Quaternions & Relativité
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| Format: | Recurso digital |
| Langue: | français |
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Zenodo
2014
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| _version_ | 1866902116573904896 |
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| author | Hardt Lalinne, Gregory |
| author_facet | Hardt Lalinne, Gregory |
| contents | <p><strong>Context:</strong> Titled "Quaternions & Relativité", this 2013-2014 research project (MA1) provides the physical and intuitive foundations for the author's later work. While the 2015 Master's Thesis focuses on Möbius transformations and compass-and-straightedge constructions, this monograph explores the relativistic model with a broader and more detailed physical scope.</p> <p><strong>Key Highlights:</strong></p> <ul> <li> <p><strong>Kinematics & Relativity:</strong> Detailed exploration of the <strong>Twin Paradox</strong> with original illustrations and worked examples, using unit quaternions to represent velocity.</p> </li> <li> <p><strong>Velocity Addition:</strong> Introduction of a preliminary quaternionic addition formula, supported by empirical validation via <strong>Python simulations</strong> (testing the non-commutative case).</p> </li> <li> <p><strong>Algebraic & Geometric Digressions:</strong> Study of <strong>Hurwitz Quaternions</strong>, the Four-Square Theorem, and "Spherical Trigonometry" through involutive automorphisms of the Real Projective Plane.</p> </li> <li> <p><strong>Differential Structure:</strong> Early treatment of quaternions as a differential (non-commutative) algebra, using commutators as derivations.</p> </li> </ul> <p>This document is the "conceptual lab" where the core ideas were born, providing the detailed physical intuitions that were sometimes abbreviated in the more formal 2015 Thesis (DOI: 10.5281/zenodo.18320378).</p> <p>Together with the 2015 Thesis, this manuscript serves as the historical and mathematical precursor to the author's forthcoming 2026 monograph (<a title="Quaternionic Möbius Transformations: a Different Approach to Relativistic Kinematics" href="https://doi.org/10.5281/zenodo.18344596" rel="noopener">10.5281/zenodo.18344596</a>).</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18322428 |
| institution | Zenodo |
| language | fra |
| publishDate | 2014 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Quaternions & Relativité Hardt Lalinne, Gregory Quaternions Special Relativity Twin Paradox Velocity Addition Formula Hurwitz Quaternions Four-Square Theorem Spherical Trigonometry Noncommutative Algebra Differential Algebra Python Simulation Kinematics Real Projective Plane Quaternionic Möbius Transformations Gyrogroup Poincaré Half-Space <p><strong>Context:</strong> Titled "Quaternions & Relativité", this 2013-2014 research project (MA1) provides the physical and intuitive foundations for the author's later work. While the 2015 Master's Thesis focuses on Möbius transformations and compass-and-straightedge constructions, this monograph explores the relativistic model with a broader and more detailed physical scope.</p> <p><strong>Key Highlights:</strong></p> <ul> <li> <p><strong>Kinematics & Relativity:</strong> Detailed exploration of the <strong>Twin Paradox</strong> with original illustrations and worked examples, using unit quaternions to represent velocity.</p> </li> <li> <p><strong>Velocity Addition:</strong> Introduction of a preliminary quaternionic addition formula, supported by empirical validation via <strong>Python simulations</strong> (testing the non-commutative case).</p> </li> <li> <p><strong>Algebraic & Geometric Digressions:</strong> Study of <strong>Hurwitz Quaternions</strong>, the Four-Square Theorem, and "Spherical Trigonometry" through involutive automorphisms of the Real Projective Plane.</p> </li> <li> <p><strong>Differential Structure:</strong> Early treatment of quaternions as a differential (non-commutative) algebra, using commutators as derivations.</p> </li> </ul> <p>This document is the "conceptual lab" where the core ideas were born, providing the detailed physical intuitions that were sometimes abbreviated in the more formal 2015 Thesis (DOI: 10.5281/zenodo.18320378).</p> <p>Together with the 2015 Thesis, this manuscript serves as the historical and mathematical precursor to the author's forthcoming 2026 monograph (<a title="Quaternionic Möbius Transformations: a Different Approach to Relativistic Kinematics" href="https://doi.org/10.5281/zenodo.18344596" rel="noopener">10.5281/zenodo.18344596</a>).</p> |
| title | Quaternions & Relativité |
| topic | Quaternions Special Relativity Twin Paradox Velocity Addition Formula Hurwitz Quaternions Four-Square Theorem Spherical Trigonometry Noncommutative Algebra Differential Algebra Python Simulation Kinematics Real Projective Plane Quaternionic Möbius Transformations Gyrogroup Poincaré Half-Space |
| url | https://doi.org/10.5281/zenodo.18322428 |