Hans Bethe

Strasbourg, Frankfurt, and a boy who counted in his head

Hans Albrecht Bethe was born on 2 July 1906 in Strasbourg, then part of the German Empire, in a household where physics and mathematics were the family business. His father Albrecht was a physiologist who would later hold a chair at Frankfurt. His mother Anna, the daughter of a professor of medicine, was Jewish, a detail of no apparent consequence in 1906 and of life-altering consequence twenty-seven years later. Friends of the family remembered Hans as a quiet child who taught himself to read at four and who at six was already filling notebooks with arithmetic done for sport, the way other children doodled. By the time he reached the gymnasium in Frankfurt his teachers had stopped giving him problems and started giving him books.

In 1924 he entered the University of Frankfurt to read physics, and two years later moved south to Munich to study under Arnold Sommerfeld, the same Sommerfeld whose seminar had already turned out Heisenberg, Pauli, and Debye. Sommerfeld assigned the new student a problem on electron diffraction in crystals; Bethe disposed of it inside a year and produced, in 1928, a doctoral thesis that is still cited in solid-state physics today. He was 22.

The Handbuch article that taught a generation

Between 1928 and 1933 Bethe wandered the European theoretical landscape on fellowships: Frankfurt, Stuttgart, Cambridge with Ralph Fowler, Rome with Enrico Fermi. The Rome year mattered. Fermi was the opposite of Sommerfeld in temperament, more interested in getting the right answer fast than in proving it elegantly, and Bethe absorbed the style. He always said afterward that Sommerfeld had taught him how to calculate and Fermi had taught him what to calculate.

In 1933 the Handbuch der Physik, the German encyclopedia of physics, asked the 27-year-old Bethe to write the article on the quantum mechanics of one- and two-electron atoms. The result, co-authored with Edwin Salpeter in a later edition, ran to several hundred pages and became the reference work on hydrogenic atoms for the next half century. Students of the period would refer to it simply as “the Handbuch article” the way a literary scholar might say “the OED.” Every formula a working atomic physicist needed for hydrogen, helium, or the lithium ion was in there, derived from first principles, with the numerical tables computed by hand. Bethe’s habit of grinding out numerical answers, alongside the analytical derivations, would become a signature of every paper he wrote for the next seventy years.

Hans Albrecht Eduard Bethe (; ; July 2, 1906 – March 6, 2005) was a German-American physicist who made major contributions to nuclear physics, astrophysics, quantum electrodynamics and solid-state physics, and received the Nobel Prize in Physics in 1967 for his work on the theory of stellar nucleosynthesis. For most of his career, Bethe was a professor at Cornell University.

1933 and the long walk west

In April 1933 the Nazi government passed the Law for the Restoration of the Professional Civil Service, the statute that purged Jews and political opponents from German universities. Bethe was an instructor at Tübingen. His mother’s Jewish ancestry made him a non-Aryan under the new code; the letter of dismissal arrived within weeks. He never forgot the timing. He had been at Tübingen exactly eight months.

He spent the rest of 1933 in Manchester as a visiting lecturer at William Lawrence Bragg’s invitation, and the academic year 1934 at Bristol with Nevill Mott. In early 1935 a telegram arrived from Cornell University in upstate New York offering an assistant professorship at a yearly salary of three thousand dollars. Bethe accepted by return cable, sailed for New York in February, and arrived in Ithaca to find a small physics department in a small Ivy League town in a country he had never seen. He would stay for seventy years.

His mother, after extended difficulty, joined him in 1941. Many of the relatives who did not get out died in the camps. Bethe rarely spoke about it. When the topic came up in interviews near the end of his life, he would say only that he had been lucky and that those who had not been lucky had been the better physicists. It was the kind of statement, characteristic of him, that contained both genuine modesty and a quiet refusal to soften the facts.

Energy production in stars

The problem of why stars shine was one of the oldest in physics. Lord Kelvin had calculated in the 1860s that if the Sun were burning ordinary fuel it could last only a few thousand years, and that even gravitational contraction could supply at most twenty million years of output. The geologists, looking at sedimentary rock, kept finding evidence that the Earth was much older than that. By the 1920s Arthur Eddington had guessed that nuclear processes deep in the stellar core might supply the missing energy, but no one knew which nuclear processes or at what rate.

In April 1938 the physicist Charles Critchfield, then a graduate student at George Washington University, wrote to Bethe describing a calculation he had done on a possible reaction in which two protons fuse, emit a positron and a neutrino, and produce a deuteron. Bethe took the calculation apart, rebuilt it, and saw that Critchfield was right but that the proton-proton chain alone could not power the brighter stars. Something else had to be happening in stars more massive than the Sun.

He went to a conference in Washington that same month, listened for four days to astrophysicists describe what they knew about stellar interiors, and on the train ride back to Ithaca worked out, on the back of timetables and conference programs, the rest of the answer. By the time he reached Cornell he had identified the carbon-nitrogen- oxygen catalytic cycle, what we now call the CNO cycle, in which carbon-12 absorbs a proton, undergoes four further reactions, and returns to carbon-12 having converted four protons into a helium nucleus. Carbon goes in, carbon comes out; the net reaction is the fusion of hydrogen into helium with the release of about 26 MeV.

