Erich Kretschmann
Encyclopedia
Erich Justus Kretschmann (July 14, 1887 in Berlin
-1973) was a German
physicist
.
He obtained his D.Phil. at Berlin University in 1914 with his dissertation entitled "Eine Theorie der Schwerkraft im Rahmen der ursprünglichen Einsteinschen Relativitätstheorie (A theory of gravity in the framework of the original Einstein theory of relativity)". His advisors were Max Planck
and Heinrich Rubens
. After working as a Gymnasium (school)
teacher
, he became Privatdozent
for theoretical physics
at the University of Königsberg
in 1920, where he eventually became professor extraordinarius in 1926. From 1946 until 1952, Kretschmann was professor for theoretical physics and director of the institute for theoretical physics at the University of Halle-Wittenberg
.
. In his 1915 papers he also introduced, though not in name, the point coincidence argument in relativity. Similar ideas appeared in Einstein's writings on general relativity
. Historians Don Howard and John Norton suggest that Einstein may have failed to adequately acknowledge Kretschmann's contribution. Kretschmann's use of the argument was more topological while Einstein's use involved physical measurements.
Kretschmann is most famous for his 1917 claim that Einstein's use of the principle of covariance
in General Relativity is vacuous. Kretschmann claimed that the demand that a theory be put in generally covariant form does not limit or restrict the range of acceptable theories, but is simply a challenge to the mathematician's ingenuity. According to Kretschmann, any theory can be put in generally covariant form. Einstein responded that even if general covariance is not a purely formal limitation on acceptable theories, it plays "an important heuristic role" in the formulation of General Relativity.
Einstein wrote concerning Kretschmann's objection:"Although it is true that every empirical law can be put in a generally covariant form, yet the principle of relativity possesses a great heuristic power....Of two theoretical systems, both of which agree with experience, the one is to be preferred which, from the point of view of the absolute differential calculus is the simpler and more transparent. Let one express Newtonian mechanics four-dimensionally in the form of generally covariant equations and one will surely be convinced that the principle of relativity excludes this theory from the practical, though not the theoretical, viewpoint." (1918, p. 242)
Einstein suggested that Newtonian theory would be impossibly complex if put in covariant form, although since Einstein made that claim it has been formulated in covariant form by several physicists, including Elie Cartan in 1923 and Friedrichs in 1927. Misner, Thorne, and Wheeler, in their textbook Gravitation (1973) Ch. 12 present the covariant version of Newton.
In a letter of 1925 Arnold Sommerfeld wrote favorably of Kretschmann's work in relativity and the statistics of atoms, but said that he needed to get a different teaching position (get away from Königsberg) in order to be able to do more research.
The issue of whether covariance is a real restriction and if so in what sense appears in various contributions to the philosophical debate concerning Einstein's "hole argument." This argument initially had led Einstein in 1913 for a time to reject generally covariant theories, because a region of space/time without forces would undermine determinism or unique extension of trajectories. He later concluded that space/time points without gravity would not be individuated.
It has been claimed also that Kretschmann discovered that the conformal geometry of General Relativity corresponds to the light cone structure, a point rediscovered by and extensively exploited by Hermann Weyl, and since then developed by Jürgen Ehlers and collaborators.
Kretschmann's prose is so convoluted and obscure that reception and appreciation of his work was generally delayed. James Anderson, in the mid-1960s made Kretschmann's work more well-known, though he used it as an object of criticism with respect to Kretschmann's claims concerning the symmetry groups of special and general relativity.
Kretschmann published half a dozen less noted papers during the 1920s and early 1930s, the last in 1934, though he continued to live in Germany for decades. Whether the Nazi seizure of power had anything to do with his ceasing to publish should be investigated.
Einstein's Response to Kretschmann:
Einstein, Albert, 1918 "Principielles zur allgemainen Relativitãtstheorie," Annalen der Physik
, vol. 55.
