乔治·乌伦贝克George Uhlenbeck

乔治·乌伦贝克的祖先最初来自德国，但后来的几代人是荷兰人，并在荷兰殖民地服役。他的父亲Eugenius Marius Uhlenbeck出生在爪哇，当时称为荷属东印度，即现在的印度尼西亚。1893年，在荷属东印度军队服役的Eugenius 乌伦贝克与Anne Marie Beeger结婚，她是荷兰一位少将的女儿。他们的两个孩子幼年死于疟疾，但有四个活了下来。在活下来的孩子中，乌伦贝克是第二个孩子，有一个姐姐Annie和两个弟弟Willem Jan和Eugenius 西门·马里乌斯。

当乌伦贝克六岁时，全家永久移居荷兰，在海牙安了家。在那里，乌伦贝克先上小学，然后上中学，或者当时所称的高级市民学校。乌伦贝克说[3]：-

我是一个非常听话的学生，非常听话。我总是非常有规律地学习，在班上总是非常优秀。直到中学最后几年，我才明确自己将来要做什么。

然而，和许多人一样，他受到了一位优秀学校教师的影响。在学校的最后两年，他的物理老师大力鼓励他，给他微分和积分学的文本，并建议他阅读数学和物理学的本科教材。使他热衷于物理学的书籍之一是亨德里克·洛伦兹的Lectures on Physics，他在海牙的皇家图书馆读了这本书。

乌伦贝克在1918年7月的学校毕业考试中表现极为出色，但由于他的学习不包括希腊语和拉丁语，他不能进入大学。这不是他的过错，只是他所上的学校不提供这些科目。他别无选择，只能进入代尔夫特技术学院。他选择在那里学习化学工程，但不久之后，当荷兰政府修改规定，大学入学不再要求希腊语和拉丁语时，他离开了技术学院。他只学了一个学期的化学工程，就开始了在莱顿大学的大学学习。

乌伦贝克能够搬家，感到加倍高兴，首先因为他一直想在大学学习物理和数学，但也因为他觉得自己没有从事实用学科所需的灵巧。在莱顿，物理由保罗·埃伦费斯特、H K Onnes和J P Kuenen讲授，而亨德里克·洛伦兹当时已从讲席退休，每周来上一次课。乌伦贝克买了一本路德维希·玻尔兹曼的Lectures on gas dynamics，利用自己的时间学习，继续他在学校养成的学习方式。起初他发现几乎无法理解，但在读了保罗·埃伦费斯特的一篇百科全书文章后，它开始变得有意义了。在他所听的讲座中，关于分析基础的讲座令他非常喜欢，他发现分析的严格性特别令他满意。后来在他的职业生涯中，保罗·埃伦费斯特会鼓励他以较少的严格性来呈现他的数学。

乌伦贝克的父母发现为他提供大学所需的经济支持并不容易。为了压低开支，他每天从海牙前往莱顿，这是一段漫长而疲惫的旅程。在本科第二年，乌伦贝克学习了詹姆斯·克拉克·麦克斯韦的理论，并非常详细地写了出来。这项令人印象深刻的工作使他在第三年学习时获得奖学金，从而减轻了父母的经济负担。正如他在学校时一样，乌伦贝克异常努力，并在1920年12月的期末考试中表现出色。

毕业后，他在保罗·埃伦费斯特的指导下在莱顿开始研究生学习。然而，为了在经济上支持自己，他不得不工作。他在莱顿的一所女子学校做兼职教师，这给了他足够的钱租一个房间。终于，每日的奔波结束了。他安定下来攻读硕士学位，这涉及参加讲座课程。5写道[5]：-

保罗·埃伦费斯特的研究生讲座包括一个为期两年的课程：詹姆斯·克拉克·麦克斯韦理论，以电子理论和一些相对论结束，一年；以及统计力学，以原子结构和quantum theory结束，另一年。乌伦贝克参加了这些讲座，并接受了额外的数学指导。

1922年9月，在获得硕士学位之前，乌伦贝克利用机会在意大利工作，当时他接受了荷兰驻罗马大使儿子的私人导师职位。他一直担任这份工作直到1925年6月，但每年夏天他都会回到荷兰。他又花了一年时间完成硕士学位的工作，然后在1923年9月接受考试并获得学位。获得学位后不久，乌伦贝克回到意大利，并在保罗·埃伦费斯特的建议下，与恩里科·费米取得了联系。这对两人来说都是一段重要的友谊。

