Quaternions and Special Relativity

Abstract

We reformulate Special Relativity by a quaternionic algebra on reals. Using {\em real linear quaternions}, we show that previous difficulties, concerning the appropriate transformations on the $3+1$ space-time, may be overcome. This implies that a complexified quaternionic version of Special Relativity is a choice and not a necessity.

17 pages, latex, no figures

References in corpus (4)

• Generalized quantum dynamics
• Representations of U(1,q) and Constructive Quaternion Tensor Products
• Translations between Quaternion and Complex Quantum Mechanics
• Quaternion Higgs and the Electroweak Gauge Group

Cited by in corpus (23)

• Right eigenvalue equation in quaternionic quantum mechanics
• Octonionic Electrodynamics
• Clifford algebra approach of 3D Ising model
• Quaternionic differential operators
• Quaternions for Guts
• A comparative study of quaternionic rotational Dirac equation and its interpretation
• Matrix Representation of Octonions and Generalizations
• Mathematical structure of three - dimensional (3D) Ising model
• Octonionic Representations of GL(8,R) and GL(4,C)
• Geometrical Applications of Split Octonions
• Rotations in the Space of Split Octonions
• Quaternion Electromagnetism and the Relation with 2-Spinor Formalism
• On the quaternion transformation and field equations in curved space-time
• Quaternionic Electroweak Theory and CKM Matrix
• Imaginary in all directions: an elegant formulation of special relativity and classical electrodynamics
• A Nature-Inspired Feature Selection Approach based on Hypercomplex Information
• Generalized quaternionic free rotational Dirac equation and spinor solutions in the electromagnetic field
• A possibility of Klein Paradox in quaternionic (3+1) frame
• Extensions of real numbers using coset groups
• Exact solution of the three-dimensional (3D) Z2 lattice gauge theory
• Explicit Baker-Campbell-Hausdorff-Dynkin formula for Spacetime via Geometric Algebra
• Dirac and Maxwell systems in split octonions
• Enhancing Hyper-To-Real Space Projections Through Euclidean Norm Meta-Heuristic Optimization