A Hierarchy of Selection Problems

Abstract

This chapter brings together Einstein’s 1907 vision of ‘quantization as selection problem’ (see Section 5.1) and our explorations of the possible and impossible (momentum) configurations in Chapter 4. The hierarchy is formulated in terms of the latter ones and consists of Newtonian systems, non-Newtonian classical systems, non-classical systems and non-mechanical systems. These explorations are assisted by an overview on selection problems in classical and quantum theory, by further reasonings for Einstein’s vision and by few explanations about alternative and harmony in Euler’s axioms of classical mechanics. Two fundamental conclusions for non-classical systems can be drawn already at this stage. (i), The notion of path as a point-wise relationship between the configurations and the momentum configurations looses its meaning. (ii), there are no longer coordinates describing the boundaries of a system in (momentum) like the classical turning points of an oscillator.

Keywords: Einstein, Impossible configuration, Impossible momentum configuration, Newtonian mechanics, Non-classical mechanics, Non-Newtonian classical mechanics, Possible configuration, Possible momentum configuration, Selection problem.