# Contrastive analysis of two energy gradients in the ultra-strong magnetic fields

## TL;DR

This paper uses complex-octonions to analyze how ultra-strong magnetic fields influence the variable gravitational mass and energy gradients of particles, revealing that gravitational mass is not intrinsic but varies with field conditions.

## Contribution

It introduces a complex-octonion framework to analyze electromagnetic and gravitational fields simultaneously, deriving equations that show gravitational mass varies with field strength and energy.

## Key findings

- Gravitational mass is variable, not intrinsic.
- Energy gradients are measurable despite tiny mass variations.
- Octonion-based equations reveal new insights into field interactions.

## Abstract

The paper aims to apply the complex-octonions to explore the variable gravitational mass and energy gradient of several particles in the external ultra-strong magnetic fields. J. C. Maxwell was the first to introduce the algebra of quaternions to study the physical properties of electromagnetic fields. Some scholars follow up this method in the field theories. Nowadays, they employ the complex-octonions to analyze simultaneously the physical quantities of electromagnetic and gravitational fields, including the field potential, field strength, field source, linear momentum, angular momentum, torque, and force. When the octonion force is equal to zero, it is able to deduce eight independent equilibrium equations, especially the force equilibrium equation, precession equilibrium equation, mass continuity equation, and current continuity equation. In the force equilibrium equation, the gravitational mass is variable. The gravitational mass is the sum of the inertial mass and a few tiny terms. These tiny terms will be varied with not only the fluctuation of field strength and of potential energy, but also the spatial dimension of velocity. The study reveals that it is comparatively untoward to attempt to measure directly the variation of these tiny terms of gravitational mass in the ultra-strong magnetic field. However it is not such difficult to measure the energy gradient relevant to the variation of these tiny terms of gravitational mass. In the complex-octonion space, the gravitational mass is a sort of variable physical quantity, rather than an intrinsic property of any physical object. And this inference is accordant with the academic thought of `the mass is not an intrinsic property any more' in the unified electro-weak theory.