# Pascual Jordan

**Ernst Pascual Jordan** (German: [ˈjɔɐ̯daːn]; 18 October 1902 – 31 July 1980) was a German theoretical and mathematical physicist who made significant contributions to quantum mechanics and quantum field theory. He contributed much to the mathematical form of matrix mechanics, and developed canonical anticommutation relations for fermions. Jordan algebra is employed for and is still used in studying the mathematical and conceptual foundations of quantum theory, and has found other mathematical applications.^{[1]}

Pascual Jordan | |
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Pascual Jordan in the 1920s | |

Born | 18 October 1902 |

Died | 31 July 1980 | (aged 77)

Nationality | Germany |

Known for | Quantum mechanics Quantum field theory Matrix mechanics Skew lattice Jordan algebra Jordan–Brans–Dicke theory Jordan and Einstein frames Jordan map Jordan–Wigner transformation |

Awards | Max Planck Medal (1942), Carl Friedrich Gauß Medal (1955) |

Scientific career | |

Fields | Theoretical physics |

Institutions | Technical University of Hannover University of Göttingen |

Doctoral advisor | Max Born |

Doctoral students | Jürgen Ehlers, Engelbert Schücking |

## Family historyEdit

An ancestor of Pascual Jordan named Pascual Jordan^{[2]} was a Spanish nobleman and cavalry officer who served with the British during and after the Napoleonic Wars. Jordan eventually settled in Hannover, which in those days ruled the United Kingdom. The family name was eventually changed to Jordan (pronounced in the German manner, [ˈjɔʁdaːn] or [ˈjɔɐ̯daːn]). A family tradition held that the first-born son in each generation be named Pascual.^{[3]} Jordan was raised with a traditional religious upbringing. At age 12 he attempted to reconcile a literal interpretation of the Bible with Darwinian evolution; his teacher of religion convinced him there was no contradiction between science and religion (Jordan would write numerous articles on the relationship between the two throughout his life).^{[3]}

Jordan enrolled in the Technical University of Hannover in 1921 where he studied zoology, mathematics, and physics. As was typical for a German university student of the time, he shifted his studies to another university before obtaining a degree. The University of Göttingen, his destination in 1923, was then at the very zenith of its powers in mathematics and the physical sciences, such as under the guidance of mathematician David Hilbert and the physicist Arnold Sommerfeld. At Göttingen Jordan became an assistant to the mathematician Richard Courant for a time, and then he studied under the physicist Max Born for his doctorate.

## Scientific workEdit

Together with Max Born and Werner Heisenberg, Jordan was a coauthor of an important series of papers on quantum mechanics.^{[4]} He went on to pioneer early quantum field theory^{[4]} before largely switching his focus to cosmology before World War II.

Jordan devised a type of nonassociative algebras, now named Jordan algebras in his honor, in an attempt to create an algebra of observables for quantum mechanics and quantum field theory. Today, von Neumann algebras are also employed for this purpose. Jordan algebras have since been applied in projective geometry, number theory, complex analysis, optimization, and many other fields of pure and applied mathematics, and continue to be used in studying the mathematical and conceptual underpinnings of quantum theory.

In 1966, Jordan published his 182-page work *Die Expansion der Erde. Folgerungen aus der Diracschen Gravitationshypothese* (The expansion of the Earth. Conclusions from the Dirac gravitation hypothesis)^{[5]} in which he developed his theory that, according to Paul Dirac's hypothesis of a steady weakening of gravitation throughout the history of the universe, the Earth may have swollen to its current size, from an initial ball of a diameter of only about 7,000 kilometres (4,300 mi). This theory could explain why the ductile lower sima layer of the Earth's crust is of a comparatively uniform thickness, while the brittle upper sial layer of the Earth's crust had broken apart into the main continental plates. The continents having to adapt to the ever flatter surface of the growing ball, the mountain ranges on the Earth's surface would, in the course of that, have come into being as constricted folds.^{[6]} Despite the energy Jordan invested in the expanding Earth theory, his geological work was never taken seriously by either physicists or geologists.^{[7]}

## Political activitiesEdit

Germany's defeat in the First World War and the Treaty of Versailles had a profound effect on Jordan's political beliefs. While many of his colleagues believed the Treaty to be unjust, Jordan went much further and became increasingly nationalistic and right-wing. He wrote numerous articles in the late 1920s that propounded an aggressive and bellicose stance. He was an anti-communist and was particularly concerned about the Russian Revolution and the rise of the Bolsheviks.^{[3]}

In 1933, Jordan joined the Nazi party, like Philipp Lenard and Johannes Stark, and, moreover, joined an SA unit. He supported the Nazis' nationalism and anti-communism but at the same time, he remained "a defender of Einstein" and other Jewish scientists. Jordan seemed to hope that he could influence the new regime; one of his projects was attempting to convince the Nazis that modern physics developed as represented by Einstein and especially the new Copenhagen brand of quantum theory could be the antidote to the "materialism of the Bolsheviks". However, while the Nazis appreciated his support for them, his continued support for Jewish scientists and their theories led him to be regarded as politically unreliable.^{[8]}^{[9]}

Jordan enlisted in the Luftwaffe in 1939 and worked as a weather analyst at the Peenemünde rocket center, for a while. During the war he attempted to interest the Nazi party in various schemes for advanced weapons. His suggestions were ignored because he was considered "politically unreliable", probably because of his past associations with Jews (in particular: Courant, Born, and Wolfgang Pauli) and the so-called "Jewish physics".

