Diana Preston - Before the Fallout

It was Sommerfeld who brought Heisenberg with him from Munich to hear Niels Bohr at Gottingen. The lecture hall was crammed. Heisenberg was excited not only by what the Dane had to say but also, as he later recalled, by how he said it: “Each one of his carefully formulated sentences revealed a long chain of underlying thoughts, of philosophical reflections, hinted at but never fully expressed.” At the end of Bohr’s third lecture Heisenberg summoned enough courage to voice a critical remark. Bohr listened gravely and at the end of the lecture invited Heisenberg for a walk over the Hain Mountain. During it, Bohr asked him to visit Copenhagen. Heisenberg later wrote, “My real scientific career began only that afternoon.”

Also that year, 1922, Sommerfeld suggested that Heisenberg attend a scientific congress in Leipzig where Einstein was speaking. As Heisenberg entered the lecture hall, a young man pressed a red handbill into his hand. It attacked Einstein and derided relativity as wild, dangerous speculation alien to German culture and put about by the Jewish press. The lecture went ahead, but Heisenberg was too disturbed by the eruption into science of such “twisted political passions” to concentrate. He had no heart, at the end, to seek an introduction to Einstein. It was his first, but by no means last, experience of what he called “the dangerous no-man’s land between science and politics.”

After completing his doctorate at Munich, Heisenberg moved to Gottingen as Max Born’s assistant. He also made frequent visits to Bohr in Copenhagen. During long walks he and the Dane became good friends while debating quantum theory. Heisenberg was becoming increasingly troubled by the theory’s reliance on the unobservable and hence the unmeasurable. Hypothesizing about what was happening within the atom and about orbiting electrons was, he felt, all very well, but he yearned for proof of what was actually occurring. He therefore decided to focus on what could be observed—the frequencies and amplitudes of light emitted from inside the atom—and to seek mathematical correlations between them.

It was a complex task, but in 1925 Heisenberg had something akin to a vision. A severe bout of hay fever sent him to the bracingly windy, relatively pollen-free North Sea island of Heligoland. He arrived with a face so swollen his landlady thought he had been in a fight. He worked late in his room, churning out reams of calculations until he felt that “through the surface of atomic phenomena, I was looking at a strangely beautiful interior, and felt almost giddy at the thought that I now had to probe this wealth of mathematical structures nature had so generously spread out before me.” He was so exhilarated that, instead of going to bed, he went out and climbed a jutting sliver of rock and waited for the sun to rise.

Down from “the mountain” and back at Gottingen, Heisenberg was sufficiently sure of himself to parade his thoughts to Max Born and his colleagues. Together they evolved what Heisenberg called “a coherent mathematical framework… that promised to embrace all the multifarious aspects of atomic physics.” This new approach was the earliest version of “quantum me­chanics”—a tool using experimental evidence to predict physical phenomena. It was based on matrix algebra, a species of mathematics originally developed in the 1850s, and later refined, as a means of analyzing large amounts of numbers using a system of grids. In keeping with his original aim, Heisenberg’s quantum mechanics focused on what could be observed—like radiation emitted from an atom—and otherwise involved only the use of fundamental constants. In contrast with the Rutherford-Bohr model, Heisenberg’s abstract mathematics provided nothing in the way of a picture of atomic structure, but its predictions proved remarkably accurate.

Heisenberg s approach had a competitor: “wave mechanics,” outlined just a few weeks later by an urbane Austrian physicist, Erwin Schrodinger. Building on an idea of the Frenchman Louis de Broglie that particles such as electrons behave like waves, Schrodinger invented a neat equation capable of embracing those wavelike characteristics. An important feature was the incorporation in the calculation of a likelihood of occurrence—a probability—which meant, for example, that the location of an electron was not predicted as a point but rather as a smear of probability whose density gave the likelihood of the electron being found at any point. At first, Schrodinger’s different approach appeared to threaten Heisenberg’s quantum mechanics, and the respective proponents indulged in vigorous debate. Heisenberg wrote crossly to Wolfgang Pauli, that, “The more I think about the physical portion of Schrodinger’s theory, the more repulsive I find it…. What Schrodinger writes about the visualizability of his theory is probably not quite right, in other words it’s crap.” However, Schrodinger proved that his “wave equation,” as it became known, provided results mathematically equivalent to Heisenberg’s formulas and that the two theories complemented each other rather than conflicted. Schrodinger’s waves and Heisenberg’s matrices were analogous.

Heisenberg’s next step, in 1927, was his renowned “uncertainty principle.” It grew out of an intellectual pummeling from Bohr over whether apparent ambiguities in atomic physics could be reconciled. A cold walk under a starlit sky in Copenhagen led Heisenberg to a conclusion that some uncertainties were unavoidable. Given the atom’s tiny dimensions, the scientist’s ability to measure events must be inherently limited. The more accurately one aspect was measured, the more uncertain another must become. Although it was possible accurately to observe either the speed or the position of a nuclear particle, doing both simultaneously was impossible. “The more precisely the position is determined,” he wrote, “the less precisely its momentum is known and vice versa.” In the mechanical world of Newtonian physics, future behavior could be predicted with certainty, just as what had happened in the past could be accurately determined. Under Heisenberg’s principle, while past behavior could be known accurately and future behavior could generally be predicted using a series of approximations based on probability, the future behavior of an individual atom was subject to inherent uncertainty.

Heisenberg’s ideas at first provoked a fierce reaction from Bohr, who taxed him with flying in the face of previous interpretations and reduced him to tears with his vehemence. When both had cooled off, they agreed that their approaches could, after all, be reconciled. Bohr incorporated Heisenberg’s uncertainty principle into a broader thesis of his own: “complementarity.” He argued that conflicting or ambiguous findings should be placed side by side to build a comprehensive picture—the particle and wave nature of matter should be accepted—and each aspect should recognize “the impossibility of any sharp separation between the behaviour of atomic objects and the interaction with measuring instruments.” He borrowed the word complementarity from the Latin complementum, meaning “that which completes.” Bohr’s and Heisenberg’s friendship emerged unscathed from their confrontation. However, Heisenberg’s uncertainty principle sparked a famous row with Einstein, who argued that probability was far too vague a tool for assessing the physical world: “It seems hard to sneak a look at God’s cards. But that He plays dice and uses telepathic methods… is something that I cannot believe for a single moment.” Nor did he or any other scientist yet believe that this rash of new intellectual tools would be used to predict how atoms could be split to release their latent energy explosively.