<b>The Invariance of Spacetime, the Light Cone Structure, and Quaternion Algebra</b>

This article explores the foundational principles of special relativity through the framework of quaternion algebra. It demonstrates how the Minkowski spacetime interval and the causal structure of the light cone (timelike, spacelike, lightlike) can be derived from the norm of a quaternion. The paper also discusses how the algebraic properties of quaternions naturally distinguish between the directed nature of time (real part) and the isotropic nature of space (imaginary part). Furthermore, it shows how Lorentz transformations, including rotations and boosts, can be represented elegantly using quaternion and biquaternion operations, suggesting a deep connection between the symmetries of physics and fundamental algebraic structures.

Publication Details

Journal
Figshare
Published
2025-01-01
DOI
https://doi.org/10.6084/m9.figshare.29847368.v1
Primary Topic
Algebraic and Geometric Analysis
Type
article
Field-Weighted Citation Impact
0.00
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The Invariance of Spacetime, the Light Cone Structure, and Quaternion Algebra

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Algebraic and Geometric Analysis
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The Invariance of Spacetime, the Light Cone Structure, and Quaternion Algebra

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Abstract

This article explores the foundational principles of special relativity through the framework of quaternion algebra. It demonstrates how the Minkowski spacetime interval and the causal structure of the light cone (timelike, spacelike, lightlike) can be derived from the norm of a quaternion. The paper also discusses how the algebraic properties of quaternions naturally distinguish between the directed nature of time (real part) and the isotropic nature of space (imaginary part). Furthermore, it shows how Lorentz transformations, including rotations and boosts, can be represented elegantly using quaternion and biquaternion operations, suggesting a deep connection between the symmetries of physics and fundamental algebraic structures.

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Openalex Percentile: Top 41%
Algebraic and Geometric Analysis
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<b>The Invariance of Spacetime, the Light Cone Structure, and Quaternion Algebra</b> · Figshare (2025) | TGRS Research Map | TGRS