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Symmetries and Reflections

E. P. Wigner

posted on 15 January 2002

reviewed by Joe McCauley

Although simply written, this is not a book for beginers. On the other hand it doesn't hurt to read it early and think about it for a long time, rereading it from time to time, in order finally to get the main point. Wigner points out that the basis for answering the question posed by him, 'Why is it possible to discover laws of nature?' is explained in every elementary physics text but the point is too subtle, is therefore lost on nearly every reader. The answer, he explains convincingly, lies in invariance principles. As an example, were local Galilean invariance not true it would have been impossible for Galileo to have discovered any law of motion at all. The same holds for local translational, rotational and time-translational invariance. Inherent in Wigner's argument is the explanation why the so-called principle of general covariance is not the foundation of general relativity, which also is grounded in the local invariance principles of special relativity.

Contrast this with the nonsense propagated in the first chapter of Samuelson's well-sold Economics text, where he asserts on the basis of a hokey picture that the difference between physics and the social sciences is not as great as it seems. In fact, there are no known invariance principles in the socio-economic sciences, and no corresponding laws of socio-economic motion (motion of money, e.g.). At best, there are intelligent gambling strategies like the equations for predicting option pricing, but these depend on market statistics that can change from one era to the next. Nor is it guaranteed that options traders will forever favor the dalta-hadging strategy and it's refinements. The last word: mathematical modelling and computer simulations are a completely different cat than approximate predictions based on laws of nature, like the laws of physics and genetics. The fact that we cannot yet (if ever) solve the Navier-Stokes
equations for turbulence, which are grounded in local invariance principles and physical law, has nothing to do with ourgeneral inability to model human behavior mathematically.