Equivalence without relativity

[Chronos]

Here is a very interesting read on SR. Were Gould not the author, I probably would have glossed and flossed this paper.
http://www.arxiv.org/abs/astro-ph/0504486
E = mc^2 Without Relativity
Authors: Andrew Gould

[jdavel]

Chronos,

Get out your floss!

Maybe I'm missing something, but in the introductory book "Special Relativity" by Anthony French, there's a derivation of E=mc2 that doesn't assume constant c. A 1906 paper by Einstein (Ann. Phys., 20, 627-633) is cited. Gould's derivation seems along the same lines (momentum of EM radiation) although he takes longer to get to the result than Einstein did.

But, like I said, maybe I'm missing something!

[yogi]

Interesting tutorial - the second part (3.1) is bootstrap however - since it assumes c constant in any reference frame, it recovers the relativistic mass (eq 10), but that assumption is part of SR, which is what the author seeks to prove.

[Chronos]

The more interesting point that Gould raises is how one could have derived the principle of equivalence using only the tools available in 1884. He takes the long way around because he deliberately avoids using any assumptions that were not accessible at that time.

[SpaceTiger]

Interesting tutorial - the second part (3.1) is bootstrap however - since it assumes c constant in any reference frame, it recovers the relativistic mass (eq 10), but that assumption is part of SR, which is what the author seeks to prove.

Care to elaborate? It looks to me like he explicitly avoids doing that.

[pmb_phy]

Here is a very interesting read on SR. Were Gould not the author, I probably would have glossed and flossed this paper.
http://www.arxiv.org/abs/astro-ph/0504486
E = mc^2 Without Relativity
Authors: Andrew GouldA buddy of mine told me about this paper today. It turns out that the author referenced an article I (ref 2 - "Brown, P.M.") wrote last year. Please note that my article is in the physics archive and not in the astro-ph archive. The author of this article is not the first to derive E = mc^2 by the method he uses. Fritz Rorhlich did this several years ago. It appears in the American Journal of Physics.

jdavel - The author does not use the Lorentz transformation nor does he use time dilatation. He approximates red shift using the classical relation rather than the relativistic one (which assumes c = invariant).

Pete

[yogi]

Space Tiger - top of page 5 ..."but c is constant in any one frame" One way isotropy is a premise of SR.

[SpaceTiger]

Space Tiger - top of page 5 ..."but c is constant in any one frame" One way isotropy is a premise of SR.

Ok, I thought you were saying that he was assuming its constantcy across reference frames. Although single-frame constancy is an assumption which is implicit to SR, it seems like that assumption was also implicit to Maxwell's equations, work done prior to relativity.

[Ich]

Ok, I thought you were saying that he was assuming its constantcy across reference frames. Although single-frame constancy is an assumption which is implicit to SR, it seems like that assumption was also implicit to Maxwell's equations, work done prior to relativity.
I think the interpretation of Maxwell´s equation was that c is constant only in one special frame (the aether).
further, if I were a scientist back then and would know nothing about photons, I would rather believe that my calculation was oversimplyfied than announce that E=mc².

[SpaceTiger]

I think the interpretation of Maxwell´s equation was that c is constant only in one special frame (the aether).

From what I understand about the aether theories, they were claiming that c was simply a different constant, depending on your motion with respect to the aether. This would make sense because they were looking to preserve Galilean relativity. When you apply this to Maxwell's equations, you will simply find that c is a different constant, but constant nonetheless.

[Ich]

From what I understand about the aether theories, they were claiming that c was simply a different constant, depending on your motion with respect to the aether. This would make sense because they were looking to preserve Galilean relativity. When you apply this to Maxwell's equations, you will simply find that c is a different constant, but constant nonetheless.
Michelson and Morley expected to find different c in different directions, just like you would expect for sound.

[PeteSF]

I the impression that the E=mc^2 equation was independently derived more than once before the advent of relativity?

Heaviside is a name that rings a bell in this context.

[JesseM]

I the impression that the E=mc^2 equation was independently derived more than once before the advent of relativity?

Heaviside is a name that rings a bell in this context. There were some people who wrote down the equation, but in each case they either meant for it only to apply to some very specific physical situation rather than being a general relation, or their derivation was wrong, or both. This page (http://users.net.yu/~mrp/chapter23.html) shows Heaviside came up with the equation E = (3/4)mc^2 in 1889 (equation 23.44 on that page). Besides the extra 3/4 factor there, he did seem to only mean for it to apply to a specific case: from what I could gather, the equation was just supposed to describe the energy contained in the electromagnetic field of a moving electron, where the electron was modeled as a small charged sphere of finite radius. Some others who wrote down the equation before Einstein are discussed on this thread (http://www.iidb.org/vbb/showthread.php?t=119631) from another forum.