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The world’s most famous equation is undoubtedly E=mc2, also known as the ‘energy-mass equivalence’.

Although I had seen it countless times, it wasn’t until writing this article that I realised that it makes predictions so extreme that I struggled to see how they could possibly be true.

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At the same time, it’s quite literally Albert Einstein’s most famous and recognisable contribution to science, so I was pretty sure that he had it right.

This is how it works. At first glance, it seems pretty simple.

Mass is a type of energy.

Mass is the same thing as weight unless you’re on a rocket or another planet where gravity is different. Everything around us from fruit juice, to sofas, to the air around us, has mass.

A bottle of fruit juice has a mass of 1 kilogram, and a sofa about 80 kilograms.

To work out how much energy is contained within these things, you use the E=mc2 formula.

• E is what you solve for, it gives the amount of energy in joules.
• M is the mass in kilograms.
• C is the speed of light, which you have to square.

If two objects have the same mass, they contain the same amount of energy. Even though burning 1 kilogram of rocket fuel releases more energy than burning 1 kilogram of fruit juice, this is because rocket fuel’s molecules give up their energy more easily in a chemical reaction.

So far so good. Until you actually plug some numbers in.

I’ve embedded a calculator below so you can play with this yourself, but it doesn’t show up in consistently in every browser and email. If it doesn’t work, just click through to the website here, or just take my word for it.

1 kilogram of mass contains 89,875,517,873,681,764 joules of energy.

Using WolframAlpha, that is equivalent to:

• 24.48 megatons of TNT, about the same as a hydrogen bomb
• 0.6x the energy of the Krakatoa eruption
• 0.8x the surface energy of the 2004 Indian Ocean earthquake and tsunami

Or perhaps more productively, if there was a way to completely convert a bottle of fruit juice into electricity, it would power a city many times over.

The amount of energy that’s contained in ordinary objects through their mass is outstanding.

It is theoretically possible to access it, although we don’t have the right materials at the moment. By mixing the juice with a kilogram of exotic particles called antimatter, both would cease to exist and would erupt into an explosion of heat and gamma radiation.

Awesome.

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The E=mc2 equation was used in the development of the atomic bomb, which uses neutrons to split uranium atoms. When the atoms split, a tiny portion of their mass is converted to radiation and heat, and this is where their explosive power comes from.

But this is where the theory gets really strange. If matter can be converted into different forms of energy, the same thing could be done in reverse.

Scientists are currently working on something called the ‘Breit–Wheeler process’, which is the creation of subatomic particles from colliding particles of light. But it remains a technological challenge.

One day in the distant future we may be able to 3D print any object using light. This technology is at the moment pure science fiction, but if it comes to fruition the effects in society would be utterly transformative.

Imagine a world where we didn’t grow our food, we collected the energy required to forge it.

Or where instead of going to a supermarket, you choose what you want on a screen and it materialises in front of you.

Instead of getting blueprints for a new house, you might have the house emailed to you, and you can print an exact model at 1:30 of the size.

All waste would surely be recycled for the energy in its mass.

What I find most interesting about the energy-mass equivalence is that it shows how vast nature’s theoretical limits are, and the potential of a technologically advanced future.

In the Star Trek universe, ‘matter replicators’ do just that. They turn energy into any material object. Their invention turned the Star Trek world into a post-scarcity economy, where all people’s material wants and needs are met.

### Ben McCarthy

Ben is the Founder of Discover Earth and the author of the Big Ideas Network.