1. ## Help With Sources

I just started Physics III yesterday, and I talked to my professor about doing research for the class. He recommended that I write a paper on how Maxwell came up with the equation $\displaystyle dP=\frac{dU}{c}$, where P is momentum, U is energy (forget which one at the moment) and c is the speed of light. After this, he wants me to do the following:

$\displaystyle dP=\frac{dU}{c} \implies E=mc^2$

He wants me to derive Einstein's Famous equation from Maxwell's. Can anyone give suggestions on how to start, or even suggestions on books that I can take a look at?

--Chris

2. Originally Posted by Chris L T521
I just started Physics III yesterday, and I talked to my professor about doing research for the class. He recommended that I write a paper on how Maxwell came up with the equation $\displaystyle dP=\frac{dU}{c}$, where P is momentum, U is energy (forget which one at the moment) and c is the speed of light. After this, he wants me to do the following:

$\displaystyle dP=\frac{dU}{c} \implies E=mc^2$

He wants me to derive Einstein's Famous equation from Maxwell's. Can anyone give suggestions on how to start, or even suggestions on books that I can take a look at?

--Chris
If you ever find out how to do this I'd like to know. I don't think it can be done. As I recall your given equation only holds for massless particles. You see given your original equation:
$\displaystyle dp = \frac{dU}{c}$

$\displaystyle \frac{dU}{dp} = c$

$\displaystyle U = pc$
where U is the total internal energy of the particle, ie. U = E, and this is indeed true for a massless particle.

E = pc also comes from Einstein's equation. The actual equation derived by Einstein is
$\displaystyle E^2 = (pc)^2 + (mc^2)^2$

If the particle is massless we have E = pc like we had above. If the particle is at rest (ie. no momentum) we get the celebrated $\displaystyle E = mc^2$.

I cannot think where the Maxwell equation would be found, but Maxwell's work in this case is for bosons (subatomic particles with integer spins) and probably would be found under a search on spin-statistics correlations. You can find a derivation of Einstein's equation in just about any Modern Physics text. That will give you a starting point anyway.

-Dan