Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-06-05T06:31:51.330Z Has data issue: false hasContentIssue false

The Philosophy of Symmetry

Published online by Cambridge University Press:  21 May 2024

Nicholas Joshua Yii Wye Teh
Affiliation:
University of Notre Dame

Summary

This Element is a concise, high-level introduction to the philosophy of physical symmetry. It begins with the notion of 'physical representation' (the kind of empirical representation of nature that we effect in doing physics), and then lays out the historically and conceptually central case of physical symmetry that frequently falls under the rubric of 'the Relativity Principle,' or 'Galileo's Ship.' This material is then used as a point of departure to explore the key hermeneutic challenge concerning physical symmetry in the past century, namely understanding the physical significance of the notion of 'local' gauge symmetry. The approach taken stresses both the continuity with historically important themes such as the Relativity Principle, as well as novel insights earned by working with contemporary representational media such as the covariant phase space formalism.
Get access
Type
Element
Information
Online ISBN: 9781009008600
Publisher: Cambridge University Press
Print publication: 20 June 2024

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, I. M. (1989). The variational bicomplex (Tech. Rep.). Utah State Technical Report, 1989, http://math.usu.edu/~fg~mpGoogle Scholar
Anscombe, G. E. M. (1971). Causality and determination: An inaugural lecture. CUP Archive.Google Scholar
Belot, G. (2000). Geometry and motion. British Journal for the Philosophy of Science, 51(4), 561595.CrossRefGoogle Scholar
Belot, G. (2018). Fifty million Elvis fans can’t be wrong. Noûs, 52(4), 946981.CrossRefGoogle Scholar
Blau, M. (2011). Lecture notes on general relativity. Albert Einstein Center for Fundamental Physics Bern.Google Scholar
Brading, K., & Brown, H. R. (2004). Are gauge symmetry transformations observable? British Journal for the Philosophy of Science, 55(4), 645665.CrossRefGoogle Scholar
Brown, H. (2005). Physical relativity: Space-time structure from a dynamical perspective. Clarendon Press. https://books.google.com/books?id=LbAUDAAAQBAJCrossRefGoogle Scholar
Brown, H., & Brading, K. (2002). General covariance from the perspective of Noether’s theorems. Diálogos, 5986.Google Scholar
Brown, H. R., & Sypel, R. (1995). On the meaning of the relativity principle and other symmetries. International Studies in the Philosophy of Science, 9(3), 235253.CrossRefGoogle Scholar
Callender, C., & Cohen, J. (2006). There is no special problem about scientific representation. Theoria. Revista de teoría, historia y fundamentos de la ciencia, 21(1), 6785.Google Scholar
Carrozza, S., & Hoehn, P. A. (2021). Edge modes as reference frames and boundary actions from post-selection. arXiv preprint arXiv:2109.06184.Google Scholar
Cartwright, N. (1999). The dappled world: A study of the boundaries of science. Cambridge University Press. https://books.google.com/books?id=tOFv_i9oiAgCCrossRefGoogle Scholar
Cattaneo, A. S., Mnev, P., & Reshetikhin, N. (2014). Classical bv theories on manifolds with boundary. Communications in Mathematical Physics, 332(2), 535603. https://dx.doi.org/10.1007/s00220-014-2145-3CrossRefGoogle Scholar
Chandrasekaran, V., Flanagan, E. E., Shehzad, I., & Speranza, A. J. (2021). A general framework for gravitational charges and holographic renormalization. arXiv preprint arXiv:2111.11974.Google Scholar
Chang, H. (2022). Realism for realistic people. Cambridge University Press.CrossRefGoogle Scholar
De Haro, S. (2021). Noether’s theorems and energy in general relativity. arXiv preprint arXiv:2103.17160.Google Scholar
Delacrétaz, L. V., Endlich, S., Monin, A., Penco, R., & Riva, F. (2014). (re-) inventing the relativistic wheel: Gravity, cosets, and spinning objects. Journal of High Energy Physics, 2014(11), 131.CrossRefGoogle Scholar
Donnelly, W., & Freidel, L. (2016). Local subsystems in gauge theory and gravity. Journal of High Energy Physics, 2016(9). https://dx.doi.org/10.1007/JHEP09(2016)102.CrossRefGoogle Scholar
Einstein, A. (1905). On the Electrodynamics of Moving Bodies. Annalen der Physik, 17, 891921.CrossRefGoogle Scholar
