https://doi.org/10.4081/peasa.5
Symmetry and symmetry breaking in science and arts
Published: December 30, 2022
Abstract Views: 428
PDF: 38
Publisher's note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.
In this review article, symmetry and symmetry breaking are considered as complementary principles in science and arts. It starts with symmetry and symmetry breaking in early world views of nature and art. Then, symmetries are definied as fundamental structures of mathematics. Mathematical models of symmetry and symmetry breaking are used to explain the emergence of space-time and matter in modern physics. Even molecular structures in chemistry are distinguished by mathematical symmetries. Their elegance and beauty seem to realize aesthetical categories in nature. In biological evolution, the question arises how symmetry breaking (e.g. molcular chirality) can be explained. In modern arts, symmetry and symmetry breaking are "hidden" structures which can be found in music, painting, and architecture. In a philosophical outlook, symmetry and symmetry breaking are highlighted as regulative guiding ideas of research.
_______________________________________________________________________________________________________________________________________________________
This article is an extended version and English translation of my article "Symmetrie und Symmetriebrechung. Von der Urmaterie zu Kunst und Leben,“ in: Schriftenreihe der Heisenberg-Gesellschaft: Quanten 2 (ed. Konrad Kleinknecht), S. Hirzel Verlag, 9-59. An abridged version was presented in the EASA Colloquium Science meets Art (https://www.youtube.com/watch?v=nIUVNEQ7AR8 )
Audretsch, Jürgen/Mainzer, Klaus (Eds.) (1994), Philosophie und Physik der Raum-Zeit. Grundlagen der exakten Naturwissenschaften Bd. 7, Mannheim: B.I. Wissenschaftsverlag 2nd ed.
Audretsch, Jürgen/ Mainzer, Klaus (Eds.) (1990), Vom Anfang der Welt. Wissenschaft, Philosophie, Religion, Mythos, München: C.H. Beck 2nd ed.
Audretsch, Jürgen/Mainzer, Klaus (1996), Wieviele Leben hat Schrödingers Katze? Zur Physik und Philosophie der Quantenmechanik, Heidelberg: Spektrum Akademischer Verlag 2nd ed.
Ball.P (2016) Patterns in nature, University of Chicago Press, US.
Bernstein, J. (1974), Spontaneous symmetry breaking, gauge theories, the Higgs mechanism and all that, in: Revise Reports of Modern Physics 46, 7-48.
DOI: https://doi.org/10.1103/RevModPhys.46.7
Claus, R. (1980), Symmetrie in der Musik. Zur Anwendung gruppentheoretischer Methoden, in: A. Preisinger (ed.), Symmetrie, Springer: Vienna/New York.
DOI: https://doi.org/10.1007/978-3-7091-5506-6_4
Conway, J.H., Heidi Burgiel , Chaim Goodman-Strauss (2008) The symmetries of things, Taylor & Francis Inc.
Commins, E.D.; Bucksbaum, P.H. (1983), Weak Interactions of Leptons and Quarks, Cambridge University Press: Cambridge.
Doncel, Manuel G.; Hermann, Achim: Michel, Louis; Pais, Abraham (Eds.) (1987), Symmetries in Physics 1600-1980, Bellaterra (Barcelona).
Ehlers, Jürgen (1973), The Nature and Structure of Spacetime, in: Mehra, Jagdish (Ed.), The Physicist’s Conception of Nature, Dordrecht: Kluwer Academic Publisher.
DOI: https://doi.org/10.1007/978-94-010-2602-4_6
Eudoxos (1966), Die Fragmente des Eudoxos von Knidos (Ed. transl. comm. François Lasserre), De Gruyter: Berlin.
DOI: https://doi.org/10.1515/9783110828931
Feynman, Richard Philips; Leighton, Robert; Sands, Matthew (1966), The Feynman Lectures on Physics, Reading, Mass. [et al.], Addison-Wesley. 2nd ed.
Gell-Mann, Murry; Ne’eman, Yuval (1964), The Eightfold Way, New York.
Georgi, Howard; Glashow, Sheldon Lee (1974), Unity of all elementary-particle forces, in: Phys. Rev. Lett. 32, 438-441.
DOI: https://doi.org/10.1103/PhysRevLett.32.438
Georgi, Howard (1980), Why unify? In: Nature 288, 649-651.
DOI: https://doi.org/10.1038/288649a0
Greenberg, O.W. (2002): CPT violation implies violation of Lorentz invariance. in: Physical Review Letters 89, 2002, 231602.
DOI: https://doi.org/10.1103/PhysRevLett.89.231602
Groom, D.E. et al. (2000), Review of Particle Physics, in: European Physics Journal C15, 1-4.
Heisenberg, Werner (1959), Wandlungen in den Grundlagen der Naturwissenschaften, Stuttgart: S. Hirzel: 9th ed.
Higgs, Peter Ware (1964), Broken symmetries, massless particles and gauge fields. Phys. Lett. 12, 132.
DOI: https://doi.org/10.1016/0031-9163(64)91136-9
Hollas, John Michael (1975), Die Symmetrie von Molekülen, Berlin, De Gruyter.
