# Relativity in Clifford's Geometric Algebras of Space and Spacetime

@article{Baylis2004RelativityIC, title={Relativity in Clifford's Geometric Algebras of Space and Spacetime}, author={William E. Baylis and Garret Sobczyk}, journal={International Journal of Theoretical Physics}, year={2004}, volume={43}, pages={2061-2079} }

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…

## 39 Citations

### The Complex Algebra of Physical Space: A Framework for Relativity

- Mathematics
- 2012

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…

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- Physics
- 2010

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

- Physics
- 2015

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

- Physics
- 2007

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…

### RELATIVITY GROUPOID INSTEAD OF RELATIVITY GROUP

- Mathematics, Physics
- 2007

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”

- Physics
- 2008

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

- Mathematics
- 2017

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

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- 2008

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

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- 2013

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

- Physics
- 2004

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…

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