In 1922, Sommerfeld decided to spend a year the University
of Wisconsin as a visiting professor, so Heisenberg took the opportunity to
transfer to Göttingen to work with Max Born, succeeding Pauli as
his assistant. With Born, Heisenberg constructed mathematical methods
that furthered knowledge of the relationships of the periodic table.
However, he again provoked the disagreement of Bohr and now Pauli,
who had relocated to Copenhagen. Meanwhile, Heisenberg completed
work for a dissertation on the less controversial topic of hydrodynamics.
In particular, he focused on solving convoluted equations for the
stability and turbulence of flowing fluids. Though Heisenberg's
answers were incomplete, his dissertation was passed on the grounds
that his handling was evidence of strong ability, and moreover
because the subject had been an unusually difficult one for a student
to tackle.
Heisenberg encountered much less sympathy at his oral
examination, however. The stubborn experimentalist Willy Wien was shocked
at Heisenberg's lack of preparation for questions on experimental
physics. Wien perhaps took Heisenberg's incompetence personally,
as he had spent much time lecturing on these very basic problems.
Wien saw no reason to grant Heisenberg his degree, resulting in
one of the great clashes between theory and experiment. Finally,
Heisenberg was passed with the grade of III, cum laude, where
a IV would have meant passing with no honors. Heisenberg was naturally
shocked and embarrassed. He had been accustomed to handling oral
examinations and defenses expertly, even in front of the biggest
names in his field. He was so distraught that he took the evening
train back to Göttingen, though he had planned to spend some time
on leave in Munich.
As Heisenberg was completing his doctorate in July of
1923, Germany was facing increasing challenges to its economic
and political stability. Inflation had made living conditions difficult
for everyone, including the isolated scientists. Many had to turn
to American benefactors to support their research. The political
situation had a direct effect on physics as well. On two occasions, Heisenberg
had lost the opportunity to see and meet Einstein because the latter
had had to back out due to anti-Semitic threats. Although these
circumstances troubled him, Heisenberg made no active opposition
and continued believing that science should rise above politics.
Just as inflation had exploded to the point that a nationwide
state of emergency was called, Heisenberg was proposing his groundbreaking
Zeeman principle. The new theory was based on Bohr's own quantum
postulate of 1913:
hv = E(2) - E(1)
This translates into h (Planck's constant)
times v (frequency) equals the difference between
the two energy states when an electron jumps from E(2) to E(1).
Heisenberg saw that this postulate was inconsistent, for while the
energies were calculated by classical Newtonian mechanics, the
frequency was related not to the energy of one state but to the
difference between two. Heisenberg, therefore, replaced the classical
energies with a new function that served as an average, or integral,
of the classical energy. From this new principle he was able to
reproduce the results of previous findings, while also satisfying
the Zeeman effect. More important, after applying it to his original
core model–with alterations of course–Heisenberg was able to reconcile
other principles he had earlier attempted to discard.
This time, before rushing to publication, Heisenberg first
sent a copy to Bohr and asked for feedback from others as well.
Bohr responded with an invitation to Copenhagen. Much of their
time together was once again spent on philosophical debate, specifically avoiding
technical details. Bohr also encouraged Heisenberg to plant himself
in the institute library to read physics textbooks, so that his
general physics understanding could be improved. As his friend
Pauli had hoped, Heisenberg left after two weeks with a broader
appreciation for physics.
Shortly afterward, Heisenberg coauthored a paper with
Alfred Landé, modifying his Zeeman principle. With its publication,
the science faculty at Göttingen voted on July 28, 1924, to habilitate the
young scientist, certifying his qualification to lecture at all
levels in Germany.
