Editing Max Born (section)

==Career==
===Berlin and Frankfurt===
Born settled in as a young academic at Göttingen as a {{lang|de|[[Privatdozent]]}}. In Göttingen, Born stayed at a [[boarding house]] run by Sister Annie at Dahlmannstraße 17, known as El BoKaReBo.  The name was derived from the first letters of the last names of its boarders: "El" for Ella Philipson (a medical student), "Bo" for Born and Hans Bolza (a physics student), "Ka" for [[Theodore von Kármán]] (a {{lang|de|Privatdozent}}), and "Re" for Albrecht Renner (another medical student). A frequent visitor to the boarding house was [[Paul Peter Ewald]], a doctoral student of [[Arnold Sommerfeld]] on loan to Hilbert at Göttingen as a special assistant for physics. [[Richard Courant]], a mathematician and {{lang|de|Privatdozent}}, called these people the "in group".{{sfn|Greenspan|2005|pp=49–55}}

In 1912, Born met Hedwig (Hedi) Ehrenberg, the daughter of a [[Leipzig University]] law professor, and a friend of Carl Runge's daughter [[Iris Runge|Iris]]. She was of Jewish background on her father's side, although he had become a practising [[Lutheran]] when he got married, as did Max's sister Käthe. Despite never practising his religion, Born refused to convert, and his wedding on 2 August 1913 was a garden ceremony. However, he was baptised as a Lutheran in March 1914 by the same pastor who had performed his wedding ceremony. Born regarded "religious professions and churches as a matter of no importance".{{sfn|Greenspan|2005|pp=61–62}} His decision to be baptised was made partly in deference to his wife, and partly due to his desire to assimilate into German society.{{sfn|Greenspan|2005|pp=61–62}} The marriage produced three children: two daughters, Irene, born in 1914, and Margarethe (Gritli), born in 1915, and a son, [[Gustav Victor Rudolf Born|Gustav]], born in 1921.{{sfn|Born|2002|p=225}} Through marriage, Born is related to jurists [[Victor Ehrenberg (jurist)|Victor Ehrenberg]], his father-in-law, and [[Rudolf von Jhering]], his wife's maternal grandfather, as well as to philosopher and theologian [[Hans Ehrenberg]], and is a great uncle of British comedian [[Ben Elton]].{{sfn|Born|2002|pp=238–241}}

By the end of 1913, Born had published 27 papers, including important work on relativity and the dynamics of crystal lattices (3 with [[Theodore von Karman]]),{{sfn|Greenspan|2005|pp=56–62}} which became a book.{{sfn|Kemmer|Schlapp|1971|p=20}} In 1914, he received a letter from [[Max Planck]] explaining that a new [[professor extraordinarius]] chair of [[theoretical physics]] had been created at the [[University of Berlin]]. The chair had been offered to [[Max von Laue]], but he had turned it down. Born accepted.{{sfn|Greenspan|2005|pp=63–67}} The [[First World War]] was now raging. Soon after  arriving in Berlin in 1915, he enlisted in an Army signals unit. In October, he joined the [[Artillerie Prüfungskommission]], the Army's Berlin-based artillery research and development organisation, under [[Rudolf Ladenburg]], who had established a special unit dedicated to the new technology of [[sound ranging]]. In Berlin, Born formed a lifelong friendship with Einstein, who became a frequent visitor to Born's home.{{sfn|Greenspan|2005|pp=70–75}} Within days of [[Armistice with Germany|the armistice]] in November 1918, Planck had the Army release Born. A chance meeting with [[Fritz Haber]] that month led to discussion of the manner in which an [[ionic compound]] is formed when a [[metal]] reacts with a [[halogen]], which is today known as the [[Born–Haber cycle]].{{sfn|Greenspan|2005|pp=83–86}}

