西奥多·卡鲁扎Theodor Kaluza

西奥多·卡鲁扎的父亲是Max Kaluza。他属于一个在拉蒂博尔（今波兰拉齐布日）居住了约300年的家族。Max Kaluza是一位优秀学者，虽为德国人，却是英语语言和英国文学方面的顶尖专家，其专长领域是乔叟研究。卡鲁扎是独生子，在学校表现出极大前途，他进入柯尼斯堡大学学习数学。

卡鲁扎在柯尼斯堡继续学业，在Meyer指导下攻读博士学位。他的教授资格论文（Habilitation）学位论文是关于埃伦弗里德·瓦尔特·冯·切恩豪斯变换的，1910年发表在Archiv der Mathematik und Physik上。前一年他已通过考试并获得在大学授课的资格。卡鲁扎于1909年结婚，取得任教资格后成为柯尼斯堡大学的Privatdozent，这个职位几乎不给他带来任何收入。大多数学者在成为编外讲师几年后就会晋升，但卡鲁扎显然被认为功绩不足，因为他做了20年编外讲师。然而，有一个人对卡鲁扎评价很高，那就是阿尔伯特·爱因斯坦。

1919年4月，他在柯尼斯堡任教时写信给阿尔伯特·爱因斯坦，告诉他自己关于统一阿尔伯特·爱因斯坦的引力理论和詹姆斯·克拉克·麦克斯韦的光理论的想法。阿尔伯特·爱因斯坦鼓励他发表这些极具独创性的想法，他于1921年在关于物理学统一问题的论文中这样做了——Zum Unitätsproblem der Physik Ⓣ（论物理学中的统一问题），发表于Sitzungsberichte Preussische Akademie der Wissenschaften 96 (1921), 69。正是阿尔伯特·爱因斯坦于1921年12月8日提交了这篇论文。

卡鲁扎的思想涉及引入第五维，尽管他因将这一想法作为纯数学观念引入而受到批评，但他的工作很重要，并被其他人所探索。他在这篇论文中说，他的理论具有：-

……几乎无与伦比的形式统一性……这不可能仅仅是反复无常的偶然事件那种诱人的把戏。

这一理论的统一性特征在于，它统一了阿尔伯特·爱因斯坦的引力理论和詹姆斯·克拉克·麦克斯韦的电磁理论。正如⟦N2⟧在[3]中所写：-

……这位不知名的科学家提议一举将科学已知的两大场论，即詹姆斯·克拉克·麦克斯韦的和阿尔伯特·爱因斯坦的，通过在第五维中混合它们而结合起来。

卡鲁扎因卡鲁扎-奥斯卡·克莱因（以数学家奥斯卡·克莱因命名）场论而被人们记住，该理论涉及五维空间中的场方程。该理论最初是研究的热门话题，但随着量子力学的引入很快失宠。

1926年11月，阿尔伯特·爱因斯坦写信支持卡鲁扎，试图让人们认识到他是一位提出了非凡新颖想法的数学家，其价值远远超过他仍然占据的Privatdozent职位。卡鲁扎仍然未能获得晋升，然后在1929年，恰好在他被任命为Privatdozent 20年后，他被任命为基尔大学的教授。1935年，他被任命为哥廷根大学的正教授，直到1954年去世，距他本应退休还有两个月。

卡鲁扎过于专注于他在理论物理学中的想法，以至于无法做出他显然有能力做出的数学贡献。他继续提出与原子核模型有关的想法，并撰写了关于相对论的著作。也许他最出色的数学著作是教科书Höhere Mathematik für die Pracktiker Ⓣ（实践中的高等数学），该书与G Joos合著，于1938年出版。⟦N2⟧写道[1]：-

在这部著作中，他更多地表现为一位数学家，而不是数学物理学家。

他的儿子，也叫卡鲁扎，提供了关于他父亲个人生活的细节，这些内容被收入1。这些叙述让我们感受到卡鲁扎的性格：-

……一个兴趣广泛的人。尽管数学抽象令他极为欣喜，他也对语言、文学和哲学深感兴趣。他学习了超过十五种语言，包括希伯来语、匈牙利语、阿拉伯语和立陶宛语。他有敏锐的幽默感。他不会游泳，曾通过读一本游泳书来展示理论知识的威力，然后第一次尝试就成功游了起来（他完成这一壮举时已年过三十）。卡鲁扎热爱自然和科学，也喜欢孩子。