Einstein, A. (1998). Collected papers of Albert Einstein: The Berlin years (trans suppl) (Schulmann, Ed.). Princeton University Press.Google Scholar
Freidel, L., Geiller, M., & Pranzetti, D. (2020). Edge modes of gravity. Part i. corner potentials and charges. Journal of High Energy Physics, 2020(11), 152.Google Scholar
Freidel, L., Oliveri, R., Pranzetti, D., & Speziale, S. (2021). Extended corner symmetry, charge bracket and Einstein’s equations. Journal of High Energy Physics, 2021(9), 138.CrossRefGoogle Scholar
Freidel, L., & Teh, N. (2022). Substantive general covariance and the Einstein -Klein dispute: A Noetherian approach. In Read, J. & Teh, N. (eds.), The philosophy and physics of Noether’s theorems. Cambridge University Press.Google Scholar
Frigg, R., & Hartmann, S. (2020). Models in science. In Zalta, E. N. (ed.), The Stanford encyclopedia of philosophy (Spring 2020 ed.). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/spr2020/entries/models-science/Google Scholar
Frigg, R., & Nguyen, J. (2020). Modelling nature: An opinionated introduction to scientific representation. Springer.CrossRefGoogle Scholar
Galilei, G. (1967). Dialogue concerning the two world systems. Drake,(trans.), Berkeley CA: University of California Press.(Original work published in 1632).Google Scholar
Geiller, M., & Jai-Akson, P. (2020). Extended actions, dynamics of edge modes, and entanglement entropy. Journal of High Energy Physics, 2020(9), 157.CrossRefGoogle Scholar
Gomes, H. (2019). Gauging the boundary in field-space. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 67, 89110.CrossRefGoogle Scholar
Gomes, H. (2021). Holism as the empirical significance of symmetries. European Journal for Philosophy of Science, 11(3), 141.CrossRefGoogle Scholar
Gomes, H., Hopfmüller, F., & Riello, A. (2019). A unified geometric framework for boundary charges and dressings: Non-abelian theory and matter. Nuclear Physics B, 941, 249315. https://dx.doi.org/10.1016/j.nuclphysb.2019.02.020CrossRefGoogle Scholar
Gomes, H., & Riello, A. (2017). The observer’s ghost: Notes on a field space connection. Journal of High Energy Physics, 2017(5), 131.CrossRefGoogle Scholar
Greaves, H., & Wallace, D. (2014). Empirical consequences of symmetries. The British Journal for the Philosophy of Science, 65(1), 5989.CrossRefGoogle Scholar
Harlow, D., & Wu, J.- q. (2020). Covariant phase space with boundaries. Journal of High Energy Physics, 2020(10), 152.CrossRefGoogle Scholar
Khavkine, I. (2014). Covariant phase space, constraints, gauge and the Peierls formula. International Journal of Modern Physics A, 29(05), 1430009.CrossRefGoogle Scholar
Kosmann-Schwarzbach, Y., Schwarzbach, B. E., & Kosmann-Schwarzbach, Y. (2011). The Noether theorems. Springer.CrossRefGoogle Scholar
Kretschmann, E. (1918). Über den physikalischen sinn der relativitätspostulate, a. einsteins neue und seine ursprüngliche relativitätstheorie. Annalen der Physik, 358(16), 575614.CrossRefGoogle Scholar
Lehmkuhl, D. (2023). Einstein’s principles: On the interpretation of gravity. Oxford University Press.Google Scholar
Martens, N. C., & Read, J. (2020). Sophistry about symmetries? Synthese. https://philsci-archive.pitt.edu/17184/Google Scholar
Martz, L. (1990). Thomas more: The search for the inner man. Yale University Press. https://books.google.com/books?id=R45XD3gZIt0CGoogle Scholar
Mathieu, P., Murray, L., Schenkel, A., & Teh, N. J. (2019). Homological perspective on edge modes in linear Yang–Mills and Chern–Simons theory. arXiv preprint arXiv:1907.10651.Google Scholar
Mathieu, P., & Teh, N. (2021, Jul). Boundary electromagnetic duality from homological edge modes. Journal of High Energy Physics, 2021(7). https://dx.doi.org/10.1007/JHEP07(2021)192 doi: 10.1007/jhep07(2021)192Google Scholar
McCraw, D. (1986). The poetry of Chen Yuyi. Stanford University PhD dissertation.Google Scholar
Nguyen, J., Teh, N. J., & Wells, L. (2020). Why surplus structure is not superfluous. The British Journal for the Philosophy of Science, 71(2), 665695.CrossRefGoogle Scholar
Noether, E. (1918). Invariante variations probleme, math-phys. Klasse, 1918, 235257.Google Scholar
Norton, J. D. (1993). General covariance and the foundations of general relativity: Eight decades of dispute. Reports on progress in physics, 56(7), 791858.CrossRefGoogle Scholar
