乔治·勒梅特Georges Lemaître

乔治·勒梅特的父母是Joseph Lemaître和Maguerite Lannoy。1911年，他进入鲁汶天主教大学攻读工程学学位。然而在1914年，当他还是本科生时，第一次世界大战爆发了。他自愿参军，在比利时军队中担任炮兵军官。他因勇敢而受到嘉奖，获得了军事十字勋章，但他在战场上目睹的可怕屠杀深深困扰着他，并改变了他的人生。战争结束后，他回到大学继续学业，但他的兴趣此时已从工程学转向数学。1920年，他在夏尔-让·德拉瓦莱·普桑的指导下提交了学位论文l'Approximation des fonctions de plusieurs variables réelles Ⓣ（多实变量函数的逼近），获得了数学科学博士学位。

战争经历给他的人生带来的另一个变化是，他进入了梅赫伦大主教区的神学院Maison Saint Rombaut，并于1923年被任命为神父，成为Abbé 勒梅特。此时，凭借从夏尔-让·德拉瓦莱·普桑那里学习获得的深厚数学背景，勒梅特转向了数学天文学，并前往英国剑桥，在1923-24学年期间师从亚瑟·爱丁顿，随后他前往美国，在接下来的学年中于马萨诸塞州的哈佛大学天文台度过。1925年，他接受了比利时鲁汶天主教大学兼职讲师的职位，但继续在哈佛大学和美国麻省理工学院度过时光。1927年，他因提交给麻省理工学院的学位论文The gravitational field in a fluid而获得博士学位。他在麻省理工学院的导师是哈罗·沙普利。他进行的研究，部分在哈佛、部分在麻省理工学院、部分在鲁汶完成，被写成Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extragalactiques Ⓣ（一个质量恒定且半径增长的均匀宇宙，解释了河外星云径向速度），并于1927年发表在Annales de la Société Scientifique de Bruxelles上。

在这篇开创性的论文中，勒梅特推导出了现在被称为爱德文·哈勃定律的关系，即星系远离的速度与其距离之间的关系。1927年，著名的索尔维会议召开，大多数顶尖物理学家都出席了。阿尔伯特·爱因斯坦参加了会议，他在布鲁塞尔对勒梅特说，他1927年论文中的想法已由亚历山大·弗里德曼在1922年提出，但他也说，尽管他认为勒梅特对广义相对论方程的解在数学上是正确的，但它们给出的解在物理上是不可行的。阿尔伯特·爱因斯坦说：-

你的计算是正确的，但你对物理学的理解糟透了。

阿尔伯特·爱因斯坦并不是唯一一个认为勒梅特的想法完全不可接受的人；相反，这几乎是所有科学家的意见。然而在1929年，爱德文·哈勃发表了著作，提出了更多宇宙膨胀的证据，与当时公认的静态宇宙理论相矛盾。亚瑟·爱丁顿和皇家天文学会的其他成员开始着手工作，试图解决理论与观测之间的差异所带来的问题。勒梅特随后将他1927年的论文副本寄给了亚瑟·爱丁顿，后者立即看出它提供了一种解释。亚瑟·爱丁顿安排将勒梅特的论文英译发表在Monthly Notices of the Royal Astronomical Society上，它确实于1931年3月出现在那里。勒梅特的理论中仍有一部分是包括亚瑟·爱丁顿在内的科学家们认为无法接受的，即宇宙在过去某个有限时间有一个开端的含义。几乎所有人都愿意相信宇宙一直存在。我们留给读者去思考这样一个想法：也许勒梅特深厚的基督教信仰使得世界在过去某个有限时间开始（如《创世记》所声称的）这一想法更容易被接受。

勒梅特在1931年5月发表于Nature的一篇论文中回应了对其理论的反对意见。他写道：-

如果世界始于一个单一的量子，那么空间和时间的概念在开端时将完全没有任何意义；只有当最初的量子被分割成足够数量的量子时，它们才开始具有可理解的意义。如果这个建议是正确的，那么世界的开端发生在空间和时间开端之前不久。

这是目前公认的“大爆炸”理论的首次明确表述。我们应该注意到，尽管大多数科学家接受了它，但弗雷德·霍伊尔并不接受这一理论，而“大爆炸”一词是弗雷德·霍伊尔在1950年一次广播中对勒梅特理论的嘲讽性描述。1933年，阿尔伯特·爱因斯坦和勒梅特在加利福尼亚做了一系列讲座。在其中一次研讨会上听完勒梅特解释他的理论后，阿尔伯特·爱因斯坦站起来说：-

