Wednesday, August 24, 2011

Did Einstein discover E=mc2?

A lot of people have strong opinions about that, as is clear from the comments that have followed on from my article of this title for Physics World. (I particularly liked "For an objective account, see Albert Einstein: The Incorrigible Plagiarist." Yup, sounds like an objective book to me.) The piece is here, but the pre-edited version is below. There's a fair bit more that I'd have liked to explore here - it's a deeply interesting issue. The biggest revelation for me was not so much seeing that there were several well-founded precursors for the equivalence of mass and energy, but finding that this equivalence seems to have virtually nothing to do with special relativity. Tony Rothman said to me that "I've long maintained that the conventional history of science, as presented in the media, textbooks and by the stories scientists tell themselves is basically a collection of fairy tales." I'd concur with that.

Who discovered that E=mc2? It’s not as easy a question as you might think. Scientists ranging from James Clerk Maxwell and Max von Laue to a string of now obscure early twentieth-century physicists have been proposed as the true discovers of the mass-energy equivalence now popularly credited to Einstein’s theory of special relativity. These claims have spawned headlines accusing Einstein of plagiarism, but many are spurious or barely supported. Yet two physicists have now shown that Einstein’s famous formula does have a complicated and somewhat ambiguous genesis – which has little to do with relativity.

One of the more plausible precursors to E=mc2 is attributed to Fritz Hasenörhl, a physics professor at the University of Vienna. In a 1904 paper, Hasenörhl clearly wrote down the equation E=3/8mc2. Where did he get it from, and why is the constant of proportionality wrong? Stephen Boughn of Haverford College in Pennsylvania and Tony Rothman of Princeton University examine this question in a preprint.

“I had run across Hasenöhrl's name a number of times with no real explanation as to what he did”, Rothman explains. “One of my old professors, E.C.G. Sudarshan, once remarked that he gave Hasenöhrl credit for mass-energy equivalence. So around Christmas time last year, I said to Steve, ‘why don't we spend a couple hours after lunch one day looking at Hasenöhrl's papers and see what he did wrong?’ Well, two hours turned into eight months, because the problem ended up being extremely difficult.”

Hasenöhrl’s name has a certain notoriety now, as he is commonly invoked by anti-Einstein cranks. His reputation as the man who really discovered E=mc2 owes much to the efforts of the anti-Semitic and pro-Nazi physics Nobel laureate Philipp Lenard, who sought to separate Einstein’s name from the theory of relativity so that it was not seen as a product of ‘Jewish science’.

Yet all this does Hasenörhl a disservice. He was Ludwig Boltzmann’s student and successor at Vienna, and was lauded by Erwin Schrödinger among others. “Hasenohrl was probably the leading Austrian physicist of his day”, says Rothman. He might have achieved much more if he had not been killed in the First World War.

The relationship of energy and mass was already widely discussed by the time Hasenörhl considered the matter. Henri Poincaré had stated that electromagnetic radiation had a momentum and thus effectively a mass according to E=mc2. German physicist Max Abraham argued that a moving electron interacts with its own field E0 to acquire an apparent mass given by E0=3/4mc2. All this was based on classical electrodynamics, assuming an ether theory. “Hasenöhrl, Poincaré, Abraham and others suggested that there must be an inertial mass associated with electromagnetic energy, even though they may have disagreed on the constant of proportionality”, says Boughn.

Robert Crease, a philosopher and historian of science at Stony Brook University in New York, agrees. “Historians often say that, had there been no Einstein, the community would have converged on special relativity shortly”, he says. “Events were pushing them kicking and screaming in that direction.” Boughn and Rothman’s work, he says, shows that Hasenöhrl was among those headed this way.

Hasenörhl approached the problem by asking whether a black body emitting radiation changes in mass when it is moving relative to the observer. He calculated that the motion adds a mass of 3/8c2 times the radiant energy. The following year he corrected this to 3/4c2.

