数学家传记
沃尔夫冈·泡利因其在量子力学方面的工作而获得诺贝尔奖。
沃尔夫冈·泡利 是 泡利 Joseph 和 Berta Camilla Schütz 的儿子。泡利 Joseph 曾在布拉格接受过医学博士培训。取得资格后,他在维也纳行医并迅速走红。1898 年,他改名为 泡利 Joseph Pauli,并在次年从犹太教皈依为罗马天主教徒。他于 1899 年 5 月与 Berta Schütz 结婚,但此时他已放弃医疗实践,转而从事化学和物理学研究,成为一名大学教授。
泡利 Joseph 受 Ernst Mach 启发而学习科学,当他的第一个孩子出生时,他给他取名为 泡利 Ernst Pauli,并给他中间名 Ernst 以纪念 Mach。泡利 的中间名不仅来自 Mach,Mach 还是他的教父,在他于 1900 年 5 月 31 日受洗时送给他一个银杯。
泡利 在维也纳上学,在那里他在 Döblingen 文理中学(Gymnasium) 开始了对数学和物理学的深入研究。他肯定不是一个典型的学生,因为他在还在文理中学时就读了 阿尔伯特·爱因斯坦 关于相对论的论文。学校功课对才华横溢的 泡利 来说很无聊,他把 阿尔伯特·爱因斯坦 的论文藏在课桌下,在课堂上研究它们。上课不专心并没有阻碍 泡利,因为他于 1918 年 7 月以优异成绩从文理中学毕业。
离开文理中学后,他进入慕尼黑路德维希-马克西米利安大学。离开学校两个月内,他就提交了第一篇关于相对论的论文。还在慕尼黑读本科时,他又写了两篇关于相对论的文章。在慕尼黑,泡利由阿诺·索末菲授课,后者很快认出了他的天才。阿诺·索末菲在泡利上大学仅两年时就请他Encyclopädie der mathematischen Wissenschaften撰写一篇关于相对论的评论文章,这标志着他对泡利的高度重视。这种尊重是相互的,因为泡利对阿诺·索末菲作为个人和科学家的尊重超过了对任何其他人的尊重。
泡利 在写到他在慕尼黑的学生时代时写道(见 [17] 中给出的 泡利 1945年诺贝尔奖演讲摘录):-
当每一位习惯于经典思维方式的物理学家第一次了解到玻尔的quantum theory基本假设时,所经历的那种震撼,我也未能幸免。
1920年6月,他写下了关于量子物理的第一篇论文,这是一项关于物质磁性的工作。1920年正是维尔纳·海森堡来到慕尼黑、也成为阿诺·索末菲学生的那一年。在[21]中,Pais引用了维尔纳·海森堡对泡利当时生活方式的描述:——
泡利是个典型的夜猫子。他更喜欢城里,喜欢在咖啡馆消磨夜晚,之后便会以极大的强度和极大的成功投入物理学工作。因此,令阿诺·索末菲沮丧的是,他很少去听上午的课,直到中午前后才会露面。
1921年7月,泡利在阿诺·索末菲的指导下获得了博士学位,学位论文是关于电离分子氢的量子理论的。在关于这篇论文的报告中,阿诺·索末菲写道,它显示出:——
……如同他许多已经发表的较小研究和他那篇较大的百科全书文章一样,对数学物理工具的充分掌握。
阿诺·索末菲对这篇论文大加赞扬无疑是正确的,但它令泡利失望,因为他所证明的理论结果与实验证据不符。现在来看,它表明,当时所表述的量子理论本身并不能提供必要的结构,以便在此基础上建立一种与实验证据相符的合乎逻辑的原子结构理论。
获得博士学位两个月后,泡利的相对论综述问世,此时已扩展为一部237页的著作。他的天才立即得到阿尔伯特·爱因斯坦的认可,后者在阅读了泡利关于相对论的专著后,写了一篇评论[21]:-
无论谁研究这部成熟而构思宏大的著作,都可能不相信其作者是一个二十一岁的年轻人。人们会思忖最令人钦佩的是什么,是对思想发展的心理学理解,是数学推演的确定性,是深刻的物理洞察力,是清晰、系统阐述的能力,是对文献的了解,是对主题的完整处理,还是批判性评价的确定性。
泡利随后于1921年10月起被任命为哥廷根的马克斯·玻恩的助手。正是在哥廷根,他第一次亲自见到了尼尔斯·玻尔,他说(例如见[17]):-
