Abstract
E. T. Jaynes' resolution of Bertrand's paradox in terms of invariance principles is criticized. An experimental setup is considered which generates general solutions to Bertrand's problem by rotating a line around a point a distancer+d from a circle of radiusr. The general solution obtained is neither translationally nor scale invariant, but depends on the value ofr/d. Only in the limitr/d » 0, when the line is just translating across the circle, is the distribution translationally invariant and scale invariant. In this limiting case the distribution found is just that obtained by Jaynes.
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Reference
E. T. Jaynes,Found. Phys. 3, 477 (1973).
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Friedman, K.S. A problem posed. Found Phys 5, 89–91 (1975). https://doi.org/10.1007/BF01100318
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DOI: https://doi.org/10.1007/BF01100318