Ernst Pascual Jordan


Born: 18 October 1902 in Hannover, Germany
Died: 31 July 1980 in Hamburg, West Germany

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Pascual Jordan's parents were Ernst Pasqual Jordan (1858-1924) and Eva Fischer. Ernst Jordan, the father of the subject of this biography, was a painter who was renowned for his portraits and landscapes. He was an associate professor of art at Hanover Technical University when his son was born. The family name was originally Jorda and it was of Spanish origin. The first born sons were all given the name Pasqual or the version Pascual. The family settled in Hannover after Napoleon's defeat at the Battle of Waterloo in 1815 and at some stage changed their name from Jorda to Jordan. Ernst Jordan married Eva Fischer in 1892. Pascual leant much from his parents. In an interview in 1963 he spoke about things he learnt from them:-
My father used to read popular books about natural science especially the series of 'Kosmos' books which was popular at the beginning of this century. Each year several books came out in this series, written by people such as Eilhelm Bölsche who was well-known as a popular author. All these 'Kosmos' books belonged to my first reading in natural science. ... My mother knew a good deal about plants, flowers, birds and stars. I learnt from her that light takes eight minutes in coming from the sun to the earth. She was also interested in numbers and calculation; I learnt arithmetic from her.
When he was around eleven years old Jordan was attracted to painting and architecture, topics in which his father was highly skilled. His father strongly encouraged him to follow these interests but soon Jordan became attracted to biology. He said in the 1963 interview:-
Very early when I was a little boy, I was very fond of animals. I was often taken to the zoological gardens and I began collecting pictures of extinct animals.
He attended the Reform Gymnasium in Hannover and, by the age of fourteen, he was reading books such as August Pauly's 1905 work Darwinismus und Lamarckismus. Entwurf einer psychophysischen Teleologie . There he learnt of the ideas of Charles Darwin and Jean Baptiste Lemarck. He also read Friedrich Albert Lange's Geschichte des Materialismus und Kritik seiner Bedeutung in der Gegenwart (1866) and began to think deeply about fundamental questions such as whether organic life was understandable from a purely mechanical and physical perspective. He worried whether there was a contradiction between Darwin's theories and the Bible but his teacher of religion at the Gymnasium convinced him that there was no contradiction between Christian teaching and the sciences. In order to gain further understanding he studied classical physics and the theory of forces. He decided that there was no reason to prevent man building a rocket which could travel to the moon. These thoughts made him enthusiastic about studying science.

At the age of sixteen, he became interested in advanced mathematics through reading the classic book by Walther Nernst and Arthur Schönflies Einführung in die Mathematische Behandlung der Naturwissenschaften (1895) and the same two authors' book Kurzgefasstes Lehrbuch Der Differential Und Integralrechnung (1895). Concerning this last book he remarked (in 1963):-

It presents differential calculus and the beginnings of integral calculus, also some considerations about multiple integrals and such things, with specific application to scientific problems. ... I could not read it all at once; at first I read only the first few chapters, then stopped, but later I read on further. It thus took me several years to read completely, up to the first year of my university studies.
Among other mathematics books he read while at the Gymnasium, we mention Konrad Knopp's Funktionentheorie (1913).

Against his father's wishes, after Jordan graduated from the Gymnasium in 1921, he entered the Hanover Technische Hochschule in the summer of that year to study mathematics and physics. His father had pressed him hard to study architecture but Jordan resisted and followed his own wishes. The teaching of physics at the Technische Hochschule disappointed Jordan and he studied mostly mathematics taking courses on differential equations, methods of integration, and algebra. He also attended an electrical engineering course, a physical chemistry course and zoology courses. Since the physics teaching was not up to the standard he hoped for, he left the Technische Hochschule and enrolled at the University of Göttingen in the summer of 1922. His father still pressed for Jordan to remain at the Technische Hochschule and study architecture there but Jordan's mother persuaded her husband to relent and accept that their son would study physics. However, when Jordan began studying at Göttingen he discovered that the physics lectures were all before 9 o'clock in the morning. This was not to his liking since he had developed the habit of going to bed late and rising late in the mornings, so again Jordan took mainly mathematics courses. In particular he enrolled in Richard Courant's differential equations course and Courant quickly realised that he had an exceptionally talented student. He helped Courant with the writing of Courant and Hilbert's Methoden der mathematischen Physik (1924). The two would meet daily to discuss problems and Courant expressed his thanks to Jordan in the Foreword of the book.

