Introduction to the special issue Hermann Weyl and the philosophy of the ‘New Physics’. (English) Zbl 1382.81011
Summary: This Special Issue Hermann Weyl and the Philosophy of the ‘New Physics’ has two main objectives: first, to shed fresh light on the relevance of Weyl’s work for modern physics and, second, to evaluate the importance of Weyl’s work and ideas for contemporary philosophy of physics. Regarding the first objective, this Special Issue emphasizes aspects of Weyl’s work (e.g. his work on spinors in \(n\) dimensions) whose importance has recently been emerging in research fields across both mathematical and experimental physics, as well as in the history and philosophy of physics. Regarding the second objective, this Special Issue addresses the relevance of Weyl’s ideas regarding important open problems in the philosophy of physics, such as the problem of characterizing scientific objectivity and the problem of providing a satisfactory interpretation of fundamental symmetries in gauge theories and quantum mechanics. In this Introduction, we sketch the state of the art in Weyl studies and we summarize the content of the contributions to the present volume.
MSC:
| 81P05 | General and philosophical questions in quantum theory |
| 00A79 | Physics |
| 00A30 | Philosophy of mathematics |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 81-03 | History of quantum theory |
| 01A60 | History of mathematics in the 20th century |
| 81-06 | Proceedings, conferences, collections, etc. pertaining to quantum theory |
| 00B10 | Collections of articles of general interest |
Biographic References:
Weyl, HermannReferences:
| [1] | Afriat, A., Weyl’s gauge argument, Foundations of Physics, 43, 5, 699-705 (2013) · Zbl 1286.83046 |
| [2] | Balents, L., Weyl electrons kiss, Physics, 4, 36 (2011) |
| [3] | Bernard, J., Becker-Blaschke problem of space, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 52, 251-266 (2015) · Zbl 1329.70008 |
| [4] | Bueno, O., Weyl and von Neumann: Symmetry, Group Theory, and Quantum Mechanics (2001), (Preprint) |
| [5] | (Chandrasekharan, K., Hermann Weyl: 1885-1985; centenary lectures delivered by C. N. Yang, R. Penrose, and A. Borel at the Eidgenössische Technische Hochschule Zürich (1986), Springer: Springer Berlin) |
| [6] | Coleman, R.; Korté, H., Hermann Weyl: Mathematician, physicist, philosopher, (Scholz, E., Hermann Weyl’s Raum - Zeit - Materie and a general introduction to his scientific work. Hermann Weyl’s Raum - Zeit - Materie and a general introduction to his scientific work, Deutsche Mathematiker-Vereinigung seminar, Vol. 30 (2001), Birkhäuser: Birkhäuser Basel), 161-386 |
| [7] | Eckes, C., Groupes, invariants et géométries dans l’oeuvre de Weyl (2011), University of Lyon, (Ph.D. diss.) |
| [8] | Eckes, C., Weyl’s philosophy of physics, from apriorism to holism (1918-1927), Philosophia Scientiae (2017), ( in press) |
| [9] | Ehlers, J., Hermann Weyl’s contributions to the general theory of relativity, (Deppert, W.; Hübner, K., Exact Sciences and Their Philosophical Foundations: Exakte Wissenschaften und ihre philosophische Grundlegung. Vorträge des internationalen Hermann-Weyl-Kongresses (1988), Peter Lang Verlag: Peter Lang Verlag Frankfurt/M - Bern), 83-105 |
| [10] | Feist, R., Weyl’s appropriation of Husserl’s and Poincaré’s thought, Synthese, 132, 273-301 (2002) · Zbl 1015.03504 |
| [11] | (Feist, R., Husserl and the sciences (2004), University of Ottawa Press) |
| [12] | Feist, R., Husserl and Weyl: Phenomenology, mathematics, and physics, (Feist, R., Husserl and the sciences (2004), University of Ottawa Press), 153-172 |