Even before Born had taken up the chair in Berlin, von Laue had changed his mind, and decided that he wanted it after all.{{sfn|Greenspan|2005|pp=63–67}}  He arranged with Born and the faculties concerned for them to exchange jobs. In April 1919, Born became [[professor ordinarius]] and Director of the Institute of Theoretical Physics on the science faculty at the [[University of Frankfurt am Main]].{{sfn|Kemmer|Schlapp|1971|p=20}} While there, he was approached by the University of Göttingen, which was looking for a replacement for [[Peter Debye]] as Director of the Physical Institute.{{sfn|Kemmer|Schlapp|1971|p=21}} "Theoretical physics," Einstein advised him, "will flourish wherever ''you'' happen to be; there is no other Born to be found in Germany today."{{sfn|Greenspan|2005|p=96}}  In negotiating for the position with the education ministry, Born arranged for another chair, of experimental physics, at Göttingen for his long-time friend and colleague [[James Franck]].{{sfn|Kemmer|Schlapp|1971|p=21}}

In 1919 [[Elisabeth Bormann]] joined the Institut für Theoretische Physik as his assistant.<ref>{{Cite book |title=Biografien bedeutender österreichischer Wissenschafterinnen: "Die Neugier treibt mich, Fragen zu stellen"|date=2018|first1=Ilse Erika |last1=Korotin |first2=Nastasja |last2=Stupnicki|isbn=978-3-205-20238-7|location=Wien |publisher=Böhlau Verlag |oclc=1038390215}}</ref> She developed the first atomic beams. Working with Born, Bormann was the first to measure the [[Mean free path|free path]] of atoms in gases and the size of molecules.<ref>{{cite web|title=Goethe-Universität — "Historic Site" Plaque for Frankfurt Physics|url=https://www.goethe-university-frankfurt.de/81694072/Historic_Site__Plaque_for_Frankfurt_Physics|access-date=2021-08-03|website=www.goethe-university-frankfurt.de}}</ref><ref>{{Cite journal|last=Toennies|first=J. Peter|title=Serendipitous Meanderings and Adventures with Molecular Beams|date=June 2004|url=http://www.annualreviews.org/doi/10.1146/annurev.physchem.55.081203.151413|journal=Annual Review of Physical Chemistry|language=en|volume=55|issue=1|pages=1–33|doi=10.1146/annurev.physchem.55.081203.151413|pmid=15117245|bibcode=2004ARPC...55....1T|issn=0066-426X|access-date=4 August 2021|archive-date=3 August 2021|archive-url=https://web.archive.org/web/20210803205238/https://www.annualreviews.org/doi/10.1146/annurev.physchem.55.081203.151413}}</ref>

===Göttingen===
[[File:Solvay conference 1927.jpg|thumb|left|[[Solvay Conference]], 1927. Born is second from the right in the second row, between [[Louis de Broglie]] and [[Niels Bohr]]. ]]

For the 12 years Born and Franck were at the [[University of Göttingen]] (1921 to 1933), Born had a collaborator with shared views on basic scientific concepts—a benefit for teaching and research. Born's collaborative approach with experimental physicists was similar to that of [[Arnold Sommerfeld]] at the [[University of Munich]], who was ordinarius professor of theoretical physics and Director of the Institute of Theoretical Physics—also a prime mover in the development of [[Quantum field theory|quantum theory]].  Born and Sommerfeld collaborated with experimental physicists to test and advance their theories. In 1922, when lecturing in the United States at the [[University of Wisconsin–Madison]], Sommerfeld sent his student [[Werner Heisenberg]] to be Born's assistant.  Heisenberg returned to Göttingen in 1923, where he completed his habilitation under Born in 1924, and became a {{lang|de|Privatdozent}} at Göttingen.{{sfn|Greenspan|2005|pp=113, 120, 123}}{{sfn|Jungnickel|McCormmach|1986|pp=274, 281–285, 350–354}}