Had Jordan not joined the Nazi party, it is conceivable that he could have won a Nobel Prize in Physics for his work with Max Born. Born would go on to win the 1954 Physics Prize with Walther Bothe.^{[10]}^{[11]}

Wolfgang Pauli declared Jordan to be "rehabilitated" to the West German authorities some time after the war, allowing him to regain academic employment after a two-year period. He then recovered his full status as a tenured professor in 1953. Jordan went against Pauli's advice, and reentered politics after the period of denazification came to an end under the pressures of the Cold War. He secured election to the Bundestag standing with the conservative Christian Democratic Union. In 1957 Jordan supported the arming of the Bundeswehr with tactical nuclear weapons by the Adenauer government, while the Göttingen Eighteen (which included Born and Heisenberg) issued the Göttinger Manifest in protest. This and other issues were to further strain his relationships with his former friends and colleagues.^{[3]}

## Selected worksEdit

- Born, M.; Jordan, P. (1925). "Zur Quantenmechanik".
*Zeitschrift für Physik*.**34**(1): 858. Bibcode:1925ZPhy...34..858B. doi:10.1007/BF01328531. - Born, M.; Heisenberg, W.; Jordan, P. (1926). "Zur Quantenmechanik. II".
*Zeitschrift für Physik*.**35**(8–9): 557. Bibcode:1926ZPhy...35..557B. doi:10.1007/BF01379806. - Jordan, P. (1927). "Über quantenmechanische Darstellung von Quantensprüngen".
*Zeitschrift für Physik*.**40**(9): 661–666. Bibcode:1927ZPhy...40..661J. doi:10.1007/BF01451860. - Jordan, P. (1927). "Über eine neue Begründung der Quantenmechanik".
*Zeitschrift für Physik*.**40**(11–12): 809–838. Bibcode:1927ZPhy...40..809J. doi:10.1007/BF01390903. - Jordan, P. (1927). "Kausalität und Statistik in der modernen Physik".
*Die Naturwissenschaften*.**15**(5): 105–110. Bibcode:1927NW.....15..105J. doi:10.1007/BF01504228. - Jordan, P. (1927). "Anmerkung zur statistischen Deutung der Quantenmechanik".
*Zeitschrift für Physik*.**41**(4–5): 797–800. Bibcode:1927ZPhy...41..797J. doi:10.1007/BF01395485. - Jordan, P. (1927). "Über eine neue Begründung der Quantenmechanik II".
*Zeitschrift für Physik*.**44**: 1–25. Bibcode:1927ZPhy...44....1J. doi:10.1007/BF01391714. - Jordan, P.; von Neumann, J.; Wigner, E. (1934). "On an Algebraic Generalization of the Quantum Mechanical Formalism".
*Annals of Mathematics*.**35**(1): 29–64. doi:10.2307/1968117. JSTOR 1968117.

## ReferencesEdit

**^**McCrimmon, Kevin (2004).*A taste of Jordan algebras*(PDF). New York: Springer. ISBN 0-387-95447-3.**^**Jones, Sheilla (2008).*The quantum ten : a story of passion, tragedy, ambition and science*. Oxford: Oxford University Press. ISBN 9780195369090.- ^
^{a}^{b}^{c}^{d}Schroer, Bert (2003). "Pascual Jordan, his contributions to quantum mechanics and his legacy in contemporary local quantum physics". arXiv:hep-th/0303241. - ^
^{a}^{b}Silvan S. Schweber,*QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga*, Princeton: Princeton University Press, 1994, ISBN 0-691-03327-7. **^**Die Wissenschaft, vol. 124. Friedrich Vieweg & Sohn, Braunschweig 1966**^**Heinz Haber: "Die Expansion der Erde" [The expansion of the Earth].*Unser blauer Planet*[*Our blue planet*]. Rororo Sachbuch [Rororo nonfiction] (in German) (Rororo Taschenbuch Ausgabe [Rororo pocket edition] ed.). Reinbek: Rowohlt Verlag. 1967 [1965]. pp. 48, 52, 54–55.**^**Kragh, Helge (2015). "Pascual Jordan, Varying Gravity, and the Expanding Earth".*Physics in Perspective*.**17**(2): 107–134. Bibcode:2015PhP....17..107K. doi:10.1007/s00016-015-0157-9.**^**Schucking, E. L. (1999). "Jordan, Pauli, Politics, Brecht, and a Variable Gravitational Constant".*Physics Today*.**52**(10): 26–31. Bibcode:1999PhT....52j..26S. doi:10.1063/1.882858.**^**Schroer, Bert (27 March 2003). "Pascual Jordan, his contributions to quantum mechanics and his legacy in contemporary local quantum physics". arXiv:hep-th/0303241.**^**Bernstein, Jeremy (2005). "Max Born and the quantum theory".*Am. J. Phys*.**73**(11): 999–1008. Bibcode:2005AmJPh..73..999B. doi:10.1119/1.2060717.**^**Bert Schroer (2003). "Pascual Jordan, his contributions to quantum mechanics and his legacy in contemporary local quantum physics". arXiv:hep-th/0303241.

## Further readingEdit

Wikimedia Commons has media related to .Pascual Jordan |

- Schroer, B. (2011). "Pascual Jordan's legacy and the ongoing research in quantum field theory".
*European Physical Journal H*.**35**(4): 377–434. arXiv:1010.4431. Bibcode:2010EPJH...35..377S. CiteSeerX 10.1.1.612.5751. doi:10.1140/epjh/e2011-10015-8. - Duncan, Anthony; Janssen, Michel (2012). "(Never) Mind your p's and q's: Von Neumann versus Jordan on the Foundations of Quantum Theory".
*The European Physical Journal H*.**38**(2): 175. arXiv:1204.6511. Bibcode:2013EPJH...38..175D. doi:10.1140/epjh/e2012-30024-5.

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