Title: Non-Euclidean Geometry and Quantum Entanglement

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

This paper explores the potential for unifying geometric properties with quantum phenomena through the development of a novel framework, termed "resonant geometry." We propose a mathematical model wherein geometric shapes exhibit emergent quantum behavior, driven by a dynamically adjustable operator that mimics the quantum state of the shape. The core claim is to establish a bridge between discrete quantum systems and continuous space, potentially unveiling new physics and offering a deeper understanding of fundamental geometric concepts. The paper details the introduction of a new mathematical operator and outlines a preliminary exploration of its effects on geometric transformations and quantum entanglement. We argue that this approach represents a significant departure from traditional geometric methods and opens avenues for investigating the interplay between space, quantum mechanics, and geometry.

DOI: 10.5281/zenodo.22269433

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