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Title: Quantum State Collapse Analysis via Geometric Topology

Jincheng Zhang

Published Sep 6, 2026• 0 citations
Publisher

Abstract

Quantum state collapse is a fundamental and perplexing problem in quantum mechanics, posing a significant challenge to our understanding of reality. This paper proposes a novel framework for analyzing this collapse, leveraging geometric topology to represent and predict the emergence of specific quantum states. We argue that classical mechanics, while useful for describing macroscopic phenomena, fails to adequately capture the intricate dynamics of quantum systems. This work introduces a new mathematical model – geometric topology – that allows us to visualize and analyze the collapse process with unprecedented precision. The framework will provide a new way to study the transition between quantum and classical states. We aim to develop a predictive tool that can assist in exploring the limits of quantum mechanics and potentially lead to a deeper comprehension of its underlying principles.

DOI
10.5281/zenodo.22515030

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Quantum state collapse is a fundamental and perplexing problem in quantum mechanics, posing a significant challenge to our understanding of reality. This paper proposes a novel framework for analyzing this collapse, leveraging geometric topology to represent and predict the emergence of specific quantum states. We argue that classical mechanics, while useful for describing macroscopic phenomena, fails to adequately capture the intricate dynamics of quantum systems. This work introduces a new mathematical model – geometric topology – that allows us to visualize and analyze the collapse process with unprecedented precision. The framework will provide a new way to study the transition between quantum and classical states. We aim to develop a predictive tool that can assist in exploring the limits of quantum mechanics and potentially lead to a deeper comprehension of its underlying principles.
Quantum state collapse is a fundamental problem in quantum mechanics, challenging our understanding of how quantum systems transition from a superposition of states to a definite outcome. This paper explores the application of geometric group theory to analyze this process, proposing a novel mathematical framework that offers a potentially more robust and intuitive model. The core claim is to develop a new mathematical framework for analyzing the collapse of quantum states, leveraging geometric group theory to understand the probabilistic nature of quantum processes. This involves creating a set of geometric transformations that can be applied to quantum states and deriving a probabilistic model based on these transformations. The paper details the theoretical foundation, proposes a specific geometric transformation scheme, and provides a preliminary analysis of its potential implications for understanding collapse. We argue that this approach enhances our ability to model and predict the behavior of quantum systems, particularly in the context of collapse analysis.
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