然而，尽管与科学家有这些接触，乌伦贝克的学术兴趣转向了历史。当他在意大利的任命结束并回到荷兰时，他几乎决定成为一名历史学家。保罗·埃伦费斯特急于让他继续做科学家，建议他为自己工作一段时间，并给乌伦贝克一个为期两年的助理任命。他接替了获得洛克菲勒奖学金的迪尔克·扬·斯特勒伊克。接受任命后不久，乌伦贝克与研究生皮埃尔·萨米埃尔 Goudsmit合作，做出了他最重要的科学发现，即发现了电子自旋。

1925年1月，沃尔夫冈·泡利提出电子应被赋予一个额外的第四量子数，该数为半整数。这是导致乌伦贝克得出电子自旋思想的线索之一。他写道（例如见[2]）：-

……我想到，既然（我了解到）每个量子数对应电子的一个自由度，那么沃尔夫冈·泡利的第四量子数必定意味着电子有一个额外的自由度——换句话说，电子必定在旋转。

这一概念立即引起了尼尔斯·玻尔、沃尔夫冈·泡利、阿尔伯特·爱因斯坦、维尔纳·海森堡以及其他对量子理论感兴趣的人的兴奋。乌伦贝克的工作进展顺利，尤其重要的是奥斯卡·克莱因被任命到莱顿。两人很快成为朋友并交换想法，特别是关于奥斯卡·克莱因的五维相对论思想。

乌伦贝克的博士工作是在哥本哈根完成的，他在那里花了两个月专注于学位论文的密集写作。这在量子力学中具有根本重要性，系统化了统计概念，并扩展了两年前宣布的电子自旋思想。在论文答辩后，乌伦贝克立即被任命到密歇根。他于1927年8月与Else Ophorst结婚，然后在接下来的一个月，他抵达安娜堡就职。

他于1935年回到荷兰，在乌得勒支担任讲席。该讲席之所以空缺，是因为其持有者汉斯·克拉莫斯转往莱顿，接替保罗·埃伦费斯特自杀后留下的讲席。1938年，他从乌得勒支请假，前往纽约哥伦比亚大学担任访问教授一年，但回到荷兰不久后，又于1939年8月，即第二次世界大战爆发前不久，再次前往美国。

从1943年到1945年，乌伦贝克在麻省理工学院工作，是雷达研发团队的一员。战争结束后，他回到安娜堡，在1948-49年间在普林斯顿度过一段时间后，于1954年被任命为密歇根大学的Henry Cahart教授。四年后，即1960年，他搬到纽约的洛克菲勒研究所，一直在那里工作，直到1971年退休。

除了量子力学的基础工作外，乌伦贝克还研究原子结构和物质的动理论。他将路德维希·玻尔兹曼的方程推广到稠密气体，并写了两篇关于布朗运动的重要论文。他整个职业生涯中研究的主要主题是统计物理。这一主题的目标是理解原子层次物理与宏观层次物理之间的关系。1955年，他解释了这个领域对他的吸引力：-

对我来说，统计物理的巨大魅力在于它与数学某些部分的联系，否则人们很少接触到这些部分。

乌伦贝克对统计力学产生了非常重大的影响，把一个极为多样且零散不整的领域带入了某种有结构的整体之中。他总是非常热衷于清晰性，以及对他所研究的一切问题采取逻辑的方法。乌伦贝克的学生Cohen在2中告诉了我们许多关于乌伦贝克性格的事情。

……[乌伦贝克]常常告诫我，与其试图追求原创，远为重要的是做到清晰和正确，并按照保罗·埃伦费斯特的传统对一个领域的现状作出批判性的总结。他明智地指出，往往具有持久价值的并不是对某个问题的第一个原创性贡献，而是最终那篇写得清晰而带有批判性的综述。这 certainly 正是他在这篇布朗运动论文中所做的！

至于乌伦贝克论文的风格，Cohen写道：-

乌伦贝克的论文全都相对简短，并以简洁、精确和清晰而著称，经过精心打磨，以加深对统计物理学中某个基本问题的理解。它们不包含冗长的形式推导，而且几乎全都针对具体问题。……它们具有一种古典的高贵、数学的纯粹和清晰……他觉得真正原创的东西一个人一生只做一次——就像电子自旋那样——其余的时间都花在澄清基础之上。

Cohen还在[2]中评论了乌伦贝克教学的高质量：-

他是一位鼓舞人心的教师。凭借组织得极为出色、极其清晰的讲课，他让所有人都能看到统计力学的美妙结构，这一结构建立在奠基者詹姆斯·克拉克·麦克斯韦、路德维希·玻尔兹曼和约西亚·威拉德·吉布斯的原理之上。就这样，他把他所理解的过去的精华以及通向未来的道路传给了更年轻的一代。在此过程中，他以本世纪罕见的方式培养了数代统计力学物理学家。

