“It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing — a somewhat unfamiliar conception for the average mind.” -

Albert Einstein

You’ve heard and seen it plenty of times: Einstein’s most famous equation, E = mc^{2}. I’ve taken you inside this equation before, which lays out how much energy is stored in matter-at-rest, and tells you how much energy you need to create matter in the first place.

That’s right, you can create matter *directly* from energy; we do it all the time, in fact. In particle accelerators, in stars like the Sun, around black holes and neutron stars, and in cosmic catastrophes, we’re constantly creating new matter purely out of energy. It’s pretty simple: take two protons with enough energy, smash them together, and you get out three protons and one antiproton. (This is the exact process that used to take place at the old Fermilab accelerator!)

This is how we’ve made the vast majority of antimatter here on Earth, and if you add up all the kinetic energy of the four particles that come out, you’ll find that it’s smaller than the kinetic energy of the two protons you started with by exactly… the mass of a proton and an antiproton, times the speed of light squared.

That’s what E = mc^{2} tells us: that mass is just *one form of energy*, and that mass can be created or destroyed very easily, so long as you convert that mass into another form of energy. (There are other conservation rules that you may need to obey as well, but you must *always* conserve the total amount of energy, as far as our experiments can tell.)

But there’s a far more common and even mundane application of Einstein’s most famous equation: every single nuclear and chemical reaction, *ever*.

You’ve heard of a nuclear reaction: it’s where we either take lower mass nuclei and combine them to make one or more higher mass nucleus (that’s fusion), or we take heavy nuclei and split them apart into lower mass ones (that’s fission). In both cases, the amount of energy that comes out is *huge*, even though the changes in mass are relatively tiny. The most powerful nuclear explosion in history — the Tsar Bomba — which released nearly 60 MegaTons of energy, converted less than **50 grams** (under 2 ounces) of mass into energy.

^{2}comes into play in much less spectacular places than that: the paltry chemical reactions that underlie all the biological (and inorganic) processes of everyday life are all based on how electrons are bound to atoms and molecules. There are different energy levels and configurations that electrons transitions between; bonds are formed, broken and re-formed, and energy is either absorbed or emitted to balance each individual reaction out.

The crazy part? When a plant absorbs a photon for photosynthesis, it *increases* in mass in direct proportion to the energy of the photon it absorbed, following the law of E = mc^{2}. When a human burns through his-or-her chemical fuel in order to maintain their body temperature, they lose mass in direct proportion to the energy released from the breaking of those chemical bonds. In fact, if I did something as simple as weighed a free electron and a free proton on one end of a scale, and weighed a neutral, ground-state hydrogen atom on the other end, I’d find that the free electron and proton weighed more by 13.6 eV/c^{2}, exactly the mass-equivalent of the energy needed to ionize a neutral hydrogen atom!

When you combust hydrogen gas with oxygen gas to make water, it gives off energy, as made famous by the Hindenburg disaster.

Yet the water that’s the product of the reaction actually is slightly lower in mass than the hydrogen and oxygen that came before. How much lower in mass? By the exact amount of energy that was released, divided by the speed-of-light squared. (Because if E = mc^{2}, then it’s also true that E / c^{2} = m.)

So every time you do something that releases energy, you’re *losing mass* in direct proportion to the amount of energy that’s released.

And similarly, every time you absorb energy, you *gain mass* in direct proportion to the amount of energy that’s absorbed.

So what this means is that mass is a form of energy, and that these two quantities, no matter what you do to a system, are proportional to one another. In terms of an equation, E ∝ m.

But to turn that proportional symbol (∝) into an equal sign, you need to get the conversion factor right. The conversion factor is what tells you *how* energy is related to mass, **quantitatively**.

And that conversion factor is the speed-of-light, squared. Figuring all of this out was just one of Einstein’s great contributions to our understanding of the Universe.

And that was 108 years ago, already, believe it or not. Even though you probably never think about it, E = mc^{2} (or E / c^{2} = m) affects practically everything that occurs in our world; each time you bat an eyelid, flex a muscle, breathe in or out, think a thought or beat your heart, you’re converting mass into energy, and each time you digest a meal, you’re converting energy back into mass. Everything that adds or subtracts energy from a system causes its mass to change, and we can even figure out, down to the tiniest amounts measurable, by how much.

How?

Through E = mc^{2}.