Commentary:
Robert Rynasiewicz, "Kretshmann's Analysis of Covariance and Relativity Principles," in The Expanding Worlds of General Relativity ed. Hubert Goeener, et al., Boston: Birkhãuser, 1999, 431-462.
Other and Later Works of Kretschmann:
Beitrag zur Kritik der Blochschen Theorie der Elektrizitätsleitung. Z. f. Physik 87, 518-534(1934)
Über die Resonanzbedingung und über die Beschleunigung der Elektronen in der
Blochschen Theorie der Elektrizitätsleistung. Z. f. Physik 88, 792-799. (1934)
Beitrag zur Theorie des elektrischen Widerstandes und der Supraleitfähigkeit
der Metalle. Annalen d. Physik (5) 13, 564-598. 1932
Atom und Welle. Schriften Königsberg 6, 216-231. 1929
Eine Bemerkung zu Herrn A. Sommerfelds Arbeit: ``Zur Elektronentheorie der
Metalle auf Grund der Fermischen Statistik. Z. f. Physik 48, 739-744.(1928)
Die Supraleitfähigkeit nach Schrödingers Wellengleichung und Fermis
Statistik. Annalen d. Physik (4) 86, 914-928.(1928)
Theorie der Dauerströme in Supraleitern. Annalen d. Physik (4) 80, 109-136. Berichtigung. Annalen d. Physik (4) 80,532. (1926)
Über die Ableitung der Helmholtzschen Wirbelsätze in der Lorentz-Einsteinschen Relativitätstheorie. Schriften Königsberg 1, 179-191.(1925)
Zur Theorie der Supraleitfähigkeit und der gewöhnlichen elektrischen
Leitfähigkeit der Metalle. Schriften Königsberg 1, 193-204. (1925)
Das Maxwell-Boltzmannsche Geschwindigkeits- und Energieverteilungsgesetz in
der Relativitätstheorie. Phys. Zs. 25, 162-165. 192
Das statische Einkörperproblem in der Einstein'schen Theorie. Antwort an
Hrn. A. Gullstrand. Ark. för Mat., Astron, och Fys. 17, Nr. 25, 4 S. 1923
Eine Bemerkung zu Hrn. A. Gullstrands Abhandlung: ``Allgemeine Lösung des
statischen Einkörperproblems in der Einsteinschen Gravitationstheorie".
Ark. för Mat., Astron. och Fys. 17, Nr. 2, 4 S. (1922)
Der Liouvillesche Satz und die Relativitätstheorie. Physik. Zs. 21, 484-487.192
Eine Theorie der Schwerkraft im Rahmen der ursprünglichen {\it
Einstein}schen Relativitätstheorie. Berlin, 113 1914
Berlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
-1973) was a German
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
.
He obtained his D.Phil. at Berlin University in 1914 with his dissertation entitled "Eine Theorie der Schwerkraft im Rahmen der ursprünglichen Einsteinschen Relativitätstheorie (A theory of gravity in the framework of the original Einstein theory of relativity)". His advisors were Max Planck
Max Planck
Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...
and Heinrich Rubens
Heinrich Rubens
Heinrich Rubens was a German physicist.He played a direct role in the genesis of the quantum theory, providing the experimental results that pushed Max Planck to provide the first quantum hypothesis.He also combined scientific ideas to create the Rubens' tube.-External links:*...
. After working as a Gymnasium (school)
Gymnasium (school)
A gymnasium is a type of school providing secondary education in some parts of Europe, comparable to English grammar schools or sixth form colleges and U.S. college preparatory high schools. The word γυμνάσιον was used in Ancient Greece, meaning a locality for both physical and intellectual...
teacher
Teacher
A teacher or schoolteacher is a person who provides education for pupils and students . The role of teacher is often formal and ongoing, carried out at a school or other place of formal education. In many countries, a person who wishes to become a teacher must first obtain specified professional...
