How to explain the world’s most famous equation (E=mc²) to your granny or kids

Why should you know about E=mc²?

There’s a saying. If you can’t explain it back to kids (or granny for that matter!) then you haven’t truly understood it. Mathematics and physics is a whole different kettle of fish. Even the guides and explanations that aim to describe a concept are themselves complex. Usually, what happens is that a new theory in mathematics appears. The book behind it starts off dense. As the years pass and understanding improves, the books get thinner and thinner. Think of Pythagoras’ Theorem for example. It features in every elementary child’s school now. When it was first discovered, it was groundbreaking.

Einstein’s E=mc² is the world’s most famous equation. Simple as that. It is short, it is elegant, and it describes a phenomenon so crucial that everyone should know about it. The problem is, the explanations aren’t always easy to follow. Let’s take an attempt to explain it again in a very simple manner.

Early disclaimer: some of the descriptions have been simplified to illustrate the point. I’m sure you can pick out certain points if you were to nit-pick, but for the audience, this is intended for (the mass), the explanations will perfectly suffice.

The backstory

The equation itself is not too old in terms of history, at only just over 100 years old. Some equations have been around for hundreds of years, thousands even. Taking that into account, we’re talking about a baby equation here. Albert Einstein was back then a young mid-twenties office clerk in Switzerland, reading through patent applications all day. Albert would use whatever time he could muster in his job to daydream about deep things physics. Everyone at the time thought of the universe in two big buckets. One bucket was about energy, the other was about mass.

What does it mean?

The equation is telling us that energy and mass are essentially the same thing and that you can go from one to the other using a constant value. That constant value turns out to be the square of the speed of light. Basically, the formula is saying e = m x c x c, or E=mc².

So why does it matter? What’s so great about it?

Energy and mass were considered separate things by the science community before Einstein came along. Unrelated. Einstein managed to figure out that actually they were related after all. They’re connected by the speed of light, strange as that may sound. The finding revolutionized the world because it allowed us to convert energy to mass and vice versa. Something the science community previously didn’t know.

Einstein must have been the grand-daddy of geniuses?

Actually no. Einstein did something very admirable. He took everything back to basics and questioned previously well-established schools of thought. There’s a lesson here that everyone should absorb. Always come up with your own conclusions. Einstein wasn’t the greatest mathematician, nor was he particularly successful at school. But what Einstein did have was the ability to think critically and think for a very long time without getting distracted.

His ideas were also not entirely new. Those before him had also thought about E=mc². When the equation became public information, the public asked him why this fact was not known earlier. He responded saying it’s the same as a rich man who never spends. How would you know he was rich?

Why does this equation matter? How does it impact us in the real world?

Think about the profundity of the equation for a moment. What it’s telling us is that small amounts of mass can be converted into huge amounts of energy and vice versa. E=mc². Imagine how that could help us. Small things generating big energy. Clean energy perhaps? The engine in your car will convert very tiny amounts of matter into the energy your car needs to run. In a nuclear reactor, tiny amounts of matter is created into electrical energy. It’s fascinating really to think of how much energy is around us.

Why is it the most famous equation of all?

It’s short, snappy and easy to remember. But its fame also has a lot to do with using the formula to help create one of the most devastating weapons of all time — the atomic bomb. It’s an incredibly powerful equation.

What’s freaky is that the energy inside us, one human being, is thousands of times more explosive than the amount of energy that destroyed an entire city in Japan during the World Wars.

Hold on a second. How can mass and energy be the same thing?

Energy is all about the things happening around us such as wheels in motion, a weightlifter using all his ‘energy’ to lift weights, storms, lightning. Power. That’s what energy is about. Then you have mass. Big planets, big buildings, and tiny babies who keep growing and growing until they become massive toddlers.

They must, of course, be two different things, correct? Up until just over 100 years ago, that’s exactly what everyone thought. These must be two separate concepts. Unrelated.

Actually, they’re not.

