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The British Journal for the Philosophy of Science 2008 59(2):143-168; doi:10.1093/bjps/axn009
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© The Author (2008). Published by Oxford University Press on behalf of British Society for the Philosophy of Science. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

A Puzzle about Laws, Symmetries and Measurability

John T. Roberts

Department of Philosophy, University of North Carolina, C. B. #3125 Chapel Hill NC 27599, USA

johnroberts{at}unc.edu


  Abstract

I describe a problem about the relations among symmetries, laws and measurable quantities. I explain why several ways of trying to solve it will not work, and I sketch a solution that might work. I discuss this problem in the context of Newtonian theories, but it also arises for many other physical theories. The problem is that there are two ways of defining the space-time symmetries of a physical theory: as its dynamical symmetries or as its empirical symmetries. The two definitions are not equivalent, yet they pick out the same extension. This coincidence cries out for explanation, and it is not clear what the explanation could be.

  1. The Puzzle: Symmetries, Measurability and Invariance
    1.1 The symmetries and the measurable quantities of Newtonian mechanics
    1.2 The puzzle
  2. Two Easy Answers
  3. Another Unsuccessful Solution: Appeal to Geometrical Symmetries
  4. Locating the Puzzle
  5. The Relation between Laws and Measurability
  6. A Possible Solution


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