Observing Nonclassical Paths by Measuring Bohmian Velocities in Multi-Slit Interferometer with Electron

TL;DR

This paper demonstrates that non-classical paths significantly influence electron velocities in multi-slit interferometers, measurable through weak measurement techniques, challenging traditional interpretations of wave superposition.

Contribution

It introduces a method to observe non-classical paths via Bohmian velocities in electron multi-slit experiments, providing quantitative analysis of their effects.

Findings

Non-classical paths cause a 10^{-3} deviation in Bohmian velocity.

The deviation is observable with weak measurement techniques.

Non-classical paths contribute to multi-slit interference beyond traditional superposition.

Abstract

Superposition principle of wave function in multi-slit interference experiment has been widely accepted by many quantum mechanics textbooks, however the expression ${\psi _{AB}} = {\psi _A} + {\psi _B}$ does not strictly hold. The non-classical paths in Feynman path integral provide an explanation to the multi-path interference effect, and can be used to quantitatively analyse the multi-slit interference effect. In this work, we apply quantities in Bohmian mechanics to the measurement of multi-order interference by analysing the contribution of non-classical paths to Bohmian velocity in electron's multi-slit interferometer. The result shows that the non-classical paths effect will cause a relative deviation of $10^{-3}$ in electron's Bohmian velocity, which is observable by doing weak measurement similar to previous work.