EXCLUSION OF INTRINSICALLY CLASSICAL DOMAINS AND THE PROBLEM OF QUASI-CLASSICAL EMERGENCE

One difficulty with the correspondence principle is its vagueness. To what should the quantum theory correspond in the quasiclassical domain? Here we show that, whatever it is, it cannot be Hamilton's equations. This is done using Weinberg's generalized nonlinear quantum theory [S. Weinberg, Ann. Phys. (N.Y.) 194, 336 (1989)[ by exploiting the fact that it contains an exact copy of classical dynamics [K.R.W. Jones, Phys. Rev. D 45, R2590 (1992)]. An enlarged dynamical theory incorporating mixed quantum and classical interactions is shown to have some desirable properties in relation to measurement. By studying this system, we show that the existence of observable physical domains obeying intrinsically classical laws would violate the uncertainty principle, thereby ruling out an entire class of such larger theories. We interpret this result as a demonstration that the correspondence principle is essentially approximate. Further, the given exclusion is suggestive as a guide to physical models of quasiclassical emergence in a scenario based upon environmental noise and stochastic reduction.