Hyperbolic Relational Spacetime

In this work, we present an idea unifying aspects of Special Relativity (SR) and quantum mechanics through the concept of worldline coherence and decoherence. We show that both relativistic effects—such as simultaneity and time dilation—and quantum-like superposition emerge relationally, becoming physically observable only upon intersection of worldlines. Building on this relational approach, we introduce a toy metric generated by hyperbolic functions of relative rapidity between worldlines. This emergent geometry produces curvature and geodesic bending analogous to gravitational effects, providing a conceptual bridge between spacetime structure and gravitation. Importantly, this framework: Derives time and apparent causal order as emergent from relational interactions, not as absolute properties. Recovers the phenomenology of Special Relativity and quantum superposition in a unified relational picture. Produces emergent curvature and “gravity-like” effects without introducing mass or energy explicitly. Highlights sensitivity to initial spacetime configuration, paralleling emergent retrocausal phenomena. Unlike Loop Quantum Gravity or other discrete spacetime approaches, this framework does not rely on spin networks or pre-quantized geometry, but rather on continuous relational coherence between worldlines. The relational nature of both time and metric implies that: Effects such as time dilation are frame-dependent and manifest only upon worldline intersection. Quantum superposition is naturally represented by multiple possible configurations prior to intersection (decoherence). Emergent curvature can mimic gravitational phenomena in a toy model, though it does not yet produce Newton’s constant or the Einstein Field Equations. This work suggests a paradigm where spacetime, time, and curvature are relationally emergent, providing a conceptually simpler, potentially more intuitive framework than current quantum gravity approaches, while remaining fully consistent with Special Relativity. It lays the foundation for future explorations of gravity, quantum information, and retrocausality as emergent properties of relational spacetime configurations. This manuscript is current in Official Peer Review. Not final version.Copyright©2026 Alex De Giuseppe.All rights reserved. This work is protected by copyright. Any form of plagiarism, unauthorized reproduction, or misappropriation of ideas, mathematically results, or text without proper citation constitutes a violation of academic and intellectual property standards and common laws. No commercial use, adaptation, or derivative works are permitted without explicit written permission from the author. For correspondence, citations, collaboration inquiries, or feedback please contact:[e-mail] The hash files that determine ownership have been created本研究提出了一种通过世界线相干性（worldline coherence）与退相干（decoherence）概念统一狭义相对论（Special Relativity）与量子力学核心内涵的思路。我们证明，相对论效应（如同时性与时间膨胀（time dilation））以及类量子叠加均以关系性方式涌现，仅当世界线相交时才具备可观测的物理意义。 基于这一关系性研究框架，我们引入了由世界线间相对快度（relative rapidity）的双曲函数生成的玩具模型度规。该涌现几何会产生曲率与测地线弯曲，其特性与引力效应类似，为时空结构与引力之间搭建了概念性桥梁。值得注意的是，本框架具备如下特点： - 将时间与表观因果序推导为关系性相互作用的涌现产物，而非绝对固有属性。 - 在统一的关系性图景中复现狭义相对论与量子叠加的现象学特征。 - 无需显式引入质量与能量，即可生成涌现曲率与“类引力”效应。 - 凸显对初始时空构型的敏感性，这与涌现逆因果现象相一致。 与圈量子引力（Loop Quantum Gravity）及其他离散时空研究路径不同，本框架不依赖自旋网络（spin networks）或预量子化几何，而是基于世界线间的连续关系性相干性。时间与度规的关系性本质意味着： - 诸如时间膨胀的效应依赖参考系，且仅在世界线相交时才会显现。 - 量子叠加可自然地表示为相交前的多种可能构型，即退相干过程。 - 玩具模型中的涌现曲率可模拟引力现象，但目前尚未能推导出牛顿引力常数或爱因斯坦场方程（Einstein Field Equations）。 本研究提出了一种时空、时间与曲率均为关系性涌现的范式，相较于当前量子引力研究路径，该范式在概念上更为简洁直观，且完全契合狭义相对论的理论框架。它为后续将引力、量子信息与逆因果性作为关系性时空构型的涌现属性开展探索奠定了基础。 本稿件目前处于正式同行评审阶段，尚未定稿。版权所有©2026 Alex De Giuseppe，保留所有权利。 本作品受版权保护。任何形式的抄袭、未经授权复制或未经适当引用即挪用本文的思想、数学结果或文本，均违反学术规范与知识产权准则及普通法。 未经作者明确书面许可，不得进行商业使用、改编或创作衍生作品。 如需通信、引用、合作咨询或反馈，请联系：[e-mail] 已创建用于确定权属的哈希文件。