Resonant inelastic x-ray incarnation of Young’s double-slit experiment

The Borsuk-Ulam theorem (BUT) is a general topological principle subtending several physical and biological real-world phenomena. The theorem states that, given a continuous function, two antipodal features with matching description lying on a n-dimensional convex manifold (e.g., a three –dimensional sphere termed S2) project to a single feature on a n-1 dimensional manifold (e.g., a two-dimensional Euclidean space termed R2). Here we ask: might the BUT-related mechanism of topological projections and mappings display physical, quantifiable counterparts? The answer is positive, if we take into account double-slit experiments, which demonstrate that light and matter display not just features of both classically defined waves and particles, but also the probabilistic nature of quantum mechanics. In double-slit experiments, a wave is split into two separate oscillations that later combine into a single one. Changes in path lengths result in phase shifts which produce interference patterns. Despite the wave nature of light causes bright and dark bands on the screen, the light is always found to be absorbed at the screen as individual particles, the interference pattern progressively appearing through the varying density of particle hits on the screen.

A BUT-framed explanation of the double-slit experiment may be drawn. When a plain wave passes through two slits of the proper size, it splits in two different waves that interfere one each other and then reach the detection screen. In a BUT account, the two interfering waves are located inside a sphere S2, which is endowed in the three-dimensional space between the two slits and the screen. The interference patterns detected by Revelli et al. (2019) through resonant inelastic x-ray scattering reveal intrinsic symmetries: this means that there exist antipodal interfering oscillations in S2 which display matching description. According to the quantum dictates, when the two waves reach the 2D screen R2, they give rise to a single detection point. This means, in BUT terms, that two opposite features with matching description in S2 project to a single feature in R2. Therefore, BUT-framed projections describe the counterintuitive notion of light as equipped with both oscillatory and particle-like behavior in the double-slit experiment: the continuous, oscillatory components of the quantum wave are located inside the three-dimensional manifold S2, while the discrete particle components are located inside the two-dimensional manifold (standing for R2). This means that BUT allows the description of physical phenomena, in particular in the quantum realm where the classical logic, based on the Aristotelian principle of non-contradiction and temporal/causal relationships, does not hold anymore.

Arturo Tozzi
Center for Nonlinear Science, Department of Physics, University of North Texas, Denton, Texas, USA
tozziarturo@libero.it
Arturo.Tozzi@unt.edu