137 - Arthur I. Miller [47]
At this point Kepler and his family were living in an apartment in the wall surrounding the city of Linz, which was constantly under siege. They often had to admit soldiers to fire their guns through their windows. When the siege was lifted in 1626, Kepler finally left. He died in Regensburg on November 15, 1630. The cemetery in which he was buried was obliterated in the Thirty Years War.
Fludd died seven years later in London. Like a lightning rod his ideas had attracted sharp controversies, most notably with Kepler. His will stated that all those at his funeral should return to the local pub and entertain themselves at his expense.
Three or four?
To Pauli, Kepler and Fludd were a study in opposites. At first he sided with Kepler but over time came to realize that Fludd’s worldview included science, music, religion, and the mind. For Fludd four was “the eternal fountainhead of nature.” For Kepler the perfect number was three. “I hit upon Kepler as trinitarian and Fludd as quaternarian—and with their polemic, I felt an inner conflict resonate within myself. I have certain features of both,” Pauli wrote.
Like Kepler, Pauli brooded about his work, suffering over problems he couldn’t solve, far removed from the world of ordinary people. In 1924, when he discovered the exclusion principle, perhaps like Kepler he felt that he had tapped into something that went beyond science. Moving from three to four quantum numbers was a momentous step. It meant a complete break with the iconic imagery of the Bohr atom as a miniscule solar system. It was a step into the unknown, into a world without any visual images. Perhaps Pauli had in mind one of Bohr’s favorite sayings from the eighteenth-century German poet Friedrich Schiller:
Only fullness leads to clarity
And truth lies in the abyss.
In his day Kepler stopped short at the number three, basing this decision on the three-dimensionality of space, on the one hand, and the Holy Trinity on the other. The deep mysteries of alchemy with its emphasis on the number four overwhelmed him.
Pauli, Heisenberg, and the Great Quantum Breakthrough
EVERYONE AGREED with Pauli that there should be four not three quantum numbers. His exclusion principle had shown that no two electrons in an atom could have the same four quantum numbers. Beyond that his colleagues could see that the principle must have huge implications. But no one could yet see what they were.
By the beginning of 1925 it was clear that Bohr’s theory of the atom as a miniature solar system no longer provided even an adequate basis for understanding the atom, let alone for the exclusion principle or the anomalous Zeeman effect. Bohr’s theory by now was under attack from all sides.
The demise of Bohr’s theory of the atom
Pauli, despite his best intentions, had been one of the key wielders of the knife. As he had discovered, the theory had failed to produce a realistic model of either a hydrogen-molecule ion or a helium atom. Then new data appeared showing that the hydrogen atom did not respond to being hit by light as if it were a tiny solar system. This model produced spectral lines for the struck light that did not agree with those found in the laboratory.
Bohr fought back with a variation of his theory in which the invisible orbits of the invisible electrons were replaced by invisible electrons on springs, each emitting light at the frequency of an observed spectral line. To emphasize that these invisible electrons were an intermediate kind of reality, he referred to them as “virtual oscillators.” Pauli wanted nothing to do with them. He had had enough of bizarre models and