hoc old quantum theory with modern quantum mechanics. The central premise was that the classical concept of motion does not fit at the quantum level, as electrons in an atom do not travel on sharply defined orbits. Rather, their motion is smeared out in a strange way: the Fourier transform of its time dependence only involves those frequencies that could be observed in the quantum jumps of their radiation. Heisenberg's paper did not admit any unobservable quantities like the exact position of the electron in an orbit at any time; he only allowed the theorist to talk about the Fourier components of the motion. Since the Fourier components were not defined at the classical frequencies, they could not be used to construct an exact trajectory, so that the formalism could not answer certain overly precise questions about where the electron was or how fast it was going. According to one account: "Heisenberg's paper marked a radical departure from previous attempts to solve atomic problems by making use of observable quantities only. 'My entire meagre efforts go toward killing off and suitably replacing the concept of the orbital paths that one cannot observe,' he wrote in a letter dated 9 July 1925." It was actually Einstein who first raised the problem to Heisenberg in 1926 upon their first real discussion. Einstein had invited Heisenberg to his home for a discussion of matrix mechanics upon its introduction. As Heisenberg describes the discussion: "On the way home, he questioned me about my background, my studies with Sommerfeld. But on arrival he at once began with a central question about the philosophical foundation of the new quantum mechanics. He pointed out to me that in my mathematical description the notion of 'electron path' did not occur at all, but that in a cloud-chamber the track of the electron can of course be observed directly. It seemed to him absurd to claim that there was indeed an electron path in the cloud-chamber, but none in the interior of the atom." In this situation, of course, we [Heisenberg and Bohr] had many discussions, difficult discussions, because we all felt that the mathematical scheme of quantum or wave mechanics was already final. It could not be changed, and we would have to do all our calculations from this scheme. On the other hand, nobody knew how to represent in this scheme such a simple case as the