保罗·狄拉克Paul Dirac

保罗·狄拉克的父亲是Charles Adrien Ladislas 狄拉克，母亲是Florence Hannah Holten。Charles Dirac是瑞士公民，出生于瑞士瓦莱州的蒙泰，而他的母亲来自英格兰的康沃尔。Charles曾在日内瓦大学接受教育，后于1888年左右来到英格兰，在布里斯托尔教授法语。在那里他遇到了Florence，她的父亲曾作为一艘布里斯托尔船只的船长移居布里斯托尔，当时她正在那里的图书馆工作。Charles和Florence于1899年结婚，搬进了布里斯托尔Bishopston的一所房子，他们以Charles出生的城镇将其命名为蒙泰。此时Charles在布里斯托尔商人冒险家技术学院附属中学教授法语。

狄拉克是三个孩子之一，他的哥哥是Reginald Charles Felix Dirac，他的妹妹是Beatrice Isabelle Marguerite Walla 狄拉克。狄拉克有着非常严格的家庭教养。他的父亲坚持在餐桌上只说法语，因此，狄拉克是唯一一个在餐厅与父亲一起吃饭的人。狄拉克的父亲对他的儿子们如此严格，以至于两人都被疏远，狄拉克在一个有些不幸的家庭中长大。

狄拉克就读的第一所学校是Bishop Primary school，在这所学校里，他的数学天赋已经让老师们刮目相看。十二岁时，他进入中学，就读于他父亲任教的那所中学，该校是商人冒险家技术学院的一部分。大约在狄拉克进入这所学校的时候，第一次世界大战爆发了，这对狄拉克来说反而有利，因为学校里年龄较大的男孩都去服兵役了，年龄较小的男孩有更多机会使用科学实验室和其他设施。狄拉克本人在[14]中这样描述他的学生时代：-

Merchant Venturers是一所优秀的学校，理科和现代语言都很出色。那里不教拉丁语或希腊语，我对此相当高兴，因为我不欣赏古老文化的价值。我认为自己能进入这所学校非常幸运。……我被快速送过低年级，在特别小的年纪就在高年级接触了数学、物理和化学的基础。在数学方面，我学习的课本大多超出了班上其他同学的进度。这种快速进步对我后来的职业生涯帮助很大。

他于1918年完成中学教育，随后在布里斯托尔大学学习电气工程。此时该大学已与商人冒险家技术学院合并，因此狄拉克仍在他中学四年学习时的那栋楼里学习。尽管数学是他最喜欢的科目，他还是选择在大学学习工程课程，因为他认为数学家唯一可能的职业是学校教书，而他当然想避开这个职业。他于1921年获得工程学位，但此后，在一家工程厂做了一份平平无奇的暑期工作后，他没能找到固定职位。此时他对数学产生了真正的热情，但他试图去剑桥学习的努力却因相当奇怪的原因而失败。

1921年6月参加剑桥奖学金考试时，他获得了在剑桥圣弗瑞兹·约翰学院学习数学的奖学金，但这不足以支持他的生活。原本期望从当地教育当局获得额外支持，但他被拒绝支持，理由是他的父亲成为英国公民的时间不够长。狄拉克获得了免学费在布里斯托尔学习数学的机会，他这样做了，并于1923年获得一等荣誉学位。此后，他获得了一笔在剑桥进行研究的资助，并于1923年开始在那里学习。

狄拉克一直希望由埃比尼泽·坎宁安指导他的研究，因为此时狄拉克已经迷上了广义相对论，想就这个课题进行研究。埃比尼泽·坎宁安已经收了他愿意接收的那么多研究生，因此狄拉克由Ralph 拉尔夫·福勒指导。[13]的作者写道：-

Fowler当时是剑桥的顶尖理论家，精通原子的quantum theory；他自己的研究主要是统计力学。他在狄拉克身上发现了一个能力非凡的学生。在他的影响下，狄拉克研究了一些统计力学问题。到剑桥后六个月内，他就这些问题写了两篇论文。毫无疑问，拉尔夫·福勒激发了他对量子理论的兴趣，1924年5月，狄拉克完成了他的第一篇处理量子问题的论文。到1925年11月，他又完成了四篇论文。