DOI: https://doi.org/10.1515/9783110830538
Itzyson, Claude; Zuber, Jean-Bernard (1980), Quantum Field Theory, New York: McGraw-Hill.
Jencks, Charles (1978), Die Sprache der postmodernen Architektur. Die Entstehung einer alternativen Tradition, Stuttgart: DVA.
Johnston, I.G., Kamaludin Dingle, Sam F. Greenbury and Ard A. Louis (2022) Symmetry and simplicity spontaneously emerge from the algorithmic nature of evolution. PNAS 119;e2113883119.
DOI: https://doi.org/10.1073/pnas.2113883119
Klee, Paul (1928), Exakte Versuche im Bereich der Kunst, in: Bauhaus. Zeitschrift für Bau und Gestaltung 2 No. 2/3, Dessau.
Le Corbusier (1925), Urbanism, in: U. Conrads (ed.), Programme und Manifeste zur Architektur des 20. Jahrhunderts, Bauwelt Fundamente vol. 1, Berlin: Ullstein 1964.
T. D. Lee, T.D.; C. N. Yang, C.N. (1956), Question of Parity Conservation in Weak Interactions, in: Phys. Rev. 104, 254; Erratum Phys. Rev. 106, 1371 (1957).
DOI: https://doi.org/10.1103/PhysRev.106.1371
Mainzer, Klaus (1980), Geschichte der Geometrie, Mannheim: B.I. Wissenschaftsverlag.
Mainzer, Klaus (1981), Grundlagenprobleme in der Geschichte der Exakten Wissenschaften, Konstanz: Universitätsverlag.
Mainzer, Klaus (German: 1988, English: 1996), Symmetries of Nature, Berlin/New York: De Gruyter: Berlin.
Mainzer, Klaus (2014), Die Berechnung der Welt. Von der Weltformel zu Big Data, München: C.H. Beck.
DOI: https://doi.org/10.17104/9783406661310
Mainzer, Klaus (2005), Symmetry and Complexity. The Spirit and Beauty of Nonlinear Science, World Scientific Publishing Singapore.
DOI: https://doi.org/10.1142/9789812569400
Mittelstraß, Jürgen (1970), Die Rettung der Phänomene. Ursprung und Geschichte eines antiken Forschungsprinzips, Berlin: De Gruyter.
Noether, Emmy (1918), Invariante Variationsprobleme, in: Nachr. Ges. Wiss. Göttingen, Math. Phys. Klasse, 235-257.
Perkins, Donald H. (2000), Introduction to High Energy Physics, Cambridge University Press: Cambridge 4th edition.
Primas, Hans (1985), Kann Chemie auf Physik reduziert werden? Erster Teil. Das Molekulare Programm. Chemie in unserer Zeit 19:100-119.
DOI: https://doi.org/10.1002/ciuz.19850190402
Quack, Martin (1986), On the measurement of parity violating energy difference between enantiomers. Chemical Physics Letters 132;147-153.
DOI: https://doi.org/10.1016/0009-2614(86)80098-7
Schmutzer, Ernst (1972), Symmetrien und Erhaltungssätze der Physik, Pergamon Press: Oxford, Vieweg: Braunschweig.
DOI: https://doi.org/10.1515/9783112596302
Schrödinger, Erwin (1962), Was ist ein Naturgesetz? München: R. Oldenbourg.
Tranter, G.E. (1986), Paritätsverletzung: Ursache der biomolekularen Chiralität, in: repr. Chem. Techn. Lab. 34:866.
DOI: https://doi.org/10.1002/nadc.19860340905
van Doesburg, Theo; van Eesteren, Cornelis (1924), Auf dem Weg zu einer kollektiven Konstruktion, in: De Stijl 12, Issue 6/7.
Warwick, Roger; Williams, Peter (Ed.) (1973), Gray’s Anatomy, Edinburgh: Longman.
Weinberg, Steven (1985), Vereinheitlichte Theorie der elektro-schwachen Wechselwirkung, in: Dosch, Hans Günter (Ed.), Teilchen, Felder und Symmetrien. Spektrum der Wissenschaft, Heidelberg 2nd ed.
Werker, Wilhelm (1922), Studien über Symmetrie im Bau der Fugen und die motivische Zusammengehörigkeit der Präludien und Fugen des Wohltemperierten Klaviers von J.S. Bach, Leipzig: Breitkopf und Härtel.
Weyl, Hermann (1918), Gravitation und Elektrizität, in: Sitz. Ber. d. Preuß. Akad. d. Wissensch. 465-480.
Weyl, Hermann (2015), Symmetry, Berlin: De Gruyter.
How to Cite
Mainzer, K. (2022). Symmetry and symmetry breaking in science and arts. Proceedings of the European Academy of Sciences and Arts, 1(1). https://doi.org/10.4081/peasa.5
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Copyright (c) 2023 The Author(s)
PAGEPress has chosen to apply the Creative Commons Attribution NonCommercial 4.0 International License (CC BY-NC 4.0) to all manuscripts to be published.