Student Years: 1920 - 1927
The Sad Story of Heisenberg's Doctorate

The title page of Heisenberg's doctoral dissertation on hydrodynamics. Click here to enlarge.

Heisenberg returned to Munich from Göttingen, where he had been a visiting student, in May 1923 to finish out his last semester while writing his doctoral dissertation. Knowing Heisenberg's reputation for controversial solutions to problems in quantum theory, his Munich mentor, Arnold Sommerfeld, suggested that he write his dissertation in the more traditional field of hydrodynamics. Heisenberg also had to take the four-hour laboratory course in experimental physics offered by Prof. Wilhelm Wien. Wien insisted that any physicist, even Sommerfeld's brilliant theorists, must be fully prepared in experimental physics. Physics in those days still meant primarily experimental physics. Theoretical physics, though rising in status, had not yet reached full acceptance as a branch of physics equal to experimental research. Wien and Sommerfeld both sat on the candidate's final oral exam and both had to agree on a single grade in physics.

In the handling of the present problem, Heisenberg shows once again his extraordinary abilities: complete command of the mathematical apparatus and daring physical insight.

--Arnold Sommerfeld, evaluation of the thesis, 1923.

Wilhelm Wien, professor of experimental physics in Munich

While Heisenberg struggled through Wien's lab course (much to Wien's displeasure at the results), he prepared his dissertation. He submitted the work, a 59-page calculation titled "On the Stability and Turbulence of Fluid Flow," to the Munich faculty on July 10, 1923. The topic arose from an earlier research contract Sommerfeld had received from a company channeling the Isar River through Munich. The problem was to determine the precise transition of a smoothly flowing fluid (laminar flow) to turbulent flow. It was an extremely difficult mathematical problem; in fact, it was so difficult that Heisenberg offered only an approximate solution. "I would not have proposed a topic of this difficulty as a dissertation to any of my other pupils," wrote Sommerfeld. The faculty accepted the thesis and Wien accepted it for publication in the physics journal he edited (Annalen der Physik). When the mathematician Fritz Noether raised objections to the results in 1926,  they remained in doubt for nearly a quarter century until they were finally confirmed.

Arnold Sommerfeld, Heisenberg's doctoral advisor, ca. 1930.

Trouble began when acceptance of the dissertation brought admission of the candidate to the final orals. The examining committee consisted of Sommerfeld and Wien in physics, along with representatives in Heisenberg's two minor subjects, mathematics and astronomy. Much was at stake, for the only grades a candidate received for his studies were those based on the dissertation and final oral: one grade for each subject and one for overall performance. The grades ranged from I (equivalent to an A) to V (an F).
As the 21-year-old Heisenberg appeared before the four professors on July 23, 1923, he easily handled Sommerfeld's questions and those in mathematics, but he began to stumble on astronomy and fell flat on his face on experimental physics. In his laboratory work Heisenberg had to use a Fabry-Perot interferometer, a device for observing the interference of light waves, which the class had studied extensively. But Heisenberg had no idea how to derive the resolving power of the interferometer nor, to Wien's surprise, could he derive the resolution (ability to distinguish objects) of such common instruments as the telescope or the microscope. When an angry Wien asked him how a storage battery works, the candidate was still lost. Wien saw no reason to pass the young man, no matter how brilliant he might be in other branches of physics. An argument arose between Sommerfeld and Wien over the relative importance of  theoretical physics in relation to experimental physics. The result was that Heisenberg received a III, equivalent to a C, in physics and for the overall grade for his doctorate.  Both of these grades were probably averages between Sommerfeld's grade (an A) and Wien's grade (an F).

Fabry-Perot interferometer Photo credit

Sommerfeld was shocked. Heisenberg was mortified. Accustomed to being always at the top of his class, Heisenberg found it hard to accept a mediocre grade for his doctorate. Sommerfeld held a small party at his home later that evening for the new Dr. Heisenberg, but Heisenberg excused himself early, packed his bag, and took the midnight train to Göttingen, showing up in Max Born's office the next morning. Born had already hired Heisenberg as his teaching assistant for the coming school year. After informing Born of the debacle of his orals, Heisenberg asked sheepishly, "I wonder if you still want to have me."

Max Born in Göttingen

Born did not answer until he had gone over the questions Heisenberg had missed. Convincing himself that the questions were "rather tricky," Born let his employment offer stand. But that fall Heisenberg's worried father wrote to the famed Göttingen experimentalist James Franck, asking Franck to teach his boy some experimental physics. Franck did his best, but he could not overcome Heisenberg's complete lack of interest and gave up the effort. If Heisenberg was going to survive at all in physics it would be only as a theorist.

The Quantum Mechanic


University Student

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Heisenberg's Doctoral Dissertation



About this Exhibit

1998 - American Institute of Physics and David Cassidy ()