In light of the lessons learned in the last 35 years from the quantum statistical mechanics description of phase transitions, I argue that the dichotomy in the evolution of quantum systems proposed by von Neumann, and pursued by Wigner in spite of the Einstein--Bohr criticisms on the attendent lack of resolution in terms of classical reality, fails to take into account the middle term suggested by the existence of superselection rules, Wigner's own discovery (with Wightmann and Wick). I claim that the part of the measurement problem concerned with the stable transfer of microscopic information to macroscopic physics can be treated
entirely within the framework of a deterministic, conservative evolution of the joint system, i.e. without requiring the type of evolution von Neumann proposed besides that governed by the Schroedinger equation. I sustain this claim with the use of an exactly solvable model akin to the x-y model of statistical mechanics and involving its thermodynamical limit.
Some of the proto-history of the theory of wavelets was written as Quantum Mechanics was first developed; but a long consolidation period had to occur before the magic clouds dissipated to let the more general structures energy, ready for applications which the Founders were not anticipating. This lecture will recount some of the salient episodes belonging in the earlier part of this saga--and bow out at the threshold of the history of wavelets proper, thus focusing on the hatching grounds provided by coherent states.
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