# Why the c in mc^2?

1. Dec 25, 2009

In the mass-energy equivalent equation, E=mc^2, why is it related to the speed of light?

2. Dec 25, 2009

### espen180

That is the formula for rest energy predicted by Special Relativity.

From the postulates of SR (Invariance of c, physical laws are the same in all inertial frames) one can derive the equations describing energy:
$$E_{tot}=\gamma mc^2$$
$$E_k=(\gamma -1)mc^2$$
which lead to the conclusion that a mass has a rest energy $$E_0=mc^2$$ which is called the mass-energy equivalence.

So the the short answer is that it follows from the postulates of SR.

For a more in depth description detailing how the equation is derived, see
http://en.wikipedia.org/wiki/Mass-energy_equivalence#Background

3. Dec 25, 2009

### tiny-tim

Merry Christmas!

He DeadCat_86! Have a bouncy Christmas!

e is energy, which is ML2/T2, while m is of course just M,

so the conversion factor must have dimensions of L2/T2, ie it has to be a velocity squared …

and c is the only non-arbitrary velocity for such a general equation!

4. Dec 25, 2009

### Nabeshin

Re: Merry Christmas!

Dimensional analysis saves the day yet again!