Considerations on an Optical Test of Popper's Experiment

TL;DR

This paper analyzes a ghost imaging realization of Popper's experiment, showing that the unmeasured particle's spread depends on system geometry rather than virtual confinement, and proposes an alternative setup with different behavior.

Contribution

It provides a detailed optical diffraction analysis of Popper's experiment, clarifies the dependence of particle spread on system geometry, and suggests an alternative configuration for expected behavior.

Findings

In the original setup, the unmeasured particle's spread is determined by the system's numerical aperture.

The spread does not inversely relate to the virtual slit width in the original configuration.

An alternative configuration is proposed where the spread increases with the virtual slit width.

Abstract

We present a detailed analysis of a previously published realization of Popper's experiment using entangled ghost imaging. Our analysis, which is based on optical diffraction integrals, shows that, for the configuration previously described, the transverse spread of an unmeasured particle (the signal photon here) does not increase in inverse proportion to the width of its virtual confinement when its entangled twin is confined in transverse dimension by a physical slit. Rather we show that the spread of the unmeasured particle carries no dependence on the width of its virtual confinement in the published configuration. Instead, it spreads geometrically at a rate determined by the numerical aperture of the ghost imaging system. We further propose an alternative configuration for which the spread of the unmeasured particle does increase in inverse proportion to the width of its virtual confinement. We discuss the relation of these results to the predictions of Popper.