……当我第一次亲自见到尼尔斯·玻尔时,我科学生活的新阶段开始了。这是在1922年,当时他在哥廷根做了一系列客座讲座,报告了他关于元素周期系统的理论研究。在这些会面期间,玻尔问我是否能来哥本哈根一年。
泡利急切地接受了邀请,并在玻尔研究所度过了1922-23年[17]:-
应玻尔的邀请,我于1922年秋天前往哥本哈根,在那里我认真努力地解释所谓的‘反常埃里克·克里斯托弗·齐曼效应’,……这是一种磁场中谱线分裂的类型,不同于正常的三重线。
1923年,泡利被任命为汉堡privatdozent[17]:-
1923年我回到汉堡大学后不久,就在那里以私人讲师的身份作了关于元素周期系统的就职演讲。演讲的内容让我感到很不满意,因为电子壳层闭合的问题没有得到进一步的阐明。
1924年,泡利为电子提出了一个量子自旋数。他最著名的是1925年提出的Pauli exclusion principle,该原理指出原子中不可能有两个电子具有相同的四个量子数。在这篇维尔纳·海森堡发表后不到一年,他就提交了关于量子力学的文章,这篇文章将改变整个研究该主题的方法。泡利此前已开始觉得,用当时存在的理论无法取得进一步进展,但他很快利用维尔纳·海森堡的新思想取得了进展,并在1925年底之前从新理论推导出了氢光谱。
1927年,泡利遭遇了个人悲剧,与他非常亲近的母亲自杀身亡。次年,他的父亲再婚,这给泡利带来了更加不幸的处境,他称父亲的新妻子为“邪恶的继母”。1929年5月6日,泡利离开了罗马天主教会,但其原因并不完全清楚。更多的不幸接踵而至,他于1929年12月23日在柏林与Käthe Margarethe Deppner结婚。这桩婚姻从未成功,即使在最初几个月也是如此,他们于1930年11月29日在维也纳离婚。
尽管有个人问题,泡利的事业进展顺利。1928年,他被任命为苏黎世联邦理工学院理论物理学教授,并很快取得了一些显著进展。1931年,他通过数学预测,守恒定律要求存在一种新粒子,他提议将其称为“中子”。他首次在1930年12月4日的一封信中提到了支持这种粒子的理论证据,并于1931年6月16日在帕萨迪纳的一次会议上公开宣布。《纽约时报》6月17日报道:-
今天,当瑞士苏黎世理工学院的W 泡利博士假设存在他称之为“中子”的粒子或实体时,原子核心的新居民被介绍给了物理学界。
然而,泡利仍不清楚这种粒子的存在和性质,直到1933年他才将他的预测付印发表。当时他首次声称该粒子质量为零。我们现在所知的中子是由查德威克于1932年发现的。泡利的粒子于1934年被恩里科·费米命名为中微子,当时他正确地指出它不是原子核的组成部分。后来它被实验发现。
泡利这段科学发现时期恰逢他个人困难日益增多的时期。也许是由于他不幸的婚姻,他开始酗酒,并因此咨询了心理学家卡尔·古斯塔夫·荣格。他并未接受荣格的治疗,而是由荣格的一位助手帮助了泡利。然而,泡利详细记录了1000多个梦,并在多年间寄给荣格,荣格基于其中一些梦发表了著作。泡利显然像相信物理学一样相信心理学。他晚年在一封给派斯的信中写道(例如见[21]):-
我个人的看法是,在未来的科学中,实在既不是“心理的”也不是“物理的”,而是以某种方式既是两者又都不是。
1934年4月4日泡利与弗朗西斯卡·贝特拉姆结婚后,情况好转了。与他第一次灾难性的婚姻相比,他的第二次婚姻证明是对他的巨大支持。他去世后,弗朗西斯卡泡利这样评价她的已故丈夫:-
他很容易受伤,因此会拉下帷幕。他试图不承认现实而生活。而他的不谙世事恰恰源于他相信这是可能的。
1931年,泡利是密歇根大学的访问教授,然后在1935-1936年,他是普林斯顿高等爱德华·斯图迪的访问教授。他回到苏黎世,但在1939年第二次世界大战爆发后,他发现自己处境尴尬,因为德国在1938年吞并奥地利后,使他成为了德国公民。1940年,他收到普林斯顿的聘书,大大松了一口气,并被任命为那里的理论物理讲席,1941年作为密歇根大学的访问教授,1942年作为普渡大学的访问教授。
