# E=mc²

### The Famous Equation

Everyone's heard of it, a lot of people know what it means - or think they do. When Einstein wrote up his Theory of Relativity in Two Flavours (Special and General), he managed to work out somehow that mass equals energy. In fact, it equals energy times the speed of light times the speed of light again. And when the speed of light equals 299792458 ms-1 (about 670,000,000 miles per hour), that's a huge amount of energy for even a little mass, like a few subatomic particles cuaght up in a nuclear explosion, for example.

### The Ugly Truth

Of course, since this is physics, it's not as simple as that. In fact, to give the full equation:

E=√(m2c4 + p2c2)

So what does this mean? Well, the m and c stand for mass and speed of light still, but p stands for momentum, a handy way of keeping track of mass and speed1, so if the object in question isn't moving (something which has whole new connotations in relativity), it has a 'rest energy' of mc², which is what everyone remembers. But, if the object is moving, so it has momentum, then the energy is greater than mc². As with all things in physics, if a given set of rules explains a system well, then a set of rules explaining a bigger system has to approximate to the previous set of rules within the smaller sub-system. In this case, the rule for relativistic energy is pretty close to the Newtonian rules for energy when velocity is small compared to the speed of light.

Another thing to note is that if mass is zero, as is close enough to the case with light, but it is moving, as is the case with light, it still has energy, which makes perfect sense. In that case, E=pc, which provides a handy relation between energy and momentum, which can then be linked with the frequency (or 'colour') of the light as well.

1The fancy-schmancy physics term for speed is actually velocity