The German Genius

quantum theory. According to this theory, energy—like light—was emitted in tiny packets, but according to classical physics it was emitted continuously. How could that be? Heisenberg returned to Göttingen enthused by his time in Copenhagen but also confused. And so, toward the end of May 1925, when he suffered one of his many attacks of hay fever, he took two weeks’ holiday in Helgoland, a narrow strip of land off the German coast on the North Sea, where there was next to no pollen, and he cleared his head with long walks and bracing dips in the sea. The idea that came to Heisenberg in that cold, fresh environment was the first example of what came to be called quantum weirdness. Heisenberg formed the view that if something is measured as continuous at one point, and discrete at another, that is the way of reality. If the two measurements exist, it makes no sense to say that they disagree: they are just measurements.
    This was Heisenberg’s central insight, but in a hectic three weeks he went further, developing a method of mathematics known as matrix math, originating from an idea by David Hilbert, in which the measurements obtained are grouped in a two-dimensional table of numbers where two matrices can be multiplied together to give another matrix. 5 In Heisenberg’s scheme, each atom would be represented by one matrix, each “rule” by another. If one multiplied the “sodium matrix” by the “spectral line matrix,” the result should give the matrix of wavelengths of sodium’s spectral lines. To Heisenberg’s, and Bohr’s, great satisfaction, it did: “For the first time, atomic structure had a genuine, though very surprising, mathematical base.” Heisenberg called his creation/discovery quantum mechanics, though Nancy Thorndike Greenspan’s recent biography of Max Born confirms how his role in the conception of the probabilistic nature of quantum waves, and of matrices themselves, was underacknowledged in the past by the likes of Heisenberg. Born won the Nobel Prize in 1954, but his contribution has now been properly positioned. 6
    The acceptance of Heisenberg’s idea was made easier by a new theory of Louis de Broglie in Paris, also published in 1925. Both Planck and Einstein had argued that light, hitherto regarded as a wave, could sometimes behave as a particle. Broglie reversed this idea, arguing that particles could sometimes behave like waves. No sooner had he broached this theory than experimentation proved him right. The wave-particle duality of matter was the second weird notion of physics, but it caught on quickly and one reason was the work of the Austrian Erwin Schrödinger, who was disturbed by Heisenberg’s idea and fascinated by Broglie’s. Schrödinger added the notion that the electron, in its orbit around the nucleus, is not like a planet but like a wave. Moreover, this wave pattern determines the size of the orbit, because to form a complete circle the wave must conform to a whole number, not fractions (otherwise the wave would descend into chaos). In turn this determined the distance of the orbit from the nucleus.
    The final layer of weirdness came in 1927, again from Heisenberg. It was late February, and Bohr had gone skiing in Norway. In his room high up in Bohr’s institute, Heisenberg decided he needed some air, so he trudged across the muddy soccer fields nearby. As he walked, an idea began to germinate in his brain. Could it be, Heisenberg asked himself, that at the level of the atom there was a limit to what could be known? To identify the position of a particle, it must impact on a zinc-sulphide screen. This alters its velocity, meaning it cannot be measured at the crucial moment. Conversely, when the velocity of a particle is measured—by scattering gamma rays from it, say—it is knocked into a different path, and its exact position at the point of measurement is changed. Heisenberg’s uncertainty principle, as it came to be called, posited that the exact position and precise velocity of an electron could not be determined at the same time (Heisenberg said: “To measure is to disturb,” “ messen ist stören ”). This was certainly disturbing both practically and philosophically, because it implied that in the subatomic world cause and effect could never be measured. The only way to understand electron behavior was statistical, using the rules of probability. “Even in principle,” Heisenberg was affirming, “we cannot know the present in all