Elastic Universe Theory: Quaternionic and Elastic Unification of Physical Realitym

This work presents a comprehensive formulation of the Elastic Universe Theory (TUE), a unifying physical model where all observed phenomena—mass, time, energy, fields, and space-time curvature—emerge from the elastic deformation of the physical vacuum. The theory proposes that the vacuum is not empty but structured, continuous, and capable of tension and quantized oscillation.<br>We compare and integrate TUE with the quaternionic formalism developed by Danielewski and Sapa (2020), demonstrating that the quaternionic wavefunction naturally encodes the same internal geometry assumed by the elastic field. By representing the elastic displacement field as a quaternion , we show that mass, spin, curvature, and gauge interactions arise from internal rotation, amplitude, and orientation of this unified field.<br>The article includes seven chapters: theoretical foundations, formal postulates, detailed comparison with the Polish quaternionic model, structural unification, physical implications, cosmological consequences, and future research directions. The final unified model reproduces major observable constants (H₀, particle masses, CMB features) within experimental margins and proposes a falsifiable and testable geometric framework.<br>All content is original by the author Andrea Zanette, with editorial and mathematical assistance by ChatGPT-4 (OpenAI). This document is intended for open-access publication on Figshare.

本研究系统性阐述了弹性宇宙理论（Elastic Universe Theory, TUE）——这一统一物理模型认为，所有可观测现象——包括质量、时间、能量、场及时空曲率——均源于物理真空的弹性形变。该理论提出，真空并非空无一物，而是具有结构化、连续性特征，且可产生张力与量子化振荡。
本研究将TUE与Danielewski及Sapa于2020年提出的四元数形式体系进行对比并整合，证明四元数波函数可自然编码弹性场所假定的同一内在几何结构。通过将弹性位移场表示为四元数，本研究证明质量、自旋、曲率及规范相互作用均源于该统一场的内禀旋转、振幅与取向。
本文共包含七章：理论基础、形式公设、与波兰四元数模型的详细对比、结构统一、物理内涵、宇宙学推论以及未来研究方向。最终构建的统一模型可在实验误差范围内复现主要可观测常数（哈勃常数H₀、粒子质量、宇宙微波背景（Cosmic Microwave Background, CMB）特征），并提出了一个可证伪且可检验的几何框架。
本文所有内容均为作者Andrea Zanette的原创成果，ChatGPT-4（OpenAI）提供了编辑与数学协助。本文档拟于Figshare平台进行开放获取出版。