Some theorems in gravitational and electromagnetic fields

TL;DR

This paper explores how velocity curl and field strength influence fundamental theorems in gravitational and electromagnetic fields using quaternion algebra, deriving key conservation laws and examining their dependencies.

Contribution

It introduces a quaternion-based framework to analyze the effects of field strength and velocity curl on classical theorems in physics, providing new insights into their interrelations.

Findings

Field strength directly affects some theorems.

Velocity curl influences certain theorems.

Quaternion algebra facilitates derivation of conservation laws.

Abstract

The paper discusses the influences of velocity curl and field strength on some theorems in the electromagnetic field and gravitational field. With the characteristics of the algebra of quaternions, the theorem of linear momentum, conservation of linear momentum, and conservation of angular momentum etc. can be deduced from the quaternionic definitions of physical quantities. And the strength of gravitational field and electromagnetic field have an influence on some theorems directly. While the velocity curl has an effect on some theorems also.