Symmetries and invariances in classical physics

Symmetry, intended as invariance with respect to a transformation (more precisely, with respect to a transformation group), has acquired more and more importance in modern physics. This Chapter explores in 8 Sections the meaning, application and interpretation of symmetry in classical physics. This is done both in general, and with attention to specific topics. The general topics include illustration of the distinctions between symmetries of objects and of laws, and between symmetry principles and symmetry arguments (such as Curie's principle), and reviewing the meaning and various types of symmetry that may be found in classical physics, along with different interpretative strategies that may be adopted. Specific topics discussed include the historical path by which group theory entered classical physics, transformation theory in classical mechanics, the relativity principle in Einstein's Special Theory of Relativity, general covariance in his General Theory of Relativity, and Noether's theorems. In bringing these diverse materials together in a single Chapter, we display the pervasive and powerful influence of symmetry in classical physics, and offer a possible framework for the further philosophical investigation of this topic.
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Diego Romero-Maltrana (2015). Symmetries as by-Products of Conserved Quantities. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52:358-368.
Olimpia Lombardi, Mario Castagnino & Juan Sebastián Ardenghi (2010). The Modal-Hamiltonian Interpretation and the Galilean Covariance of Quantum Mechanics. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (2):93-103.

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