# The Vector Algebra War: A Historical Perspective

@article{Chappell2015TheVA, title={The Vector Algebra War: A Historical Perspective}, author={James M. Chappell and Azhar Iqbal and John Gideon Hartnett and Derek Abbott}, journal={IEEE Access}, year={2015}, volume={4}, pages={1997-2004} }

There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs' three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, and quaternions used to describe rigid body rotations and vectors defined in Clifford geometric algebra. With such a range of vector formalisms in use, it thus appears that there is as yet no general agreement on a vector formalism suitable for science as a whole. This is surprising, in that, one…

## 22 Citations

### Time As a Geometric Property of Space

- MathematicsFront. Phys.
- 2016

The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which {\it `flows equably without relation to anything external'}. In the…

### The Simplest Form of the Lorentz Transformations

- Physics
- 2017

We report the simplest possible form to compute rotations around arbitrary axis and boosts in arbitrary directions for 4-vectors (space-time points, energy-momentum) and bi-vectors (electric and…

### The Poor Man ’ s Introduction to Tensors

- Education
- 2017

When solving physical problems, one must often choose between writing formulas in a coordinate independent form or a form in which calculations are transparent. Tensors are important because they…

### Dimensional scaffolding of electromagnetism using geometric algebra

- PhysicsEuropean Journal of Physics
- 2020

Using geometric algebra and calculus to express the laws of electromagnetism we are able to present magnitudes and relations in a gradual way, escalating the number of dimensions. In the…

### Algorithmic structure for geometric algebra operators and application to quadric surfaces

- Mathematics, Computer Science
- 2018

The proposed method is a hybrid solution that includes precomputed code with fast execution for low dimensional vector space, which is somehow equivalent to the state of the art method and for high dimensional vector spaces, a new recursive scheme is introduced and it is proved that associated algorithms are efficient both in terms of computationnal and memory complexity.

### Does Geometric Algebra Provide a Loophole to Bell’s Theorem?

- PhilosophyEntropy
- 2020

This paper aims to serve as a useful resource to those who need to evaluate new “disproofs of Bell’s theorem”, and identifies devices and misinterpretations in common use by other Bell critics.

### Time as a geometric property of space Frontiers in Physics, 2016; 4:44-1-44-6

- Mathematics
- 2016

of time itself. In order to answer this question we begin by exploring the geometric properties of three-dimensional space that we model using Clifford geometric algebra, which is found to contain…

### Explicit Baker–Campbell–Hausdorff–Dynkin formula for spacetime via geometric algebra

- MathematicsInternational Journal of Geometric Methods in Modern Physics
- 2021

We present a compact Baker–Campbell–Hausdorff–Dynkin formula for the composition of Lorentz transformations [Formula: see text] in the spin representation (a.k.a. Lorentz rotors) in terms of their…

### Comment on “Dr. Bertlmann’s Socks in a Quaternionic World of Ambidextral Reality”

- PhysicsIEEE Access
- 2021

I point out critical errors in the article “Dr. Bertlmann’s Socks in a Quaternionic World of Ambidextral Reality” by J. Christian, published in IEEE ACCESS, and suggest that a possible role for Geometric Algebra is still wide open and deserves further investigation.

### Why Newton’s Second Law is not F=ma

- PhysicsActa Scientiae
- 2019

The second law enunciated by Isaac Newton in the Principia is not equivalent to , as it is popularly known. The latter was described by Leonhard Euler, in 1752. However, for some historians, this…

## References

SHOWING 1-10 OF 49 REFERENCES

### Functions of Multivector Variables

- MathematicsPloS one
- 2015

A number of elementary functions extended to act over the skew field of Clifford multivectors, in both two and three dimensions are detailed, finding one key relationship that a complex number raised to a vector power produces a quaternion thus combining these systems within a single equation.

### Quaternion and Clifford Fourier Transforms and Wavelets

- Mathematics
- 2013

Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics,…

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

- Physics, Mathematics
- 2004

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…

### Why Does the Geometric Product Simplify the Equations of Physics?

- Mathematics
- 2002

In the last decades it was observed that Clifford algebras and geometric product provide a model for different physical phenomena. We propose an explanation of this observation based on the theory of…

### Geometric Algebra for Physicists

- Mathematics, Physics
- 2003

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…

### Geometric algebra for computer science - an object-oriented approach to geometry

- Computer ScienceThe Morgan Kaufmann series in computer graphics
- 2007

An introduction to Geometric Algebra that will give a strong grasp of its relationship to linear algebra and its significance for 3D programming of geometry in graphics, vision, and robotics is found.

### Geometry of Paravector Space with Applications to Relativistic Physics

- Physics
- 2004

Clifford’s geometric algebra, in particular the algebra of physical space (APS), lubricates the paradigm shifts from the Newtonian worldview to the post-Newtonian theories of relativity and quantum…

### 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…

### LIGHT POLARIZATION : A GEOMETRIC-ALGEBRA APPROACH

- Physics
- 1993

The geometric algebra of three‐dimensional space (the ‘‘Pauli algebra’’) is known to provide an efficient geometric description of electromagnetic phenomena. Here, it is applied to the…

### A geometric algebra reformulation of geometric optics

- Mathematics, Physics
- 2004

We present a tutorial on the Clifford (geometric) algebra Cl3,0 and use it to reformulate the laws of geometric optics. This algebra is essentially a Pauli algebra, with the Pauli sigma matrices…