137 - Arthur I. Miller [53]
The crux of the problem was this: how could ordinary language, with its visual connotations, be used to describe a realm of nature that defied the imagination?
While Bohr and Heisenberg were deliberating in Copenhagen, Pauli had an idea. He immediately wrote it up and mailed it to Heisenberg. It was based on an insight Born had had, looking into Schrödinger’s wave equation.
Born had suggested that the wave function was a wave of probability for an electron moving between stationary states. Pauli pushed the idea further. He realized that the wave function gave the probability of an electron being detected in a certain region of space. In his usual way, he didn’t bother to write a paper to publish this idea and in the end Born took the credit.
But as he was working out the mathematics for Heisenberg, he came up with another extraordinary discovery: if he could determine a particle’s position accurately, he could not determine its momentum with the same accuracy. Pauli was puzzled as to why this should be so. Why couldn’t he determine both with the same degree of accuracy? Heisenberg was struck by the insight. He was, he wrote to Pauli, “more and more inspired by the content of your last letter every time I reflect on it.”
By February 1927 Bohr and Heisenberg had hit an impasse in their discussions on the deep meaning of the quantum theory, which seemed to be riddled with ambiguities. Bohr took a skiing break. Left to his own devices, Heisenberg set to work. The result was a paper that he called “On the Intuitive Content of the Quantum-Theoretical Kinematics and Mechanics.” Hidden behind this daunting title was one of the most earth-shattering discoveries of modern physics: the uncertainty principle.
Heisenberg realized that the supposed ambiguities of the quantum theory were essentially a problem of language. The issue was how to define words such as “position” and “velocity” in the ambiguous realm of the atom, a world in which “things” can be both wave and particle at the same time. He used the term “intuitive” in the title of his paper, for his goal was to redefine the word in the world of the atom.
Certain concepts in quantum physics, Heisenberg claimed, such as “position” and “momentum” (mass times velocity), were “derivable neither from our laws of thought nor from experiment.” Instead we would have to look into the peculiar mathematics of quantum mechanics, which should have alerted us all along that in the realm of the atom we would have to apply such words with great care.
In his paper Heisenberg made the amazing assertion that the more accurately we measure an electron’s momentum in a certain experiment, the less accurately we can measure its position in that experiment. This quickly became known as the uncertainty principle. It was earth-shattering in that it questioned our understanding of the inherent nature of the physical world as completely as Einstein’s relativity theory.
In the classical physics of Newton we can measure the position and momentum of an object with the same degree of accuracy by observing how it moves. Using a telescope and a clock we can measure both the location of a falling stone and how fast it is moving with an accuracy limited only by the width of the telescope’s crosshairs and the clock’s mechanism. If we make these errors as small as possible we can deduce very precisely the stone’s position and momentum. In principle, the product of the errors in measurements of position and momentum can both be zero. In quantum mechanics this is not possible.
Heisenberg wrote all this down in a detailed fourteen-page letter to Pauli. He asked for “severe criticism” after all, it was Pauli who had given him the key idea. Pauli was elated. “It becomes day in the quantum theory,” he declared.