Conceptual Analog to Wave Interference with Discrete Particles

We present a numerical implementation of the proposed Source–Detector Resonance (SDR) as a conceptual analog of a Double-Slit Interference Experiment with discrete particles. Two periodic streams of particles are emitted from two point sources at random integer multiples of a fundamental period P and corresponding frequency ω=2π/P and fly out towards a detection screen. The screen consists of a deep set of identical oscillators with eigenfrequency ω0=2π/P0. In the SDR scenario, ω≈ω0. When the particles reach the screen, they implement a periodic forcing of its oscillators at the stream’s fundamental frequency ω0. As a result, an oscillating pattern develops along the screen. The amplitude of oscillation of each oscillator saturates at a value that is determined by the balance between the periodic particle forcing and the damping of each oscillator. This is clearly proportional to the number of particles that reach a certain oscillator per unit time times the fraction of particles that reach it at its resonant frequency. The latter fraction is equal to the ratio of the Power Spectral Density (PSD) of the time series of the particles that reach the oscillator at its resonance frequency PSD(ω0) over the PSD at zero frequency PSD(0). If we further assume that each oscillator absorbs a particle and announces a detection with a probability that is proportional to the square of the ratio PSD(ω0)/PSD(0); the pattern of particle detections that develops over a thick layer of oscillators is shown to be the same as that of a Double-Slit Interference Experiment. Our result shows that when macroscopic resonant detectors interact with and detect periodic streams of discrete particles, they may create the illusion of an interference measurement, as if each discrete particle manifests a phase of its own.