尽管狄拉克作为研究生在学业上取得了明显的成功，但这段时期对他来说并不轻松。他的兄弟雷金纳德狄拉克在此期间自杀了。自杀的原因似乎不为人知，但狄拉克与父亲本已紧张的关系在此之后似乎几乎完全断绝，这确实表明狄拉克觉得父亲至少负有部分责任。他本就是一个朋友很少的人，这一个人悲剧使他变得更加孤僻。

尽管他在研究生涯中已经有了一个极好的开端，但更令人印象深刻的工作还在后面。这是由于狄拉克在1925年夏天获赠了一篇维尔纳·海森堡的论文校样来阅读。当狄拉克在乡间散步时，维尔纳·海森堡的对易子的代数性质的意义击中了他。他意识到维尔纳·海森堡的不确定性原理是关于量子力学可观测量不可交换性的陈述。他意识到这与哈密顿力学中的西莫恩·德尼·泊松括号的类比。希格斯在[14]中写道：-

这种相似性提供了线索，引导他首次系统地阐述了一种与哈密顿力学相对应的、数学上一致的量子力学一般理论。

这些思想在狄拉克的博士论文Quantum mechanics中得到了阐述，他因此于1926年被授予博士学位。值得注意的是，狄拉克在提交博士论文之前已有十一篇论文发表。获得学位后，他前往哥本哈根与尼尔斯·玻尔合作，并于1927年2月转到哥廷根，在那里他与罗伯特·奥本海默、马克斯·玻恩、詹姆斯·弗兰克和俄罗斯人伊戈尔·塔姆进行了交流。接受保罗·埃伦费斯特的邀请，他在返回剑桥的途中在莱顿逗留了几周。他于1927年当选为剑桥圣约翰学院的研究员。

狄拉克于1928年访问苏联。这是许多次访问中的第一次，因为他在1929年、1930年、1932年、1933年、1935年、1936年、1937年、1957年、1965年和1973年又去了。同样在1928年，他发现了相对论与量子力学之间的联系，即他著名的自旋1/2的狄拉克方程。1929年，他首次访问美国，在威斯康星大学和密歇根大学讲学。访问之后，他与维尔纳·海森堡一起横渡太平洋，在日本讲学。他经西伯利亚大铁路返回。

1930年，狄拉克发表了The principles of Quantum Mechanics，并因此项工作于1933年被授予诺贝尔物理学奖。德法西奥在评论[4]时，这样评价这本书：-

狄拉克没有受到当时实验现象学中那种狂热追捧的影响。这赋予了狄拉克的书……一种持久的品质，很少有著作能与之匹敌。

[13]的作者评论道，这本书——

……反映了狄拉克非常典型的方法：抽象但简单，总是选取要点，并以无懈可击的逻辑进行论证。

讣告[2]指出——

他在剑桥的讲座紧密以[量子力学原理]为蓝本，它们向一代代学生传达了量子理论之连贯与优雅的强烈印象。这些讲座构成了他对教育的主要贡献，因为他很少招收研究生。

同样在1930年，狄拉克当选为皇家学会的会士。这一荣誉在他首次被提名时就到来了，这本身是相当不寻常的事，充分说明了狄拉克的科学家同行们对他评价极高。

狄拉克于1932年被任命为剑桥大学卢卡斯数学讲席教授，他担任此职37年。1933年，他发表了一篇关于拉格朗日量子力学的开创性论文，这篇论文成为理查德·费曼后来建立其路径积分思想的基础。同年，狄拉克获得诺贝尔物理学奖，与埃尔温·薛定谔共享。关于狄拉克的性格，一个有趣的评论是，他的第一个念头是拒绝该奖，理由是他讨厌出风头。然而，当有人向他指出，如果他拒绝该奖，他会受到多得多的关注时，他接受了。关于这一事件的另一则评论是，狄拉克被告知可以邀请父母参加在斯德哥尔摩举行的颁奖典礼，但他选择只邀请母亲而不邀请父亲。

