The Wobbling Plate Behind a Nobel Prize, and Why Feynman Got It Backward

Sometime around 1947, in a cafeteria at Cornell University, someone fooling around tossed a dinner plate into the air. It went up spinning and wobbling, the way a badly thrown Frisbee does, and somebody in the room was paying closer attention than anyone could have guessed. The plate had the university’s red medallion printed on the rim, and as it flew, a young physics professor named Richard Feynman, not yet 30, watched the medallion go around and the plate’s tilt rock back and forth. He wondered how the two motions were related.

Nearly forty years later, in his best-selling memoir Surely You’re Joking, Mr. Feynman!, he claimed that the doodling that followed led straight to the work that won him the 1965 Nobel Prize in Physics. “The diagrams and the whole business that I got the Nobel Prize for,” he wrote, “came from that piddling around with the wobbling plate.”

It is one of the most beloved stories in science, and it has two twists. The first is that Feynman got the physics backward. The second is that the man who caught the mistake was an expert on a much bigger wobbling object, one we are all standing on.

A physicist who had stopped having fun

Feynman arrived at Cornell in the autumn of 1945, straight from Los Alamos, where he had worked on the atomic bomb under Hans Bethe. The war years had been brutal for him personally. His first wife, Arline, died of tuberculosis in June 1945, weeks before the Trinity test, and his father died suddenly in October 1946. At Cornell he taught well but could not make himself do research. He felt, as he later put it, burned out.

Universities kept sending him job offers anyway, including the Institute for Advanced Study in Princeton, and each one made him feel worse, because he was sure he would never live up to them. His way out was to give himself permission not to care. Physics had once been fun, he reasoned, back when he played with it simply because it was interesting. So he would play again. “Just like I read the Arabian Nights for pleasure,” he wrote, “I’m going to play with physics, whenever I want to, without worrying about any importance whatsoever.”

Within a week, he said, the plate went up in the cafeteria.

“There’s no importance whatsoever”

What caught Feynman’s eye was the relationship between the spin and the wobble. A thrown plate does two things at once. It spins around its own center, which you can track by following a mark on the rim, and its tilted face rocks around in a circle, which is the wobble. To Feynman, “it was pretty obvious” that the medallion went around faster than the wobbling.

With nothing better to do, he worked it out. For a small tilt, his equations told him there was a neat ratio between the two motions: two to one. Not satisfied with a formula, he went back and worked out how the forces on every bit of the plate balanced to produce that ratio. “It was effortless,” he remembered. “It was like uncorking a bottle.”

He took the result to Bethe, by then a colleague down the hall. Bethe was not impressed. “Feynman, that’s pretty interesting, but what’s the importance of it? Why are you doing it?” Feynman’s answer is the line people quote: “Hah! There’s no importance whatsoever. I’m just doing it for the fun of it.”

But play has a way of wandering. From wobbling plates, Feynman wrote, he went on to “work out equations of wobbles,” then to how electron orbits move in relativity, then to the Dirac equation, the relativistic description of the electron, and from there to quantum electrodynamics, the theory of how light and matter interact. Spinning objects have a long record of catching physicists’ attention in exactly this way. Niels Bohr and Wolfgang Pauli were famously photographed crouched over a tippe top that flips itself over, and a coin spun on a table, Euler’s Disk, still puzzles people today.

From a cafeteria plate to the electron

Quantum electrodynamics, or QED, was in trouble in the late 1940s. Its equations worked to a first approximation, but any attempt to calculate more precisely produced answers that blew up to infinity. In June 1947, at a small conference at the Ram’s Head Inn on Shelter Island, off the tip of Long Island, experimenters made the problem impossible to ignore. Willis Lamb reported a tiny shift between two energy levels of hydrogen that the existing theory said should not exist.

Bethe worked out a rough explanation of the Lamb shift within days, by cutting off the troublesome infinities in a sensible way. A proper relativistic version still needed doing. Feynman attacked it with the tools he had been building for himself: a new way of adding up every possible path a particle could take, and a shorthand of little line drawings to keep track of the terms. When he presented the approach at the Pocono Conference in 1948 it fell flat. Paul Dirac, Edward Teller and Niels Bohr all raised objections, and the audience found his doodles baffling.