The paper, “Energy Production in Stars,” appeared in the Physical Review in March 1939. It runs to 36 pages and is one of the densest, most consequential papers of the twentieth century. In it Bethe considered every plausible thermonuclear reaction that could occur in a stellar core, computed the rate of each as a function of temperature and density, and showed that two and only two channels mattered: the proton-proton chain for stars like the Sun and below, and the CNO cycle for stars hotter than about 18 million Kelvin. The rates matched the observed luminosities of stars across the main sequence. The age of the Sun came out to about ten billion years, consistent with the age of the Earth and the age of meteorites. The problem that had troubled astronomy since the 1860s had been solved.

For this work Bethe received the Nobel Prize in Physics in 1967, twenty-nine years later. The committee usually moves faster. The delay was partly the war and partly Bethe’s habit of refusing to lobby for himself, but the citation when it came was unambiguous: “for his contributions to the theory of nuclear reactions, especially his discoveries concerning the energy production in stars.”

Los Alamos

In April 1943 J. Robert Oppenheimer asked Bethe to lead the Theoretical Division of the new laboratory at Los Alamos. Bethe accepted. He was 36. The division grew from a handful of physicists to over a hundred, and Bethe spent the next two and a half years calculating the dynamics of nuclear explosives: critical masses, neutron transport, the timing of the implosion lens, the radiation hydrodynamics of the fireball. He worked alongside Feynman, Teller, Peierls, Serber, von Neumann, and a younger generation of theorists who would dominate American physics for the next forty years. The T Division did not invent the bomb; it computed it.

Bethe never repudiated his Los Alamos work. He believed at the time, and still believed in 2003, that beating the Germans to the weapon had been a moral necessity, and that the use of the bomb against Japan, while terrible, had probably shortened the war. What he did repudiate, immediately and for the rest of his life, was the postwar nuclear arms race. He testified against Edward Teller’s hydrogen-bomb program in 1949 (and then, when the program proceeded without him, worked on it briefly to make sure the calculations were not botched). He helped found the Federation of American Scientists. He served on the President’s Science Advisory Committee under Eisenhower and Kennedy. He worked for the partial test ban of 1963, the ABM Treaty of 1972, the SALT and START treaties of the 1970s and 1980s. He campaigned, late in life, against missile defense and against the development of so-called bunker-buster nuclear weapons.

When the Second World War began, Bethe wanted to contribute to the war effort, but was unable to work on classified projects until he became a citizen. Following the advice of the Caltech aerodynamicist Theodore von Kármán, Bethe collaborated with his friend Edward Teller on a theory of shock waves that are generated by the passage of a projectile through a gas. Bethe considered it one of their most influential papers. He also worked on a theory of armor penetration, which was immediately…

He gave his last public statement on nuclear weapons in 1995, at 89, an open letter to all working scientists, asking them to refuse on conscience to participate in the design of new nuclear weapons. It is a remarkable document, not least because the man writing it had personally led the calculations that produced the first such weapons fifty years earlier.

The Cornell decades and a Lamb shift in a railway carriage

Bethe returned to Cornell in 1946 and resumed teaching. In June 1947 he attended the Shelter Island conference at which Willis Lamb announced his measurement of the small splitting between the 2s and 2p levels of hydrogen, a 1058 MHz shift that the bare Dirac equation said should not exist. The shift had to be a quantum-electrodynamical effect, and theorists had been trying to compute it for years without success: the integrals diverged.

On the train back from Shelter Island, in a Pullman car somewhere between New York and Schenectady, Bethe did the calculation. He used a non-relativistic approximation, subtracted the divergent mass-shift term that an unbound electron would also have, and got 1040 MHz, within four percent of Lamb’s experimental value. The result was crude. He knew it was crude. But it was the first time anyone had extracted a finite number from the otherwise divergent jungle of quantum electrodynamics, and it gave Feynman, Schwinger, Tomonaga, and Dyson the courage to attack the full relativistic theory in the two years that followed. The modern method of renormalization is descended, in a clean line, from Bethe’s afternoon on a train.

For the next sixty years Bethe remained at Cornell, generating one or two important papers a year on nuclear matter, neutron stars, supernova mechanisms, solar neutrinos, and reactor physics. He co-authored, in his eighties and nineties, papers on Type II supernova explosions and on the missing solar neutrino problem, both of which were eventually resolved in his favor. He never retired in any meaningful sense. He kept his office in Newman Laboratory until the last few months of his life, walking up the same staircase he had first climbed in 1935.

What Bethe means to the quantum story

Bethe died at home in Ithaca on 6 March 2005, eight months short of his 99th birthday. He had been doing physics for 80 years. The obituaries called him the last of the giants of twentieth-century physics, which was both true and inadequate. He was the physicist who showed how the stars burn. He was the physicist who, on a train, made quantum electrodynamics into a theory that could predict real numbers. He was the physicist who built the first nuclear weapons and spent the rest of his life trying to put that genie back. The thread that runs through all of it is the same instinct: take a physical problem, however vast or however small, and grind through the calculation until a real number falls out at the end. He is the man who taught quantum mechanics to do its arithmetic in public.