Hostname: page-component-7bb8b95d7b-fmk2r Total loading time: 0 Render date: 2024-09-20T12:47:00.798Z Has data issue: false hasContentIssue false
  • English
  • Français

Mirroring as an A Priori Symmetry

Published online by Cambridge University Press:  01 January 2022

Simon Saunders
Get access Rights & Permissions [Opens in a new window]

Abstract

A relationist will account for the use of ‘left’ and ‘right’ in terms of relative orientations, and other properties and relations invariant under mirroring. This analysis will apply whenever mirroring is a symmetry, so it certainly applies to classical mechanics; we argue it applies to any physical theory formulated on a manifold: it is in this sense an a priori symmetry. It should apply in particular to parity violating theories in quantum mechanics; mirror symmetry is only broken in such theories as a special symmetry.

Type
Research Article
Information
Philosophy of Science , Volume 74 , Issue 4 , October 2007 , pp. 452 - 480
Copyright
Copyright © The Philosophy of Science Association

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.)

Footnotes

‡

My thanks to a number of audiences, too numerous to mention, who have heard me speak on various of these ideas or their precursors, and for helpful discussions over the years to Harvey Brown, Nick Huggett, Oliver Pooley, David Wallace, and Graeme Segal, none of whom may entirely agree with my conclusions. My special thanks to Oliver Pooley for persuading me of the irrelevance of PCT symmetry to the treatment of mirroring.

References

Bartlett, S., Rudolph, T., and Spekkens, R. (2005), “Reference Frames, Superselection Rules, and Quantum Information”, quant-ph/0610030.Google Scholar
Brown, H. (2005), Physical Relativity. Oxford: Clarendon Press.CrossRefGoogle Scholar
Brown, H., and Sypel, R. (1986), “On the Meaning of the Relativity Principle and Other Symmetries”, On the Meaning of the Relativity Principle and Other Symmetries 9:235–253.Google Scholar
Crawford, F., Cresti, M., Good, M., Gottstein, K., Lyman, E., Solmitz, F., Stevenson, M., and Ticko, H., (1957), “Detection of Parity Nonconservation in Λ Decay”, Detection of Parity Nonconservation in Λ Decay 108:1102–1103.Google Scholar
Davis, W. (1970), Classical Fields, Particles, and the Theory of Relativity. New York: Gordon & Breach.Google Scholar
Earman, J. (1989), World Enough and Space-Time. Cambridge, MA: MIT Press.Google Scholar
Earman, J., and Norton, J. (1987), “What Price Substantivalism? The Hole Story”, What Price Substantivalism? The Hole Story 38:515–525.Google Scholar
Gardner, M. (1964), The Ambidextrous Universe: Mirror Asymmetry and Time-Reversed Worlds. New York: Basic Books.Google Scholar
Hegstrom, R., Rein, D., and Sanders, P., (1979), “Parity Non-conserving Energy Difference between Mirror Image Molecules”, Parity Non-conserving Energy Difference between Mirror Image Molecules 71:499–502.Google Scholar
Hoefer, C. (2000), “Kant’s Hands and Earman’s Pions: Chirality Arguments for the Substantival Space”, Kant’s Hands and Earman’s Pions: Chirality Arguments for the Substantival Space 14:237–256.Google Scholar
Huggett, N. (2000), “Reflections on Parity Non-conversation”, Reflections on Parity Non-conversation 67:219–241.Google Scholar
Letokhov, V. S. (1975), “On Difference of Energy Levels of Left and Right Molecules Due to Weak Interactions”, On Difference of Energy Levels of Left and Right Molecules Due to Weak Interactions 53:275–276.Google Scholar
Mason, S., and Tranter, G. (1985), “The Electroweak Origin of Biomolecular Handedness”, The Electroweak Origin of Biomolecular Handedness 397:45–65.Google Scholar
Nozick, R. (2001), Invariances: The Structure of the Objective World. Cambridge, MA: Harvard University Press.Google Scholar
Peskin, Michael E., and Schroeder, Daniel V. (1995), An Introduction to Quantum Field Theory. Reading, MA: Addison-Wesley.Google Scholar
Pooley, O. (2003), “Handedness, Parity Violation, and the Reality of Space”, in Brading, K. and Castellani, E. (eds.), Symmetries in Physics: Philosophical Reflections. Cambridge: Cambridge University Press, 250–280.CrossRefGoogle Scholar
Rein, D. (1974), “Some Remarks on Parity Violating Effects of Intramolecular Interactions”, Some Remarks on Parity Violating Effects of Intramolecular Interactions 4:15–22.Google ScholarPubMed
Saunders, S. (2003), “Indiscernibles, General Covariance, and Other Symmetries: The Case for Non-reductive Relationalism”, in Ashtekar, A., Howard, D., Renn, J., Sarkar, S., and Shimony, A. (eds.), Revisiting the Foundations of Relativistic Physics: Festschrift in Honour of John Stachel. Dordrecht: Kluwer, 151–175.CrossRefGoogle Scholar
Stachel, J. (1993), “The Meaning of General Covariance”, in Janis, A., Rescher, N., and Massey, G. (eds.), Philosophical Problems of the Internal and External Worlds: Essays Concerning the Philosophy of Adolf Grünbaum. Pittsburgh: University of Pittsburgh Press, 129–160.CrossRefGoogle Scholar
Ulbricht, T. L. V. (1959), “Asymmetry: The Nonconservation of Parity and Optical Activity”, Quarterly Reviews (London) 13:48–60.CrossRefGoogle Scholar
Wald, R. (1984), General Relativity. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Weyl, H. (1952), Symmetries. Princeton, NJ: Princeton University Press.Google Scholar
Zel’dovich, B., Saakyan, D., and Sobel’man, I. (1977), “Energy Difference between Right-Hand and Left-Hand Molecules, Due to Parity Nonconservation in Weak Interactions of Electrons with Nuclei”, Energy Difference between Right-Hand and Left-Hand Molecules, Due to Parity Nonconservation in Weak Interactions of Electrons with Nuclei 25:94–97.Google Scholar