Relativity in Clifford's Geometric Algebras of Space and Spacetime

  title={Relativity in Clifford's Geometric Algebras of Space and Spacetime},
  author={William E. Baylis and Garret Sobczyk},
  journal={International Journal of Theoretical Physics},
Of the various formalisms developed to treat relativistic phenomena, those based on Clifford's geometric algebra are especially well adapted for clear geometric interpretations and computational efficiency. Here we study relationships between formulations of special relativity in the spacetime algebra (STA) Cℓ1,3 of the underlying Minkowski vector space, and in the algebra of physical space (APS) Cℓ3. STA lends itself to an absolute formulation of relativity, in which paths, fields, and other… 

The Complex Algebra of Physical Space: A Framework for Relativity

A complex and, equivalently, hyperbolic extension of the algebra of physical space (APS) is discussed that allows one to distinguish space-time vectors from paravectors of APS, while preserving the

On the value of geometric algebra for spacetime analyses using an investigation of the form of the self-force on an accelerating charged particle as a case study

The ability to treat vectors in classical mechanics and classical electromagnetism as single geometric objects rather than as a set of components facilitates physical understanding and theoretical

An Interpretation of Relativistic Spin Entanglement Using Geometric Algebra

Entangled states are often given as one of the most bizarre examples of “weirdness” described as inherent to quantum mechanics. The present work reinterprets entanglement as not being a property of

Quantum/Classical Interface: Fermion Spin

Although intrinsic spin is usually viewed as a purely quantum property with no classical analog, we present evidence here that fermion spin has a classical origin rooted in the geometry of


In 1908, Minkowski [13] used space-like binary velocity-field of a medium, relative to an observer. In 1974, Hestenes introduced, within a Clifford algebra, an axiomatic binary relative velocity as a

A Relativistic Algebraic Approach to the Q/C Interface: Implications for “Quantum Reality”

Abstract.Clifford’s geometric algebra, in particular the algebra of physical space (APS), provides a new relativistic approach to the Quantum/Classical interface. It describes classical relativistic

Spinors in Spacetime Algebra and Euclidean 4-Space

This article explores the geometric algebra of Minkowski spacetime, and its relationship to the geometric algebra of Euclidean 4-space. Both of these geometric algebras are algebraically isomorphic

Special relativity in complex vector algebra

Special relativity is one of the monumental achievements of physics of the 20thCentury. Whereas Einstein used a coordinate based approach [1], which ob-scures important geometric aspects of this

The covariant description of electric and magnetic field lines of null fields: application to Hopf–Rañada solutions

The concept of electric and magnetic field lines is intrinsically non-relativistic. Nonetheless, for certain types of fields satisfying certain geometric properties, field lines can be defined

Relativity in introductory physics

A century after its formulation by Einstein, it is time to incorporate special relativity early in the physics curriculum. The approach advocated here employs a simple algebraic extension of vector



Geometric Algebra for Physicists

Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with

Clifford Algebra: A Computational Tool for Physicists

1. A Taste of Clifford Algebra in Euclidean 3-Space 2. A Sample of Clifford Algebra in Minkowski 4-Space 3. Clifford Algebra for Flat n-Dimensional Spaces 4. Curved Spaces Embedded in Higher

Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics

1 / Geometric Algebra.- 1-1. Axioms, Definitions and Identities.- 1-2. Vector Spaces, Pseudoscalars and Projections.- 1-3. Frames and Matrices.- 1-4. Alternating Forms and Determinants.- 1-5.

Clifford algebra: What is it?

  • E. Bolinder
  • Mathematics
    IEEE Antennas and Propagation Society Newsletter
  • 1987
The participants, about 70 people from 20 countries constituted a motley crowd of mathematicians, physicists, and engineers, and the Proceedings of the workshop has been published as a book.

Quaternionic and Clifford Calculus for Physicists and Engineers

Electrodynamics: A modern geometric approach


  • 15, 1768–1777
  • 1974


  • Letters A :45–48 Jul
  • 1981

Acta Phys

  • Pol., Vol.B12, 509-521
  • 1981