Calculation of the electron two-slit experiment using a quantum mechanical variational principle

Abstract

A nonlocal relativistic variational principle (VP) has recently been proposed as an alternative to the Dirac wave equation of standard quantum mechanics. We apply that principle to the electron two-slit experiment. The detection system is modeled as a screen made of atoms, any one of which can be excited by the incident electron, but we avoid restricting the detection mechanism further. The VP is shown to predict that, at the time the electron reaches the screen, its wavefunction will be localized to the neighborhood of a single atom, resulting in a position-type measurement. In an ensemble of such experiments (‘identically prepared’ except that the initial phase of the wavefunction—the hidden variable in the VP formulation—is sampled over the expected uniform distribution), the distribution of measured positions will reproduce the interference pattern predicted by the Dirac equation. We also demonstrate that with a detection system designed fundamentally to detect the electron's transverse wavelength rather than its position, the VP predicts that one such mode will be detected, that is, a wavelength measurement will result. Finally, it is shown that these results are unchanged in the ‘delayed choice’ variant of the experiment.