Beyond Superposition and Collapse: Double-Slit Interference from Trembling Spacetime Geodesics

Nico F. Declercq

Published May 15, 2025• 0 citations

Abstract

The double-slit experiment has long been interpreted as evidence of wave-particle duality and quantum superposition. Here we propose a deterministic alternative rooted in Trembling Spacetime Relativity Theory (TSRT), where particles always follow localized proper-time geodesics within a causally structured but metrically fluctuating spacetime. Apparent interference fringes arise not from wavefunction superposition, but from the deterministic redirection of particle geodesics due to curvature perturbations shaped by the slit geometry. The observed distribution of arrival positions is governed by two geometric mechanisms: (i) the slit separation, which sets the angular deflection range of redirected geodesics, and (ii) a minimal action threshold that enforces a resolution limit based on causal distinguishability. Planck’s constant emerges naturally from this causal constraint as the smallest resolvable geodesic action difference, without any quantum postulates. TSRT provides analytical predictions for fringe spacing and intensity distribution across a wide range of particles—photons, electrons, and neutrons—by applying geometric deflection laws to causally permitted geodesics. These predictions align closely with established experimental results. In addition, the TSRT framework enables simulation of arbitrary configurations by modeling ensembles of geodesics subject to metric trembling, providing a fully geometric alternative to quantum superposition.

DOI: 10.5281/zenodo.15425853

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