The plasticine ball argument. Hermann Weyl, the homogeneity of space and Mach’s principle. (English) Zbl 1442.83003
Bernard, Julien (ed.) et al., Weyl and the problem of space. From science to philosophy. Cham: Springer. Stud. Hist. Philos. Sci. (Dordr.) 49, 295-345 (2019).
Summary: Hermann Weyl’s work is difficult to classify as physics, mathematics, philosophy or history of science. Perhaps because of his wide audience, perhaps also because of his aesthetic preferences, Weyl likes to use analogies and metaphors in order to provide insights about the most difficult and abstract problems of the twentieth-century science.
For the entire collection see [Zbl 1426.00002].
For the entire collection see [Zbl 1426.00002].
MSC:
| 83-03 | History of relativity and gravitational theory |
| 01A60 | History of mathematics in the 20th century |
| 83F05 | Relativistic cosmology |
Biographic References:
Weyl, HermannReferences:
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| [7] | Bernard, Julien. 2013. L’idéalisme dans l’infinitésimal. Weyl et l’espace à l’époque de la relativité. Prix Paul Ricœur 2012. Presses Universitaires de Paris Ouest, 2013. ISBN:2840161311. |
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| [21] | Georges Darmois. 1927. Les équations de la gravitation einsteinienne. Mém. Sc. Math. 25. · JFM 53.0816.03 |
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| [24] | Einstein, Albert. 1916. Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik und Chemie. · JFM 46.1293.01 |
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| [28] | Einstein, Albert, and Marcel Grossman. 1913. Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation. Leipzig: B.G.Teubner. · JFM 44.0770.02 |
| [29] | Giovanelli, Marco. 2013a. Erich Kretschmann as a proto-logical-empiricist: Adventures and misadventures of the point-coincidence argument. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44:115-134. · Zbl 1281.83007 · doi:10.1016/j.shpsb.2012.11.004 |
| [30] | Giovanelli, Marco. 2013b. Leibniz equivalence. On Leibniz’s (Bad) influence on the logical empiricist interpretation of general relativity. From a preprint, Unpublished. · Zbl 1281.83007 |
| [31] | Iftime, Mihaela, and John Stachel. 2006. The hole argument for covariant theories. General Relativity and Gravitation 38:1241-1252. · Zbl 1175.83011 · doi:10.1007/s10714-006-0303-4 |
| [32] | Pierre Kerszberg. 1986. Le principe de Weyl et l’invention d’une cosmologie non-statique. Archive for History of Exact Sciences 35(1):1-89. · Zbl 0589.01008 · doi:10.1007/BF00330002 |
| [33] | Pierre Kerszberg. 1989. The Einstein-de Sitter controversy of 1916-1917 and the rise of relativistic cosmology. In Einstein and the history of general relativity, ed. D. Howard and John Stachel, 1-325. Boston: Birkhäuser. |
| [34] | Laugwitz, Detlef. 1958. Über eine Vermutung von Hermann Weyl zum Raumproblem”. Archiv der Mathematik 9:128-133. · Zbl 0084.37301 · doi:10.1007/BF02287072 |
| [35] | Lense, Josef, and Hans Thirring. 1918. Über den Einfluß der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Physikalische Zeitschrift 19:156-163. · JFM 46.1317.01 |
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| [37] | Michel, Alain. 2006. La fonction de l’histoire dans la pensée mathématique et physique d’Hermann Weyl. In Kairos, 27. |
| [38] | Norton, John D. 1987. Einstein, the hole argument and the reality of space. In Measurement, realism, and objectivity, Australasian studies in history and philosophy of science, vol. 5, 153-188. Dordrecht/Boston: D. Reidel. |
| [39] | Norton, John D. 1993. General covariance and the foundations of general relativity: Eight decades of dispute. Reports of Progress in Physics 56:791-861. Institute of Physics. |
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| [41] | Poincaré, H. 1902. La science et l’hypothèse. Bibliothèque de philosophie scientifique, New edition: 2000. E. Flammarion. · JFM 34.0080.12 |
| [42] | Reinhardt, Michael. 1973. Mach’s principle – a critical review. Zeitschrift für Naturforschung A. 28(3-4):529-537. |