| [13] | French, S., The reasonable effectiveness of mathematics: Partial structures and the application of group theory to physics, Synthese, 125, 1, 103-120 (2000) · Zbl 1007.81005 |
| [14] | Friedman, M., Carnap and Weyl on the foundations of geometry and relativity theory, (Reflections on Spacetime (1995), Springer: Springer Netherlands), 127-140 |
| [15] | Howard, D., A Peek behind the Veil of Maya. Einstein, Schopenhauer and the historical background of the conception of space as a ground for the individuation of physical systems, (Earman, J.; Norton, J. D., The cosmos of science: Essays of exploration (1997), Pittsburgh University Press: Pittsburgh University Press Pittsburgh), 87-150 |
| [16] | Kerszberg, P., Perseverance and adjustment: On Weyl’s phenomenological philosophy of nature, (Boi, L.; Kerszberg, P., Rediscovering Phenomenology: Phenomenological essays of mathematical beings, physical reality, perception and conscioussness (2007), Springer: Springer Dordrecht), 173-194 |
| [17] | Majorana, E., Teoria simmetrica dell’elettrone e del positrone, Il Nuovo Cimento (1924-1942), 14, 4, 171 (1937) · Zbl 0016.42707 |
| [18] | Mancosu, P.; Ryckman, T., Mathematics and phenomenology: The correspondence between O. Becker and H. Weyl, Philosophia Mathematica, 3, 10, 130-202 (2002) · Zbl 1032.01024 |
| [19] | Muller, F. A.; Saunders, S., Discerning fermions, British Journal for the Philosophy of Science, 59, 499-548 (2008) · Zbl 1152.81657 |
| [20] | O’Raifeartaigh, L.; Straumann, N., Gauge theory: Origins and modern developments, Reviews of Modern Physics, 72, 1 (2000) · Zbl 1205.81106 |
| [21] | Röller, N., Medientheorie im epistemischen Übergang: Hermann Weyls Philosophie der Mathematik und Naturwissenschaften und Ernst Cassirers Philosophie der symbolischen Formen in Wechselverhältnis (2002), VDG: VDG Weimar |
| [22] | Ryckman, T., The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism, (Brading, K.; Castellani, E., Symmetries in physics: Philosophical reflections (2003), Cambridge University Press: Cambridge University Press Cambridge), 61-88 |
| [23] | Ryckman, T., The reign of relativity: Philosophy in physics 1915-1925 (2005), Oxford University Press: Oxford University Press New York |
| [24] | Scheibe, E., Über das Weylsche Raumproblem, Journal für Mathematik, 197, 3/4, 162-207 (1957), (Dissertation Göttingen 1955) · Zbl 0083.36201 |
| [25] | Scheibe, E., Hermann Weyl and the nature of spacetime, (Deppert, W.; Hübner, K., Exact Sciences and Their Philosophical Foundations: Exakte Wissenschaften und ihre philosophische Grundlegung. Vorträge des internationalen Hermann-Weyl-Kongresses (1988), Peter Lang Verlag: Peter Lang Verlag Frankfurt/M - Bern), 61-82 |
| [26] | Scholz, E., Weyl’s infinitesimalgeometrie, 1917-1925, (Scholz, E., Hermann Weyl’s Raum - Zeit - Materie and a general introduction to his scientific work (2001), Birkäuser: Birkäuser Basel), 48-104 |
| [27] | Scholz, E., Hermann Weyl’s analysis of the “problem of space” and the origin of gauge structures, Science in Context, 17, 165-197 (2004) · Zbl 1181.01038 |
| [28] | Scholz, E., Local spinor structures in V. Fock’s and H. Weyl’s work on the Dirac equation (1929), (Kouneiher, J.; Nabonnand, P.; Szczeciniarz, J.-J., Géométrie au XXe siècle, 1930-2000: Histoire et horizons (2005), Presses internationales Polytechnique), 284-301 |
| [29] | Scholz, E., Introducing groups into quantum theory (1926-1930), Historia Mathematica, 33, 4, 440-490 (2006) · Zbl 1130.01011 |
| [30] | Scholz, E., Leibnizian Traces in H. Weyl’s Philosophie der Mathematik und Naturwissenschaft, (New essays on Leibniz Reception (2012), Springer: Springer Basel), 203-216 |
