The Double-Slit Experiment as Observer-Bundle Transform: A Computational Demonstration of the OQM → OMeas Quotient Structure

We present a computational demonstration that the apparent wave-particle duality inthe double-slit experiment emerges naturally from the quotient structure connecting two observerbundles: the quantum-coherent bundle OQM (which perceives interference patternsand superposition) and the measurement bundle OMeas (which perceives discrete detectionevents). Through numerical simulations, we show that individual detection eventsappear random and particle-like while statistical accumulation reveals the underlying wavepattern—without invoking wave function collapse. Crucially, this analysis adopts the epistemic structuralism of Scale-Relative DistinguishabilityTheory (SRDT): we make no claims about the intrinsic nature of fundamental dynamicsF. The wave function ψ(x, t) is what OQM perceives; discrete detections are whatOMeas perceives. Both are quotients of F, denoted F/∼O. Asking “is the electron reallya wave or a particle?” is asking about F’s intrinsic nature—a question that lies beyondembedded-observer access. Our simulations validate the quotient structure quantitatively: pattern visibility metricsshow smooth transitions from particle-like to wave-like statistics as detection number Nincreases, with correlation coefficients exceeding 0.99 between simulated and theoreticaldistributions. We derive testable predictions for the critical detection number Ncritical ∝(δx)2 as a function of detector resolution. We further demonstrate that the double-slit experiment instantiates universal SRDTpatterns appearing across multiple physics transforms: wave-particle duality dissolves asobserver-relative descriptions of an F-unity, and the wave-to-particle transition is structurallyisomorphic to the Wave Optics → Geometrical Optics transform. The question“which slit did the photon go through?” is shown to be a category error analogous to askingfor the temperature of a specific microstate.