Did Einstein discover E = mc2?

Aug 23, 2011

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 20th-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 Hasenöhrl, a physics professor at the University of Vienna. In a 1904 paper Hasenöhrl 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 paper submitted to the arXiv preprint server.

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 antisemitic 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”.

‘Leading Austrian physicist of his day’

Yet all this does Hasenöhrl a disservice. He was Ludwig Boltzmann’s student and successor at Vienna, and was lauded by Erwin Schrödinger among others. “Hasenöhrl was probably the leading Austrian physicist of his day”, Rothman told physicsworld.com. 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 being widely discussed by the time Hasenöhrl 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 = 3/4 mc2. 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.

Photo of Fritz Hasenöhrl
Photo of Fritz Hasenöhrl published in 1933. (Courtesy: AIP Emilio Segrè Visual Archives, Brittle Books Collection, Physics Today Collection)Photo of Fritz Hasenöhrl published in 1933. (Courtesy: AIP Emilio Segrè Visual Archives, Brittle Books Collection, Physics Today Collection) Fritz Hasenöhrl

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.

Hasenöhrl 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.

A different style of scientific paper

However, no-one has properly studied Hasenöhrl’s derivation to understand his reasoning or why the prefactor is wrong, claim 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 Hasenöhrl’s papers properly before concluding wrongly that the discrepant 3/4 prefactor was due to the electron self-energy identified by Abraham.

“What Hasenöhrl 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, perhaps 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.”

A controversial issue

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 account for some of the reluctance of historians of physics to comment when contacted by physicsworld.com.

Did Einstein know of Hasenöhrl’s work? “I can’t prove it, but I am reasonably certain that Einstein must have 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 Hasenöhrl 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.

Rothman told physicsworld.com that he had run across Hasenöhrl’s name a number of times but with no real explanation as to what he did. “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.”

About the author

Philip Ball is a science writer based in the UK