Carlos Graef Fernández’s heart was racing as he stood at the doorstep of Albert Einstein’s Princeton, New Jersey, home. The 33-year-old Mexican physicist had good reason to be nervous: He was about to defend the merits of a two-year-old theory of gravitation that fundamentally clashed with Einstein’s celebrated general theory of relativity.

Graef’s visit to 112 Mercer Street in December 1944 didn’t change Einstein’s mind. Nor has the theory Graef championed proved superior to general relativity. Yet the story of the two physicists’ spirited debate, chronicled in a 1956 interview of Graef, is significant in what it says about the rapid rise in prominence of Mexican science. As one of the country’s first professional physicists, Graef, along with colleagues such as Alberto Barajas and Manuel Sandoval Vallarta, helped transform a country with no graduate programs in physics or mathematics into a respected hub for physical science research.

General relativity in Mexico and the US

Graef and Einstein’s meeting was a result of two decades of increased scientific collaboration between the US and Mexico. In 1933, as part of his new Good Neighbor Policy, President Franklin Roosevelt invited a group of Latin American scientists to meet with their US peers. The timing was ideal for the Mexican science community, which had just begun a concerted effort to modernize and engage in cutting-edge research.

Carlos Graef Fernández. Credit: Archive of Sociedad Mexicana de Física

In February 1942 astronomer Luis Enrique Erro held a congress in Puebla, Mexico, to celebrate the opening of the National Astrophysical Observatory of Tonantzintla. At the urging of Sandoval, then a professor at MIT, an impressive group of American scientists attended, including astronomer Harlow Shapley and mathematician George David Birkhoff, both from Harvard. During the meeting, Birkhoff presented a new, still-unpublished gravitational theory.

In contrast with general relativity, which considers spacetime as a dynamic, curved structure, Birkhoff’s theory used Hermann Minkowski’s rigid, flat spacetime. Moreover, Birkhoff suggested that a strange matter filled the universe. His hypothesized perfect fluid, essentially an ether that obeyed Lorentz’s transformations, would exert forces on massive objects moving in space. Birkhoff showed that the three principal predictions of general relativity at the time—the precession of Mercury’s orbit, the deflection of light by the Sun, and the gravitational redshift of light—could also be explained with his novel proposal.

Graef and Barajas were among the Mexican scientists present at the Puebla congress. The two had become friends as undergraduate engineering students at the National Autonomous University of Mexico (UNAM). They then became among the country’s first graduate students in mathematics and physics. Graef got his PhD with Sandoval at MIT and then returned to Mexico in 1941 to become a tenured professor at UNAM’s science school. Meanwhile, Barajas stayed in Mexico, earning a master’s degree in mathematics in 1942.

Graef and Barajas were so impressed with Birkhoff’s ideas that they immediately began collaborating with him from afar to develop the theory. In subsequent months the three researchers demonstrated that by multiple measures Birkhoff’s theory was as predictive as Einstein’s, with the advantage that it was easier to work with. For example, whereas general relativity requires approximations or numerical analysis to solve the two-body problem, in Birkhoff’s theory Graef was able to find an analytical solution. Barajas and Graef showed that Birkhoff’s universe would expand and also obey the equivalence principle.

From left: Astronomer Donald H. Menzel, Albert Einstein, George Birkhoff, and Carl Shapley (Harlow Shapley’s son) pose for a photo at Harvard College Observatory in 1935. Credit: AIP Emilio Segrè Visual Archives, Shapley Collection

In November 1944, Barajas accepted a John Simon Guggenheim Foundation fellowship to pursue gravitational research with Birkhoff at Harvard. Twelve days after Barajas’s arrival, Birkhoff died at the age of 60. Though devastated by the passing of their dear friend and mentor, Barajas and Graef decided to pick up the torch and further develop Birkhoff’s gravitational theory.

A few weeks later, Graef arrived at Princeton University to begin work as a visiting professor in the mathematics department. He abruptly received an unexpected invitation to visit Einstein at his home. Graef was excited and terrified. Only days before, Erro had reported astronomical observations that matched the predictions of Birkhoff’s theory. Graef felt sorry that his friend had died before knowing about the finding, which Erro would later present at a meeting of the American Astronomical Society. Now Graef would have to stand in Birkhoff’s place to defend the theory to Einstein.

