Coordinate transformations in quaternion spaces

TL;DR

This paper explores how quaternion spaces can be used to derive various coordinate transformations, including Lorentz and Galilean, and introduces transformations with variable light speed in electromagnetic and gravitational fields.

Contribution

It presents a method to derive coordinate transformations in quaternion spaces, extending traditional transformations to include variable light speed scenarios.

Findings

Derived Lorentz and Galilean transformations in quaternion spaces

Introduced coordinate transformations with variable light speed

Connected quaternion properties to electromagnetic and gravitational fields

Abstract

The quaternion spaces can be used to describe the property of electromagnetic field and gravitational field. In the quaternion space, some coordinate transformations can be deduced from the feature of quaternions, including Lorentz transformation and Galilean transformation etc., when the coordinate system is transformed into others. And some coordinate transformations with variable speed of light can be obtained in the electromagnetic field and gravitational field.