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Note on the two-slit experiment

N. G. van Kampen

Journal of Statistical PhysicsOct 1, 19942 citations

Reinterpreting Double-Slit Quantum Interference as Relational Frame Geometry: A Definitive URPD-Based Resolution

A.I. Trinity Lab

This paper presents a URPD-based geometric reconstruction of the double-slit interference experiment. In this formulation, the electron does not behave as a wave or a particle; instead, the interference pattern emerges from geodesic overlap relations within the relational frame manifold CPN−1\mathbb{CP}^{N-1}CPN−1. The relative phase between the two paths arises from the Kähler geometry of the Fubini–Study metric, and the disappearance of interference under which-path measurement follows from displacement-constrained frame collapse. No wave–particle duality, hidden variables, or ad hoc collapse mechanisms are required. The double-slit paradox thus becomes a direct consequence of informational-geometric structure, fully consistent with the Born rule and relativistic causality.This paper presents a URPD-based geometric reconstruction of the double-slit interference experiment. In this formulation, the electron does not behave as a wave or a particle; instead, the interference pattern emerges from geodesic overlap relations within the relational frame manifold CPN−1\mathbb{CP}^{N-1}CPN−1. The relative phase between the two paths arises from the Kähler geometry of the Fubini–Study metric, and the disappearance of interference under which-path measurement follows from displacement-constrained frame collapse. No wave–particle duality, hidden variables, or ad hoc collapse mechanisms are required. The double-slit paradox thus becomes a direct consequence of informational-geometric structure, fully consistent with the Born rule and relativistic causality.

Nov 22, 20250 citations

A Numerical Experiment with the Double Slit Geometry

Al Rabeh, H Riadh

PrPhJul 1, 20103 citations

Geometric viewpoint on the quantization of a fuzzy logic

Davide Pastorello

Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel [Formula: see text]-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations. Considering the geometric formulation of quantum mechanics we give a description of quantum propositions in terms of fuzzy events in a complex projective space equipped with Kähler structure (the quantum phase space) obtaining a quantized version of a fuzzy logic by deformation of the product [Formula: see text]-norm.Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel [Formula: see text]-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations. Considering the geometric formulation of quantum mechanics we give a description of quantum propositions in terms of fuzzy events in a complex projective space equipped with Kähler structure (the quantum phase space) obtaining a quantized version of a fuzzy logic by deformation of the product [Formula: see text]-norm.

arXiv:2004.03395International Journal of Geometric Methods in Modern PhysicsSep 10, 20200 citations

On the uncertainty of Cantorian geometry and the two-slit experiment

Mohamed Saladin El Naschie

Chaos Solitons & FractalsMar 1, 1998272 citations

Entanglement and products

Tatyana Barron, Noah Wheatley

We address a general question whether geometry of submanifolds of an integral compact Kähler manifold is characterized by invariants that come from analysis. In geometric quantization, we have an integral compact Kähler manifold M and a holomorphic line bundle L on this manifold. There is a known procedure how to associate a sequence of mixed states (ρN), N=1,2,3,…, to a submanifold Λ of M. Do analytic properties of this sequence reflect the geometry of Λ ? In this paper, we consider the case when M is a product of two integral compact Kähler manifolds. We show that, when Λ is a product submanifold of M, then the entanglement of formation of ρN is zero for all sufficiently large N.We address a general question whether geometry of submanifolds of an integral compact Kähler manifold is characterized by invariants that come from analysis. In geometric quantization, we have an integral compact Kähler manifold M and a holomorphic line bundle L on this manifold. There is a known procedure how to associate a sequence of mixed states (ρN), N=1,2,3,…, to a submanifold Λ of M. Do analytic properties of this sequence reflect the geometry of Λ ? In this paper, we consider the case when M is a product of two integral compact Kähler manifolds. We show that, when Λ is a product submanifold of M, then the entanglement of formation of ρN is zero for all sufficiently large N.

arXiv:2104.10597Linear and Multilinear AlgebraMar 5, 20220 citations

On a Fuzzy Kähler-like Manifold which is Consistent with the Two Slit Experiment

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