• # Question: Why does E=MC squared?

Asked by nosyt21 to Antonia, Douglas, Hugh, Matt, Tom on 26 Jun 2010 in Categories: .
• Matthew Hurley answered on 13 Jun 2010:

It just does, OK?

• Douglas Blane answered on 24 Jun 2010:

E is energy, m is mass and c is the speed of light. Squared just means you multiply it by itself.

What this equation says is that you can change mass into energy or energy into mass.

Mass is frozen energy, if you like. This was a new discovery Albert Einstein made with his special theory of relativity. The equation says more than that though. It tells you how much energy you can get from a lump of matter, if you convert it all to energy.

It says the energy you get is the mass multiplied by the speed of light multiplied by the speed of light.

So let’s do a wee sum. Suppose you have a paper clip that weighs 1 gram. How much energy could you get from that if you knew how to convert all its mass to energy?

Well if m is in kilograms and c is in metres a second, E comes out to be joules – which I’ll explain in a minute.

The speed of light c is 300,000,000 metres per second.

So here we go: E = .001 x 300,000,000 x 300,000,000

=90000000000000 joules

So you get 90 million million joules from one paper clip.

Is that a lot?

How much?

Well it’s roughly twice the energy you’d get in one day from wind turbines, if you covered the entire United Kingdom with them.

That’s quite a lot of energy.

Can we get any of this energy that comes from mass? Some but not all – unless you know where to get your hands on anti-matter.

Nuclear fission, which goes on in nuclear power stations, and nuclear fusion in the sun and stars both get their energy from converting fairly small amounts of mass to pretty big amounts of energy.

And it all works because of E = m c squared