1934-35学年对狄拉克来说在个人和职业两方面都很重要。他访问了普林斯顿的爱德华·斯图迪高等研究院，并在那里与尤金·维格纳交好。当狄拉克在那里时，尤金·维格纳住在布达佩斯的妹妹Margit来看望她的哥哥。这次偶然的相遇导致狄拉克于1937年1月在伦敦与Margit结婚。Margit此前结过婚，从第一次婚姻中育有两个孩子Judith和Gabriel Andrew。两个孩子都改姓狄拉克，Gabriel Andrew Dirac后来成为著名的纯数学家，尤其对图论有贡献，成为丹麦奥胡斯大学的纯数学教授。

1937年，也就是他结婚的同一年，狄拉克发表了他的第一篇关于大数和宇宙学问题的论文。我们在下面进一步评论他的宇宙学思想。他在1938年发表了他关于经典电子理论的著名论文，其中包括质量重正化和辐射反作用。狄拉克在第二次世界大战期间从事铀分离和核武器的工作。特别是，他担任伯明翰一个从事原子能研究的小组的顾问。这种联系导致狄拉克在战争结束后被英国政府阻止访问苏联；直到1957年他才得以再次访问。

我们在上文注意到，狄拉克于1930年当选为皇家学会的会士。他于1939年被授予皇家学会的皇家奖章，该学会又于1952年授予他科普利奖章——

以表彰他在量子力学中粒子相对论动力学方面的杰出贡献。

1969年，狄拉克从剑桥大学卢卡斯数学讲席退休，与家人前往美国佛罗里达。他在迈阿密大学和佛罗里达州立大学担任访问职务。随后，1971年，狄拉克被任命为佛罗里达州立大学物理学教授，并在那里继续他的研究。

1973年和1975年，狄拉克在列宁格勒物理工程研究所讲学。在这些讲座中，他谈到了宇宙学问题，或者更准确地说，谈到了世界常数的无量纲组合问题。

狄拉克对物理学做出了极其重要的贡献，重要的是要认识到他总是受到数学美原则的激励。狄拉克统一了量子力学和相对论，但他也因在磁单极子、基本长度、反物质、d函数、bra-kets等方面的杰出工作而被人们铭记。

关于狄拉克有一个标准的民间传说，主要围绕狄拉克说话精确，不多说一个字。有一次，有人在晚餐时礼貌地闲聊，评论说风很大，狄拉克离开餐桌走到门口，向外看了看，回到餐桌回答说确实风很大。有人开玩笑说，他的口语词汇只有“是”、“不”和“我不知道”。当然，当苏布拉马尼扬·钱德拉塞卡向狄拉克解释他的想法时，他不断插话“是”，然后向苏布拉马尼扬·钱德拉塞卡解释说，“是”并不意味着他同意他所说的话，只是希望他继续。他曾说：-

我在学校被教导，在不知道句子结尾的情况下绝不要开始一个句子。

这或许可以解释很多关于他谈话的方式，以及他书中和论文中那些写得很漂亮的句子。

狄拉克因其工作获得了许多荣誉，其中一些我们已在上文提及。他拒绝接受名誉学位，但确实接受了科学院和学术团体的名誉会员资格。这些名单很长，其中包括苏联科学院（1931年）、Indian Academy of Sciences（1939年）、中国物理学会（1943年）、Royal Irish Academy（1944年）、Royal Society of Edinburgh（1946年）、法兰西研究院（1946年）、印度国家科学院（1947年）、美国物理学会（1948年）、National Academy of Sciences（1949年）、National Academy of Arts and Sciences（1950年）、Accademia delle Scienze di Torino（1951年）、里斯本科学院（1953年）、Pontifical Academy of Sciences、梵蒂冈城（1958年）、Accademia Nazionale dei Lincei、罗马（1960年）、Royal Danish Academy of Sciences（1962年）和Académie des Sciences Paris（1963年）。他于1973年被授予功绩勋章。

1985年4月19日在剑桥大学举行了一次纪念会议，会议上提交的论文发表在Tributes to Paul Dirac, Cambridge, 1985（布里斯托尔，1987年）。论文[12]、[15]、[25]、[30]、[37]、[39]和[40]来自该卷。Achuthan在评论该卷时写道：-

……我们处处生动地看到狄拉克的光辉印记，他是量子力学与相对论的统一者。每一篇不仅是对一位天赋异禀的智者的颂扬，而且记录了人类心智能够多么深刻而持久地深入数学洞察与建模的领域，同时保持一位创造性天才的美与清晰的精神。只有少数诺贝尔奖得主能与之相提并论，这位数学科学巨人的逝世无疑使原创思想的世界失去了一位最珍贵的灵魂，所幸其荣耀仍留存，供后人长久地歌颂与效仿。