It was the young English mathematician Freeman Dyson who showed, in 1949, that Feynman’s pictures, Julian Schwinger’s formidable equations and the independent work of Sin-Itiro Tomonaga in Japan were the same theory in different clothes. Within a few years almost every particle physicist was drawing Feynman diagrams. In 1965 Feynman, Schwinger and Tomonaga shared the Nobel Prize in Physics “for their fundamental work in quantum electrodynamics.”

How much of that really came from the plate is impossible to measure. Feynman’s biographers tend to read the story less as a literal chain of equations than as a turning point in mood: the moment he started enjoying physics again. Either way, he told it as the seed of his Nobel work, and the plate became part of his legend.

The twist: Feynman got it backward

Feynman died in February 1988. A year later, in February 1989, the magazine Physics Today printed a short letter from Benjamin Fong Chao, a geophysicist at NASA’s Goddard Space Flight Center. He loved the book, he wrote, and the plate story was great, “except for one little twist: A torque-free plate wobbles twice as fast as it spins when the wobble angle is slight. The ratio of spin to wobble rates is 1:2, not 2:1!”

Chao’s argument takes a few lines of the rigid-body equations Leonhard Euler wrote down in the 18th century. A spinning object with no forces twisting it keeps its angular momentum fixed in space, the same principle that lets a gyrocompass hold its direction. If the spin axis is slightly tilted away from that fixed direction, it circles around it. How fast it circles depends on the object’s shape, captured in a single number: how much harder it is to turn the object around its symmetry axis than around a line across it.

For a thin flat disc, that ratio is exactly two. Plug it in and the wobble seen from the room comes out at exactly twice the spin rate. Watch a plate long enough and its tilt rocks through two full cycles every time the medallion makes one lap. You can check this yourself with a slow-motion video of a thrown paper plate or a flying disc. A physics student did exactly that with a high-speed camera:

Chao signed off with a joke worthy of his subject. Whether the error was a slip of memory or, in the spirit of the book, “another practical joke meant for those who do physics without experimenting, we do not know and perhaps never will.” He added one more observation: the story appears on page 157 of the book, and the text is 314 pages long. Exactly half-way, or, if you like, two to one.

Some mathematicians have since argued that Feynman was not completely wrong, only careless about what he was counting. Measured from a frame that turns with the plate, the spin runs backward against the wobble, and the bookkeeping changes depending on how you define “the rotation of the medallion.” But the plain observation stands: watch the plate, and it wobbles twice for each turn.

The same equation, the size of a planet

Here is the part that makes Chao’s letter more than a correction. The formula he used for the plate also describes the Earth. Our planet is a spinning body that is slightly flattened: its radius at the equator is about 21 kilometers (13 miles) longer than at the poles. For Earth, the shape number is barely more than one, and the result is that the wobble, as seen by someone standing on the ground, is very slow: about one cycle every 305 days.

Euler worked this out in 1765. If the Earth’s spin axis was even slightly out of line with its axis of symmetry, he showed, the North Pole would trace a small circle on the ground about every ten months, and every observatory on the planet would see its latitude drift up and down by a tiny amount. Astronomers spent the next century looking for a ten-month wobble. They didn’t find one.

Chao knew all this well. According to the mathematician Semjon Adlaj, he had studied the Earth’s wobble before he ever read Feynman’s account, so he knew the right answer before he reached page 157. The plate and the planet are the same problem.

Chasing a wobble around the world

The Earth does wobble. It just doesn’t keep Euler’s schedule. In the late 1880s the German astronomer Friedrich Küstner noticed that his careful latitude measurements in Berlin were drifting. Then, in 1891, Seth Carlo Chandler Jr., a Boston actuary who did astronomy on the side with the Harvard College Observatory, did what nobody else had thought to do. Instead of hunting for a ten-month signal, he went through years of old latitude records without assuming any period at all. He found a wobble with a period of about 14 months, and soon afterward a second, yearly one tied to the seasons.