泡利担心法西斯主义可能导致欧洲科学生活的终结。为此,他积极鼓励美国和苏联的科学进展。他热衷于参加苏联的会议,参加了1939年在敖德萨举行的全联盟物理学会议和1937年在莫斯科举行的全联盟物理学会议。泡利还试图鼓励那些能留在意大利和德国的科学家这样做,因为他相信这可能确保科学文化在战后幸存。泡利没有留在美国,而是在第二次世界大战后回到了苏黎世。这对他来说不是一个容易的决定,但基本上他总是觉得自己是欧洲人,从未完全觉得自己融入了美国的生活。
泡利于1945年因其以下工作被授予诺贝尔奖:-
……通过他在1925年发现的一条新的自然定律,即不相容原理或泡利原理,做出了决定性的贡献。
他曾由阿尔伯特·爱因斯坦提名获奖。1945年他没有前往斯德哥尔摩参加颁奖典礼,但12月10日在普林斯顿为他举行了一个特别的仪式。在斯德哥尔摩,I Waller教授在泡利缺席的情况下发表了颁奖演说。他解释了不相容原理的重要性:-
泡利的研究基于对当时原子物理学中实验和理论知识深刻的分析。他发现,为了定义电子的能量状态,通常需要四个量子数。然后他提出了他的原理,该原理可以表述为:当每个能量状态被完全定义时,每个能量状态中不能有一个以上的电子。只有三个量子数可以与电子绕原子核的旋转相关联。第四个量子数的必要性证明了电子存在有趣的性质。
其他物理学家发现,这些性质可以通过说明电子具有“自旋”来解释,即它在某种程度上表现得好像它围绕通过其重心的轴快速旋转。
泡利自己表明,电子构型通过不相容原理变得完全可理解,因此该原理对于阐明不同元素的特征物理和化学性质至关重要。在那些必须借助泡利原理才能解释的重要现象中,我们提到金属的导电性和物质的磁性。
在1925年和1926年,量子理论——原子物理学的基础——取得了另一类重要的进展。描述粒子运动的新颖且革命性的方法被发展出来。
自旋的提议,赋予了泡利的第四个量子数以意义,最早由乔治·乌伦贝克在1925年提出。泡利于次年12月13日在斯德哥尔摩发表了他的诺贝尔演讲。
在[20]中,Laurikainen写到了二战后泡利的工作将他引向的其他方向:-
在他生命的最后10至15年里,泡利花费大量时间研究科学史与科学哲学。他的出发点是量子力学哲学,但这将他引向心理学、思想史以及许多其他领域,尤其是宗教与自然科学的关系。
除了诺贝尔奖之外,泡利因其工作还获得了许多荣誉。他于1953年当选为伦敦皇家学会会士,还当选为瑞士物理学会、美国物理学会和美国科学促进会会员。1931年10月,他在阿姆斯特丹被授予亨德里克·洛伦兹奖章。
[3]的作者写道:-
……他有一种天赋,能抓住某个可以变得简单的要点,并且一经呈现便立刻显出重要性。这就是他天才的特质——而他天性中以及思维中的那种简洁,也使他深受爱戴。
Wolfgang Pauli was the son of Wolfgang Joseph and Berta Camilla Schütz. Wolfgang Joseph had trained as a medical doctor in Prague. After qualifying, he practised as a doctor in Vienna and quickly became popular. In 1898 he changed his name to Wolfgang Joseph Pauli and, in the following year, converted from Judaism to become a Roman Catholic. He married Berta Schütz in May 1899 but by this time he had given up his medical practice for research in chemistry and physics, becoming a university professor.