乌伦贝克因其工作获得了许多荣誉。这些包括1955年被任命为亨德里克·洛伦兹教授，以及1959年担任美国物理学会主席。他于1965年被授予马克斯·普朗克奖章，1970年被授予荷兰皇家科学院的亨德里克·洛伦兹奖章，1977年获得美国国家科学奖章，1979年获得沃尔夫物理学奖。

George Uhlenbeck's ancestors had come first from Germany but then later generations were Dutch and served in the Dutch colonies. His father, Eugenius Marius Uhlenbeck was born in Java in what was then called the Dutch East Indies but is now Indonesia. In 1893 Eugenius Uhlenbeck, who served in the Dutch East Indian Army, married Anne Marie Beeger who was the daughter of a Dutch major general. Two of their children died of malaria at a very young age but four survived. Of the surviving children George was the second child, with an older sister Annie and two younger brothers Willem Jan and Eugenius Marius.

When George was six years old the family moved permanently to Holland, setting up home in The Hague. There George attended elementary school followed by high school, or the higher burger school as it was then called. Uhlenbeck said [3]:-

I was a very dutiful student, very dutiful. I always worked very regularly and I was always very good in class. I was certainly not clear until the last years in high school what I was going to do.

However, as with so many people, he was influenced by an excellent school teacher. In his last couple of years at school his physics teacher strongly encouraged him, gave him texts on the differential and integral calculus and suggested that he read undergraduate texts on mathematics and physics. One of the books which made him enthusiastic about physics was Lorentz's Lectures on Physics which he read in the Royal Library in The Hague.

Although Uhlenbeck performed extremely well in his final school examinations in July 1918, he was not allowed to enter a university since his studies had not included Greek and Latin. This was not his fault, simply that the school he attended did not offer these topics. He had no choice but to enter the Institute of Technology in Delft. He chose to study chemical engineering there but shortly after, when the rules were changed by the Dutch government so that Greek and Latin were no longer required for university entrance, he left the Institute of Technology. Having spent just one semester studying chemical engineering he began his university study at the University of Leiden.

Uhlenbeck was doubly glad to be able to make the move, firstly because he had always wanted to study physics and mathematics at university, but also because he felt he did not have the dexterity to undertake a practical subject. At Leiden physics was taught by Ehrenfest, H K Onnes and J P Kuenen while Lorentz, by that time retired from his chair, came in to lecture once a week. Uhlenbeck bought a copy of Boltzmann's Lectures on gas dynamics and he studied this in his own time, continuing the way of learning which he had adopted at school. At first he found it almost impossible to understand but after reading an encyclopaedia article by Ehrenfest it began to make sense. Of the lectures he attended those on the foundations of analysis he found greatly to his liking, finding that the rigour of analysis was particularly pleasing to him. Later in his career Ehrenfest would encourage him to present his mathematics with less rigour.

Uhlenbeck's parents did not find it easy to provide the necessary financial support for him at university. To keep down the expense, he travelled every day from The Hague to Leiden, a long and tiring journey. In his second year as an undergraduate Uhlenbeck studied Maxwell's theory which he wrote out in great detail. This impressive piece of work led to him being awarded a scholarship for his third year of study which took the financial burden away from his parents. As he had done at school, Uhlenbeck worked exceptionally hard and performed well in his final examinations in December 1920.

After graduating, he began postgraduate studies at Leiden under the supervision of Ehrenfest. In order to support himself financially, however, he had to work. He took a part-time job as a teacher in a girls school in Leiden which gave him sufficient money to allow him to rent a room. At last the daily travelling was over. He settled down to the work for his Master's degree which involved attending lecture courses. Pais writes [5]:-

Ehrenfest's graduate lectures consisted of a two-year course: Maxwell theory, ending with the theory of electrons and some relativity, one year; and statistical mechanics, ending with atomic structure and quantum theory the other. Uhlenbeck attended these lectures and took additional instruction in mathematics.

In September 1922, before obtaining his Master's degree, Uhlenbeck took the opportunity to spend time working in Italy when he accepted an appointment as a private tutor to the son of the Dutch ambassador in Rome. He held this job until June 1925, but he returned to Holland each summer. He completed the work for his Master's degree after one more year and then he was examined and received the degree in September 1923. Shortly after the award of the degree Uhlenbeck returned to Italy and, on Ehrenfest's advice, made contact with Enrico Fermi. This proved to be an important friendship for both men.

