# Equivalence without relativity

• Chronos
In summary, the author discusses how the equation for energy, E=mc^2, was independently derived more than once before relativity was proposed.
Chronos
Gold Member
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

Chronos,

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!

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.

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.

yogi said:
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.

Chronos said:
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
A 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

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

yogi said:
Space Tiger - top of page 5 ..."but c is constant in anyone 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.

SpaceTiger said:
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.

Ich said:
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.

SpaceTiger said:
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.

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.

PeteSF said:
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. http://users.net.yu/~mrp/chapter23.html from another forum.

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## 1. What is "Equivalence without relativity"?

Equivalence without relativity refers to the concept that two systems can be considered equivalent without the need for a reference frame or a comparison to a third system. It is a fundamental principle in physics that allows for the simplification and understanding of complex systems.

## 2. How is "Equivalence without relativity" different from the theory of relativity?

The theory of relativity states that the laws of physics are the same in all inertial reference frames. However, "Equivalence without relativity" suggests that two systems can be considered equivalent without the need for a reference frame or comparison to a third system. In other words, it does not rely on the concept of a reference frame to determine equivalence.

## 3. What are some examples of "Equivalence without relativity" in science?

One example is the principle of equivalence in general relativity, which states that the effects of gravity can be equivalent to the effects of acceleration. Another example is the concept of inertial mass, which is equivalent to gravitational mass in Newton's laws of motion.

## 4. How does "Equivalence without relativity" impact our understanding of the universe?

"Equivalence without relativity" allows us to simplify complex systems and understand the fundamental principles that govern them. It also helps us make predictions and perform calculations without the need for a reference frame, making it a powerful tool in the study of the universe and its phenomena.

## 5. Can "Equivalence without relativity" be applied outside of physics?

While the concept of "Equivalence without relativity" is primarily used in physics, it can also be applied in other fields such as economics and psychology. For example, the concept of opportunity cost in economics can be seen as an equivalent trade-off without the need for a third comparison. In psychology, the concept of cognitive equivalence suggests that individuals may perceive two things as being equivalent even if they are not objectively equal.

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