Wolfgang Joseph had been inspired to study science by Ernst Mach, and when his first child was born he named him Wolfgang Ernst Pauli, giving him the middle name of Ernst in honour of Mach. Not only did Pauli's middle name come from Mach, but Mach was also his godfather giving him a silver cup when he was christened on 31 May 1900.
Wolfgang attended school in Vienna where he began a deep study of mathematics and physics at the Döblingen Gymnasium. He was certainly not a typical pupil for he read Einstein's papers on relativity while he was still at the Gymnasium. School work was boring to the brilliant Pauli and he hid Einstein's papers under his school desk and studied them during the lessons. Not paying attention in class did not hold Pauli back, for he graduated from the Gymnasium in July 1918 with distinction.
After leaving the Gymnasium he entered the Ludwig-Maximilian University of Munich. Within two months of leaving school he had submitted his first paper on the theory of relativity. While still an undergraduate at Munich he wrote two further articles on the theory of relativity. At Munich, Pauli was taught by Sommerfeld who quickly recognised his genius. Sommerfeld asked Pauli to write a review article on relativity for the Encyclopädie der mathematischen Wissenschaften when he had only been two years at university, a mark of the high regard in which he held Pauli. The respect was mutual, for Pauli showed more respect for Sommerfeld, both as a person and as a scientist, than he did for any other.
Pauli, writing about his days as a student at Munich, wrote (see the extracts from Pauli's Nobel Prize lecture in 1945 given in [17]):-
I was not spared the shock which every physicist accustomed to the classical way of thinking experienced when he came to know Bohr's basic postulate of quantum theory for the first time.
He wrote his first paper on quantum physics in June 1920, a work on the magnetic properties of matter. The year 1920 was when Heisenberg arrived in Munich, also to become a student of Sommerfeld. In [21] Pais quotes from Heisenberg's description of Pauli's way of life at this time:-
Wolfgang was a typical night bird. He preferred the town, liked to spend evenings in some café, and would thereafter work on his physics with great intensity and great success. To Sommerfeld's dismay he would therefore rarely attend morning lectures and would not turn up until about noon.
Pauli received his doctorate, which had been supervised by Sommerfeld, in July 1921 for a thesis on the quantum theory of ionised molecular hydrogen. In his report on the thesis Sommerfeld wrote that it showed:-
... like his many already published smaller investigations and his larger encyclopedia article, the full command of the tools of mathematical physics.
Sommerfeld was certainly right to heap much praise on the thesis but it had been a disappointment to Pauli since the theoretical results he had proved did not agree with experimental evidence. Looking at it now one can see that it showed that quantum theory, as then formulated, was not in itself going to provide the necessary structure on which to build a logical theory of atomic structure which agreed with experimental evidence.
Two months after the award of his doctorate Pauli's survey of the theory of relativity appeared, by this time having grown into a work of 237 pages. His genius was immediately recognised by Einstein who, after reading Pauli's monograph on relativity, wrote a review [21]:-
Whoever studies this mature and grandly conceived work might not believe that its author is a twenty-one year old man. One wonders what to admire most, the psychological understanding for the development of ideas, the sureness of mathematical deduction, the profound physical insight, the capacity for lucid, systematical presentation, the knowledge of the literature, the complete treatment of the subject matter, or the sureness of critical appraisal.