这是我所听过的最美妙、最令人满意的关于创世的解释。

勒梅特于1933年在L'univers en expansionⓉ（膨胀的宇宙）中发表了他理论的更详细版本。M A H MacCallum翻译的这篇论文的英译本于1997年出版。他在1933年论文中提出的观点传到了大众媒体那里，媒体称他为世界领先的宇宙学家。New York Times上的一篇文章刊登了阿尔伯特·爱因斯坦和勒梅特的照片，并配有说明文字：-

他们彼此怀有深深的敬意和钦佩。

当然，勒梅特既是顶尖科学家又是天主教神父这一事实，正是大众媒体着迷的部分原因。在同一篇文章中，作者写道：-

“宗教与科学之间没有冲突，”勒梅特在这个国家一次又一次地告诉听众……他的观点有趣且重要，不是因为他是一位天主教神父，不是因为他是我们时代领先的数学物理学家之一，而是因为他两者兼具。

来自不同来源的荣誉纷纷授予他，例如1934年的弗朗基奖。该奖项由利奥波德三世国王授予勒梅特，是比利时所能授予的最高科学荣誉。1936年，他被教皇庇护十一世引入宗座科学院。他于1941年当选为比利时皇家科学院成员，1951年成为首位由皇家天文学会授予亚瑟·爱丁顿奖章的人，并于1960年至1966年担任宗座科学院主席。

勒梅特于1927年被任命为鲁汶大学教授，并在那里度过了余下的职业生涯。让我们看看他后来的一些出版物，特别是那些更具数学性质的。1942年，他出版了L'itération rationnelle Ⓣ（有理迭代），其中讨论了他将卡尔·弗里德里希·高斯的逐次逼近法应用于两个未知数的两个方程组成的系统，以根据三次观测确定行星的轨道。勒梅特随后将这些思想应用于加速正统的迭代过程，以一阶微分方程的埃米尔·皮卡迭代解为例。他在同年发表的另一篇论文中应用了同样的技术，即Intégration d'une équation différentielle par itération rationnelle Ⓣ（用有理迭代积分微分方程）。在Sur un cas limite du problème de Stormer Ⓣ（关于Stormer问题的一个极限情况）（1945年）中，他研究了电子在磁偶极场力线附近的轨迹，然后在Interpolation dans la méthode de Runge-Kutta Ⓣ（卡尔·龙格-马丁·威廉·库塔方法中的插值）（1947年）中回到了对一阶微分方程数值解的研究。1948年，他发表了一篇将数学技术应用于天文学问题的论文，出版了Modèles mécaniques d'amas de nébuleuses Ⓣ（星云团的力学模型）。B L J Bok在对此论文的评论中写道：-

作者关注的是星系团中单个成员存在大随机速度所引发的问题。是否有可能解释星系或多或少永久集中的存在，其中没有单个星系长期停留在同一位置？本文的双重目的是描述潜在的力学模型并写下问题的基本方程。文中展示了如何将这些方程应用于解决均匀膨胀宇宙中均匀分布这一著名问题。

同年发表的另一篇论文 Modèles de nébuleuses à vitesses radiales Ⓣ（具有径向速度的星云模型），这次是与R Vander Borght合作，关注的是具有径向对称且只允许径向速度而不允许横向速度的恒星系统的平衡构型研究。1949年，他在Cosmological application of relativity中回到了对膨胀宇宙的研究。霍华得·帕西·罗伯特森写道：-

论文以对广义相对论引力理论的快速阐述性回顾开篇，包括对运动学、守恒定律、球对称性以及卡尔·史瓦西和威廉·德西特在共动坐标下的解的讨论。接着叙述了亚历山大·弗里德曼的均匀膨胀宇宙模型，并专门讨论了红移和时间尺度观测所要求的类型。论文剩余的三分之一关注模型中的非均匀性效应，简要叙述了作者关于宇宙线起源、它们凝聚成云、星云和星云团的形成等假设和预测，并解释了氢和氦的普遍存在是动能物质化的结果。

