It is said that the world’s top scientists are always working, even while on vacation; although not of course in the same way as CEOs who must be available 24/7, taking business calls on the beach while wading into the sea, their thoughts still trapped within their office walls. Scientists, though, keep working even when science is the last thing on their minds.

We can learn from the history of science that some of the most innovative ideas were discovered just as their discoverers relaxed from painstaking work. Let us consider one such event that took place a little less than a hundred years ago and caused a major revolution in physics.

Summer island vacation

Helgoland (Wikipedia)
Helgoland (Wikipedia)

Helgoland is a small island in the North Sea, not far from Hamburg. It boasts distinctive steep red cliffs and lush green grassland, offering a perfect escape from the summer heat. Seeking refuge from his annual attack of hay fever, the young German physicist Werner Heisenberg arrived at this idyllic piece of land in June-1925. A few days later, dipping his feet in the cold seawater, he was struck by an idea that brought an important new turn in the development of quantum physics. To understand fully the importance of young Heisenberg’s idea, we need to shed some light on what was going on in science at that time. But first, a short introduction to the hero of this summertime story is in order.

Werner Heisenberg was a typical representative of the generation of young physicists who concluded their studies after the First World War. Their characteristic traits included a certain lack of respect for senior colleagues. This young generation found it essential to figure out new approaches to scientific problems, and regarded the old academic establishment largely as an obstacle.

Mens sana in corpore sano

Heisenberg’s father was a classical philologist. He introduced his son to ancient philosophy and literature at an early age. Young Werner joined the German Youth Movement, whose members lived by the credo “Mens sana in corpore sano (healthy mind in a healthy body)”. Despite his love for classical music (he was an exceptional pianist), he became increasingly interested in the natural sciences.

Heisenberg studied in Munich with professor Arnold Sommerfeld, who invited him as an up-and-coming scientist to attend a physics conference in Göttingen in 1921. There the most prominent scientists discussed all the burning issues of that time. Heisenberg initially planned to be a mathematician, but changed his mind after a long conversation in Göttingen with the Danish physicist Niels Bohr. He was so fascinated with the new problems in atomic theory that he decided to pursue a career in physics. He realized that abstract mathematics was becoming increasingly important for the understanding of new problems in physics, and the connection between purely abstract mathematical thought and the real world intrigued him the most. When he obtained his PhD in 1924 with professor Sommerfeld, he went to Denmark to work with Bohr on problems raised in the newly established field of atomic physics.

When a brewery subsidizes alkaline science

Niels Bohr’s long-time wish was to create a working environment where scientists would be free to discuss technical problems regardless of the hierarchy between professors and students. In 1920 funds from Danish companies (including the Carlsberg brewery) helped make his wish a reality and the Niels Bohr Institute in Copenhagen was founded. Bohr gathered brilliant young students from Europe, America and Russia to work together in the new field of atomic physics.

Heisenberg fitted perfectly into this environment. He was surrounded by geniuses who in a few years’ time became leading experts in their fields. What they all had in common was their brilliant knowledge and intelligence accompanied by an enormous amount of confidence, nurturing a strong belief that they were always right. They weren’t discouraged by society’s wider lack of interest in their work. Nothing could undermine their conviction that they were headed for new discoveries that would completely transform physics and our understanding of the world.

The crucial summer idea that changed physics forever

After a year at Bohr’s institute, Heisenberg took a position as assistant with Max Born, who then chaired the Göttingen University Institute for Theoretical Physics. But only a few months into his new job, he decided to take a short break to order his thoughts. Upon arriving on the tiny island in the north of Germany, an idea occurred to him that set a new foundation for the theory of quantum physics.

Like the majority of physicists at that time, Heisenberg directed most of his energy to explaining the way atoms emit light. The central problem then was how to explain the fact that atoms only diffuse light in certain colors. What goes on inside the atoms to make them produce not the full spectrum of light but only certain colors?

How abstract mathematics explained atomic behavior

Heisenberg’s illuminating insight, which flashed into his mind during his vacation on Helgoland, revealed that the key question might not lie with what was going on inside the atom, but rather with how to formulate mathematically what was already known about the atom. What if we stopped searching for mechanisms to explain the functioning of atoms, and instead used numbers to describe the colours they emit? He quickly found out that these descriptive numeric sequences formed clear formal mathematical patterns of connection, which meant they could be calculated and predicted.

Upon returning from his vacation, Heisenberg shared his findings with Born, who immediately noticed that the numeric sequences in fact form mathematical matrices. As is well known, a matrix is a generalized idea of a number, an idea represented by, for example, a square list of numbers, consisting of the same number of rows and columns. Mathematicians have long known the rules for the addition and multiplication of matrices. To Born and Heisenberg it seemed that matrices, and not numerals, offered the right language for describing atomic behaviour.

Then Niels Bohr sets off on vacation

Heisenberg’s groundbreaking idea triggered a wave of debates and theories on possible improvements. Even though physicists were swift to work out equations on how to predict the color of light absorbed or emitted by individual atoms in different circumstances, they weren’t able to understand fully the processes this phenomenon involved. And they became increasingly frustrated.

The scientists at Bohr’s Institute tried hard to explain these new findings in the atomic world. Bohr, Heisenberg and other physicists spent a year at the Copenhagen Institute, discussing how even to begin interpreting quantum physics. They were on the verge of giving up, but Bohr’s optimism kept them going. Yet by February 1927 Bohr himself was so exhausted that he needed a break. Since it was the middle of winter, he decided to go on an alpine touring trip to the Norwegian mountains north of Oslo.

The origins of today’s textbook equations

While on holiday, alone with his thoughts, the basic interpretation of quantum physics, the very same that still dominates today’s physics textbooks, occurred to Bohr. The basic premise of his realization goes as follows: each time we ask a question about nature, we need to specify how to interpret its answer. As Bohr said himself: “It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.”

While Bohr was away, Heisenberg too made a revelatory finding, following a long discussion with his colleagues, which contributed further to the foundations for interpreting quantum physics. Both he and Bohr reached very similar conclusions. Heisenberg came up with the famous uncertainty principle, while Bohr conceived the principle of complementarity. Both principles form the core of the Copenhagen interpretation of quantum mechanics.

Please note that leaving for vacation doesn’t necessarily mean you will experience a profound scientific insight. It is what you do between your vacations that really matters.