June/July 1925: Werner Heisenberg pioneers quantum mechanics

In 1925, quantum theory was in crisis. Physicists’ understanding of the structure of atoms and the nature of light wasn’t consistent with experimental observations. The great physicists of the day tried fix after fix, but they couldn’t resolve the problem.

On June 6, a swollen-faced, stuffy-nosed Werner Heisenberg, then 23 years old and suffering from hay fever, left his home in central Germany for the fresh air of the North Sea island of Helgoland, hoping for relief. There, he had a breakthrough, becoming the first to articulate a mathematical framework of quantum mechanics and resolve the then-glaring contradictions of quantum theory — while raising uncomfortable questions about the nature of reality.

Heisenberg was born in Würzburg, Germany, in 1901. Growing up during World War I and disgusted by its aftermath, he became a leader in his local New Boy Scouts, which promoted nationalistic ideas and embraced German romanticism through poetry, music, and natural beauty. (Hitler banned such groups in 1933.)

Heisenberg was also a brilliant student. In the fall of 1920, he started his doctorate at the University of Munich, where he published well-regarded papers on quantum theory — but struggled in the lab. Despite his deep interest in the nature of light, he couldn’t answer questions during his orals about microscopes, telescopes, and the interferometer he’d used in his lab course. He received the equivalent of a “C” grade, which humiliated him. While he was a skilled theoretician, he was no experimentalist.

Still, Heisenberg graduated in just three years’ time, and went on to a postdoc with Niels Bohr in Göttingen. By this time, the problems with quantum theory had become impossible to ignore.

Bohr had articulated the current picture of the atom, made up of electrons circling around a nucleus like planets around the Sun. “It was quite visual,” says physics historian and CNRS research director emeritus Olivier Darrigol. “You could describe the shapes of their orbits, or at least try to.”

Even Bohr knew this theory was inadequate. It couldn’t predict the observed behavior of atoms, particularly their spectra — how they absorbed and emitted light. And physicists could not actually observe the orbits of electrons.

Faced with this impasse, Heisenberg made a bold leap into abstraction. If the orbits of electrons could not be observed, why insist that they existed? “The genius of Heisenberg is that he was able to conceive a brand-new theory without picturing it,” says Darrigol.

He decided to derive quantum mechanics based on observable quantities: atomic spectra. He focused his calculations on the frequency and intensity of light emitted by the simplest atom, hydrogen.

Heisenberg was working on his calculations in the months leading up to his allergy-driven escape to Helgoland in 1925, but he was stuck. So were his colleagues, collaborators, and correspondents. In May, Wolfgang Pauli wrote to Ralph Kronig, “Physics is at the moment once again very wrong.”

According to Heisenberg’s account decades later, it was during an all-nighter in his lodgings at Helgoland that he made his breakthrough. After writing into the early morning, he triumphantly climbed a rock at the edge of the island and watched the sun rise (although some historians have raised doubts about this romanticized story.)

Heisenberg’s equation described quantum mechanics not based on electron motion, but on atomic energies and arrays of probabilities.

Accounting for electron motion required complex, abstract math. When an electron jumps from one state to the next lowest one, then to the one below that, “the two emitted frequencies must add together to produce the frequency that is actually observed,” writes physics historian David C. Cassidy in his biography of Heisenberg, Beyond Uncertainty. “Heisenberg found that, mathematically, if the frequencies do add together, then the two amplitudes do not simply multiply together but are subjected to a new and strange multiplication rule involving all of the possible intermediary states — just in case the electron takes a circuitous route in getting from one place to another.”

The new approach made the movement of the electron abstract. Heisenberg said as much, declaring in a July 9 letter to Pauli, “My entire meager efforts go toward killing off and suitably replacing the concept of the orbital paths that one cannot observe.”

In July, Heisenberg submitted this work to the journal Zeitschrift für Physik, which published the paper in September.

Heisenberg provided “a theory without a picture,” says Darrigol. “It’s a discovery based on completely counterintuitive ideas.” For that reason, though many of these ideas had been hashed out in letters and conversations with Bohr, Pauli, and others, Heisenberg may have needed time alone to make the leap. “The fact that he was isolated, not talking to other people, may have helped,” says Darrigol.

Physicist Max Born recognized that Heisenberg’s arrays resembled the matrices used in linear algebra, and worked with his assistant Pascual Jordan to expand the mathematics of what would come to be called “matrix mechanics.” Heisenberg and Pauli also added to the theory to account for electron spin, which made it possible for matrix mechanics to account for the effects of magnetic fields on atomic spectra — previously a hole in the theory.

Physicists were excited about the predictive power of matrix mechanics, but dismayed and even repulsed by its abstraction. Einstein called matrix mechanics “a true witches’ multiplication table.”

Many were drawn to Shrödinger’s alternative quantum mechanics, described in a series of papers in early 1926. Shrödinger treated electrons as waves — something people could picture. And physicists versed in optics were already comfortable with wave equations. In May 1926, Shrödinger proved that matrix mathematics and wave mechanics were equivalent, but he still pushed for his version, and Heisenberg for his.

Experimental results seem to suggest a strange world: Light, for instance, behaves like particles sometimes and a wave at other times. Physicists have had to accept this duality. “The present version of quantum mechanics is a mix of Heisenberg and Shrödinger,” says Darrigol.

While Heisenberg shaped quantum mechanics and articulated the uncertainty principle soon after, his legacy is complex. In 1937, an SS publication called him a “white Jew,” and he was investigated by the Gestapo for a year. After the war started, Heisenberg visited occupied countries as a representative of the German government. He told a Dutch colleague that democracy was not strong enough to prevail in Europe and warned that either his country or the Soviet Union would take over the continent — and he favored Nazi Germany.

He also worked on Nazi Germany’s atomic bomb project. Historians disagree about why this project was unsuccessful, but it’s possible that Heisenberg’s limited skills as an experimentalist were a factor.

One hundred years later, physicists are celebrating Heisenberg’s 1925 breakthrough as part of the International Year of Quantum Science and Technology. In June, a century after Heisenberg fled to the island, physicists gathered on Helgoland for a weeklong conference in his honor.

“The struggle continues today to understand the quantum mechanical behavior of events at the smallest levels,” writes Cassidy in Beyond Uncertainty. Indeed, Heisenberg’s work raised questions that remain unanswered — something he acknowledged in a lecture some 30 years after his breakthrough paper.

“The mathematical forms that represent the elementary particles will be solutions of some eternal law of motion for matter,” he said in that lecture. “This is a problem which has not yet been solved.”