However, no-one has properly studied Hasenörhl’s derivation to understand his reasoning or why the prefactor is wrong, say Bough and Rothman. That’s not easy, they admit. “The papers are by today’s standards presented in a cumbersome manner and are not free of error. The greatest hindrance is that they are written from an obsolete world view, which can only confuse the reader steeped in relativistic physics.” Even Enrico Fermi apparently did not bother to read Hasenörhl’s papers properly before concluding wrongly that the discrepant 3/4 prefactor was due to the electron self-energy identified by Abraham.

“What Hasenörhl really missed in his calculation was the idea that if the radiators in his cavity are emitting radiation, they must be losing mass, so his calculation wasn't consistent”, says Rothman. “Nevertheless, he got half of it right. If he had merely said that E is proportional to m, history would probably have been kinder to him.”

But if that’s the case, where does relativity come into it? Actually, it doesn’t. While Einstein’s celebrated 1905 paper ‘On the electrodynamics of moving bodies’ clearly laid down the foundations of relativity by abandoning the ether and making the speed of light invariant, his derivation of E=mc2 did not depend on those assumptions. You can get the right answer with classical physics, says Rothman, all in an ether theory without c being either constant or the limiting speed. “Although Einstein begins relativistically, he approximates away all the relativistic bits, and you are left with what is basically a classical calculation."

Physicist Clifford Will of Washington University in St Louis, a specialist on relativity, considers the preprint “very interesting”. Boughn and Rothman “are well regarded physicists”, he says, and as a result he “tend[s] to trust their analysis”. However, the controversies that have been previously aroused over the issue of priority perhaps accounts for some of the reluctance of historians of physics to comment when contacted by Physics World.

Did Einstein know of Hasenörhl’s work? “I can't prove it, but I am reasonably certain that Einstein must done, and just decided to do it better”, says Rothman. But failure to cite it was not inconsistent with the conventions of the time. In any event, Einstein asserted his priority for the mass-energy relationship when this was challenged by Johannes Stark (who credited it in 1907 to Max Planck). Both Hasenörhl and Einstein were at the famous first Solvay conference in 1911, along with most of the other illustrious physicists of the time. “One can only imagine the conversations”, say Boughn and Rothman.


JimmyGiro said...

One of the corollaries of the equation, was the splitting of gamma photons into electron-positron pairs, with the energy of the photon and the masses of the particles, and their kinetic energy, being accounted for by the equation. And it was presumed that the reverse process of electron positron mutual annihilation would yield a suitably energetic photon.

One of the many things that perplex me is: if the electron is held off from falling into the proton of a hydrogen atom, on the grounds of 'quantum forces', then why isn't the electron-positron collision also not 'held off' in similar manner?

Eleanor said...

Einstein attempted to prove E = mc2 on four separate equations throughout his life, beginning in 1906. Each time he failed - in his own eyes, not his critics.
Read the detailed history in "Albert Einstein's Special Theory of Relativity" - Arthur I. Miller pp. 334-359.

Incidentally, ask yourself how an electron loses some of its inertial mass when it interacts with another remote electron? (Hint: Maxwell's theory is statistical.)

Mark Teller said...

No, not by a long shot... see

ErkDemon said...

If you imagine a light-complex initially in equilibrium, trapped in a perfectly reflecting container, an attempt to change the motion of the container results in an increased resisting radiation pressure against the advancing wall, and a reduced pressure against the receding wall. So the enclosed light appears to an outsider to have increased the inertial mass of the container.

We can work out how much apparent mass results from a lightcomplex with energy E in the container's rest frame, by transforming the energy of the individual rays according to a Doppler equation and then working out the resulting momentum of the light-complex when it's moving.

Regardless of whether we do this calculation using the "relativistic Doppler" equations of special relativity, or the simpler (but also technically relativistic) equations of Newtonian optics, we get precisely the same result, that in the rest frame, the lightcomplex with energy E contributes E/c^2 of apparent mass to the container, giving us E=mc^2.

I think that when Einstein published his SR-based calculation he's likely to have realised that older theory gave precisely the same result ... but back in 1905 he may have been more interested in presenting E=mc^2 as an exciting prediction of his new theory, rather than as something more general that also agreed with older theory.