Superposition and Macroscopic Observation

Abstract

The principle of superposition has long plagued the quantum mechanics of macrosopic bodies. Macroscopic objects are taken to be composed of a large number of interacting constituents, each in its interaction with others governed by the laws of quantum mechanics. For any two systems already represented, quantum theory represents the composite by a vector in the tensor product of the Hilbert spaces representing the systems separately. Thus, an n-body system is represented by a vector in the Hilbert space ${H^n} = {H_I} \otimes {H_{II}} \otimes ... \otimes {H_N}$. When n becomes large enough to constitute a macroscopic body the treatment is problematic. Macroscopic states, it appears, do not superpose. Macroscopic bodies seem to possess sharp values for all observable quantities simultaneously.