1995年11月，一块纪念狄拉克的牌匾在威斯敏斯特教堂揭幕。该卷[9]收录了为此场合向皇家学会提交的演讲。纪念演说由史蒂芬·霍金发表，他是狄拉克在剑桥卢卡斯数学讲席的继任者，该讲席也曾是艾萨克·牛顿的讲席。

Paul Dirac's father was Charles Adrien Ladislas Dirac and his mother was Florence Hannah Holten. Charles Dirac was a Swiss citizen born in Monthey, in the Valais Canton of Switzerland, while his mother came from Cornwall in England. Charles had been educated at the University of Geneva, then came to England in around 1888 and taught French in Bristol. There he met Florence, whose father had moved to Bristol as Master Mariner on a Bristol ship, when she was working in the library there. Charles and Florence married in 1899 and they moved into a house in Bishopston, Bristol, which they named Monthey after the town of Charles's birth. By this time Charles was teaching French at the secondary school attached to the Merchant Venturers Technical College in Bristol.

Paul was one of three children, his older brother being Reginald Charles Felix Dirac and his younger sister being Beatrice Isabelle Marguerite Walla Dirac. Paul had a very strict family upbringing. His father insisted that only French be spoken at the dinner table and, as a result, Paul was the only one to eat with his father in the dining room. Paul's father was so strict with his sons that both were alienated and Paul was brought up in a somewhat unhappy home.

The first school which Paul attended was Bishop Primary school and already in this school his exceptional ability in mathematics became clear to his teachers. When he was twelve years old he entered secondary school, attending the secondary school where his father taught which was part of the Merchant Venturers Technical College. At about the time Paul entered this school, World War I began and this had a beneficial effect for Paul since the older boys in the school left for military service and the younger boys had more access to the science laboratories and other facilities. Paul himself wrote about his school years in [14]:-

The Merchant Venturers was an excellent school for science and modern languages. There was no Latin or Greek, something of which I was rather glad, because I did not appreciate the value of old cultures. I consider myself very lucky in having been able to attend the school. ... I was rushed through the lower forms, and was introduced at an especially early age to the basis of mathematics, physics and chemistry in the higher forms. In mathematics I was studying from books which mostly were ahead of the rest of the class. This rapid advancement was a great help to me in my latter career.

He completed his school education in 1918 and then studied electrical engineering at the University of Bristol. By this time the University had combined with the Merchant Venturers Technical College so Dirac remained in the same building as he had studied during his four years at secondary school. Although mathematics was his favourite subject he chose to study an engineering course at university since he thought that the only possible career for a mathematician was school teaching and he certainly wanted to avoid that profession. He obtained his degree in engineering in 1921 but following this, after an undistinguished summer job in an engineering works, he did not find a permanent position. By this time he was developing a real passion for mathematics but his attempts to study at Cambridge failed for rather strange reasons.

Taking the Cambridge scholarship examinations in June 1921 he was awarded a scholarship to study mathematics at St John's College, Cambridge, but it did not provide enough to support him. Additional support would have been expected from his local education authority, but he was refused support on the grounds that his father had not been a British citizen for long enough. Dirac was offered the chance to study mathematics at Bristol without paying fees and he did so being awarded first class honours in 1923. Following this he was awarded a grant to undertake research at Cambridge and he began his studies there in 1923.

Dirac had been hoping to have his research supervised by Ebenezer Cunningham, for by this time Dirac had become fascinated in the general theory of relativity and wanted to undertake research on this topic. Cunningham already had as many research students as he was prepared to take on and so Dirac was supervised by Ralph Fowler. The authors of [13] write:-

Fowler was then the leading theoretician in Cambridge, well versed in the quantum theory of atoms; his own research was mostly on statistical mechanics. He recognised in Dirac a student of unusual ability. Under his influence Dirac worked on some problems in statistical mechanics. Within six months of arriving in Cambridge he wrote two papers on these problems. No doubt Fowler aroused his interest in the quantum theory, and in May 1924 Dirac completed his first paper dealing with quantum problems. Four more papers were completed by November 1925.

