# 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…

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