In 1919 and 1920, Max Born became displeased about the large number of objections<ref>The Born Einstein Letters, Walker and Company, New York, 1971, page 72</ref> against Einstein's relativity, and gave speeches in the winter of 1919 in support of Einstein. Born received pay for his relativity speeches which helped with expenses through the year of rapid inflation. The speeches in German language became a book published in 1920 of which Einstein received the proofs before publication.<ref>The Born Einstein Letters, Walker and Company, New York, 1971, page 30</ref> A third edition was published in 1922 and an English translation was published in 1924. Born represented light speed as a function of curvature,<ref>Einstein's Theory Of Relativity, Max Born, Dover, New York, 1965, page 357</ref> "the velocity of light is much greater for some directions of the light ray than its ordinary value c, and other bodies can also attain much greater velocities.<ref>Einstein's Theory Of Relativity, Max Born, E. P. Dutton and Company, New York, 1924 page 285</ref>"

In 1925, Born and Heisenberg formulated the [[matrix mechanics]] representation of [[quantum mechanics]]. On 9 July, Heisenberg gave Born a paper entitled ''[[Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen]]'' ("Quantum-Theoretical Re-interpretation of Kinematic and Mechanical Relations") to review, and submit for publication. In the paper, Heisenberg formulated quantum theory, avoiding the concrete, but unobservable, representations of electron orbits by using parameters such as transition probabilities for quantum jumps, which necessitated using two indexes corresponding to the initial and final states.{{sfn|Heisenberg|1925|pages=879–893}}{{sfn|Segrè|1980|pp=153–157}} When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices,{{sfn|Pais|1991|pp=275–279}} which he had learned from his study under Jakob Rosanes at [[Breslau University]].<ref name=Born1954>{{cite web |url=http://nobelprize.org/nobel_prizes/physics/laureates/1954/born-lecture.pdf |title=The Statistical Interpretation of Quantum Mechanics—Nobel Lecture |year=1954 |first=Max |last=Born |publisher=Official Web Site of the Nobel Prize |access-date=9 March 2013 |archive-url=https://web.archive.org/web/20121019194414/http://www.nobelprize.org/nobel_prizes/physics/laureates/1954/born-lecture.pdf |archive-date=19 October 2012 }}</ref>

Up until this time, matrices were seldom used by physicists; they were considered to belong to the realm of [[pure mathematics]]. [[Gustav Mie]] had used them in a paper on electrodynamics in 1912, and Born had used them in his work on the lattices theory of crystals in 1921.  While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics.{{sfn|Jammer|1966|pp=206–207}} With the help of his assistant and former student [[Pascual Jordan]], Born began immediately to make a transcription and extension, and they submitted their results for publication; the paper was received for publication just 60 days after Heisenberg's paper.{{sfn|Born|Jordan|1925}} A follow-on paper was submitted for publication before the end of the year by all three authors.{{sfn|Born|Heisenberg|Jordan|1925|pp=557–615}} The result was a surprising formulation:

:<math> p q - q p =  { h \over 2 \pi i } I </math>

where ''p'' and ''q'' were matrices for location and [[momentum]], and ''I'' is the [[identity matrix]]. The left hand side of the equation is not zero because [[matrix multiplication]] is not [[commutative]].<ref name=Born1954/> This formulation was entirely attributable to Born, who also established that all the elements not on the diagonal of the matrix were zero. Born considered that his paper with Jordan contained "the most important principles of quantum mechanics including its [[quantum electrodynamics|extension to electrodynamics]]."<ref name=Born1954/> The paper put Heisenberg's approach on a solid mathematical basis.{{sfn|Kemmer|Schlapp|1971|p=35}}

Born was surprised to discover that [[Paul Dirac]] had been thinking along the same lines as Heisenberg. Soon, [[Wolfgang Pauli]] used the matrix method to calculate the energy values of the hydrogen atom and found that they agreed with the [[Bohr model]]. Another important contribution was made by [[Erwin Schrödinger]], who looked at the problem using [[wave|wave mechanics]]. This had a great deal of appeal to many at the time, as it offered the possibility of returning to deterministic classical physics. Born would have none of this, as it ran counter to facts determined by experiment.<ref name=Born1954/> He formulated the now-standard interpretation of the [[probability amplitude|probability density function]] for ψ*ψ in the [[Schrödinger equation]], which he published in July 1926.{{sfn|Born|1926|pp=863–867}}{{sfn|Kemmer|Schlapp|1971|p=35}}

