Werner Heisenberg Study Guide: Uncertainty

Following the publication of the quantum mechanics papers, Heisenberg became the most sought after theoretical physicist in Germany. Several key chairs had opened up due to deaths or retirement, but Heisenberg had already accepted an appointment at Copenhagen. Most of his colleagues urged him to take advantage of the opportunity to serve as Bohr's assistant, but his family pressured him to accept the professorship offered at Leipzig. Turning down an appointment offer usually meant damaging one's future chances, at least temporarily, but Heisenberg and his colleagues recognized that he would learn a lot more by working with Bohr. He decided to turn down Leipzig with the hope that he would continue to perform notable research and earn more offers in the future.

The direct impetus for the uncertainty principle was a letter from Pauli. Max Born had started things with his statistical interpretation of Schrödinger's wave equation. He treated the function as a probability wave, rather than a matter wave, as Schrödinger had proposed. Pauli theorized from this statistical interpretation the existence of a "dark point," where we cannot exactly observe the path of a particle. This meant that if the position of the particle were controlled, then its momentum had to be uncontrolled.

Heisenberg extended this idea to focus not on an uncontrollable variable but rather the indeterminacy of both in a reciprocal manner. That is, the more accurately we measure one variable, the less accurately it will be possible to measure the other. The reason for this is that the very act of measurement affects the particle's velocity (momentum and velocity are affected the same way, since momentum is equal to velocity times mass). To determine a particle's position, one must use light, and the use of light means the addition of energy.

The consequences of the uncertainty principle are vast. For one, it limits the notion of causality. The hope of physics previously had been that if all forces were understood, then the exact position and velocity of a particle could be determined for any given moment in the future. However, such determinism was impossible if the exact measurement of original position and velocity could not be accomplished. Indeed, the best that one could attain would be the range of possibilities at any future time; therefore, the laws of quantum mechanics were really statistical rather than exact. In later philosophical works and lectures, Heisenberg would challenge the principles of Kant, whose epistemology depended on the validity of causality. Heisenberg did not, of course, attempt to propose solutions, but rather directed people in other professions in their search and the factors to consider.

Published in 1927, Heisenberg's uncertainty paper, entitled "On the Perceptual Content of Quantum Theoretical Kinematics and Mechanics," met with varying reactions and interpretations, though its significance was universally acknowledged. Schrödinger and, perhaps more famously, Einstein, flatly disapproved. Einstein and Bohr would continue to debate over indeterminacy for the rest of their lives, the former stubborn in his belief that indeterminacy was not the final answer, but merely indicative of our current inability to make exact measurements.

On the other hand, disagreements brewed between Heisenberg and Bohr as well. Bohr, who had begun to recognize the merits of wave mechanics, was now arguing that the best theory would have to accommodate the wave-particle dualism. Bohr readily accepted the fact of uncertainty, but he believed that its origin lie in the forced choice between treating the wave or the particle. Bohr attempted to show Heisenberg that his own analysis implicitly treated light as a wave.

Heisenberg yielded only months later, in writing. In the meantime, Bohr was in the process of formulating his principle of complementarity, an extension of uncertainty. Complementarity attempted to incorporate both sides of dualisms in general, arguing that neither side was sufficient in itself to account for reality. Instead, we should–as one example–consider both the wave and particle properties of matter and light to attain the most complete understanding possible.

The publication of Heisenberg's uncertainty paper had positive consequences for his career. Having spent a year with Bohr, he was prepared to return to Germany for a post. Despite prior achievements, such an offer was never guaranteed. August Heisenberg was especially concerned about the stability of his son's career, himself knowing nothing about physics or the extent of his son's work. The increasing popularity of Schrödinger's interpretation threatened to overshadow Heisenberg's own achievements. The publication of the uncertainty paper helped to reestablish Heisenberg's reputation, however, and his former mentor Sommerfeld lobbied heavily on his behalf. Sommerfeld hinted that Heisenberg would be able to succeed him at Munich soon, but in the meantime Heisenberg was happy to accept another offer from Leipzig, as it was as close to home as he could get. At the age of twenty-six, he was Germany's youngest full professor.

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