So came the big day. Graef later recounted the conversation in a 1956 interview with reporter Samuel Kaplan for American Scientist. Although Einstein unfortunately did not offer his own version of events, Graef’s recollections give us an engaging account of his visit to Mercer Street. For Graef, this was the great battle, one that could get on Birkhoff’s team the greatest possible ally.

After exchanging their greetings, the battle began.

“A born rebel”

One might think that the duel between the two men would include some dramatic episodes, perhaps some furious equation-writing on a blackboard. However, both men knew the successful results of Birkhoff’s and Einstein’s theories—the mathematics involved were clear. Einstein was more focused on discussing the ontology of Birkhoff’s theory than its quantitative details.

The first bulletin of the Mexican Mathematical Society, published in 1944, includes George Birkhoff’s 1942 lecture on his theory of gravitation along with subsequent research by Carlos Graef Fernández and Alberto Barajas.

Einstein, according to Graef in the American Scientist interview, started the proceedings: “I think the principal difference between Birkhoff’s point of view and mine lies in what we consider to be the scientific explanation of a physical system. Now what is your opinion in this matter, Graef?” Graef, in his recollection, calmly returned the thrust: “I think a person who has a set of formulae which enables him to predict accurately the future of the solar system has completely explained that system.”

That answer did not satisfy Einstein. They soon moved on to the ontology of the two theories. They reached a critical point when Einstein harshly criticized Birkhoff’s idea of employing a perfect fluid, branding it a step back in the progress of physics.

Graef told interviewer Kaplan that he had felt compelled to expose Einstein as guilty of the same crime. After all, the great physicist had earned the Nobel Prize in Physics for demonstrating light’s behavior as a particle, an idea that had been seemingly overturned decades before through the discovery of the wave nature of light. “The step backward which you made has in reality been a great step forward in physics,” Graef told Einstein.

Graef may have thought he had won the exchange, but Einstein was not easy to intimidate. The photon “is not like a pebble which you can throw out of the window,” Einstein replied. “There is a big difference between my photons and Newton’s particles.”

Graef responded: “Professor Einstein, Birkhoff’s fluid, though a liquid, cannot be drunk like a Coca-Cola. There is an enormous difference between Birkhoff’s perfect fluid and actual liquid.” Of course, the difference between photons and Isaac Newton’s corpuscular light was as obvious to Graef as the difference between the perfect fluid and a sugary beverage was to Einstein. They knew that the discussion was coming to an end, with no winner and no conciliation.

Before leaving, Einstein patted Graef’s shoulder and told him he was “a born rebel.” It’s possible that Einstein saw a little bit of himself in the young Mexican physicist. In 1901 a young Einstein had written, “Unthinking respect for authority is the greatest enemy of truth.” More than four decades later, Einstein was well aware that he had become the authority.

Graef’s legacy

Of course, Birkhoff’s theory has not superseded Einstein’s. Though Graef continued pursuing the alternative gravitational theory through at least 1968, it never gained traction in the physics community, and experiment after experiment has produced results consistent with general relativity.

Among Mexico’s modern physics infrastructure is the High-Altitude Water Cherenkov Observatory in the Parque Nacional Pico de Orizaba in Veracruz. Credit: J. Goodman/HAWC

After their stints in the US, Graef and Barajas returned to Mexico and spent the remainder of their careers at UNAM. Graef led UNAM’s science school, helped found the Mexican Mathematical Society, and was an original member of the Mexican Physical Society. He was also active in nuclear policy, serving as Mexico’s governor to the International Atomic Energy Agency. Barajas was a founding member of the Mexican Mathematical Society, the Mexican Physical Society, and the American Mathematical Society, and he served in several leadership positions.

Graef and Barajas supervised many students, participated in seminars, and oversaw the construction of research buildings and experimental laboratories. Over the next few decades, Mexican researchers published work not only on Birkhoff’s theory but also on cosmic rays and nuclear physics, and eventually on solid physics and atomic energy. (See the article by Sandoval, Physics Today, March 1949, page 26.) Today Mexican science has a solid infrastructure, with representation in almost every field within physics and mathematics.

Gustavo Arciniega is a theoretical physicist at the Facultad de Estudios Superiores–Aragón, in Mexico. The inspiration for the article was two auditoriums named after Barajas and Graef at the National Autonomous University of Mexico, where the author studied.