Comment on: Bohmian mechanics with complex action : A new trajectory-based formulation of quantum mechanics
Abstract
In a recent publication, Goldfarb et al. have proposed a new trajectory scheme to solve quantum problems: Bohmian mechanics with complex action BOMCA . According to these authors, their contribution represents “a novel formulation of Bohmian mechanics.” In our opinion, rather than a new formulation of Bohmian mechanics, the proposal of Goldfarb et al. consists of a novel quantum computational scheme, which is based on solving the complex trajectory equations resulting from an already known complex version of Bohmian dynamics. On the other hand, Goldfarb et al. also claimed that their numerical scheme describes “fully local complex quantum trajectories,” with the reward of a significantly higher degree of localization than in the conventional Bohmian mechanics by lowering the magnitude of the quantum potential. At least from a theoretical and interpretative point of view, we consider that it is very important to clarify what “fully local quantum trajectories” means. Bohmian mechanics is a nonlocal theory because standard quantum mechanics is a nonlocal theory. This nonlocality manifests via the presence of a quantum potential, and therefore the corresponding quantum trajectories will display features that reflect such nonlocality. Something similar should also occur for any trajectory-based approach that intends to be equivalent to standard quantum mechanics. In this Comment we would like to provide a general discussion on these two aspects arising from the work of Goldfarb…
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