The world’s most famous equation is E=mc^{2}, or the ‘energy-mass equivalence’. Although I had seen it written probably over a thousand times, it wasn’t until I researched what it really meant that I realised that it makes predictions so extreme that I struggled to see how they could possibly be true.

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.

Everything around us from bottles of fruit juice to sofas has mass (mass is the same thing as weight unless you’re on a rocket or another planet).

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=mc^{2} 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.

It doesn’t matter what type of object it is, as long as their mass is the same. 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.

But we’re calculating the total amount of energy down to the atomic level, so how the molecules behave doesn’t matter. All that matters is the mass

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

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

This is the crazy part. 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

Put another way, if there was a way to completely convert a bottle of fruit juice into electricity, it would power a city *many *times over.

This is theoretically possible, although we don’t have the right materials. By mixing the juice with a kilogram of exotic particles called antimatter, they would release all of this energy as heat and gamma radiation.

Awesome.

On a more practical level, the E=mc^{2} 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 how to create subatomic particles by colliding particles of light.

One day in the distant future we may be able to 3D print any object using light. This technology obviously has a *long *way to go, but would be one of the most transformative inventions of all time.

In the Star Trek universe, ‘matter replicators’ turn an energy source into any material object. Their invention turned the Star Trek world into a post-scarcity economy, where everyone’s material wants and needs are met.

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