Pauli was then appointed to Göttingen as Born's assistant from October 1921. It was in Göttingen that he first met Niels Bohr in person and he said (see for example [17]):-
... a new phase of my scientific life began when I met Niels Bohr personally for the first time. This was in 1922, when he gave a series of guest lectures at Göttingen when he reported on his theoretical investigations on the periodic system of elements. During these meetings, Bohr asked me whether I could come to Copenhagen for a year.
Pauli eagerly accepted the invitation and spent the year 1922-23 at Bohr's Institute [17]:-
Following Bohr's invitation, I went to Copenhagen in the autumn of 1922, where I made a serious effort to explain the so-called 'anomalous Zeeman effect', ... a type of splitting of the spectral lines in a magnetic field which is different from the normal triplet.
In 1923, Pauli was appointed a privatdozent at Hamburg [17]:-
Very soon after my return to the University of Hamburg, in 1923, I gave there my inaugural lecture as privatdozent on the periodic system of elements. The contents of the lecture appeared very unsatisfactory to me, since the problem of the closing of the electronic shells had been clarified no further.
In 1924 Pauli proposed a quantum spin number for electrons. He is best known for the Pauli exclusion principle , proposed in 1925, which states that no two electrons in an atom can have the same four quantum numbers. Less than a year after this Heisenberg submitted his article on quantum mechanics which was to change the whole approach to the topic. Pauli, who before that had begun to feel that further advances could not be made with the theory as it then existed, quickly made progress using Heisenberg's new ideas and before the end of 1925 he had derived the hydrogen spectrum from the new theory.
The year 1927 saw personal tragedy for Pauli when his mother, to whom he had been very close, committed suicide. In the following year his father remarried making an even more unhappy situation for Pauli who referred to his father's new wife as "the evil step-mother". On 6 May 1929 Pauli left the Roman Catholic Church, but his reasons for this are not entirely clear. Further unhappiness was to follow when he married Käthe Margarethe Deppner in Berlin on 23 December 1929. The marriage was never a success, even in the first few months, and they were divorced in Vienna on 29 November 1930.
Despite the personal problems, Pauli's career progressed well. In 1928 he was appointed Professor of Theoretical Physics at the Federal Institute of Technology in Zürich and soon made some remarkable progress. He predicted mathematically, in 1931, that conservation laws required the existence of a new particle which he proposed to call the "neutron". He first mentioned his theoretical evidence for this particle in a letter written on 4 December 1930 and his public announcement came at a conference in Pasadena on 16 June 1931. The New York Times of 17 June reported:-
A new inhabitant of the heart of the atom was introduced to the world of physics today when Dr W Pauli of the Institute of Technology in Zürich, Switzerland, postulated the existence of particles or entities which he christened "neutrons".
The existence and properties of the particle were still not clear to Pauli, however, and it was not until 1933 that he published his prediction in print. At that time he made the claim, for the first time, that the particle had zero mass. The particle which we now know as the neutron had been discovered by Chadwick in 1932. Pauli's particle was named the neutrino by Fermi in 1934 and at that time he correctly stated that it was not a constituent of the nucleus of an atom. It was later found experimentally.
This period of scientific discovery by Pauli coincided with a period of increasing personal difficulties for him. Perhaps as a consequence of his disastrous marriage, he began drinking and as a result consulted the psychologist Carl Gustave Jung. He was not treated by Jung, rather it was one of his assistants who helped Pauli. However, Pauli detailed over 1000 dreams which he sent to Jung over many years and Jung published work based on some of the dreams. Pauli clearly believed in psychology as much as he did physics. He wrote later in his life in a letter to Pais (see for example [21]):-
It is my personal opinion that in the science of the future reality will neither be "psychic" nor "physical" but somehow both and somehow neither.
