« No Dark Energy Required ! | Main | Playing Fermilab ? »

October 27, 2005



My textbook in highschool had an elementary derivation but I can't remember the details. I think it first derived time dilatation and the studied a cannon ball that hits a wall and destroys it (I am sure there are more pacifist examples along the same lines). The fact, that the wall gets destroyed is supposed to be a measure of the cannon ball's kinetic energy. Then you look at the same process from the perspective of a moving observer (IIRC you should move transversally to the ball). However the fact that the wall gets knocked down in both reference frames tells you something how the kinetic energy transforms (using the transformation of the velocity that you worked out earlier).

Somehow, you could compute E=mc^2 from that (be sure you know what you want to call E and m, E is something like restmass plus kinetic energy and m is the 'moving mass', mass decorated with a gamma factor).

Maybe there is also a way to get this relation by doing a gedankenexperiment that is based on the fact the energy and time are conjugate variables and of course the symplectic structure is invariant. Of course you should not say it that way in a public lecture...

m. visaya

probably the simplest explanation is GUAM.


B=((3/4)(sqrt(3)-3i)(mgv)), then

(B^T)^nT (time-T map dual)


I like m.visaya's answer. I don't know what it means, but I like the look of it (lol).
p.s. Thanks for your continuous effort.


The best thing to say to an audience about E = mc^2 is this:
OK people, I know why you care about this, it's because you think it has something to do with bombs and nuclear reactors. Well, that's wrong. A nucleus of uranium is held together by something called the strong force. Those bonds store energy, just as chemical bonds store energy. In a nuclear weapon that energy gets released and turned into another kind of energy. Absolutely nothing to do with E = mc^2 you see. No mass is being turned into energy, it's just the same old boring story: energy stored in one form released in another form. So you are all here for the wrong reason, please go home now.


The PBS.org site has a page where 10 different physicists give simple explanations of the equation. If you haven't seen it, it's worth reading. Don't know if it helps your question.



Hi Jochen,

I was having the exact same problem a few weeks ago: I was preparing lecture notes for "Physics for Poets" here in Princeton and got frustrated that I couldn't find a simple derivation of E=mc^2. This is interesting since everything else in special relativity really can be shown in quite simple terms (with little math and little prior knowledge) to non-scientists.

Finally, I discussed this with Richard Gott and we came up with a simple thought experiment. Unfortunately, it also involves photon momentum, so it doesn't qualify as something you are looking for. However, I prefer it to the center of mass argument you use. I will send you our notes in a separate email, but basically the idea is the following:
Imagine a particle travelling at low speed v and spontaneously emitting two photons. In the particle rest frame the photons have equal and opposite momenta, so the particle remains at rest. Now analyze this in the lab frame. The two photons are Doppler shifted and therefore impart unequal momenta on the two sides of the lab. But momentum has to be conserved. Where is the change in momentum of the walls of the lab coming from? The speed of the particle can't change (by symmetry of the situation in its rest frame; no kick in any direction), so its mass must change. Include the details of Doppler formulae and you get

Hope you enjoy being back in London.

Best, Daniel

Edward Sawka

In a book The Einstein Paradox
by Colin Bruce
page 163 the equations for deriving e=mc^2.
is it correct.
How does he get momentum to = e/c/m ?

Edward Sawka

In a book The Einstein Paradox
by Colin Bruce
page 163 the equations for deriving e=mc^2.
is it correct.
How does he get momentum to = e/c/m ?

Jochen Weller

Hi Edward

this is exactly the problem I was running up against, that most books assumed the expression
for momentum.
For a derivation of this you can look in
Feynman lectures.


I think time dilation is wrong due to inertia.



I'm a Grade 12 student who is just beginning to learn about Quantum Physics and E= mc^2. My teacher wanted the class to find an explanation of the equation over the christmas holidays: is there an explanation that a class of Grade 12 Physics students could understand?

From my research, I found out that Einstein was trying to make a connection between Mass and Energy, and that he basically tried to explain Mass in terms of Energy. I understand how the speed of light is the constant in the equation: it doesn't change in any frame of reference, while the mass and energy can change: they are the variables. What I don't fully understand is how and why Mass can be turned into Energy and back again.

Thanks a lot!

p.s. also, what is this GUAM that m. visaya mentioned in one of the past comments??


By the way, I've written out everything I understand on this topic so far on my blog space, if you'd like to see it:


Thanks again!

The comments to this entry are closed.