勒梅特在20世纪50年代教学较少，但继续发表他在40年代感兴趣的相同主题的论文。他的论文包括Application des méthodes de la mécanique céleste au problème de Stormer Ⓣ（天体力学方法在Stormer问题中的应用）（1950年）、Modèles mécaniques d'amas de nébuleuses Ⓣ（星云团的力学模型）（1951年）、Coordonnées symétriques dans le problème des trois corps Ⓣ（三体问题中的对称坐标）（1952年）和Régularisation dans le problème des trois corps Ⓣ（三体问题中的正则化）（1954年）。然而，勒梅特的研究中出现了一个与计算机引入数学研究相关的新兴趣。他开发了计算机语言，提出了新的计算技术，并继续他对计算数学的兴趣。一些关于计算的论文有Comment calculer? Ⓣ（如何计算？）（1954年），其中他提议用纸和打字机取代纸笔计算。他提议不使用阿拉伯数字0-9，而是使用右手容易触及的四个字母i, j, k, l，给出一种特殊的二进制编码十进制表示。在Pourquoi de nouveaux chiffres? Ⓣ（为什么要新数字？）（1955年）中，他讨论了十进制系统甚至阿拉伯数字的缺点。强调了二进制系统的某些优点，例如它使玩Nim游戏失去乐趣。他在Why new digits?（1955年）中再次提出了反对阿拉伯数字的论点。他在Le calcul élémentaire Ⓣ（初等计算）（1956年）中强调了二进制系统的优点。他的算术体系由Lipnik在[12]中讨论。

勒梅特于1964年退休，当时他被授予荣誉教授。他继续发表有趣的论文，如The expansion of the Universe（1967年）和The principle of continuity according to Jean-Victor Poncelet（1967年）。我们以R N Tiwari对[5]的评论中的引文结束这篇传记，因为它在许多方面既总结了勒梅特的贡献，又提出了一些引人入胜的问题供读者思考：-

勒梅特 毕业于工程专业，他的学业因第一次世界大战而中断。他参军入伍，引用作者的话说，“在经历了53个月的战争磨难和军营生活后，他对职业生涯失去了兴趣，决定成为一名神父”；这最终导致他从工程转向数学科学，特别是广义相对论，这标志着 勒梅特 一生中一个非常显著的转折点。这种思想转变是由于战争，还是这种想法的种子本就存在于他心中并在适当的时候萌发，以及教会环境及其先验原则是否对他的科学发现（如宇宙从原始原子演化、初始时期奇点的存在等）有任何影响，无法得出确切的推断。然而，作者叙述的事件序列表明，勒梅特 一再被指责（特别是被 阿尔伯特·爱因斯坦）利用科学推理“来捍卫教会的（宗教）教条”。果真如此吗？勒梅特 这位科学家是否受到 勒梅特 这位天主教神父的引导？作者将这些观点留给读者自行判断。然而，他评论道：“对于现代科学宇宙学家来说，尽管他们可能对这种原始奇点感到不安，但其创始者思想的客观性是毋庸置疑的”。

Georges Lemaître's parents were Joseph Lemaître and Maguerite Lannoy. In 1911 he entered the Catholic University of Louvain to study for a degree in engineering. However in 1914, while he was still an undergraduate, World War I broke out. He volunteered and served as an artillery officer in the Belgian army. He was decorated for bravery, receiving the Military Cross, but the dreadful carnage he had seen on the battlefields troubled him deeply and changed his life. After the war ended he returned to his university studies but his interests now moved away from engineering and towards mathematics. He graduated with the degree of Docteur en Sciences in mathematics in 1920 after submitting his thesis l'Approximation des fonctions de plusieurs variables réelles Ⓣ written under guidance from de la Vallée Poussin.

Another change in his life brought about by his wartime experiences came about when he enrolled at the Maison Saint Rombaut, a seminary of the Archdiocese of Malines, and was ordained in 1923, becoming Abbé Lemaître. Now, with the strong mathematical background obtained from his studies with de la Vallée Poussin, Lemaître turned towards mathematical astronomy and went to Cambridge in England where he studied with Eddington during the academic years 1923-24, then he went to the United States spending the next academic year at the Harvard College Observatory in Massachusetts. In 1925 he accepted a position as a part-time lecturer at the Catholic University of Louvain in Belgium but continued to spend time at Harvard and at the Massachusetts Institute of Technology in the United States. He was awarded a Ph.D. in 1927 for his thesis The gravitational field in a fluid submitted to MIT. His supervisor at MIT had been Harlow Shapley. The research he had undertaken, partly at Harvard, partly at MIT and partly at Louvain, was written up as Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extragalactiques Ⓣ and published in the Annales de la Société Scientifique de Bruxelles in 1927.