Things went better for Pauli after he married Franciska Bertram on 4 April 1934. In contrast with his first disastrous marriage his second marriage proved a great support to him. After his death, Franciska Pauli said this of her late husband:-
He was very easily hurt and therefore would let down a curtain. He tried to live without admitting reality. And his unworldliness stemmed precisely from his belief that this was possible.
In 1931 Pauli was Visiting Professor at the University of Michigan, then in 1935-1936 he was Visiting Professor at the Institute for Advanced Study, Princeton. He returned to Zürich but after the Second World War broke out in 1939 he found himself in an awkward situation since Germany, having annexed Austria in 1938, had made him a German citizen. In 1940 he was greatly relieved to receive an offer from Princeton and he was appointed to the chair of theoretical physics there, spending 1941 as Visiting Professor at the University of Michigan, and 1942 as Visiting Professor at Purdue University.
Pauli worried that fascism might bring about the end of scientific life in Europe. For this reason he actively encouraged scientific developments in the United States and also in the Soviet Union. He was keen to participate in conferences in the Soviet Union, attending the All-Union physics conference in Odessa in 1939 and the All-Union physics conference in Moscow in 1937. Pauli also tried to encourage those scientists who could remain in Italy and Germany to do so, for he believed this might ensure that scientific culture survived after the War. Pauli did not remain in the United States but he returned to Zürich after World War II. It was not an easy decision for him but basically he always felt European and never quite felt that he fitted into life in the United States.
Pauli was awarded the Nobel Prize in 1945 for his:-
... decisive contribution through his discovery in 1925 of a new law of Nature, the exclusion principle or Pauli principle.
He had been nominated for the prize by Einstein. He did not go to Stockholm for the prize ceremony in 1945 but there was a special ceremony at Princeton for him on 10 December. In Stockholm Professor I Waller delivered a presentation speech in Pauli's absence. He explained the importance of the exclusion principle:-
Pauli based his investigation on a profound analysis of the experimental and theoretical knowledge in atomic physics at the time. He found that four quantum numbers are in general needed in order to define the energy state of an electron. He then pronounced his principle, which can be expressed by saying that there cannot be more than one electron in each energy state when this state is completely defined. Three quantum numbers only can be related to the revolution of the electron round the nucleus. The necessity of a fourth quantum number proved the existence of interesting properties of the electron.
Other physicists found that these properties may be interpreted by stating that the electron has a "spin", i.e. that it behaves to some extent as if it were rapidly rotating round an axis through its centre of gravity.
Pauli showed himself that the electronic configuration is made fully intelligible by the exclusion principle, which is therefore essential for the elucidation of the characteristic physical and chemical properties of different elements. Among those important phenomena for the explanation of which the Pauli principle is indispensable, we mention the electric conductivity of metals and the magnetic properties of matter.
In 1925 and 1926 essential progress of another kind was made in the quantum theory, which is the foundation of atomic physics. New and revolutionary methods were developed for the description of the motion of particles.
The spin proposal, which gave meaning to Pauli's fourth quantum number, was first suggested by Uhlenbeck in 1925. Pauli delivered his Nobel Lecture in Stockholm on 13 December in the following year.
In [20] Laurikainen writes about other directions which Pauli's work took him in the years following World War II:-
During the last 10-15 years of his life, Pauli spent much time studying the history and philosophy of science. His starting point was the philosophy of quantum mechanics, but this led him to psychology, the history of ideas and many other fields, not least the relation of religion to natural science.
Pauli received many honours for his work in addition to the Nobel Prize. He was elected a Fellow of the Royal Society of London in 1953 and he was also elected a member of the Swiss Physical Society, the American Physical Society, and the American Association for the Advancement of Science. He was awarded the Lorentz Medal in Amsterdam in October 1931.
The author of [3] writes:-
... he had a genius of fastening on some one point which could be made simple, and so presented was seen at once to be important. That was the quality of his genius - and the simplicity that was in his nature as well as in his thinking made him also well loved.
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