Weak Measurements from the Point of View of Bohmian Mechanics

The theory of weak measurements developed by Aharonov and coworkers has been applied by them and others to several interesting problems in which the system of interest is both pre- and post-selected. When the probability of successful post-selection is very small the prediction for the weak value of the measured quantity is often “bizarre” and sometimes controversial, lying outside the range of possibility for a classical system or for a quantum system in the absence of post-selection (e.g. negative kinetic energies associated with particles found immediately after the weak measurement deep inside a classically forbidden region). In Bohmian mechanics a quantum particle is postulated to be a point-like particle which is always accompanied by a wave which probes its environment and guides its motion accordingly. Hence, from the point of view of this theory, it is natural to ask whether the measured weak value under consideration is a property of the point-like particle or of the wave (or of both) and what, if anything, it is that is actually being measured. In this paper, weak measurements of position, momentum and kinetic energy are considered for very simple case studies with these questions in mind.