In a letter to Born on 4 December 1926, Einstein made his famous remark regarding quantum mechanics: {{quote|Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the 'old one'. I, at any rate, am convinced that ''He'' is not playing at dice.{{sfn|Born|Born|Einstein|1971|p=91}} }}
This quotation is often paraphrased as '[[God does not play dice]]'.{{sfn|Born|1969|p=113}}

In 1928, Einstein nominated Heisenberg, Born, and Jordan for the [[Nobel Prize in Physics]],{{sfn|Bernstein|2005|p=1004}}{{sfn|Greenspan|2005|p=190}} but Heisenberg alone won the 1932 Prize "for the creation of quantum mechanics, the application of which has led to the discovery of the allotropic forms of hydrogen",<ref name="nobelprize.org">{{cite web |title=Nobel Prize in Physics 1933 |url=http://nobelprize.org/nobel_prizes/physics/laureates/1933/press.html |access-date=9 March 2013 }}</ref> while Schrödinger and Dirac shared the 1933 Prize "for the discovery of new productive forms of atomic theory".<ref name="nobelprize.org"/> On 25 November 1933, Born received a letter from Heisenberg in which he said he had been delayed in writing due to a "bad conscience" that he alone had received the Prize "for work done in Göttingen in collaboration—you, Jordan and I."{{sfn|Greenspan|2005|p=191}}  Heisenberg went on to say that Born and Jordan's contribution to quantum mechanics cannot be changed by "a wrong decision from the outside."{{sfn|Greenspan|2005|p=191}} In 1954, Heisenberg wrote an article honouring Planck for his insight in 1900, in which he credited Born and Jordan for the final mathematical formulation of matrix mechanics and Heisenberg went on to stress how great their contributions were to quantum mechanics, which were not "adequately acknowledged in the public eye."{{sfn|Greenspan|2005|pp=285–286}}

Those who received their PhD degrees under Born at Göttingen included [[Max Delbrück]], [[Siegfried Flügge]], [[Friedrich Hund]], [[Pascual Jordan]], [[Maria Goeppert-Mayer]], [[Lothar Wolfgang Nordheim]], [[Robert Oppenheimer]], and [[Victor Weisskopf]].<ref name="mathgene">{{MathGenealogy|id=18245}}</ref>{{sfn|Greenspan|2005|pp=142, 262}}  Born's assistants at the University of Göttingen's Institute for Theoretical Physics included [[Enrico Fermi]], Werner Heisenberg, [[Gerhard Herzberg]], Friedrich Hund, Pascual Jordan, Wolfgang Pauli, [[Léon Rosenfeld]], [[Edward Teller]], and [[Eugene Wigner]].{{sfn|Greenspan|2005|pp=178, 262}} [[Walter Heitler]]  became an assistant to Born in 1928, and completed his habilitation under him in 1929. Born not only recognised talent to work with him, but he "let his superstars stretch past him; to those less gifted, he patiently handed out respectable but doable assignments."{{sfn|Greenspan|2005|p=143}} Delbrück, and Goeppert-Mayer went on to be awarded Nobel Prizes.<ref>{{cite web |url=https://www.nobelprize.org/nobel_prizes/medicine/laureates/1969/delbruck.html |title=Max Delbrück – Biography|publisher=The Official Web Site of the Nobel Prize|access-date=10 March 2013 }}</ref><ref>{{cite web |url=https://www.nobelprize.org/educational/nobelprize_info/goeppert-mayer-edu.html |title=Maria Goeppert-Mayer – Biography|publisher=The Official Web Site of the Nobel Prize|access-date=10 March 2013 }}</ref>