In this groundbreaking paper Lemaître derived what is now known as Hubble's Law relating the speed with which a galaxy is moving away to its distance. In 1927 the famous Solvay Conference was held and most of the leading physicists attended. Einstein was at the conference and he spoke to Lemaître in Brussels telling him that the ideas in his 1927 paper had been presented by Friedmann in 1922, but he also said that although he thought Lemaître's solutions of the equations of general relativity were mathematically correct, they presented a solution which was not feasible physically. Einstein said:-

Your calculations are correct, but your grasp of physics is abominable.

Einstein was not alone in finding Lemaître's ideas totally unacceptable; rather this was the opinion of almost all scientists. However in 1929 Hubble published work presenting considerably more evidence of an expanding universe, contradicting the then accepted theory of a static universe. Eddington and other members of the Royal Astronomical Society began to undertake work to try to solve the problem brought about by the discrepancy between theory and observation. Lemaître then sent a copy of his 1927 paper to Eddington who immediately saw that it provided an explanation. Eddington arranged for an English translation of Lemaître's paper to be published in the Monthly Notices of the Royal Astronomical Society and indeed it appeared there in March 1931. There was still a part of Lemaître's theory that scientists, including Eddington, found impossible to accept, namely the implication that the universe had a beginning at a finite time in the past. Almost all wanted to believe that the universe had always existed. We leave it to the reader to ponder the thought that perhaps Lemaître's deep Christian beliefs made the thought that the world began at a finite time in the past (as the book of Genesis claims) more easily accepted.

Lemaître responded to the objections against his theory in a paper published in Nature in May 1931. He wrote:-

If the world has begun with a single quantum, the notions of space and time would altogether fail to have any meaning at the beginning; they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time.

This was the first explicit formulation of the currently accepted 'big bang' theory. We should note that, although accepted by most scientists, Fred Hoyle did not accept this theory and the term 'big bang' was Hoyle's scornful description of Lemaître's theory in a 1950 radio broadcast. In 1933 Einstein and Lemaître gave a series of lectures in California. After listening to Lemaître explain his theory in one of these seminars, Einstein stood up and said:-

This is the most beautiful and satisfactory explanation of creation to which I have ever listened.

Lemaître published a more detailed version of his theory in L'univers en expansion Ⓣ in 1933. An English translation of this paper by M A H MacCallum was published in 1997. The ideas presented in his 1933 paper reached the popular press who described him as the world's leading cosmologist. An article in the New York Times featured a photograph of Einstein and Lemaître with a caption:-

They have a profound respect and admiration for each other.

Of course, the fact that Lemaître was both a leading scientist and a Catholic Priest was part of the fascination that the popular press had. In the same article, the author wrote:-

'There is no conflict between religion and science,' Lemaitre has been telling audiences over and over again in this country .... His view is interesting and important not because he is a Catholic priest, not because he is one of the leading mathematical physicists of our time, but because he is both.

Honours from several different sources came his way such as the Francqui Prize in 1934. This prize, presented to Lemaître by King Léopold III, was the highest scientific honour that Belgium could bestow. In 1936 he was inducted into the Pontifical Academy of Sciences by Pope Pius XI. He was elected member of the Royal Academy of Sciences and Arts of Belgium in 1941, became the first to be awarded the Eddington Medal by the Royal Astronomical Society in 1951, and he served as President of the Pontifical Academy of Sciences from 1960 to 1966.

Lemaître had been appointed Professor at Louvain in 1927 and remained there for the rest of his career. Let us look at a few of his later publications, particularly those of a more mathematical nature. In 1942 he published L'itération rationnelle Ⓣ in which he discussed Gauss's method of successive approximations applied to a system of two equations in two unknowns to determine the orbit of a planet from three observations. Lemaître then applied these ideas to accelerate the orthodox process of iteration, taking the Picard iterative solution of first order differential equations as an example. He applied the same techniques in another paper published in the same year, namely Intégration d'une équation différentielle par itération rationnelle Ⓣ. In Sur un cas limite du problème de Stormer Ⓣ (1945) he studied trajectories of an electron in the neighborhood of lines of force of a magnetic dipole field, then returned to his study of numerical solutions to first order differential equations in Interpolation dans la méthode de Runge-Kutta Ⓣ (1947). In 1948 he published a paper applying mathematical techniques to a problem in astronomy publishing Modèles mécaniques d'amas de nébuleuses Ⓣ. B L J Bok writes in a review of this paper:-

The author is concerned with the problem posed by the existence of large random velocities for the individual members of clusters of galaxies. Is it possible to account for the existence of more or less permanent concentrations of galaxies in which no single galaxy remains long in the same place? The two-fold purpose of the paper is to delineate the underlying mechanical model and to write down the fundamental equations of the problem. It is shown how these equations can be applied toward the solution of the well-known problem of uniform distribution in a homogeneous, expanding universe.

