The Quantum Ratio

Abstract

The concept of quantum ratio has emerged from recent efforts to understand how Newton’s equations appear for the center of mass (CM) of an isolated macroscopic body at finite body temperatures as a first approximation of quantum mechanical equations. It is defined as Q≡Rq/L0, where the quantum fluctuation range Rq is the spatial extension of the pure-state CM wave function, whereas L0 stands for the body’s linear size (the space support of the internal bound-state wave function). The two cases Rq/L0≲1 and Rq/L0≫1 roughly correspond to the body’s CM behaving classically or quantum mechanically, respectively. In the present note, we elaborate on this concept and illustrate it through several examples. An important notion following from introduction of the quantum ratio is that the elementary particles (thus, the electron and the photon) are quantum mechanical even when environment-induced decoherence places them into a mixed state. Thus, decoherence and classical state should not be identified. This simple observation, further illustrated by consideration of a few atomic and molecular processes, may have significant implications for the way that quantum mechanics works in biological systems.