Symmetry-Based Dynamics-Independent Restrictions on Possible MeasurementsAuthor(s): Richard Spitzer (USA)
The restrictions on possible measurements termed "super-selection" are reexamined. My analysis is based on aspects of these restrictions that have not been taken into account in the literature, with essentially different results: the scope of super-selection is shown to be narrower and the nature of the symmetry-based restrictions to be broader than generally claimed. The fundamental restriction is unconditional: incompatibility of a symmetry operation and measurability of the subset of Hermitian operators connecting states distinguished by essentially different values of the phase eiα of a unimodular multiple of the identity operator generated by this symmetry; it is a purely theoretical restriction. Consequent are two mutually-exclusive conditional restrictions: (1) Exclusion of Hermitian operators connecting states with essentially different values of eiα from the subset of observables consistent with the symmetry operation, and (2) Dynamics-independent symmetry breaking upon measurement of such operators; each has both theoretical and empirical contexts. The theoretical contexts of both conditional restrictions and the empirical context of exclusion apply without exception. The empirical context of dynamics-independent symmetry breaking has been realized selectively: observed in the case of Galilean invariance but, to date, not for rotational invariance. These two symmetries collectively exemplify all aspects of my analysis.