, he became Privatdozent
Privatdozent
Privatdozent or Private lecturer is a title conferred in some European university systems, especially in German-speaking countries, for someone who pursues an academic career and holds all formal qualifications to become a tenured university professor...
for theoretical physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
at the University of Königsberg
University of Königsberg
The University of Königsberg was the university of Königsberg in East Prussia. It was founded in 1544 as second Protestant academy by Duke Albert of Prussia, and was commonly known as the Albertina....
in 1920, where he eventually became professor extraordinarius in 1926. From 1946 until 1952, Kretschmann was professor for theoretical physics and director of the institute for theoretical physics at the University of Halle-Wittenberg
University of Halle-Wittenberg
The Martin Luther University of Halle-Wittenberg , also referred to as MLU, is a public, research-oriented university in the cities of Halle and Wittenberg within Saxony-Anhalt, Germany...
.
Work
In his 1915 papers, he introduced the Kretschmann scalarKretschmann scalar
In the theory of Lorentzian manifolds, particularly in the context of applications to general relativity, the Kretschmann scalar is a quadratic scalar invariant. It was introduced by Erich Kretschmann.-Definition:...
. In his 1915 papers he also introduced, though not in name, the point coincidence argument in relativity. Similar ideas appeared in Einstein's writings on general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. Historians Don Howard and John Norton suggest that Einstein may have failed to adequately acknowledge Kretschmann's contribution. Kretschmann's use of the argument was more topological while Einstein's use involved physical measurements.
Kretschmann is most famous for his 1917 claim that Einstein's use of the principle of covariance
Principle of covariance
In physics, the principle of covariance emphasizes formulation of physical laws using only those physical quantities the measurements of which the observers in different frames of reference could unambiguously correlate....
in General Relativity is vacuous. Kretschmann claimed that the demand that a theory be put in generally covariant form does not limit or restrict the range of acceptable theories, but is simply a challenge to the mathematician's ingenuity. According to Kretschmann, any theory can be put in generally covariant form. Einstein responded that even if general covariance is not a purely formal limitation on acceptable theories, it plays "an important heuristic role" in the formulation of General Relativity.
Einstein wrote concerning Kretschmann's objection:"Although it is true that every empirical law can be put in a generally covariant form, yet the principle of relativity possesses a great heuristic power....Of two theoretical systems, both of which agree with experience, the one is to be preferred which, from the point of view of the absolute differential calculus is the simpler and more transparent. Let one express Newtonian mechanics four-dimensionally in the form of generally covariant equations and one will surely be convinced that the principle of relativity excludes this theory from the practical, though not the theoretical, viewpoint." (1918, p. 242)
Einstein suggested that Newtonian theory would be impossibly complex if put in covariant form, although since Einstein made that claim it has been formulated in covariant form by several physicists, including Elie Cartan in 1923 and Friedrichs in 1927. Misner, Thorne, and Wheeler, in their textbook Gravitation (1973) Ch. 12 present the covariant version of Newton.
In a letter of 1925 Arnold Sommerfeld wrote favorably of Kretschmann's work in relativity and the statistics of atoms, but said that he needed to get a different teaching position (get away from Königsberg) in order to be able to do more research.
The issue of whether covariance is a real restriction and if so in what sense appears in various contributions to the philosophical debate concerning Einstein's "hole argument." This argument initially had led Einstein in 1913 for a time to reject generally covariant theories, because a region of space/time without forces would undermine determinism or unique extension of trajectories. He later concluded that space/time points without gravity would not be individuated.
It has been claimed also that Kretschmann discovered that the conformal geometry of General Relativity corresponds to the light cone structure, a point rediscovered by and extensively exploited by Hermann Weyl, and since then developed by Jürgen Ehlers and collaborators.
Kretschmann's prose is so convoluted and obscure that reception and appreciation of his work was generally delayed. James Anderson, in the mid-1960s made Kretschmann's work more well-known, though he used it as an object of criticism with respect to Kretschmann's claims concerning the symmetry groups of special and general relativity.
Kretschmann published half a dozen less noted papers during the 1920s and early 1930s, the last in 1934, though he continued to live in Germany for decades. Whether the Nazi seizure of power had anything to do with his ceasing to publish should be investigated.
