Quantum-to-classical transitions

In the early days of quantum mechanics, it was reasonably expected that the Schrodinger equation should not only correctly describe facts not addressed by classical mechanics, but also reduce itself to the later when certain parameters were varied appropriately. When dealing with quantum to classical transitions, it is relevant to emphasize two fundamental properties of the Schrodinger equation: (i) it is a linear wave-equation built from single-valued conserved pure states that satisfy the superposition principle and (ii) the information provided by such states is in the form of a probability distribution because of the uncertainty principle. Even if we include the second property into a classical description by using an ensemble of trajectories with different (i.e. “uncertain”) initial conditions, the first property causes unsolvable difficulties in the transition from quantum to classical mechanics. Such difficulties were first discussed by Rosen in 1964. It is well-know that an ensemble of classical trajectories admits also a description in terms of a wave-function. However, such “classical” wave-function is non-linear(i.e. without the restriction of the superposition principle) and becomes inaccessible for the Schrodinger equation. Thus, quantum and classical domains merely intersect for some particular systems, but one domain is not contained in the other.

Work is in progress to use the ability of Bohmian mechanics to deal with a single experiment to treat quantum to classical transition.