# Quaternion algebra on 4D superfluid quantum space-time. Gravitomagnetism

## TL;DR

This paper develops a quaternionic framework for gravitomagnetism, deriving equations that resemble Maxwell's, and links them to quantum mechanics and superfluid quantum space-time, revealing new insights into gravitational and quantum phenomena.

## Contribution

It introduces a quaternion-based approach to gravitomagnetism that generates equations connecting vortex dynamics, quantum potential, and wave phenomena in superfluid quantum space-time.

## Key findings

- Derivation of gravitomagnetic equations similar to Maxwell's equations.
- Identification of vortex solutions with infinite lifetime.
- Connection of these equations to the Schrödinger equation and Planck's radiation law.

## Abstract

Gravitomagnetic equations result from applying quaternionic differential operators to the energy-momentum tensor. These equations are similar to the Maxwell's EM equations. Both sets of the equations are isomorphic after changing orientation of either the gravitomagnetic orbital force or the magnetic induction. The gravitomagnetic equations turn out to be parent equations generating the following set of equations: (a) the vorticity equation giving solutions of vortices with nonzero vortex cores and with infinite lifetime; (b) the Hamilton-Jacobi equation loaded by the quantum potential. This equation in pair with the continuity equation leads to getting the \Schrodinger equation describing a state of the superfluid quantum medium (a modern version of the old ether); (c) gravitomagnetic wave equations loaded by forces acting on the outer space. These waves obey to the Planck's law of radiation.