The 14-month motion is now called the Chandler wobble. Its period is about 433 days, and the point where the spin axis meets the surface wanders in a loop roughly 9 meters (30 feet) across. Simon Newcomb soon explained why it was slower than Euler predicted. Euler had treated the Earth as perfectly rigid, but the real planet gives a little, its rock and oceans bending as the axis shifts, and that slackness stretches the period from ten months to fourteen.

To keep watch on it, the International Geodetic Association did something remarkable for 1899. It built a chain of small observatories all on the same line of latitude, 39 degrees 8 minutes north, so that each station could measure the same stars in the same way: Mizusawa in Japan, Tschardjui in Russian Turkestan, Carloforte on the Italian island of San Pietro off Sardinia, Gaithersburg in Maryland, Cincinnati in Ohio and Ukiah in California. Each night observers swung zenith telescopes to the same pairs of stars and noted, to a fraction of an arcsecond, how far overhead they passed.

The buildings were modest. The one in Gaithersburg, according to the National Park Service, was a single room 13 feet square, with a gabled roof that rolled open on pulleys and wheels. Stations came and went with wars and budgets, but Mizusawa and Ukiah observed straight through, and the Gaithersburg site ran until 1982. Their notebooks gave the 20th century its record of a wandering pole. Today the International Earth Rotation and Reference Systems Service tracks it with radio telescopes, satellites and GPS, to within millimeters. The same kind of patient measurement had shown, decades earlier, that the planet spins at all. Visitors still line up to watch Foucault’s pendulum prove it.

What keeps the Earth wobbling

Getting the wobble’s period right raised a harder question. Because the Earth is not rigid, the Chandler wobble should die away. Its energy leaks into flexing rock and sloshing water, and on its own it would fade in a matter of decades. Estimates put its decay time at about 68 years. Yet it has kept going for well over a century. Something keeps giving the planet a nudge.

For a long time nobody knew what. Earthquakes, the atmosphere, groundwater and the molten core were all proposed and none fitted on their own. In 2000, Gross, working at NASA’s Jet Propulsion Laboratory, ran ocean and atmosphere models against the measured wobble for 1985 to 1996 and found an answer. About two-thirds of the push came from changing pressure on the floor of the ocean, as currents shifted with temperature, saltiness and wind. The remaining third came from swings in air pressure. The planet is a slightly lopsided plate, kept wobbling by its own weather.

The wobble even makes a tide of its own. As the pole moves, the oceans shift slightly in response, raising a “pole tide” only about 6 millimeters (a quarter of an inch) high. It is the only tide not raised by the Moon or Sun, and it is small but measurable. The Chandler wobble’s size has also changed over the years. Since about 2015 it has shrunk markedly, and researchers are still working out why.

Earth is no longer the only example. In 2020 researchers using 18 years of radio tracking from three Mars orbiters reported a Chandler wobble on Mars: a loop about 10 centimeters across, repeating every 207 days. For something truly unstable in rotation, look at the wing nut that flipped end over end aboard a Soviet space station, the subject of the Dzhanibekov effect. It obeys the same equations of Euler, in a far more dramatic regime.

Playing with physics

Feynman left Cornell for Caltech in 1950 and spent the rest of his career there. He kept playing, with bongo drums, safecracking and Mayan codices, and he never lost his delight in odd little problems. He even had Feynman diagrams painted on the side of his van.

The wobbling plate story survives because it is about permission as much as physics. A burned-out young professor decided to do something with no importance whatsoever, and he credited what followed with leading to a Nobel Prize. He also got the answer backward. Fittingly, the person who fixed it spent his career studying a much larger spinning body, and knew that the plate and the planet follow the same rule.

So the next time a paper plate goes sailing across a picnic, watch the rim. It is doing what the Earth does, only faster: wobbling twice for every turn.

Further reading