Invariance Principles as Regulative Ideals: From Wigner to Hilbert

Abstract

Eugene Wigner's several general discussions of symmetry and invariance principles are among the canonical texts of contemporary philosophy of physics. Wigner spoke from a position of authority, having pioneered (and won the Nobel prize in 1963) for recognition of the importance of symmetry principles from nuclear to molecular physics. But perhaps recent commentators have not sufficiently stressed that Wigner always took care to situate the notion of invariance principles with respect to two others, initial conditions (or events) and laws of nature. Wigner's first such general consideration of invariance principles, an address presented at Einstein's 70th birthday celebration, held in Princeton on 19 March 1949, began by laying out just this distinction, and in a way that seems to suggest that the three notions arise through abstraction in an analysis of the general problem of cognition in the natural sciences: The world is very complicated and it is clearly impossible for the human mind to understand it completely. Man has therefore devised an artifice which permits the complicated nature of the world to be blamed on something which is called accidental and thus permits him to abstract a domain in which simple laws can be found. The complications are called initial conditions; the domain of regularities, laws of nature. (…) the underlying abstraction is probably one of the most fruitful the human mind has made. It has made the natural sciences possible.