When Did Einstein First Write E = mc² in His Own Hand?

The version we recognize today — written as E = mc², with those specific symbols — did not enter Einstein's handwriting until 1912. Working on lecture notes for special relativity that year, Einstein replaced the L from 1905 with E, though he still wrote q for what we would now call v. The formula looked unfamiliar by today's standards, but the physics was the same.

On that manuscript page, in a note written directly beside the formula, Einstein summarized its physical meaning: the expression grows to infinity as the speed q approaches c — therefore it would require an infinite expenditure of energy to bring a body to the speed of light. The manuscript is now published as Document 1 in Volume 4 of the Collected Papers of Albert Einstein.

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Whether E = mc² was uniquely Einstein's discovery is a question historians have debated at length. Physicist Tony Rothman, writing in Scientific American, argued that Einstein was neither the first to connect mass with energy nor the person who definitively proved the relationship. This is not an unfair reduction — it confirms a real part of the history.

In 1881, J. J. Thomson calculated that the magnetic field of a moving charged sphere induced an effective mass into the sphere itself. In 1889, Oliver Heaviside simplified this result to m = (4/3) E/c². In 1900, Henri Poincaré showed that for momentum to be conserved in an electromagnetic field, the field had to behave like a fictitious fluid with a mass equivalent of E/c² — but he did not connect this to the mass of any real body. In 1904, Austrian physicist Fritz Hasenöhrl ran a thought experiment involving a cavity filled with heat radiation and arrived at a similar conclusion, though with a fundamental error he later partially corrected.

What made Einstein's 1905 contribution different? According to Rothman, Einstein was the first to equate the mass of an object not just with its electromagnetic field or its motion, but with its total energy content — a conceptually much broader claim. What remained missing was the mathematical proof: Einstein himself acknowledged within a few years that he had fallen back on classical approximations rather than fully applying his own relativistic equations.

Written on Princeton University letterhead, dated October 26, 1946. The recipient was Ludwik Silberstein, a Polish-American physicist who had spent years challenging and questioning Einstein's theories. The letter's opening is brisk: "Your question can be answered from the E = mc² formula, without any erudition."

Einstein then worked through a system of two equal masses, using the Virial theorem to calculate the energy deficit. He wrote the formula directly — in its now-standard form. The letter remained in Silberstein's personal archives until his descendants sold the collection. At the 2021 auction, five parties entered the bidding; once the price passed $700,000 it narrowed to two, closing at $1.2 million — roughly three times the pre-sale estimate.

E = mc² is not questioned today — decades of experiments have confirmed it. But among physicists there is a persistent, quiet disagreement about what the formula actually means. Some — following the view that Lev Okun argued until his death — hold that the correct equation is E₀ = mc², where E₀ denotes the energy of a body at rest. For a moving body, the full expression is E = mc²/√(1 − v²/c²). The E = mc² of popular culture is, in this reading, a special case valid only for rest energy.

This distinction is ignored in a large share of physics textbooks. Advanced treatments like Landau and Lifshitz's Classical Theory of Fields avoid the formula entirely, while most popular books present it as a universal identity. Einstein himself was inconsistent on the matter; in a 1948 letter to Lincoln Barnett he wrote plainly that the concept of a "moving mass" admits no clear definition, and that it is better to use no mass concept other than rest mass.

The history of an equation covers not just who first wrote it, but what form it has lived in. The paper trail of E = mc² shows how science actually moves — incrementally, with error margins, on the shoulders of several people converging on the same result from different directions. Einstein took a critical step in that sequence. He did not write the sequence alone.