| [31] | Sieroka, N., Weyl’s ‘agens theory’ of matter and the Zurich Fichte, Studies in the History and Philosophy of Science, 38, 84-107 (2007) |
| [32] | Sieroka, S., Husserlian and Fichtean leanings: Weyl on logicism, intuitionism, and formalism, Philosophia Scientiae, 13, 85-96 (2009) · Zbl 1244.03036 |
| [33] | Sieroka, S., Geometrization versus transcendent matter: A systematic historiography of theories of matter following Weyl, British Journal for the Philosophy of Science, 61, 769-802 (2010) |
| [34] | Sieroka, S., Hermann Weyl und Fritz Medicus: Die Zürcher FichteInterpretation in Mathematik und Physik um 1920, Fichte-Studien, 36, 129-143 (2012) |
| [35] | Sigurdsson, S., Hermann Weyl, mathematics and physics, 1900-1927 (1991), Harvard University: Harvard University Cambridge, Massachusetts, (Department of the History of Science) |
| [36] | Sigurdsson, S., Journeys in spacetime, (Scholz, E., Hermann Weyl’s Raum - Zeit - Materie and a general introduction to his scientific work. Hermann Weyl’s Raum - Zeit - Materie and a general introduction to his scientific work, Deutsche Mathematiker-Vereinigung seminar, Vol. 30 (2001), Birkhäuser: Birkhäuser Basel), 15-47 |
| [37] | Straumann, N., Ursprünge der Eichtheorien, (Scholz, E., Hermann Weyl’s Raum - Zeit - Materie and a general introduction to his scientific work (2001), Birkäuser: Birkäuser Basel), 138-155 |
| [38] | Tieszen, R., The philosophical background of Weyl’s mathematical constructivism, Philosophia Mathematica, 8, 274-301 (2000) · Zbl 0978.03004 |
| [39] | Toader, I. D., Objectivity sans intelligibility: Hermann Weyl’s symbolic constructivism (2011), University of Notre Dame, (Ph.D. dissertation) |
| [40] | Toader, I. D., Concept formation and scientific Objectivity: Weyl’s turn against Husserl, HOPOS: The Journal of the International Society for the History of Philosophy of Science 2013, 3, 2, 281-305 (2013) |
| [41] | Toader, I. D., Why did Weyl think that Formalism’s victory against intuitionism entails a defeat of pure phenomenology?, History And Philosophy Of Logic, 35, 2 (2014) · Zbl 1309.01016 |
| [42] | Weyl, H., Elektron und Gravitation, Zeitschrift für Physik, 56, 5, 330-352 (1929) · JFM 55.0513.04 |
| [43] | Weyl, H., Gruppentheorie und Quantenmechanik, (Hirzel; Leipzig, The theory of groups and quantum mechanics, 1950, Dover, NY (1931)) · JFM 57.1579.01 |
| [44] | Weyl, H. (2013). Levels of infinity: Selected writings on mathematics and philosophy. P. Pesic (ed.). NY: Dover.; Weyl, H. (2013). Levels of infinity: Selected writings on mathematics and philosophy. P. Pesic (ed.). NY: Dover. |
| [45] | Weyl, H., Symmetry (1952), Princeton University Press: Princeton University Press Princeton NJ · JFM 64.1296.02 |
| [46] | Weyl, H., Philosophy of mathematics and natural science (1949), Princeton University Press: Princeton University Press Princeton NJ · Zbl 0033.24209 |
| [47] | Weyl, H., Symmetrie (2017), Springer: Springer Berlin |
| [48] | Wilczek, F., Why are there analogies between condensed matter and particle theory?, Physics Today, 51, 11 (1998) |
| [49] | Xu, S. Y.; Belopolski, I.; Alidoust, N.; Neupane, M.; Bian, G.; Zhang, C., Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science, 349, 6248, 613-617 (2015) |
| [50] | Yang, C. N., (Chandrasekharan, K.; Weyl, H., Hermann Weyl’s contribution to physics (1986), Springer-Verlag: Springer-Verlag Berlin), 7-21, (Centenary Lectures delivered by C. N. Yang, R. Penrose, and A. Borel at the ETH Zürich) |
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