Despite the obvious academic success Dirac enjoyed as a research student this was no easy time for him. His brother Reginald Dirac committed suicide during this period. No reason for the suicide seems to be known but Dirac's relations with his father, already strained, seemed almost to end completely after this which does suggest that Dirac felt that his father carried at least some responsibility. Already a person who had few friends, this personal tragedy had the effect of making him even more withdrawn.

Although he had already made an excellent start to his research career, even more impressive work was to follow. This was as a result of Dirac being given proofs of a paper by Heisenberg to read in the summer of 1925. The significance of the algebraic properties of Heisenberg's commutators struck Dirac when he was out for a walk in the country. He realised that Heisenberg's uncertainty principle was a statement of the noncommutativity of the quantum mechanical observables. He realised the analogy with Poisson brackets in Hamiltonian mechanics. Higgs writes in [14]:-

This similarity provided the clue which led him to formulate for the first time a mathematically consistent general theory of quantum mechanics in correspondence with Hamiltonian mechanics.

The ideas were laid out in Dirac's doctoral thesis Quantum mechanics for which he was awarded a Ph.D. in 1926. It is remarkable that Dirac had eleven papers in print before submitting his doctoral dissertation. Following the award of the degree he went to Copenhagen to work with Niels Bohr, moving on to Göttingen in February 1927 where he interacted with Robert Oppenheimer, Max Born, James Franck and the Russian Igor Tamm. Accepting an invitation from Ehrenfest, he spent a few weeks in Leiden on his way back to Cambridge. He was elected a Fellow of St John's College, Cambridge in 1927.

Dirac visited the Soviet Union in 1928. It was the first of many visits for he went again in 1929, 1930, 1932, 1933, 1935, 1936, 1937, 1957, 1965, and 1973. Also in 1928 he found a connection between relativity and quantum mechanics, his famous spin-1/2 Dirac equation. In 1929 he made his first visit to the United States, lecturing at the Universities of Wisconsin and Michigan. After the visit, along with Heisenberg, he crossed the Pacific and lectured in Japan. He returned via the trans-Siberian railway.

In 1930 Dirac published The principles of Quantum Mechanics and for this work he was awarded the Nobel Prize for Physics in 1933. De Facio, reviewing [4], says of this book:-

Dirac was not influenced by the feeding frenzy in experimental phenomenology of the time. This has given Dirac's book ... a lasting quality that few works can match.

The authors of [13] comment that the book:-

... reflects Dirac's very characteristic approach: abstract but simple, always selecting the important points and arguing with unbeatable logic.

The obituary [2] notes:-

His lectures at Cambridge were closely modelled on [The principles of Quantum Mechanics], and they conveyed to generations of students a powerful impression of the coherence and elegance of quantum theory. They constituted his principal contribution to education, for he took very few research students.

Also in 1930 Dirac was elected a Fellow of the Royal Society. This honour came on the first occasion that his name was put forward, in itself quite an unusual event which says much about the extremely high opinion that Dirac's fellow scientists had of him.

Dirac was appointed Lucasian professor of mathematics at the University of Cambridge in 1932, a post he held for 37 years. In 1933 he published a pioneering paper on Lagrangian quantum mechanics which became the foundation on which Feynman later built his ideas of the path integral. In the same year Dirac received the Nobel prize for physics which he shared with Schrödinger. It is an interesting comment on Dirac's nature that his first thought was to turn down the prize on the grounds that he hated publicity. However when it was pointed out to him that he would receive far more publicity if he turned down the prize, he accepted it. Another comment about this event is that Dirac was told that he could invite his parents to the award ceremony in Stockholm, but he chose to invite only his mother and not his father.

The academic year 1934-35 was important for Dirac both for personal and professional reasons. He visited the Institute for Advanced Study at Princeton and there he became friendly with Wigner. While Dirac was there Wigner's sister Margit, who lived in Budapest, visited her brother. This chance meeting led, in January 1937, to Dirac marrying Margit in London. Margit had been married before and had two children Judith and Gabriel Andrew from her first marriage. Both children adopted the name Dirac and Gabriel Andrew Dirac went on the became a famous pure mathematician, particularly contributing to graph theory, becoming professor of pure mathematics at the University of Aarhus in Denmark.