At Göttingen, Jordan attended lectures by Edmund Landau on number theory and had discussions with Emmy Noether at the Mathematische Gesellschaft. He also attended the seminar on the structure of matter run by Max Born, David Hilbert and James Franck. Jordan became Max Born's student and assisted Born with his encyclopaedia article on crystal dynamics. After the encyclopaedia article was completed, Born became deeply interested in molecular theory and tried to interest his student Jordan in this topic for his doctoral dissertation. However, Jordan was not particularly interested in this area finding it rather specialised while he wanted to attack more fundamental questions. He read a 1923 paper by Einstein and Ehrenfest on light quanta and gave a talk on the paper in a seminar. Jordan said (in 1963):-

After listening to my seminar on light-quanta Born said that I could make that the topic of my dissertation if I liked it better. There was general scepticism about light-quanta and a belief that a different approach to the problem was needed. Born's opinion on this was not fixed and he said that since I had raised the question I could pursue it.
Jordan's doctoral dissertation was published in 'Zeitschrift für Physik' in 1924. Einstein thought that Jordan's dissertation was an ingenious piece of work but disagreed with his basic hypotheses. Einstein published a note in 'Zeitschrift für Physik' in 1925 stating his objections. Jordan was pleased that Einstein had taken an interest in his work and published a further paper on light quanta in 1925 following the approach by Planck, Einstein and Ehrenfest. In this paper Jordan thanked Einstein "for the kind interest he has taken in this investigation." However, by this time Jordan was helping James Franck in writing the book Anregung von Quantensprungen durch Stöβe . Unlike the assistance he had given previously in writing books, this time he appeared as a joint author when the book was published in 1926. The book studied spectroscopic problems but Jordan did not continue with this area for he had already become interested in quantum mechanics.

In the summer of 1925 Werner Heisenberg, who was been Born's assistant, returned to Göttingen from a visit to Copenhagen where he had worked with Niels Bohr. Back in Göttingen he showed Born his new matrix mechanics, the first version of quantum mechanics. He did not invent these concepts as a matrix algebra, however, rather he focused attention on a set of quantised probability amplitudes. These amplitudes formed a non-commutative algebra. Born read Heisenberg's manuscript and tried to make sense of it. He thought that Heisenberg's quantum objects must be related to matrices but felt he needed a young collaborator with a strong mathematical background to help him formalise his ideas. Jordan offered to help Born attack the problem and he had formalised Born's vague ideas about matrices in a few days. Born and Jordan submitted their paper Zur Quantenmechanik on matrix mechanics on 27 September 1925. It was almost entirely the work of Jordan since Born was on holiday in Switzerland for most of the time that it was being written. This paper contains the famous pq - qp equation, the first appearance of this fundamental quantum theory equation. Jordan's contributions were coming rapidly and in November 1925 Jordan, Born and Heisenberg submitted their three-author paper Zur Quantenmechanik II which was published in 1926. Before the end of the year Jordan had submitted a single author paper which suffered an unfortunate fate.

This paper [29]:-

... contained what is nowadays known as the Fermi-Dirac statistics; however it encountered an extremely unfortunate fate after its submission because it landed on the bottom of one of Max Born's (in his role as the editor of the 'Zeitschrift für Physik') suitcases on the eve of an extended lecture tour to the US, where it remained for about half a year. When Born discovered this mishap, the papers of Dirac and Fermi were already in the process of being published.
This paper by Jordan was never published, but he further developed its contents and this extended piece of work, Zur Quantenmechanik der Gasentartung , was published by Jordan in 1927. He published other, extremely significant, papers in 1927 such as Über eine neue Begründung der Quantenmechamik (in two parts) which deals with what today in called "transformation theory". His ideas here were close to those of Paul Dirac. On 24 December 1926 Dirac, who was at that time in Copenhagen visiting Niels Bohr, wrote to Jordan (see for example [16]):-
Dr Heisenberg has shown me the work you sent him, and as far as I can see it is equivalent to my own work in all essential points. The way of obtaining the results may be rather different though ... I hope you do not mind the fact that I have obtained the same results as you, at (I believe) the same time as you. Also, the Royal Society publishes papers more quickly than the Zeits. f. Phys., and I think my paper will appear in their January issue. I am expecting to go to Göttingen at the beginning of February, and I am looking forward very much to meeting you and Prof Born there.
Indeed both papers were published in January 1927, a month after being submitted, with Dirac's paper, as he had thought, appearing first. Jordan's paper was the first of the two part paper whose title we gave above. There are many other contributions that Jordan made to quantum theory in these years but we must look at another remarkable contribution he made which has had a major impact on the development of mathematics. In 1929 Jordan was appointed as extraordinary professor of physics at the University of Rostock. Bohr was delighted and wrote to Jordan saying that, since Rostock was quite close to Copenhagen, he hoped they could collaborate. Jordan was, by this time, becoming interested in applying ideas from quantum theory to biological matters. For example, Jordan published Quantenmechanik und die Grundprobleme der Biologie und Psychologie (1932) and Quantenphysikalische Bemerkungen zu Biologie und Psychologie (1934). Bohr was also interested in these ideas.

