Max Born

The mathematician who became a physicist

Max Born was born on 11 December 1882 in Breslau, a German city that is now Wrocław, Poland. His father Gustav was a professor of anatomy and embryology; his mother Margarethe, who died when Max was four, came from a wealthy Silesian industrial family. He grew up in a house where the dinner-table arguments were about cells, tissues, and the fashionable new ideas in nineteenth-century natural philosophy.

He took the long path into physics. He started at the University of Breslau in 1901, then drifted through Heidelberg and Zürich before landing at Göttingen in 1904. Göttingen at the turn of the century was the mathematical capital of the world. There he sat in the classrooms of Felix Klein, David Hilbert, and Hermann Minkowski. From the first class he attended, Hilbert spotted him as exceptional and made him his lecture scribe, the student who writes up the master’s notes so other students can study them. That apprenticeship put him inside Hilbert’s daily orbit for years.

His PhD in 1906 was on the stability of elastic wires and bands, a classical mechanics problem. The detour was telling. Born thought of himself as a mathematician all through his twenties, and only became a physicist in pieces, drawn in by Einstein’s 1905 papers on special relativity. When he tried to do his habilitation in experimental physics back in Breslau, his supervisor Otto Lummer watched him flood the lab with a burst cooling hose and told him, in plain words, that he would never be a physicist. Born returned to Göttingen and made his habilitation thesis on relativity instead. He published a paper that introduced what is still called Born rigidity, the relativistic generalisation of a rigid body. It was the work of a mathematician finding his way into physics by going through geometry.

Max Born was born on 11 December 1882 in Breslau (now Wrocław, Poland), Germany, into a family of Jewish descent. He was one of two children of anatomist and embryologist Gustav Jacob Born, who was Professor of Embryology at the University of Breslau, and Margarethe Gretchen Kauffmann, who came from a Silesian family of industrialists. Margarethe died on 29 August 1886, when Max was age four. He had a sister, Käthe, who was born in 1884, and a half-brother—Wolfgang—from his father's second…

Göttingen, 1921

In April 1921 Born became director of the Institute of Theoretical Physics at the University of Göttingen. He had taken the job partly because Einstein wrote him a letter of advice that ended with the line, “Theoretical physics will flourish wherever you happen to be; there is no other Born to be found in Germany today.” Born negotiated the move shrewdly. He insisted on a parallel chair of experimental physics for his closest friend James Franck, so the two could run their fields side by side.

The next twelve years made Göttingen one of the three great quantum capitals of the world, along with Bohr’s Copenhagen and Sommerfeld’s Munich. The cast of students and assistants who passed through Born’s institute is hard to believe when written down in one line: Werner Heisenberg, Pascual Jordan, Wolfgang Pauli, Enrico Fermi, Robert Oppenheimer, Maria Goeppert Mayer, Max Delbrück, Edward Teller, Eugene Wigner, Gerhard Herzberg, Victor Weisskopf. Several of them would win Nobel Prizes for work that began at his blackboard.

Born had a knack for handling people that ran against the stereotype of the great professor. One contemporary said that he “let his superstars stretch past him; to those less gifted, he patiently handed out respectable but doable assignments.” He was twenty-three years older than Heisenberg and a generation senior to Jordan, and he could see, from the first papers they brought him, that something was about to break.

The summer of matrix mechanics

In June 1925 the twenty-three-year-old Heisenberg, exiled to the treeless island of Helgoland by his hay fever, worked out a strange new scheme for atomic spectra. He kept only the observable quantities, transition frequencies and intensities, and abandoned the unobservable electron orbits. He brought the manuscript back to Göttingen on 9 July and handed it to Born with a note asking whether it was worth publishing.

Born read it. The arrays of numbers Heisenberg had written down, with their odd non-commuting multiplication rule, looked familiar. He had studied matrix algebra two decades earlier under Jakob Rosanes at Breslau, a topic almost no physicist of the day had touched. Born realised that Heisenberg had reinvented matrices without knowing the word. With his assistant Pascual Jordan he transcribed the scheme into proper matrix language and extended it. The famous commutation relation,

p q − q p = (h / 2πi) I

was Born’s discovery. The right-hand side is not zero, because matrix multiplication is not commutative; that single fact is the algebraic core of quantum uncertainty. The three-author follow-up paper, by Born, Heisenberg, and Jordan, appeared before the end of 1925. It is known in the field as the Dreimännerarbeit, the “three-man paper.” It is the founding document of quantum mechanics as a mathematical theory.

The footnote that became a foundation

Schrödinger published his wave equation a few months later, in early 1926. He thought of his wavefunction ψ as a real, smeared-out physical thing, like a vibrating density of charge. That picture appealed to many physicists because it offered a hope of returning to classical determinism. Born would not accept it. He kept running into a question Schrödinger could not answer: if ψ is a real density, why does an electron in a scattering experiment always arrive at one detector and not smeared across all of them?

