The emergence of classical properties through interaction with the environment

Abstract

The dependence of macroscopic systems upon their environment is studied under the assumption that quantum theory is universally valid. In particular scattering of photons and molecules turns out to be essential even in intergalactic space in restricting the observable properties by locally destroying the corresponding phase relations. The remaining coherence determines the ‘classical’ properties of the macroscopic systems. In this way local classical properties have their origin in the nonlocal character of quantum states.

The effect of the interaction depends essentially on whether it permanently ‘measures’ discrete or continuous quantities. For discrete variables (here exemplified by two-state systems) the classical properties are given by the measurement basis. The continuous case, studied for translational degrees of freedom, leads to a competition between destruction of coherence by the interaction and dispersion of the wave packet by the internal dynamics. A non-phenomenological Boltzmann-type master equation is derived for the density matrix of the center of mass. Its solutions show that the much-discussed dispersion hardly ever shows up even for small dust particles or large molecules. Instead the coherence length decreases towards the thermal de Broglie wave length of the object, whereas the incoherent spread increases. The Ehrenfest theorems are shown nevertheless to remain valid for recoil-free interactions. Some consequences of these investigations for the quantum theory of measurement are pointed out.