In 1932, in an attempt to put quantum theory into a new algebraic setting, Jordan tried to establish the basic rules satisfied in the matrix interpretation of quantum theory. He published these ideas in Über die Multiplikation quantenmechanischer Gröβen (1934) and convinced John von Neumann and Eugene Wigner that these were significant ideas. Jordan, von Neumann and Wigner published their joint ideas on this in the three-author paper On the algebraic generalization of the quantum mechanical formalism (1934). With his approach, Jordan had introduced what today are called Jordan algebras. For more details see THIS LINK.

Jordan was, as we have seen, one of the main contributors to the development of quantum theory. However, he never achieved the recognition for this that others, whose contributions appeared to be less, received. Most now believe that this was due to Jordan's political views and his support for the Nazi party. We must therefore look at this aspect of Jordan's life, partly out of interest, but also partly because of its connection with his scientific and mathematical views. Jordan's undergraduate years saw him in Göttingen at a time when most of his fellow students were feeling very hard done by because of the impact on Germany of the severe financial burdens imposed by the Allies following World War I. Jordan's views, however, went far beyond those of most of his fellow students. From the late 1920s he was publishing articles with extreme far-right political views under the pseudonym Ernst Domeier. The fact that he published these anonymously certainly shows that, at that stage, he wanted to keep his political views separate from his scientific work. We present a short quote from an article that Jordan wrote in 1930 under the name Ernst Domeier:-

Since 1918 ... instead of a subject we are an object of world politics ... All those who have anything to do with the government of our Reich ... must be inwardly filled with feelings which result with law-like necessity from the pressing sensation of powerless dependence .... Inferiority complexes create the necessity of a compensation at any price. ... Bureaucratic pomposity and bureaucrats' terrorizing of their own peoples produce the needed compensation.
In addition he being a German nationalist, he was very anti-Communist and viewed the rise of the Soviet Union as a major danger to the world. These views, of course, made him an easy target for the Nazi propaganda and indeed he joined the Nazi party in 1933, the year Hitler came to power. Things, however, are not quite as simple as they might appear and one must not think that because Jordan was a staunch and enthusiastic Nazi supporter, he believed in all the Nazi policies. For example, Jordan wrote the book Physikalisches Denken in der neuen Zeit which was published in 1935. This book contains an attack on Ludwig Bieberbach's idea of 'Deutsche Mathematik' although Jordan does not mention Bieberbach by name.

You can read an extract from the book in which Jordan attacks the idea of 'Deutsche Mathematik' at THIS LINK.

It is interesting that, as well as not subscribing to all the Nazi policies, he was actively trying to change them from inside the Nazi Party.

Another of the 'big' Nazi policies was their anti-Semitism. There is no evidence that Jordan had any anti-Semitic views and the large number of Jewish friends that he had seems to confirm this. The Nazis demanded that all German scientists omit mention of Jewish scientists in the development of their discipline but Jordan argued strongly that politics and science should be kept separate. He wrote books on the history of physics in the 20th century such as Die Physik des 20sten Jahrhunderts (1936) which gave full credit to all Jewish scientists. Of course, Jordan's views presented the leading Nazis with some difficulty. On the one hand he was putting out strong pro-Nazi propaganda which they loved, but his continued association with Jewish scientists meant that Jordan was not trusted by the authorities. There is, of course, a certain irony in the fact that Jordan was almost certainly not awarded a Nobel prize because of his Nazi views when he himself had argued with the Nazis that politics should not influence views of scientific merit.

