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Alternative quantum interpretations and the two-slit system

Jean-Guy Blouin

Published Jan 1, 1994• 0 citations
OpenAlex

Abstract

Reexamines the two-slip experiment (a basic experiment in quantum mechanics) using alternative descriptions of quantum mechanics.

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A Set-Based Alternative to the Hilbert-Space Formalism: Two-Slit Interference in the CEGS Framework This work presents a deterministic reformulation of the two-slit experiment within the Calculus of Element Generated Sets (CEGS), a set-based framework for modeling physical systems without assuming Hilbert space as a fundamental structure. Instead of representing quantum states as vectors in a complex Hilbert space, physical states are described as structured sets of phase-generating elements subject to intrinsic constraint operations prior to aggregation. Within this framework, observable quantities arise only after a coherent aggregation map acts on constrained generative sets. The standard interference pattern of the two-slit experiment is recovered exactly at the level of observable predictions, preserving empirical equivalence with conventional quantum mechanics. A central conceptual shift is that complex amplitudes are not treated as fundamental entities. Instead, they emerge as effective compressed representations of underlying distributed phase structures under observer-dependent projection. In this view, Hilbert space is interpreted as an emergent effective description rather than a primary ontological structure. The formulation provides a deterministic and structural alternative perspective on quantum interference, contributing to ongoing discussions in quantum foundations, interpretation of quantum mechanics, and set-based or non-vectorial reformulations of physical theory. The analysis is restricted to the two-slit experiment as a minimal test case, while maintaining consistency with standard quantum predictions.
The single slit, the curve-single slit, the parallel double slit, the non-parallel double slit, the curve-double slit, and the non-parallel-curve-double slit experiments show the PhotoWave phenomena. In this article, by utilize the PhotoWave concept, we interpret the mechanism of the production of the Hybrid pattern (i.e., the two interference patterns respectively embedded in two diffraction patterns) of the non-parallel-double slit experiment. Based on the interpretation, we propose the math description of the Hybrid pattern.
The single slit, the curve-single slit, the parallel double slit, the non-parallel double slit, the curve-double slit, and the non-parallel-curve-double slit experiments show the PhotoWave phenomena. In this article, by utilize the PhotoWave concept, we interpret the mechanism of the production of the Hybrid pattern (i.e., the two interference patterns respectively embedded in two diffraction patterns) of the non-parallel-double slit experiment. Based on the interpretation, we propose the math description of the Hybrid pattern.