Demonstration of the ensemble interpretation using quantum-like interference in pseudo random number generators

The electron double slit experiment is often used as a prime example for introducing the so-called wave-particle duality in quantum mechanics. In statistical or ensemble interpretation (first introduced by Einstein and later championed by Ballentine [1]), a quantum state (pure or otherwise) represents an ensemble of similarly prepared systems. In case of a single electron, an ensemble will be the conceptual (infinite) set of all single electrons which have been subjected to some state preparation (e.g., filtering of electrons) technique by interaction with a suitable apparatus (e.g., Stern-Gerlach apparatus). A momentum (/position) eigenstate represents an ensemble whose members are single electrons each having the same momentum (/position) but distributed uniformly over all positions (/momenta). Previously, Tonomura et al. [2] experimentally demonstrated double slit interference pattern using electrons. Such experiments are expensive and hard to perform. Here, we will present a simple pseudo random number generator-based single-slit diffraction and double-slit interference experiments to demonstrate the ensemble interpretation. We will show that interference disappears upon measurement or upon not including definite particle trajectory history.

1. Reviews of modern physics, 42(4), 358

2. American Journal of Physics, 57(2),117.