Let’s start to think through how Einstein came to the realization

Einstein started by looking back in history at what others had achieved and he noticed a contradiction. Two key ideas from heavyweights Galileo and Maxwell didn’t quite fit with each other.

Galileo stated that there was no such thing as just ‘moving around’. He was saying that you are ‘moving around’ in relation to something else. There must be a ‘reference’ that you’re moving against. Think of the world’s currencies. The US dollar doesn’t have its own value. Its value comes from being compared to another currency, such as the Sterling Pound, or the Euro, or even the Japanese Yen. The same concept is what Galileo was stating. When you’re inside a train, you might be sitting opposite someone. To each other, you’re both motionless, but to someone outside the train, you both are moving at the speed of the train. Get it? Your speed, your motion entirely depends on who your reference point is.

Maxwell discovered something else. He produced the equations on electromagnetism. These equations essentially stated that electromagnetic waves (the stuff that is used to transmit radio, TV, telephone and wireless signals) traveled at a constant speed, ‘c’, the same speed as light. Long story short, he suggested that light was a wave, just like how the ripples in water when you drop a penny are waves. This speed, ‘c’, was constant despite who was watching, or whose reference was being compared against. Strange. Einstein proposed that the speed of light must, therefore, be constant relative to everything. It must be a universal constant.

We’re already starting to face some contradictions. That’s what Einstein was also thinking

Why do Galileo’s ideas not quite fit into Maxwell’s? How can one idea say that motion is relative to the eye of the beholder, while the second idea says that the speed of light, it’s motion, is the same regardless of the eye of the beholder?

The speed of light is always 186,000 miles per second. Think about how fast that is for a second. The world’s fastest car probably runs somewhere close to 300 miles per hour. We’re talking about 186,000 miles per second! Not hours… seconds! That’s over 7 times around the world in one second. Who needs a plane?

What did Einstein do with the contradictions? He did thought experiments!

Einstein started with a basic assumption: no one can travel faster than the speed of light because it just does not make sense. Do you know anyone or anything that does? Exactly!

Now let’s do a thought experiment — basically running a scenario in our mind. Anything is possible in the mind.

Imagine you step into a spaceship and just like that, you travel really fast. Let’s call the speed at which you’re traveling 0.7. That’s 70% the speed of light. Now if you get another turbo boost of the exact amount, you’ll expect to get another 0.7, correct? 1.4? That would mean you’re going at 140% the speed of light, in other words, way faster than light. That’s impossible, because, back to our assumption, nothing can travel faster than light. What actually happens is that your spaceship goes faster but maybe only to 0.8. so your same effort didn’t get you as much speed as before. Diminishing returns. Another turbo boost and you’ll get faster, maybe to 0.9, then 0.92, 0.93, all the way to 0.99999, but you’re never going to reach 1.0, which is the speed of light. It’s almost as if you’re getting more massive each time, so you’re harder to push with the same effort. You can push a ball and make it move, but you can’t expect to push an elephant with the same force and make it move. It feels very much like that’s what is happening to our spaceship. Despite being the same size, it’s starting to feel more and more like transforming from a ball to an elephant.

Illustration of how the object (the blue dot) will never quite reach point B (speed of light). Each step it’s moving closer to B but the incremental gains are halving, meaning it never reaches B.

Bringing it all together

We’re starting to get to the answer. What’s happening is that the spaceship is the same mass as before, but it has more energy. That energy is its movement. So it’s as if your spaceship is gaining more mass because of that extra kinetic energy.

Wait a minute. Let’s read that again. Your spaceship is gaining more mass because of that extra kinetic energy? That sounds like we are saying energy and mass are interchangeable, one and the same.

Whoa. Energy = mass? Voila! Let that sink in for a minute.

Of course, Einstein’s explanation will be a lot more elegant than what I’ve described. What I’ve done is taken the nuts and bolts of the theory to describe what is happening.

I bet you enjoyed that thought experiment, huh? No wonder Einstein spent all his life doing it.