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Experiment to test one of the incompleteness of quantum mechanics

Michel Gondran, Alexandre Gondran

Abstract

For nearly 100 years, the incompleteness of quantum formalism and the probabilistic nature of measurement have been the subject of ongoing debate, with no interpretation achieving unanimous agreement. In double-slit interference experiments, standard quantum theory does not take particle size into account, which is not the case in de Broglie's double-solution theory. We use the large size of Rydberg atoms to propose an experiment to test the incompleteness of the standard quantum formalism. We present a variation on the double-slit experiment performed with Rydberg sodium atoms, in which a grating of very narrow slits is added between the two slits. Rydberg atoms are too big and cannot pass through the slits of the grating. We show with numerical simulations that the transmission densities in the standard interpretation and in the double-solution interpretation give very different results (a dark band appears in the center of the pattern). Experimental implementation now seems possible and would be a crucial test between these two interpretations.

Experiment to test one of the incompleteness of quantum mechanics

Abstract

For nearly 100 years, the incompleteness of quantum formalism and the probabilistic nature of measurement have been the subject of ongoing debate, with no interpretation achieving unanimous agreement. In double-slit interference experiments, standard quantum theory does not take particle size into account, which is not the case in de Broglie's double-solution theory. We use the large size of Rydberg atoms to propose an experiment to test the incompleteness of the standard quantum formalism. We present a variation on the double-slit experiment performed with Rydberg sodium atoms, in which a grating of very narrow slits is added between the two slits. Rydberg atoms are too big and cannot pass through the slits of the grating. We show with numerical simulations that the transmission densities in the standard interpretation and in the double-solution interpretation give very different results (a dark band appears in the center of the pattern). Experimental implementation now seems possible and would be a crucial test between these two interpretations.

Paper Structure

This paper contains 1 section, 2 figures.

Table of Contents

  1. Complementary data

Figures (2)

  • Figure 1: (a) Schematic drawing of the interference experiment. (b) The interference pattern (corresponding to the norm of the statistical wave function, $|\psi(y)|$) of the unexcited sodium atoms on the detection screen. This pattern is common to all interpretations. (c) Interference pattern for the double-slit experiment alone ($A_1$ and $A_1$ slits), without the $B$ grating. This also corresponds to the pattern excepted for the standard interpretation (it is as if the grating did not exist). (d) Interference pattern excepted by the double-solution theory. Same density as (b) figure with a dark band in the center. The central peak is split into two. A Rydberg atom passing through slits $A_1$ or $A_2$ is piloted by the statistical wave function $\psi$ which passes through both silts AND the $B$ grating.
  • Figure 2: Interference pattern of the 40-slit of $B$ grating alone at $2m$ after the slits.