In 1937, the same year that he married, Dirac published his first paper on large numbers and cosmological matters. We comment further on his ideas on cosmology below. He published his famous paper on classical electron theory, which included mass renormalisation and radiative reaction in 1938. Dirac worked during World War II on uranium separation and nuclear weapons. In particular he acted as a consultant to a group in Birmingham working on atomic energy. This association led to Dirac being prevented by the British government from visiting the Soviet Union after the end of the war; he was not able to visit again until 1957.

We noted above that Dirac was elected a fellow of the Royal Society in 1930. He was awarded the Royal Society's Royal Medal in 1939 and the Society awarded him their Copley Medal in 1952:-

... in recognition of his remarkable contributions to relativistic dynamics of a particle in quantum mechanics.

In 1969 Dirac retired from the Lucasian chair of mathematics at Cambridge and went with his family to Florida in the United States. He held visiting appointments at the University of Miami and at Florida State University. Then, in 1971, Dirac was appointed professor of physics at Florida State University where he continued his research.

In 1973 and 1975 Dirac lectured in the Physical Engineering Institute in Leningrad. In these lectures he spoke about the problems of cosmology or, to be more precise, to the problems of non-dimensional combinations of world constants.

Although Dirac made vastly important contributions to physics, it is important to realise that he was always motivated by principles of mathematical beauty. Dirac unified the theories of quantum mechanics and relativity theory, but he also is remembered for his outstanding work on the magnetic monopole, fundamental length, antimatter, the d-function, bra-kets, etc.

There is a standard folklore of Dirac stories, mostly revolving around Dirac saying exactly what he meant and no more. Once when someone, making polite conversation at dinner, commented that it was windy, Dirac left the table and went to the door, looked out, returned to the table and replied that indeed it was windy. It has been said in jest that his spoken vocabulary consisted of "Yes", "No", and "I don't know". Certainly when Chandrasekhar was explaining his ideas to Dirac he continually interjected "yes" then explained to Chandrasekhar that "yes" did not mean that he agreed with what he was saying, only that he wished him to continue. He once said:-

I was taught at school never to start a sentence without knowing the end of it.

This may explain much about his conversation, and also about his beautifully written sentences in his books and papers.

Dirac received many honours for his work, some of which we have mentioned above. He refused to accept honorary degrees but he did accept honorary membership of academies and learned societies. The list of these is long but among them are USSR Academy of Sciences (1931), Indian Academy of Sciences (1939), Chinese Physical Society (1943), Royal Irish Academy (1944), Royal Society of Edinburgh (1946), Institut de France (1946), National Institute of Sciences of India (1947), American Physical Society (1948), National Academy of Sciences (1949), National Academy of Arts and Sciences (1950), Accademia delle Scienze di Torino (1951), Academia das Ciencias de Lisboa (1953), Pontifical Academy of Sciences, Vatican City (1958), Accademia Nazionale dei Lincei, Rome (1960), Royal Danish Academy of Sciences (1962), and Académie des Sciences Paris (1963). He was appointed to the Order of Merit in 1973.

A memorial meeting was held at the University of Cambridge on 19 April 1985 and the papers presented at this meeting were published in Tributes to Paul Dirac, Cambridge, 1985 (Bristol, 1987). The papers [12], [15], [25], [30], [37], [39] and [40] come from this volume. Achuthan, reviewing the volume, writes:-

... we vividly see everywhere the brilliant imprints of Dirac, unifier of quantum mechanics and relativity theory. Each of the pieces not only is in praise of an exceptionally gifted intellect but also places on record how deeply and abidingly the human mind can delve into the realms of mathematical insight and modelling, keeping intact the spirit of beauty and clarity of a creative genius. Only a few Nobel laureates ever can compare as well with this giant of mathematical sciences in whose demise the world of original thinking certainly has lost one of the most precious souls retaining fortunately still the glory for others to sing and emulate for a long time to come.

In November 1995 of a plaque was unveiled in Westminster Abbey commemorating Paul Dirac. The volume [9] consists of lectures presented to the Royal Society on this occasion. The memorial address was presented by Stephen Hawking who was Dirac's successor in the Lucasian chair of mathematics at Cambridge which was also Newton's chair.