MARGINALIA
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.
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!"
» Post Comment