*[Corrected, thanks – T.]*

*[Corrected, thanks – T.]*

This derivation came very early in the development of

relativity, and the formal concept of “rest-energy” had not

yet evolved, nor had E0 been introduced to symbolize it.

Unless Einstein was willing to assume that whenever E0=0,

m=0—that all of the mass of a material entity was equivalent

to energy—he could not take the analysis any farther

than he had in September 1905. Unfortunately, he did not

overtly share his concerns about this issue with his readers.

it would not be until 1912 that he was writing statements

like: “According to this conception, we would have to view a

body with inertial mass m as an energy store of magnitude

mc^2 rest-energy of the body.” To attribute E0=mc^2 or

even worse, E=mc^2 to Einstein via the September

1905 paper is to do injustice to the gradual nature of his

development of the concepts.

Einstein made

two intuitive and seemingly innocent leaps that went beyond

what he could prove. “Since obviously here it is inessential

that the energy withdrawn from the body happens to turn into

energy of radiation rather than some other kind of energy, we

are led to the more general conclusion: The mass of a body is

a measure of its energy content [Energieinhalt]….”

The concept

of rest-energy was still unformulated, and he was not

even using the term. Without proof, Einstein guessed that the

loss of other forms of energy besides electromagnetic would

result in an equivalent loss of mass. That is no small point,

especially because many physicists at the time believed mass

was entirely electromagnetic.

An unspoken assumption was made early in the September

1905 paper that each emitted light pulse was not material,

in that it carried energy but had no intrinsic mass.

Throughout his work on the special theory, Einstein maintained

that light was other than matter. As he put it in 1911,

“the comparison of light with other ‘stuff’ is not

permissible.” Thus, Einstein avoided a more complicated

calculation by conjecturing, without discussion or proof,

that light was massless. But of course he could not prove

such a thing, one way or the other.

Finally, it should be noted that plane waves are a mathematical

contrivance. No real extended body can actually

radiate electromagnetic plane waves as required by this

thought experiment. Naturally enough Einstein said nothing

about the physical structure of the hypothetical emitting

body that could perform such a feat. This omission likely

troubled him because, as we will see, he returned to the issue

seven years later with a more elaborate emitter.

What Einstein proved in September 1905 was that if an

imaginary material body could somehow emit radiant energy

E0 which is itself massless in the form of plane waves,

that extraordinary object would diminish in mass by E0 /c^2.

He did not prove that every form of energy was equivalent to

mass; that, he simply proclaimed. Yet, he was quite aware

that his analysis had limitations, and in 1907 he discussed the

need for a more general approach.

“How Einstein confirmed E0=mc^2”, which you download from

http://www.loreto.unican.es/Carpeta2012/AJP(Hecht)Einstein2011.pdf.

Here is Hecht’s abstract:

The equivalence of mass m and rest-energy E0 is one of the great discoveries of all time. Despite the

current wisdom, Einstein did not derive this relation from first principles. Having conceived the idea

in the summer of 1905 he spent more than 40 years trying to prove it. We briefly examine all of

Einstein’s conceptual demonstrations of E0=mc2, focusing on their limitations and his awareness of

their shortcomings. Although he repeatedly confirmed the efficacy of E0=mc2, he never constructed

a general proof. Leaving aside that it continues to be affirmed experimentally, a rigorous proof of the

mass-energy equivalence is probably beyond the purview of the special theory [of relativity].

That last sentence is an important conjecture about the logic of SR.

A crucial point – which Terence emphasized he was avoiding – is whether mass changes with motion, i.e., whether mass is relativistic.

]]>