Major works by Erich Kretschmann
- Kretschmann, Erich. 1915. Über die prinzipielle Bestimmbarkeit der berechtigten Bezugssysteme beliebiger Relativitätstheorien (I), (II). Annalen der PhysikAnnalen der PhysikAnnalen der Physik is one of the oldest physics journals worldwide. The journal publishes original, peer-reviewed papers in the areas of experimental, theoretical, applied and mathematical physics and related areas...
48: 907–942, 943–982.
- ———. 1917. Über den physikalischen Sinn der Relativitätspostulate. A. Einsteins neue und seine ursprüngliche Relativitätstheorie. Annalen der PhysikAnnalen der PhysikAnnalen der Physik is one of the oldest physics journals worldwide. The journal publishes original, peer-reviewed papers in the areas of experimental, theoretical, applied and mathematical physics and related areas...
53: 575–614.
Einstein's Response to Kretschmann:
Einstein, Albert, 1918 "Principielles zur allgemainen Relativitãtstheorie," Annalen der Physik
Annalen der Physik
Annalen der Physik is one of the oldest physics journals worldwide. The journal publishes original, peer-reviewed papers in the areas of experimental, theoretical, applied and mathematical physics and related areas...
, vol. 55.
Commentary:
Robert Rynasiewicz, "Kretshmann's Analysis of Covariance and Relativity Principles," in The Expanding Worlds of General Relativity ed. Hubert Goeener, et al., Boston: Birkhãuser, 1999, 431-462.
Other and Later Works of Kretschmann:
Beitrag zur Kritik der Blochschen Theorie der Elektrizitätsleitung. Z. f. Physik 87, 518-534(1934)
Über die Resonanzbedingung und über die Beschleunigung der Elektronen in der
Blochschen Theorie der Elektrizitätsleistung. Z. f. Physik 88, 792-799. (1934)
Beitrag zur Theorie des elektrischen Widerstandes und der Supraleitfähigkeit
der Metalle. Annalen d. Physik (5) 13, 564-598. 1932
Atom und Welle. Schriften Königsberg 6, 216-231. 1929
Eine Bemerkung zu Herrn A. Sommerfelds Arbeit: ``Zur Elektronentheorie der
Metalle auf Grund der Fermischen Statistik. Z. f. Physik 48, 739-744.(1928)
Die Supraleitfähigkeit nach Schrödingers Wellengleichung und Fermis
Statistik. Annalen d. Physik (4) 86, 914-928.(1928)
Theorie der Dauerströme in Supraleitern. Annalen d. Physik (4) 80, 109-136. Berichtigung. Annalen d. Physik (4) 80,532. (1926)
Über die Ableitung der Helmholtzschen Wirbelsätze in der Lorentz-Einsteinschen Relativitätstheorie. Schriften Königsberg 1, 179-191.(1925)
Zur Theorie der Supraleitfähigkeit und der gewöhnlichen elektrischen
Leitfähigkeit der Metalle. Schriften Königsberg 1, 193-204. (1925)
Das Maxwell-Boltzmannsche Geschwindigkeits- und Energieverteilungsgesetz in
der Relativitätstheorie. Phys. Zs. 25, 162-165. 192
Das statische Einkörperproblem in der Einstein'schen Theorie. Antwort an
Hrn. A. Gullstrand. Ark. för Mat., Astron, och Fys. 17, Nr. 25, 4 S. 1923
Eine Bemerkung zu Hrn. A. Gullstrands Abhandlung: ``Allgemeine Lösung des
statischen Einkörperproblems in der Einsteinschen Gravitationstheorie".
Ark. för Mat., Astron. och Fys. 17, Nr. 2, 4 S. (1922)
Der Liouvillesche Satz und die Relativitätstheorie. Physik. Zs. 21, 484-487.192
Eine Theorie der Schwerkraft im Rahmen der ursprünglichen {\it
Einstein}schen Relativitätstheorie. Berlin, 113 1914