Norton, J. D. (2003). General covariance, gauge theories and the Kretschmann objection. In Brading, K. & Castellani, E. (eds.), Symmetries in physics: Philosophical reflections (pp. 110123). Cambridge University Press.CrossRefGoogle Scholar
Olver, P. J. (2000). Applications of lie groups to differential equations (Vol. 107). Springer Science & Business Media.Google Scholar
Podro, M. (1987). Depiction and the golden calf. In Harrison, A. (ed.), Philosophy and the visual arts (pp. 328). Royal Institute of Philosophy Conferences, vol. 4. Springer.CrossRefGoogle Scholar
Podro, M. (1998). Depiction. Yale University Press. https://books.google.com/books?id=QKaf2f30lrMCGoogle Scholar
Pooley, O. (2010). Substantive general covariance: Another decade of dispute. In Suárez, M., Dorato, M., & Rédei, M. (eds.), EPSA philosophical issues in the sciences (pp. 197209). Springer.CrossRefGoogle Scholar
Pooley, O. (2017). Background independence, diffeomorphism invariance and the meaning of coordinates. In Lehmkuhl, D., Schiemann, G., & Scholz, E. (eds.), Towards a theory of spacetime theories (pp. 105143). Birkhauser.CrossRefGoogle Scholar
Potochnik, A. (2020). Idealization and the aims of science. University of Chicago Press. https://books.google.com/books?id=CL4lEAAAQBAJGoogle Scholar
Ramírez, S. M., & Teh, N. (2020). Abandoning Galileo’s ship: The quest for non-relational empirical significance. The British Journal for the Philosophy of Science. https://philsci-archive.pitt.edu/17429/Google Scholar
Read, J. (2018). Explanation, geometry, and conspiracy in relativity theory. https://philsci-archive.pitt.edu/15253/ (to C. Beisbart, Submitted, Sauer, T. and Wuthrich, C. (eds.), “Thinking about Space and Time: 100 Years of Applying and Interpreting General Relativity”, Einstein Studies Series, Basel: Birkhauser, 2019.).Google Scholar
Rovelli, C. (2014). Why Gauge? Foundations of Physics, 44, 91104.CrossRefGoogle Scholar
Rowe, D. E. (2019). Emmy Noether on energy conservation in general relativity. arXiv preprint arXiv:1912.03269.Google Scholar
Rowe, D. E. (2021). Emmy Noether–mathematician extraordinaire. Springer.CrossRefGoogle Scholar
Scruton, R. (1997). The aesthetics of music. Oxford University Press.Google Scholar
Stevens, S. (2020). Regularity relationalism and the constructivist project. The British Journal for the Philosophy of Science, 7 1(1), 353372.CrossRefGoogle Scholar
Strocchi, F. (2011). Spontaneous symmetry breaking in classical systems. Scholarpedia, 6(10), 11195.CrossRefGoogle Scholar
Teh, N. J. (2015). A note on Rovelli’s “why gauge?”. European Journal for Philosophy of Science, 5, 339348.CrossRefGoogle Scholar
Teh, N. J. (2016). Galileo’s gauge: Understanding the empirical significance of gauge symmetry. Philosophy of Science, 83(1), 93118.CrossRefGoogle Scholar
Van Fraassen, B. C. (2010). Scientific representation: Paradoxes of perspective. Oxford University Press.Google Scholar
Vasari, G. (1900). The lives of the painters, sculptors & architects (No. v. 4). J. M. Dent. https://books.google.com/books?id=ZUQX5tbgAKgCGoogle Scholar
Wallace, D. (2019). Observability, redundancy and modality for dynamical symmetry transformations. https://philsci-archive.pitt.edu/18813/ (Revised 3/2021 to correct a few typos and add a section on Noether’s Theorem.).Google Scholar
Wallace, D. (2021a). Isolated systems and their symmetries, part i: General framework and particle-mechanics examples. https://philsci-archive.pitt.edu/19728/ (Revised version; some typos, technical errors, and stylistic infelicities corrected.).Google Scholar
Wallace, D. (2021b). Isolated systems and their symmetries, part ii: Local and global symmetries of field theories. https://philsci-archive.pitt.edu/19729/ (Revised version: Corrects various typos, technical errors, and stylistic infelicities.).Google Scholar
Wieland, W. (2021). Null infinity as an open Hamiltonian system. Journal of High Energy Physics, 2021, 95. https://doi.org/10.1007/JHEP04(2021)095.CrossRefGoogle Scholar

Save element to Kindle

To save this element to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

The Philosophy of Symmetry
Available formats
×

Save element to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

The Philosophy of Symmetry
Available formats
×

Save element to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

The Philosophy of Symmetry
Available formats
×