Causation in Science by Yemima Ben-Menahem

Author:Yemima Ben-Menahem
Language: eng
Format: epub
Publisher: Princeton University Press
Published: 2018-07-14T16:00:00+00:00

5

Symmetries and Conservation Laws

FOR THOSE WHO PONDER the “unreasonable effectiveness of mathematics in the natural sciences,” as Eugene Wigner (1960) did,1 the many applications of the notion of symmetry, and the tremendous work this notion does for the physicist, certainly provide some of the most striking examples.2 In the case of symmetry considerations, it seems, we don’t merely use mathematical language to express familiar, or conjectured, physical laws, but we actually import some segment of mathematics into physics, and then use it to derive new physical laws. More than other empirical laws, symmetries appear to have an element of aprioricity that endows them with a special grace and nobility; they belong to the nomic aristocracy, as it were. Hermann Weyl went even further: “As far as I can see, all a priori statements have their origin in symmetry” (1952, 126). And though we now know that at least some—and conceivably all—of the symmetries of physics are not, in fact, a priori, they have not completely lost their privileged status despite the recent tendency toward nomic egalitarianism.

Symmetries do indeed underscore questions regarding the relation between a mathematical structure and its physical realization(s). As we will see in more detail in this chapter, we are occasionally confronted with the existence of what Michael Redhead (2003, 128) dubbed “surplus structure,” where the same physical structure can be correlated with several distinct mathematical structures, giving us more freedom than we would like to have. This freedom creates a gap between the mathematical and physical realms, upsetting the correspondence that is generally expected to obtain between them. What physicists do in such cases, beginning with Einstein’s famous “hole argument” (Lochbetrachtung)3 and continuing with gauge theories, is impose new symmetries on the mathematical side, that is, impose equivalence relations that construe several mathematical states as the same physical state. This procedure eliminates the freedom generated by the surplus structure and restores the tight fit between the mathematical and physical realms.

This chapter focuses on the place of symmetry in the network of causal constraints. It argues that symmetry principles play a causal role on a par with that of other causal constraints, and examines some of the interconnections between symmetries and these other members of the causal family. Among the latter, conservation laws are the most closely linked to symmetries, and will therefore receive special attention. That the view presented here departs significantly from the prevailing, noncausal, portrayal of symmetries highlights the implications of the broad conception of causation set forth in this book.

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