| [43] | Renn, J. 2007. The genesis of general relativity: Sources and interpretations. Boston studies in the philosophy and history of science. Dordrecht/London: Springer. · Zbl 1216.83015 |
| [44] | Riemann, Bernhard. 1919. Über die Hypothesen, welche der Geometrie zu Grunde liegen, ed. H. Weyl with critical notes, 1st ed. Springer. · JFM 47.0770.01 |
| [45] | Ryckman, Thomas. 2009. Hermann Weyl and ‘First Philosophy’: Constituting Gauge invariance. In The Western Ontario series in philosophy of science, ed. Michel Bitbol, Kerszberg Pierre, and Petitot Jean, vol. 74, 279-298. Dordrecht: Springer. |
| [46] | Scholz, Erhard. 2004. Hermann Weyl’s analysis of the “Problem of Space” and the origin of Gauge. In Structures. Science in context, 165-197. · Zbl 1181.01038 |
| [47] | Scholz, Erhard. 2012. H. Weyl’s and E. Cartan’s proposals for infinitesimal geometry in the early 1920s. Newsletter European Mathematical Society 84:22-30. · Zbl 1263.01015 |
| [48] | Scholz, Erhard. 2018. The unexpected resurgence of Weyl geometry in late 20th-century physics. In Beyond Einstein: Perspectives on geometry, gravitation, and cosmology in the twentieth century, ed. D.E. Rowe, T. Sauer, and S.A. Walter. Einstein studies, 261-360. New York: Springer. ISBN:9781493977062. · Zbl 1402.83012 |
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| [50] | Schwarzschild, Karl. 1916a. Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. In Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin), 189-196. · JFM 46.1296.02 |
| [51] | Schwarzschild, Karl. 1916b. Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit. In Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin), 424-434. · JFM 46.1297.01 |
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| [53] | Stachel, John. 1989. Einstein’s search for general covariance. In Einstein and the history of general relativity. Einstein’s studies, vol. I, 63-100. Boston: Birkhäuser. |
| [54] | Stachel, John. 1993. The meaning of general covariance: The hole story. In Philosophical problems of the internal and external worlds, ed. John Earman and et al., 129-160. Pittsburgh: University of Pittsburg Press. · doi:10.2307/j.ctt5vkgg6.9 |
| [55] | Thirring, Hans. 1918. Über die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie. Physikalische Zeitschrift 19:33-sq. · JFM 46.1316.03 |
| [56] | Thirring, Hans. 1921. Berichtigung zu meiner Arbeit: Über die Wirkung rotierender Massen in der Einsteinschen Gravitationstheorie. Physikalische Zeitschrift 22:29-30. · JFM 48.1018.03 |
| [57] | Torretti, Roberto. 1983. Relativity and geometry. Foundations, philosophy of science, technology. New York: Pergamon Press. · Zbl 0515.53001 |
| [58] | Weyl, Hermann. 1918a. Gravitation und Elektrizität. In Sitzungsberichte des Königlichen Preußischen Akademie des Wissenschaften zu Berlin, 465-480. · JFM 46.1300.01 |
| [59] | Weyl, Hermann. 1918b. Raum, Zeit, Materie, 1st ed. Berlin: Julius Springer. · JFM 46.1277.01 |
| [60] | Weyl, Hermann. 1919a. Raum, Zeit, Materie, 3rd ed. Berlin: Julius Springer. · JFM 47.0775.01 · doi:10.1007/978-3-662-43111-5 |
| [61] | Weyl, Hermann. 1919b. Bemerkung über die axialsymmetrischen Lösung der Einsteinschen Gravitationsgleichungen. Annalen der Physik 364(10): 185-188. · JFM 47.0800.01 · doi:10.1002/andp.19193641006 |
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| [63] | Weyl, Hermann. 1923. Mathematische Analyse des Raumproblems. Vorlesungen gehalten in Barcelona und Madrid. Berlin: Julius Springer. · doi:10.1007/978-3-642-92431-6 |
| [64] | Weyl, Hermann. 1924. Massenträgheit und Kosmos. Ein Dialog. Naturwissenschaften 12:197-204. · JFM 50.0586.05 · doi:10.1007/BF01506342 |
| [65] | Weyl, Hermann. 1934. Mind and nature. Selected writings on philosophy, mathematics, and physics (2009). Princeton University Press. · JFM 60.0857.10 |
| [66] | Weyl, Hermann. 1949. Philosophy of mathematics and natural science. From an article of 1927. Princeton: Princeton University Press. · Zbl 0041.56804 |
| [67] | Weyl, Hermann. 2010. Space, time, matter. Trans. H.L. Brose. From the 4th edition. New York: Cosimo Classics. |
| [68] | Weyl, Hermann. |
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