## Even after Einstein’s death, physicists intensely debated whether they were real or not. Here’s how Feynman settled it.

“If you haven’t found something strange during the day, it hasn’t been much of a day.” –John Archibald Wheeler

Confronted with a theoretical question, such as whether or not gravitational waves exist, Richard Feynman never trusted authorities. Rather, he tried to develop and convince himself of a solution in the simplest way possible, constructing an argument from first principles. Once he managed to build a case for a particular point of view in his own mind, he felt equipped to persuade others. At the first American conference on general relativity, GR1, held in Chapel Hill in January 1957, Feynman offered a brilliant argument that gravitational waves must carry energy. The argument anticipated by almost sixty years the Laser Interferometer Gravitational-Wave Observatory (LIGO) discovery, announced in February 2016, that confirmed the reality of gravitational waves.

LIGO Scientific Collaboration, IPAC Communications & Education Team: The waves theoretically emitted from two merging, inspiraling masses.

How in the world did Feynman end up at a general relativity conference? Wasn’t he immersed in quantum electrodynamics (QED) and the world of particle physics? True, those were his major areas, recognized by his Nobel Prize and other accolades, but as with many other brilliant thinkers he had broad interests.

To understand why Feynman was invited, we look to the key organizers of the conference: French-American mathematical physicist Cécile DeWitt-Morette and her husband American field theorist Bryce DeWitt, who each had enormous respect for Feynman’s independence of thinking. We also consider the role of a major force behind the scenes, Princeton physicist John Archibald Wheeler, who invited many of the conference speakers.

DeWitt-Morette’s connection with Feynman dated back to the late 1940s, when she visited him (along with Freeman Dyson) at Cornell, discussed his path integral approach to quantum mechanics, and took steps to render it mathematically more rigorous. Her husband Bryce had been a student of Julian Schwinger, a co-developer of QED along with Feynman, and sought to construct “quantum gravidynamics:” a quantum theory of gravity. The quest proved far trickier than he thought.

Finally, Wheeler was Feynman’s PhD advisor at Princeton. While he wasn’t one of the main organizers of the conference, he was highly respected and had a thriving gravitational research group. Consequently, he was given carte blanche to bring as many students and former students to the conference as he wished. Those he brought along included Joseph Weber, who had a strong interest in gravitational waves, and Charles Misner, who, like Bryce DeWitt, was trying to recast general relativity to make it friendlier to the quantum nature of the Universe. Wheeler also invited Feynman, as he valued Feynman’s input as an outsider to the field. He hoped that Feynman’s uncanny insights and expert knowledge of QED would enable him to offer bold suggestions as to how to bring electromagnetic and gravitational theories under the same quantum umbrella.

When Feynman arrived at Raleigh-Durham Airport, the closest to Chapel Hill, he wasn’t sure which of the regional universities with “North Carolina” in the title was hosting the conference. Was it North Carolina State or the University of North Carolina? Luckily, when booking a taxi, he thought of a plan. He asked the dispatcher if he noticed anyone immersed in thought and muttering expressions such as “g mu nu” (a term from general relativity). The dispatcher did indeed, remembered which campus they were going to, and had Feynman driven to the same place.

The topic of gravitational waves, a key focus of the conference, dates back to Albert Einstein’s calculations in 1916, where it was part of one of his earliest papers on general relativity. Einstein and his assistant Nathan Rosen revisited the subject in a 1936 paper “Do Gravitational Waves Exist?” where they examined a type of solution that possessed cylindrical symmetry, like a tin can. Initially, they calculated that the waves were artifacts of the mathematical framework and didn’t really physically exist — akin to the zero mark on a meter stick having no tangible meaning, as shifting it just makes another point zero. However, when they submitted their paper to Physical Review it was rejected on the basis of an anonymous referee report — by Princeton physicist and mathematician Howard Percy Robertson (the “R” in FLRW), as we now know — that pointed to an error. Upset by the rejection, Einstein decided to resubmit to the Journal of the Franklin Institute instead. Without letting on that he was the reviewer, Robertson managed to convey to Einstein a way of rectifying the mistake — which pointed to physically real cylindrical gravitational waves after all. Einstein corrected the submission. Thus the final version of the paper predicted genuine gravitational radiation moving through space, similar to electromagnetic radiation.

Nonetheless, Rosen remained dubious. He developed an argument against gravitational waves carrying energy, on the basis of a calculation using what is called the “energy pseudotensor:” a controversial way of mapping out the gravitational energy of a local region of space. The method is controversial because a mere change of coordinate system alters its prediction. Rosen applied it to cylindrical waves moving through empty space and showed that their energy was zero at every point. Only places with actual mass or energy seemed to have gravitational energy. Everywhere else, such as the interstellar void, gravitational energy vanished; hence there could be no true gravitational radiation moving through it. After Einstein died in 1955, Rosen continued to argue against the physical validity of gravitational waves.

While Rosen did not attend the Chapel Hill conference, a paper of his was read, and his ideas about gravitational waves discussed. Wheeler, Weber, British physicist Felix Pirani, Anglo-Austrian mathematician Hermann Bondi, and others wrestled with the question of the reality of gravitational radiation and how to measure the energy it conveyed. As one of the major themes of the conference was developing a quantum theory of gravity, many saw the correct description of gravitational waves as critical to that pursuit. After all, if photons are the quantized form of electromagnetic radiation, gravitons (to use modern parlance) would be the quantized version of the gravitational equivalent, which should be equally well understood classically before quantum rules are attempted.

Enter Richard Feynman, who had distaste for unnecessary abstraction. If gravitational radiation is real, it must convey energy. Rather than debating the technical question of whether or not the pseudotensor definition of gravitational energy was correct, he turned instead to a far more intuitive line of reasoning, what has come to be known as the “sticky bead argument.”

The argument by Feynman is that gravitational waves would move masses, just as electromagnetic waves moved charges along an antenna. This would form the basis of the design of LIGO.

In his thought experiment, Feynman imagined a thin stick on which one mass is fixed and a second mass, slightly separated from the first, is free to slide back and forth, like a curtain on a rod. These two masses would be analogous to a pair of charges embedded in a vertical receiving antenna used to pick up radio signals. Just as a pulse of electromagnetic radiation would cause such charges to oscillate, the same would happen in the “gravitational antenna” if a gravitational wave passed through — with the maximum effect occurring if the wave were transverse: at right angles to the stick. Upon the impact of a gravitational wave, one of the masses would accelerate relative to the other, sliding back and forth along the stick. The rubbing movement would generate friction between the free mass and the stick, releasing heat in the process. Therefore the gravitational radiation must convey energy. Otherwise, how else did the energy arise?

Inspired, in part, by the conference, Weber built a gravitational antenna (called a “Weber Bar”) at the University of Maryland. Although, starting in the late 1960s, he claimed to have found increasing evidence for gravitational waves, the bulk of the physics community doubted that his apparatus was sensitive enough, and questioned his results, unable to reproduce them. The sensitivity of Weber Bars — both in terms of wave magnitude and frequency — seemed unlikely to yield fruitful results. But the LIGO project, situated in twin labs in Hanford, Washington and Livingston, Louisiana, respectively, used interferometry, special mirrors and masses, and a much larger apparatus to boost significantly the sensitivity and reliability of the experiment.

Feynman died in 1988, after the initial conception of LIGO but well before it first identified gravitational waves. Undoubtedly, he would have been gratified to have learned that his careful thought experiment paved the way for an incredible discovery of the energy-carrying waves that he reasoned must exist.

Edited by Ethan Siegel. Originally published in Starts with a Bang!