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Storied Theory

Science and stories are not only compatible, they're inseparable, as shown by Einstein's classic 1905 paper on the photoelectric effect

Roald Hoffmann

How Einstein Tells It

The photoelectric paper is modestly entitled, "On a Heuristic Point of View Concerning the Production and Transformation of Light." Einstein begins by stating the problem posed by the quantum hypothesis: He defines the resonators as bound electrons and takes us, with characteristic clarity, made possible by five years of experience with quanta, through Planck's derivation. He develops the characters in his tale—the radiation, Planck, his resonators, classical electromagnetic theory.

In this critical section of Einstein's 1905 paper...Click to Enlarge Image

Then Einstein does something new. He sets out to derive Planck's radiation law without any assumptions about how light is generated. How does he do that? By assigning an entropy (the measure of randomness, a concept already in wide use by then) to the light and relating that entropy to the density of the radiation. Einstein proves that the entropy of the light in the black body varies with volume just the way that entropy varies with volume for that standby of freshman chemistry, the ideal gas.

This demonstration is direct. It's not Hemingway, but for scientific prose, really exciting. Einstein is taking us somewhere—we don't know where yet, but by the way he sets the scene, by his pace and conviction, we know something is going to happen.

Pretty incredible. No resonators, just a functional analogy of atoms or molecules to light. Playing out the analogy, light of a given wavelength could be described as if its energy came in dollops of  what Einstein called Rβv/N, and today we would call hv, a constant (h) times the light's frequency (v). But that's just a way of looking at things—it's not for nothing that Einstein put the word heuristic in the title. Or is it? When do stories become real?

Back to the paper: Einstein has just rederived Planck's radiation law without resonators. Yet the discreteness of the light's energy, its quantization, is newly manifest in Einstein's work. There is no mistaking it. From this climax the paper cruises along another plateau, then swoops into a breathtaking shift of scene. Philipp Lenard had three years earlier observed "cathode rays," or beams of electrons, by shining light onto a metal. The phenomenon happened only when the frequency of that light exceeded a certain minimum; below that frequency (or above that wavelength)—nothing. After seeing the electrons, Lenard observed that their kinetic energy depended on the color of the light, their number on the intensity of the light.

This phenomenon we now call the photoelectric effect. Aside from being today a primary source of information on molecules and surfaces, the effect is behind photoelectric cells opening elevator doors, and is used in solar cells and light-sensitive diodes.

Back to 1905. Einstein just says: Let's assume light is quantized in units of hv, and that a "light quantum" (we would call it a photon today) gives up all its energy to a single electron. The electron needs a certain energy to leave the surface; if it has some left over, the extra contributes to its motion. Einstein calculates, in a couple of terse sentences, the energies involved and finds reasonable agreement with Lenard's measurements. With this and another calculation on the ionization of gases, he brings us down to experimental reality.

Except reality is not down, it is evidence. Evidence that this story of light being quantized is not just any story. This one is worth telling to our great-grandchildren.

Einstein's theory leaves us soaring, thinking what else this strange, discontinuous view of light might explain. Soon Bohr will use it to give us the first theory of an atom. This story is as exciting as Thomas Mann's 1902 Buddenbrooks, which Einstein might have been reading at the time.

The photoelectric paper was submitted to Annalen der Physik (Annals of Physics) in March 1905. But Planck's quantum theory, and the nature of light, had been on Einstein's mind for quite a while. On April 30, 1901 he wrote to his future wife, Mileva Maric, "I came recently on the idea that when light is generated, perhaps there occurs a direct conversion of kinetic energy to light. Because of the parallelism: motional energy of the molecules—absolute temperature—spectrum (energy of radiation in equilibrium). Who knows when a tunnel will be dug through these hard mountains!"

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