Bohm’s approach to quantum mechanics: Alternative theory or practical picture?

通信作者

A. S. Sanz

Department of Optics, Faculty of Physical Sciences, Universidad Complutense de Madrid,

Pza. Ciencias 1, Ciudad Universitaria E-28040 Madrid, Spain 

文章简介

This work intends to be a posthumous tribute to David Bohm on the occasion of the centennial of his birthday. He was willing to look at quantum mechanics with different eyes in times where all eyes looked on the same direction. And, in so doing, he and his works served as an inspiration to forthcoming generations of physicists. 

Since its inception Bohmian mechanics has been generally regarded as a hidden-variable theory aimed at providing an objective description of quantum phenomena. To date, this rather narrow conception of Bohm’s proposal has caused it more rejection than acceptance. Now, after 65 years of Bohmian mechanics, should still be such an interpretational aspect the prevailing appraisal? Why not favoring a more pragmatic view, as a legitimate picture of quantum mechanics, on equal footing in all respects with any other more conventional quantum picture? These questions are used here to introduce a discussion on an alternative way to deal with Bohmian mechanics at present, enhancing its aspect as an efficient and useful picture or formulation to tackle, explore, describe and explain quantum phenomena where phase and correlation (entanglement) are key elements. This discussion is presented through two complementary blocks. The first block is aimed at briefly revisiting the historical context that gave rise to the appearance of Bohmian mechanics, and how this approach or analogous ones have been used in different physical contexts. This discussion is used to emphasize a more pragmatic view to the detriment of the more conventional hidden-variable (ontological) approach that has been a leitmotif within the quantum foundations. The second block focuses on some particular formal aspects of Bohmian mechanics supporting the view presented here, with special emphasis on the physical meaning of the local phase field and the associated velocity field encoded within the wave function. As an illustration, a simple model of Young’s two-slit experiment is considered. The simplicity of this model allows to understand in an easy manner how the information conveyed by the Bohmian formulation relates to other more conventional concepts in quantum mechanics. This sort of pedagogical application is also aimed at showing the potential interest to introduce Bohmian mechanics in undergraduate quantum mechanics courses as a working tool rather than merely an alternative interpretation. 

Numerical simulation illustrating the usual Bohmian interpretation of Young’s two-slit experiment by means of Bohmian quantum trajectories (black solid lines). For the sake of clarity, these trajectories are superimposed on the contour plots of the probability density (a) and the velocity field (b). The trajectories represent the evolution in time [according to the Bohmian prescription, given by the guidance equation (8)] of a single element of quantum fluid, from any of the two slits to some final position where a scanning screen (detector) would be allocated. White arrows indicate the main (evolution) direction of the flow initially and asymptotically, which shows how from zero transversal flow the dynamics turns into a set of components traveling with different transverse speed. In part (b), the gray dashed arrows indicate the direction in which the velocity field increases at the early stages of the evolution, while the white dashed arrows show the trend motion followed by the different sub-ensembles of trajectories (downwards in the upper half of the graph; upwards in the lower half).

文章链接

A.S. Sanz, Bohm’s approach to quantum mechanics: Alternative theory or practical picture? Front. Phys. 14(1), 11301 (2019) 

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