In July 1926 Born published a short paper on the scattering of electrons by atoms. In a famous footnote, added in proof, he wrote that the squared magnitude of the wavefunction, |ψ|², was the probability of finding the particle at that point. The wavefunction itself was not a physical density. It was an amplitude whose square gave a statistical prediction. The position of the electron was not determined by the wavefunction. Only the odds were.

This is the Born rule. It was inserted, almost as an aside, into a paper about scattering, and Born himself did not at first realise its full weight. But it is the single bridge between the smooth, deterministic Schrödinger equation and the click-by-click randomness that experiments actually see. Without it, the formalism of quantum mechanics is mute. With it, the theory predicts the world.

For the 12 years Born and Franck were at the University of Göttingen (1921–1933), Born had a collaborator with shared views on basic scientific concepts, a benefit for teaching and research. His collaborative approach with experimental physicists was similar to that of Arnold Sommerfeld at the University of Munich, who was Ordinarius Professor of Theoretical Physics and Director of the Institute of Theoretical Physics—also a prime mover in the development of quantum theory. Born and Sommerfeld…

Einstein hated it. The 4 December 1926 letter from Einstein to Born contains the line everyone now misquotes, “He does not throw dice.” That line is the opening of a thirty-year argument between two close friends. The Born-Einstein correspondence, eventually published as a book, is one of the most moving documents in the history of physics: two old friends, separated by exile and by physics, arguing about the foundations of reality across decades and continents and never agreeing, but never losing the affection either.

1933: exile

In January 1933 the Nazi Party came to power. In May, Born was one of six Jewish professors at Göttingen suspended under the new race laws. James Franck had already resigned in protest. The institute Born had built over twelve years emptied within months as one faculty member after another fled the country. The losses included nearly every member of the cast list above. The physics of the twentieth century was redirected by that act, with consequences that would land at Los Alamos in 1945.

Born wrote to friends abroad looking for work. St John’s College, Cambridge, took him in as a stopgap. He wrote two of his most durable books there, a popular science volume called The Restless Universe and a textbook called Atomic Physics that ran through seven editions and trained two generations of students. In 1935 his German citizenship was revoked. A few weeks later the University of Göttingen cancelled his doctorate, the formal stamp on the work he had done thirty years earlier in their own halls.

He spent a year visiting C. V. Raman in Bangalore. Then Charles Galton Darwin, grandson of the Charles Darwin, invited him to take the Tait Chair of Natural Philosophy at the University of Edinburgh. Born accepted in October 1936. He would hold that chair for sixteen years, until his retirement at seventy in 1952. He became a British subject on 31 August 1939, one day before the Second World War broke out in Europe.

The prize, decades late

The Nobel Prize did not come quickly. In 1932 Heisenberg alone received the prize for matrix mechanics. Heisenberg, embarrassed, wrote to Born that he had a “bad conscience” about the omission and that the Göttingen work had been a collaboration “with you, Jordan and I.” Schrödinger and Dirac shared the 1933 prize for wave mechanics. Born received nothing.

He waited twenty-two years. His colleagues kept nominating him. Franck and Fermi pushed his name for the crystal-lattice work. The committee finally gave him the 1954 prize, shared with Walther Bothe, with a citation that named exactly the thing he had been overlooked for the longest: “for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction.” The footnote had become the cited work. He delivered his Nobel lecture in Stockholm on 11 December 1954, his seventy-second birthday.

Bad Pyrmont, Russell-Einstein, the granddaughter

Born retired to Bad Pyrmont in West Germany in 1954, returning to his native country thirty years after leaving it. He kept writing. He produced new editions of Optik with Emil Wolf as a fundamentally new book called Principles of Optics, which is still in print as a standard reference. He signed the Russell-Einstein Manifesto in 1955 alongside ten other Nobel laureates, calling for the abolition of nuclear weapons. It was Einstein’s final public act before his death; for Born it was one more chapter in a life spent worrying out loud about what physicists had unleashed.

He had three children. The youngest, Gustav, became an eminent pharmacologist. His daughter Irene married a Welshman named Brinley Newton-John in Cambridge, and their daughter, Born’s granddaughter, was Olivia Newton-John, the singer and actress who would later star in Grease. The historian who looks for a perfect symbol of the twentieth century could do worse than the family tree that runs from a Göttingen probability footnote to a 1978 Hollywood musical in three generations.

Max Born died on 5 January 1970 at the age of eighty-seven, in a hospital in Göttingen. He was buried in the Stadtfriedhof there, in the same cemetery that holds Planck, Hilbert, Hahn, Nernst, von Laue, and Weber. His tombstone bears the commutation relation he discovered in 1925.

What he means to the quantum story

Born is the mathematician who handed quantum mechanics its grammar, and the physicist who told us what its wavefunctions mean. Strip either contribution away and the theory does not stand. He was exiled by his own country, ignored by the Nobel committee for two decades, and outlived almost every friend he started with. What he left behind is the rule that turns the smooth Schrödinger wave into the random click of a detector, and the matrix algebra that makes the whole edifice consistent. Every probability you read off a quantum experiment is a quiet citation of Max Born.