戴维·卡西迪: 海森堡博士答辩的坎坷往事

本文作者戴维·卡西迪（就职于霍夫斯特拉大学），同时担任物理学史论坛财务秘书。文章节选自其著作《不确定性》（第149—154页），该书配套资料及更多海森堡相关内容可查阅对应网站。

取自 https://www.aps.org/archives/publications/apsnews/199801/heisenberg.cfm 

1923年5月，维尔纳·海森堡结束在哥廷根大学的访学，回到慕尼黑大学。他要完成最后一学期的学业，同时着手撰写博士论文。学界皆知，海森堡在量子理论研究中提出的解法向来颇具争议，于是他在慕尼黑的导师阿诺尔德·索末菲建议他，将论文选题转向更为经典的流体力学领域。

海森堡还必须修习威利·维恩教授开设的、时长四小时的实验物理实验课程。维恩坚持认为，所有物理研究者，即便是索末菲门下天赋出众的理论学者，也必须扎实掌握实验物理知识。博士最终答辩的评审委员包括维恩与索末菲二人，两人必须共同商议，给出物理学科的最终成绩。

海森堡在维恩的实验课上学得十分吃力，实验成果也让维恩颇为不满。与此同时，他也在推进论文工作。1923年7月10日，他向慕尼黑大学学部提交了一篇共计59页的演算论文，题为《论液流的稳定性与湍流》。该选题源自索末菲此前承接的一项企业研究项目，这家企业负责将伊萨尔河的河水引入慕尼黑城区。课题核心是探究平稳流动的层流向湍流转变的精确机理。

这是一道难度极大的数学难题。事实上，题目艰深至此，海森堡最终也只得出了近似解。索末菲曾写道：``换作我的其他学生，我绝不会把难度如此之高的题目定为毕业论文选题。'' 校方最终通过了这篇论文，维恩也同意将其刊登在自己主编的物理学期刊上。但1926年，数学家弗里茨·诺特对论文结论提出质疑，此后近二十五年间，该研究成果一直饱受争议，直到多年后才最终得到验证。

论文通过后，海森堡获得了参加最终答辩的资格，麻烦也随之而来。答辩委员会由索末菲、维恩，以及数学、天文学两门辅修科目的评审代表组成。这次答辩至关重要：毕业生的最终成绩仅由论文与答辩表现综合评定，每门科目以及整体表现都会单独打分，评分等级从一等（对应优等）至五等（不及格）依次划分。

1923年7月23日，21岁的海森堡面对四位教授展开答辩。索末菲提出的问题、数学相关考题他都对答如流，可一到天文学部分便开始支支吾吾，遇上实验物理考题更是彻底束手无策。实验课上，维恩曾详细讲解过法布里-珀罗干涉仪——一种观测光干涉现象的仪器，海森堡在实操中也接触过该设备，但他完全无法推导出这台仪器的分辨本领。更让维恩意外的是，就连望远镜、显微镜这类常见仪器的分辨本领公式，他也无从推导。维恩怒气冲冲地问起蓄电池的工作原理，海森堡依旧一问三不知。在维恩看来，即便这位青年在其他领域天赋过人，也绝不能准予通过答辩。

索末菲与维恩就此爆发争论，二人各执一词，争辩理论物理与实验物理孰轻孰重。最终，海森堡的物理学科成绩与博士综合评定均定为三等及格——这个分数是索末菲给出的最高分与维恩打出的最低分取平均后的结果。

索末菲大为震惊，海森堡更是羞愧难当。向来成绩名列前茅的他，实在难以接受博士答辩只拿到三等及格的结果。当晚，索末菲在家中为新晋博士海森堡举办了小型庆祝聚会，可海森堡早早告辞，收拾行李登上了午夜开往哥廷根的列车。次日清晨，他出现在马克斯·玻恩的办公室里。彼时玻恩早已聘请海森堡担任下一学年的助教。海森堡忐忑地讲完答辩的狼狈经历，局促地问道：``不知您是否还愿意聘用我？''

玻恩没有立刻答复，他逐一核对了海森堡答错的题目，认为这些考题本身``相当刁钻''，于是决定维持聘用决定。当年秋季，忧心忡忡的海森堡父亲写信给哥廷根知名实验物理学家詹姆斯·弗兰克，恳请他辅导儿子补上实验物理知识。弗兰克尽心施教，却始终无法提起海森堡对实验物理的兴趣，最终只得作罢。显而易见，海森堡今后若想在物理学领域立足，只能专攻理论方向。

这个故事还有一段耐人寻味的尾声。数年后，海森堡推导不确定性原理时，恰好借助了显微镜分辨本领相关知识，可他在这个知识点上依旧频频出错。尼尔斯·玻尔指出其中谬误后，海森堡再度陷入情绪低落。不过这次的波折也催生了积极成果：海森堡的思路偏差促使玻尔梳理并完善了自己的相关观点，而这些理论最终发展成为大名鼎鼎的量子力学哥本哈根诠释。

The Sad Story of Heisenberg's Doctoral Oral Exam

by David Cassidy

In May 1923 Werner Heisenberg returned to Munich from Gottingen, where he had been a visiting student, 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. Willy Wien. Wien insisted that any physicist, including Sommerfeld's brilliant theorists, must be fully prepared in experimental physics. Wien and Sommerfeld both sat on the candidate's final oral exam and both had to agree on a single grade in physics.

While Heisenberg struggled through Wien's lab course (much to Wien's displeasure at the results), Heisenberg prepared his dissertation. He submitted his dissertation, a 59-page calculation titled "On the Stability and Turbulence of Liquid Currents," 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 liquid (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, but when the mathematician Fritz Noether raised objections in 1926, the results remained in doubt for nearly a quarter century until they were finally confirmed.

Acceptance of the dissertation brought admission of the candidate to the final orals, where in this case trouble began. The examining committee consisted of Sommerfeld and Wien, along with representatives in Heisenberg's two minor subjects, mathematics and astronomy. Much was at stake, for the only grades a candidate received 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, on which Wien had lectured extensively. But Heisenberg had no idea how to derive the resolving power of the interferometer nor, to Wien's surprise, could he derive the resolving power of such common instruments as the telescope and the microscope. When an angry Wien asked how a storage battery works, the candidate was still lost. Wien saw no reason to pass the young man, no matter how brilliant he was in other fields.

An argument broke out between Sommerfeld and Wien over the relative importance of theory and experiment. The result was that Heisenberg received the lowest of three passing grades in physics and the same overall grade (cum laude) for his doctorate, both of which were an average between Sommerfeld's highest grade and Wien's lowest grade.

Sommerfeld was shocked. Heisenberg was mortified. Accustomed to being always at the top of his class, Heisenberg found it hard to accept the lowest of three passing grades 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 Gottingen, 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."

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 Gottingen experimentalist James Franck, asking Franck to teach his boy some experimental physics. Franck did his best, but 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 purely as a theorist.

There is an interesting epilogue to this story. When Heisenberg derived the uncertainty relations several years later, he used the resolving power of the microscope to derive the uncertainty relations-and he still had difficulty with it! And again, when Bohr pointed out the error, it led to emotional difficulties for Heisenberg. Likewise, this time a positive result came of the affair: Heisenberg's reaction induced Bohr to formulate his own views on the subject, which ultimately led to the so-called Copenhagen Interpretation of quantum mechanics.

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