# Do not understand why 'c' is squared in Einstein's equation

I am not a dummy but for the life of me, I do not understand why 'c' is squared in Einstein's equation. Math has never been my strength. What purpose does squaring a number (multiplying it by itself) serve?

HallsofIvy
Homework Helper

This question has absolutely nothing to do with mathematics so I am moving this to the Physics "Special and General Relativity" section. In particular, you aren't "squaring a number", you are squaring a speed, the speed of light.

You should note that, physically, it makes the units work out properly. In the "MKS" (meter, kilogram, seconds) system, energy has units of "Joules" or "kilogram meter^2/second^2". Since mass has units of kg and velocity has units of "meter/second", you must square the speed of light to get those units.

Matterwave
Gold Member

It's pretty weird to "see" E=mc^2. I guess for someone who hasn't studied special relativity, this equation seems kind of like a postulate. But really, Einstein derived this equation, and it can be derived using the postulates of special relativity (in a not-too difficult way).

One could say that the square is there to make the units work out, but it also arises from the derivation itself. Of course, at every point in the derivation, the units work out, so at the end of the derivation, the units must also work out. But you need to see the derivation to make sure that the equation is not something like a*mc^3 where a is some quantity which has units of 1/speed, or something else strange like that.

It's pretty weird to "see" E=mc^2. I guess for someone who hasn't studied special relativity, this equation seems kind of like a postulate. But really, Einstein derived this equation, and it can be derived using the postulates of special relativity (in a not-too difficult way).

Yes, that's the way Einstein did it but special relativity would also result from the postulate that energy is linear correlated with mass.

ZapperZ
Staff Emeritus

I am not a dummy but for the life of me, I do not understand why 'c' is squared in Einstein's equation. Math has never been my strength. What purpose does squaring a number (multiplying it by itself) serve?

Do you also wonder why in $P=I^2R$, that I is squared?

Zz

Pengwuino
Gold Member

FlipUnderwood said:
I am not a dummy but for the life of me, I do not understand why 'c' is squared in Einstein's equation. Math has never been my strength. What purpose does squaring a number (multiplying it by itself) serve? z

If you look at the area of a square, given a length 'L', the area is given by $Area = L^2$. It's squared because that's what makes the equation true. If you simply said $E = mc$, that wouldn't correspond to reality and the units wouldn't make sense either as has been pointed out. This is just like if you said $Area = L$. That doesn't correspond to reality and the units don't make sense either. An area can't equal a length just like an energy can't equal a mass * velocity.

HallsofIvy
Homework Helper

So we are really getting two distinct explanations- one arguing that the units are such that a speed must be squared and the other giving (or at least referring) to Einstein's proof that the formula is in fact, not just a mass and the square of a velocity but specifically $mc^2$.

The reason is this:

e=mc would be a useless equation.

The end.