A suggested experiment to distinguish between the Bohmian Interpretation and the Standard Quantum Mechanics

Abstract: Based on the double-slit experiment of electrons, we suggest a proposal of thought experiment to distinguish between the Bohmian Interpretation (BI) and the Standard Quantum Mechanics (SQM). We mainly focus on the discussion of the meaning of the wave function (Schr\"{o}dinger-$\psi$). The key technique is require to insert some slow-electrons or weak electron current into the space between the double-slit and the detector plane. We find that the two theories finally give out two totally different results about the affections which the externally inserted electrons cause to the original pattern of the interference fringes. Under the BI, the externally inserted electrons also can be influenced by the Quantum Potential (QP) in a totally same way with the electrons which come from the slits, so the positions they arrived at are preferred to certain bright zones, and the interference pattern will become more clearer. While under the SQM, the Schr\"{o}dinger-$\psi$ does not represent an objectively real field, but only a mathematical construction of the probability characteristics of the particle itself, so the externally inserted electrons and the electrons which come from the slits have no correlations with each other. No any priority positions at the detector plane the externally inserted electrons will arrive. And the affections are only the addition of a uniform bright background. In such a meaning, the dark zones of the fringes of the interference pattern have been filled.