The History Of Einstein’s Most Famous Equation

In History by Brian Koberlein

Albert Einstein is easily one of the most brilliant physicists who ever lived. His theories of general relativity changed our understanding of the cosmos, as did his work on quantum theory. But his genius has also led many to hold him up as a poor stereotype of science. The lone genius who ignores the science of his day to overturn everything with a simple brilliant theory. He’s become the icon of every crackpot who feels compelled to send emails to scientists about their idea that will revolutionize science if we only take the time to listen (and work out all the math for them). But as revolutionary as Einstein’s ideas were, they weren’t entirely unexpected. Other scientists had similar ideas, and developed similar equations. Take, for example, Einstein’s most famous equation, E = mc2

The equation appears in Einstein’s 1905 paper “Does the Inertia of a Body Depend Upon Its Energy Content?“, and it expresses a fundamental connection between matter and energy. Energy was long known to be a property of matter in terms of its kinetic motion, heat and interactions, but Einstein’s equation proposed that matter, simply by having mass, has an inherent amount of energy. It allowed us to understand how radioactive particles decay and how stars create energy through nuclear fusion. But the idea had been proposed by others before.

Like Einstein, J. J. Thompson wondered about the connection between light and matter. He thought that electromagnetism was more fundamental than Newton’s laws of motion, and tried to figure out how mass could be created by electric charge. In 1881 he showed that a moving sphere of charge would create a magnetic field, and this caused a kind of drag on its motion. This acts as an effective mass of the charge. Thompson found that the electromagnetic mass of the electron is given by m = (4/3) E/c2, which is surprisingly close to Einstein’s equation. Thompson’s derivation was rather cumbersome, but other researchers found the same result with more elegant derivations.

Thompson’s model was not without it’s problems. For one, it only applied to objects that have charge, and only when they are moving. Another problem came from Thompson’s assumption of a uniform sphere of charge. If an electron were an extended sphere of charge, some kind of force or pressure must keep the electron from flying apart. This pressure would obviously have some energy. This led Henri Poincaré to propose non-electromagnetic stresses to hold the electron together. When he calculated the energy of these stresses, he found it amounted to a fourth of an electron’s total mass. Thus, the “actual” mass of the electron due to its electric charge alone must be  m = E/c2. Poincaré’s paper deriving this result was published in June of 1905, just a few months before Einstein’s paper.

Although the equation is often attributed to Einstein’s 1905 paper, Einstein didn’t actually derive the equation from his theory of relativity. The paper is only two pages long, and only shows how the equation can arise from approximations to relativity. It’s more of a proof of concept than a formal derivation. It took other scholars to definitively prove that the equivalence between mass and energy is a consequence of special relativity.

None of this detracts from Einstein’s brilliance, but it does demonstrate that even radical ideas in science rarely come from a single individual. The ideas of Thompson,Poincaré, and others were on the right track, as were the ideas of Einstein. Over the decades the scientific evidence we’ve gathered has further confirmed Einstein’s theory as the best representation of reality. And in the end it’s the best models that win, regardless of who first thought of them.