Locality and the classical limit of quantum mechanics

I argue that conventional estimates of the criterion for classical behavior of a macroscopic body are incorrect, because they do not take into account the locality of interactions, which characterizes the behavior of all systems described approximately by local quantum field theory. Black holes are the only localized objects which do not have such a description. The deviations from classical behavior of a macroscopic body, except for those which can be described as classical uncertainties in the initial values of macroscopic variables,are exponentially small as a function of the volume of the macro-system in microscopic units. 1 Classical behavior in the non-relativistic quantum mechanics of particles In standard texts on non-relativistic quantum mechanics the classical limit is described via examples and via the WKB approximation. In particular, one often describes the spreading of the wave packet of a free particle, and estimates it as a function of time and the particle mass M . There is nothing wrong with the mathematics done in these texts, but the implication that these estimates provide the basis for an understanding of why classical mechanics is such a good approximation for macroscopic objects is not correct and therefore misleading. In particular it leads one to conclude that the corrections to decoherence for a wave function describing a superposition of two different macroscopic states is power law in the mass. I would aver that this mistake forms part of the psychological unease that many physicists feel about the resolution of Schrödinger’s cat paradox in terms of the concept of decoherence. In this introductory section, I would like to demonstrate why such estimates are wrong, using standard ideas of non-relativistic quantum mechanics. In the remainder of the paper I will discuss the basis for these calculations in quantum field theory. This will also remove the necessity to resort to HartreeFock like approximations to prove the point directly in the non-relativistic formalism. The essential point of the argument is that we must take into account the fact that a macroscopic object is made out of a huge number > 10 of microscopic constituents, in order to truly understand its classical behavior. I will argue that, as a consequence, the overlaps between states where the object follows two macroscopically different trajectories, as well as the matrix elements of all local operators between such states, are of order