Another paper published in the same year Modèles de nébuleuses à vitesses radiales Ⓣ, this time jointly with R Vander Borght, is concerned with the study of equilibrium configurations for stellar systems with radial symmetry and in which only radial and no transverse velocities are permitted. In 1949 he returned to his study of an expanding universe in Cosmological application of relativity. H P Robertson writes:-

The paper opens with a rapid expository review of the general relativity theory of gravitation, including discussion of kinematics, conservation laws, spherical symmetry, and the solutions of Schwarzschild and de Sitter in terms of comoving coordinates. There follows an account of the homogeneous expanding universe models of Friedmann, with specialization to the type demanded by red-shift and time-scale observations. The remaining third of the paper is concerned with effects of inhomogeneities in the model, with a brief account of author's hypotheses and predictions concerning the origin of cosmic rays, their condensation into clouds, formation of nebulae and clusters of nebulae, and offers an explanation of the prevalence of hydrogen and helium as materialization of kinetic energy.

Lemaître taught less through the 1950s but continued to publish on the same topics that had interested him in the 1940s. His papers include Application des méthodes de la mécanique céleste au problème de Stormer Ⓣ (1950), Modèles mécaniques d'amas de nébuleuses Ⓣ (1951), Coordonnées symétriques dans le problème des trois corps Ⓣ (1952), and Régularisation dans le problème des trois corps Ⓣ (1954). However, a new interest came into Lemaître's research related to the introduction of computers into mathematical research. He developed computer languages, proposed new calculating techniques, and continued his interests in computational mathematics. Some papers on calculating are Comment calculer? Ⓣ (1954) in which he proposes that paper and pencil computing be replaced by paper and typewriter. Instead of using the Arabic numerals 0 - 9 he proposes that the four letters i, j, k, l which lie within easy reach of the right hand be used to give a peculiar binary coded decimal representation. In Pourquoi de nouveaux chiffres? Ⓣ (1955) he discusses the shortcomings of the decimal system and even the Arabic digits. Certain advantages of the binary system are stressed such as the fact that it takes the fun out of playing Nim. His argument against the Arabic numerals is given again in Why new digits? (1955). He stresses the advantages of the binary system in Le calcul élémentaire Ⓣ (1956). His arithmetical architecture is discussed by Lipnik in [12].

Lemaître retired in 1964 when he was made professor emeritus. He continued to publish interesting papers, such as The expansion of the Universe (1967), and The principle of continuity according to Jean-Victor Poncelet (1967). We end this biography by quoting from a review by R N Tiwari of [5] since in many ways it provides both a summing up of Lemaître's contributions, but poses some fascinating questions for the reader to consider:-

Lemaître graduated in engineering, and his studies were interrupted due to World War I. He joined the army and, to quote from the author's statement, "after 53 months of war ordeals and military camps, he lost interest in a professional career and decided to become a priest"; this ultimately resulted in a change from engineering to the mathematical sciences, particularly to general relativity, which marked a very notable turning point in Lemaître's life. Whether this change of mind was due to war or the seed of such a thought was inherent in him and germinated at the appropriate time, and whether the environment of the Church and its a priori principles had any influence on his scientific discoveries (such as the evolution of the universe from a primordial atom, the existence of singularity at the initial epoch, etc.) cannot be inferred conclusively. The sequence of events narrated by the author shows, however, that time and again Lemaître was accused (especially by Einstein) of using scientific reasonings "to defend a (religious) dogma of the Church". Was it really so? Was Lemaître the scientist being guided by Lemaître the Catholic priest? The author leaves these points for readers to decide for themselves. However, he remarks that "for modern scientific cosmologists, although they may feel uneasy about this primordial singularity, the objectivity of the thinking of its initiator is beyond doubt".