, and the change releases energy. Sometimes it’s a simple change of bond angle, something like a leaf spring letting go. Sometimes there’s more than one bond angle change, in a molecule that resembles an elasticated deckchair surging from one configuration to another. And sometimes there's a whole host of bonds in play, taking a rather different shape. A familiar shape:
The myosin in your muscles looks like a mess of helical springs because that’s essentially what it is. Your muscles contract using tiny clockwork motors being repeatedly wound and released via a process called ATP hydrolysis. The molecules look like springs because they are springs. That’s the size of it. And these molecular springs aren’t just in your muscles, they’re in your skin too. Your skin is springy because of the elastin. And what does elastin look like? Like this:
Elastin looks like a heap of interconnected leaf springs because that’s exactly what it is. When stretched it’s under tension, and wants to shorten. The energy that pulls your elastic skin back in place is stored in springs that are built into the molecules of your tissues. When you get down to the atomic level, all the atoms in those molecules are held together by bonds, and these bonds rely on electrons and the electromagnetic force. They’re rather like magnets that want to pull together or push apart, only it’s electrostatic attraction and repulsion rather than the magnetic variety. This is how energy is always stored in springs, be they molecular or macroscopic, plastic or steel. It’s the same for chemical energy. Ever heard of an explosive called cubane?
”Cubane, the hydrocarbon (CH)8, is named appropriately; its skeleton is in the shape of a cube. At each corner of this cube there is a carbon atom (carrying a hydrogen) bound to three identical neighboring carbons… The large bond angle deformations in cubane make it a powerhouse of stored energy. Each strained bond is like the spring in a set mousetrap…”
Did you catch that? It’s strained. It’s under stress. Each strained bond is like the spring in a set mousetrap. Explosives are made up of molecular springs, only cubane is stable whilst nitroglycerine has a hairpin trigger. It’s similar with nuclear energy, only now we’re talking about the stuff inside the atoms rather than between the atoms, and these "springs" are stronger. That’s why we talk about the strong force rather than the electromagnetic force, but it’s the same difference. The Sun gets its energy from nuclear fusion. Squeeze hydrogen atoms together and you make helium. But when you do, twang, something lets go, there’s a material change, and things spring out between your fingers, things like neutrinos and photons. The recipe goes like this:
4 H + 2 e → He + 2 neutrinos + 6 photons.
As it happens it’s a multi-stage process, and we talk about the hydrogen in terms of protons. Two protons fuse together releasing a positron and a neutrino, then a third proton is added releasing a photon, then two trios combine to make a helium atom with two protons left over:
The squiggles in the picture above are the photons. Photons are electromagnetic radiation. The γ means gamma: these are very high frequency gamma photons, like X-rays only worse. There's only two shown above, but the two positrons will annihilate with two electrons to make four more photons. The photons might look a little like springs, and you might be thinking Spring Theory, but they're not. Because when a positron annihilates with an electron, you’re left with no springs at all. Take one positron, add one electron, and BANG, matter/antimatter annihilation occurs. The electromagnetic springs let go so totally, they’re just not there any more. It's a total material change, with no material left. The matter is totally converted to energy, and the only product is electromagnetic radiation.
Gamma rays are electromagnetic radiation, so is visible light, and so are radio waves. Electromagnetic radiation consists of photons, and the photon is of crucial interest. Particle physics often comes with mental baggage that says it’s a speck, a point, a “billiard ball” particle. But long-wave radio reminds us that photons can be 1500m long, or even longer. A photon isn’t some speck. Nor is it some kind of spring. It’s more like a ripple in a rubber mat, or the slink in a slinky spring rather than the spring itself. It's a wave, but not a longitudinal compression wave like a sound wave. A photon is a transverse wave. It ripples up and down like this ~ . And it travel through space, that vacuum void with the properties we call electrical permittivity and magnetic permeability. A photon is like a ripple on an electromagnetic ocean between the stars. A boat on an ocean can ride a ripple and the ripple just passes on by. But tie that boat to the sea bed with an elastic rope, and you can capture the energy of the ripple in a bond, just like a plant can capture the energy of sunlight and save it in starch or oil.
Of course space isn't really an ocean. It doesn’t have a surface, it isn’t a liquid, and there’s no substance to it. But the analogy is fair. A photon is a quantum of “stress-energy”. It travels in the mysterious fabric of space like a shimmy shooting through a ghostly block of transparent rubber. It's a transverse wave of travelling stress, and this stress is somehow in space itself. It’s in the space between the stars, within molecules and atoms, and is everywhere. There is nowhere in this universe where there is no space, and there is nowhere in this universe where there is no energy, so space is always stressed.
In physics, stress is the opposite of tension, and is much the same as pressure. To quantify energy and obtain the correct dimensionality, we have to know that stress is force per unit area, and energy is force multiplied by distance. We have to multiply a stress by an area and then by a distance to get energy. So we have to multiply a stress by a volume. We have to multiply the degree of stress by the volume of space that is stressed. Then we can quantify how much energy is there. And there's nothing more fundamental than space. Space isn't made of anything. We can't examine it through a microscope or annihilate it to obtain some-thing else. However we know that space always has a volume. If it didn't, it wouldn't be space, and we know that space is always stressed, because energy pervades the universe. So there's nowhere else to go, that's the end of the line. But it's quite enough for a new definition of what energy really is, and as we shall see, this new definition is utterly profound:
In barest essence energy is a volume of stressed space.
This is why you can’t hold energy in the palm of your hand. Because you can't hold a volume of stressed space in the palm of your hand. Just as you can’t hold a photon in the palm of your hand, or a sunbeam. Nothing is “pure energy”, just as there’s no such thing as pure pressure. Because energy is the property of a thing, even when it’s the very last property that makes it the thing that it is.
But oddly enough, you can hold energy in your hand. It’s a subtle difference, but it’s very simple. Just squeeze a fist. Use your right hand. Squeeze it tight. Now touch your left thumb to your right thumb. Feel that increased blood pressure. Now look at the volume of your fist. Stress is much the same thing as pressure, and there’s a volume of it in that fist. Your fist now has more energy. And if you swing that fist, it has even more. As to how, that brings us back to mass in motion. It’s all to do with pushing little circles into little helixes, like stretching a spring. And to explain that, I’ll have to explain mass.