Theodor Kaluza's father was Max Kaluza. He belonged to a family which had lived in Ratibor (now Raciborz in Poland) for around 300 years. Max Kaluza was a fine scholar and, although German, he was a leading expert on the English language and English literature, with his special field being the study of Chaucer. Theodor, who was an only child, showed great promise at school and he entered the University of Königsberg to study mathematics.

Kaluza continued his studies at Königsberg working towards his doctorate under Meyer's supervision. His habilitation thesis was on Tschirnhaus transformations and it was published in the Archiv der Mathematik und Physik in 1910. He had been examined and received the right to lecture in universities in the previous year. Kaluza married in 1909 and, after his habilitation, became a Privatdozent at the University of Königsberg, a position which left him with hardly any income. Most academics are promoted after a few years as a Privatdozent, but Kaluza clearly was not thought to be of sufficient merit for he remained a Privatdozent for 20 years. One person who thought very highly of Kaluza, however, was Einstein.

He was teaching at Königsberg in April 1919 when he wrote to Einstein and told him about his ideas to unify Einstein's theory of gravity and Maxwell's theory of light. Einstein encouraged him to publish his highly original ideas which he did in 1921 in his paper on the unity problem of physics - Zum Unitätsproblem der Physik Ⓣ published in Sitzungsberichte Preussische Akademie der Wissenschaften 96 (1921), 69. It was Einstein who communicated the paper on 8 December 1921.

Kaluza's ideas involved the introduction of a fifth dimension and, although he has been criticised for introducing this as a purely mathematical idea, his work is important and was explored by others. He says in this paper that his theory possessed:-

... virtually unsurpassed formal unity ... which could not amount to the mere alluring play of a capricious accident.

The unifying feature of this theory was that it unified Einstein's theory of gravitation and Maxwell's electromagnetic theory. As Kaku writes in [3]:-

... this unknown scientist was proposing to combine, in one stroke, the two greatest field theories known to science, Maxwell's and Einstein's, by mixing them in the fifth dimension.

Kaluza is remembered for this in Kaluza-Klein (named after the mathematician Oskar Klein) field theory, which involved field equations in five-dimensional space. The theory, initially a popular topic of research, quickly lost favour with the introduction of quantum mechanics.

In November 1926 Einstein wrote in support of Kaluza to try to impress upon people that he was a mathematician who had produced a remarkably novel idea and was worth far more than the position of Privatdozent which he still occupied. Still Kaluza failed to gain promotion, then in 1929, exactly 20 years after being appointed a Privatdozent, he was appointed as professor in Kiel. In 1935 he was made a full professor at Göttingen where he remained until his death in 1954, two months before he was due to retire.

Perhaps Kaluza became too involved with his ideas in theoretical physics to make the contributions to mathematics which he was clearly capable of making. He continued to produce ideas relating to models of the atomic nucleus, and he wrote on relativity. Perhaps his finest mathematical work is the textbook Höhere Mathematik für die Pracktiker Ⓣ which was written jointly with G Joos and published in 1938. Raman writes [1]:-

in this work he showed himself as a mathematician rather than as a mathematical physicist.

His son, also named Theodor Kaluza, contributed personal details of his father which were incorporated into [1]. These give us feeling for Kaluza's character as:-

... a man of wide-ranging interests. Although mathematical abstraction delighted him tremendously, he was also deeply interested in languages, literature, and philosophy. He studied more than fifteen languages, including Hebrew, Hungarian, Arabic, and Lithuanian. He had a keen sense of humour. A nonswimmer, he once demonstrated the power of theoretical knowledge by reading a book on swimming, then swimming successfully on his first attempt (he was over thirty when he performed this feat). Kaluza loved nature as well as science and was also fond of children.