When World War II began in 1939, Jordan enlisted in the Luftwaffe. He did not see active service but worked as a weather analyst at Peenemünde on the Baltic Sea where V-2 rockets were developed and produced. However, he continued to be more interested in his own ideas rather than in the work that was assigned to him. Peter P Wegener writes [9]:-

Jordan sat in front of his typewriter all day composing a textbook on algebra without ever consulting notes. Usually toward the end of the day he would suddenly recall the original purpose of his assignment at Peenemünde. He had never worked in fluid dynamics, but rather than read books as I did, he proceeded to derive the equations of motion of supersonic flows. He delighted in the discovery of such phenomena as shock waves.
In 1944, before the war ended, Jordan was appointed as an ordinary professor of theoretical physics at the University of Berlin to fill the chair previously held by Max von Laue who had been declared emeritus in 1943, one year before he was due to retire. Of course after Germany's defeat in the war, Jordan, as a strong Nazi supporter, was in some difficulty. Several of his colleagues, such as Werner Heisenberg and Wolfgang Pauli, spoke up in his favour. There is a nice episode when, after the war, Pauli and Jordan met. Pauli quoted some of Jordan's "Nazi propaganda" and asked, "Herr Jordan, how could you write such a thing?" Jordan replied, "Herr Pauli, how could you read such a thing?" For the two years 1945-47, Jordan was dismissed from his position at the university but in 1947 he was reinstated as a visiting professor after statements such as that by Heisenberg who said:-
I never reckoned with the possibility that Jordan could be a true National Socialist ...
Since Jordan had advertised the fact that he was a Nazi in the most vociferous of ways, this statement by Heisenberg could only mean that he wanted all Nazis reinstated. Jordan also asked Niels Bohr to support his reinstatement but Bohr was less kind in that he simply replied by sending Jordan a list of his friends and relatives murdered by the Nazis. In 1947 Jordan was offered temporary professorships at Freiburg and at Hamburg. He chose the latter and in 1953 the position became permanent and Jordan was allowed to supervise Ph.D. students. Wolfgang Kundt writes [24]:-
The first twenty years of my scientific life, 1951-71, were strongly shaped by Pascual Jordan, the dominant lecturer of my classes in theoretical physics at Hamburg University, my supervisor for the diploma, Ph.D., and habilitation, later as the head of the weekly 'Relativitätstheorieseminar', and as the scientific father who cared equally for the mental and physical wealth of his scholars.
Jordan retired from Hamburg in 1971 but before this he had had a political career being a Christian-Democratic MP in the Bundestag from 1957 to 1961. In doing so he had ignored Pauli's advice for when he spoke up for Jordan to be reinstated, he advised him not to enter politics. When in the Bundestag he frequently called for a return to the 'true front spirit'. He continued to believe in militarisation, advocated Germany being allowed to develop a nuclear bomb, remained a staunch anti-Communist, and, in 1965, argued that Germany should not recognise the Oder-Neisse line as the border between Germany and Poland. He continued to argue strongly for Germany to believe more in itself, writing in 1973:-
... what the German people most urgently need today is the overcoming of its national inferiority complex.
He objected to the fact that when he spoke out in favour of a strong Germany, he was called a fascist by those on the political Left.

Let us end our biography by quoting from [21]:-

That Jordan never won a Nobel Prize in physics is a puzzle. Some blame his inability to give elegant lectures because of a stutter; some blame his pro-Nazi politics or his support, after World War II, for a German nuclear weapons program; some blame the fact that Born misplaced Jordan's 1925 manuscript in which Fermi-Dirac statistics were first presented, thus depriving the modest Jordan of his rightful claim to priority over Pauli. But the fact remains that his contributions to the development of modern quantum theory were as fundamental and far-reaching as those of many whose achievements were recognized with a Nobel Prize. It was Jordan, more than anyone else, who developed a mathematically elegant formulation of matrix mechanics. It was Jordan who went on to consolidate matrix mechanics with Dirac's alternative operator calculus and Erwin Schrödinger's wave-mechanical formulation in the comprehensive formalism known as statistical transformation theory. It was Jordan who did more than anyone other than Dirac to inaugurate the program of quantum field theory, in ways such as developing the second quantization approach and being the first to discover the problem of divergences in quantum field theory. And it was Jordan who, along with von Neumann and Eugene Wigner, was developing more abstract algebraic frameworks for quantum mechanics. Not without reason has Jordan been described as "the unsung hero among the creators of quantum mechanics".

Article by: J J O'Connor and E F Robertson

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Mathematicians born in the same country

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