However despite this contact with scientists, Uhlenbeck's academic interests turned towards history. When his appointment in Italy ended and he had returned to Holland he was close to making a decision to become an historian. Ehrenfest, keen to keep him a scientist, suggested that he work for him for a while and gave Uhlenbeck a two year appointment as his assistant. He succeed Struik who had been awarded a Rockefeller Fellowship. Very soon after taking up the appointment, working with a graduate student Samuel Goudsmit, Uhlenbeck made his most important scientific discovery when he discovered electron spin.

In January 1925 Pauli had proposed that the electron should be given an additional fourth quantum number which was a half integer. This was one of the clues which led Uhlenbeck to arrive at the idea of electron spin. He wrote (see for example [2]):-

... it occurred to me that , since (I had learned) each quantum number corresponds to a degree of freedom of the electron, Pauli's fourth quantum number must mean that the electron had an additional degree of freedom -- in other words the electron must be rotating.

The concept immediately excited Niels Bohr, Pauli, Einstein, Heisenberg and others interested in quantum theory. Uhlenbeck's work progressed well and particularly important was Oskar Klein's appointment to Leiden. The two quickly became friends and exchanged ideas, particularly on Klein's ideas about five dimensional relativity.

Uhlenbeck's doctoral work was written in Copenhagen where he spent two months devoted to intensive writing of his dissertation. It was of fundamental importance in quantum mechanics, systematising statistical notions and expanding on the electron spin ideas which had announced two years earlier. Immediately after being examined on his thesis, Uhlenbeck was appointed to Michigan. He married Else Ophorst in August 1927 then, in the following month, he arrived in Ann Arbor to take up the appointment.

He returned to the Netherlands to take up a chair in Utrecht in 1935. The chair had become vacant due to the holder, Kramers, moving to Leiden to take up the chair left vacant there after Ehrenfest committed suicide. He took leave from Utrecht in 1938 to spend a year as visiting professor at Columbia University in New York but after a short time back in Holland he left again for the United States in August 1939 shortly before the outbreak of World War II.

From 1943 until 1945 Uhlenbeck worked at MIT as a member of the team working on the development of radar. Then, after the war ended, he returned to Ann Arbor where, after spending 1948-49 at Princeton, he was named Henry Cahart professor at Michigan in 1954. Four years later, in 1960, he moved to the Rockefeller Institute in New York where he remained on the staff until he retired in 1971.

As well as fundamental work on quantum mechanics, Uhlenbeck worked on atomic structure and the kinetic theory of matter. He extended Boltzmann's equation to dense gasses and wrote two important papers on Brownian motion. The main topic on which he worked throughout his career was statistical physics. The aim of this topic was to understand the relationship between physics at atomic level and that at macroscopic level. In 1955 he explained the attraction of the area to him:-

To me the great charms of statistical physics lies in its connection with parts of mathematics with which otherwise one rarely comes in contact.

Uhlenbeck had a very significant influence on statistical mechanics and brought an area which was very varied and disjointed into some sort of structured whole. He was always very keen on clarity and a logical approach to all the problems he studied. Cohen, a student of Uhlenbeck's, tells us much about Uhlenbeck's character in [2].

... [Uhlenbeck] often admonished me that rather than trying to be original, it was much more important to be clear and correct and to summarise critically the present status of a field in the Ehrenfest tradition. He wisely observed that what is often of lasting value is not the first original contribution to a problem, but rather the final clearly and critically written survey. That is certainly what he did in this Brownian motion paper!

As to the style of Uhlenbeck's papers, Cohen writes:-

Uhlenbeck's papers are all relatively short and stand out by their conciseness, precision, and clarity, finely honed to a deeper understanding of a basic problem in statistical physics. They do not contain long formal derivations and are almost all geared to concrete problems. ... they were of a classic nobility, mathematical purity and clarity ... He felt that something really original one did only once - like the electron-spin--the rest of one's time one spent on clarifying the basics.

Cohen also comments on the high quality of Uhlenbeck's teaching in [2]:-

He was an inspiring teacher. With superbly organised and extremely clear lectures, he laid bare for everyone to see the beautiful structure of statistical mechanics, based on the principles of the founding fathers, Maxwell, Boltzmann, and Gibbs. Thus he transmitted to a younger generation what he conceived to be the essence of the past and the way to the future. In doing so, he educated several generations of physicists in statistical mechanics in a style rare in this century.

Uhlenbeck received many honours for his work. These include his appointment at Lorentz professor in 1955, and serving as President of the American Physical Society in 1959. He was awarded the Planck Medal in 1965, the Lorentz Medal of the Royal Dutch Academy of Sciences in 1970, the National Medal of Science from the United States in 1977, and the Woolf Prize for Physics in 1979.