The Analytic Nature of Scattered Electromagnetic Fields and the Effect of Coherence on Phase Retrieval
At the Washington meeting of the American Physical Society in 1964, Wigner related that shortly after the invention of quantum mechanics he asked Von Neumann if it were not strange that the formalism failed to require analyticity. Von Neumann replied that analytic functions constituted such a restricted and special class of functions that there was no reason why they should be the only ones admitted into physics. Wigner concluded with the remark that, Von Neumann notwithstanding, the subsequent 35 years have shown that, in a deep sense, physics is based on analytic functions. G.F. Chew, who tells this story in “The Analytic S Matrix” (1966), highlights the fact that, since this meeting, a further appreciation of the relevance of analyticity to physical theories has taken place, and he asks the fundamental question: does analyticity in itself constitute a suitable a priori principle for the formulation of theories?
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