Energy as a complex number

Equations of gravity and electromagnetism exhibit structural similarities. After a convertion of units,
the pattern we see could be mathematically explained in terms of complex variables, this expression ends up capturing some aspects of both fields
in a compact notation.

: energy,

: mass,

: speed of light,

: complex unit,

: charge,

: vacuum permittivity,

: universal gravitational constant

Classical mechanics

Given that
Coulomb's inverse-square law [1]
takes the form of
Newton's law of universal gravitation [2]
if we write:

It seems reasonable to explore the use of complex numbers, as a data structure,
to treat electrostatics in a gravitational context.

Given the assumption:

Mass would be:

A complex gravitational potential defined as:

would hold enouh information to describe the classical static interaction with a different body. Which could provide a framework to justify why
we don't seem to messure direct attraction/repulsion between
mass and charge, since the representation of this interaction
is caught in the imaginary part of:

Special Relativity

Consider a complex Momentum P

: mass energy contribution

: charge energy contribution

To write:

being:

Which suggests that magnetic forces could be expressed in terms of P.

Electromagnetism

The description of Gravitoelectromagnetism [3]
already gives us a good picture of the pattern. Converting Coloumbs into Kilograms using the following convertion factor,
and allowing variables to be complex:

The full set of equations could be written as:

Subscripts m and e,
refer to massive and electric quantities.

Lastly

A complex number seems to be a suitable data structure to hold information about energy for certain calculations.
Schrodinger equation,
already deals with complex numbers, perhaps it is describing something similar.
The energy of a photon would be a complex number too, just as the energy of an electron,
making the absortion/emmision of a photon, comprehensible in terms of energy flow.

The study of a complex metric tensor, as the result of expressing it in terms of a complex potential, is left out of this document, and
would be the subject of a second document.

Schwarzschild radius would be a complex number, which suggests that a change in the frame of reference could allow us to express
the metric in terms of real numbers, forcing us to rotate, in the complex sense, the 4 momentum of a test particle, which would make
it look with a different mass/charge distribution, even with negative mass, which in turn suggests that mass could be a relative quantity.

References

1. Wikipedia, Coulomb's inverse-square law

2. Wikipedia, Newton's law of universal gravitation

3. Wikipedia, Gravitoelectromagnetism

4. Wikipedia, Minkowski metric

5. Wikipedia, Schwarzschild metric

6. Carlos Francisco Romero Madrid, Derivation of the Metric of Reissner-Nordström and Kerr-Newman Black Holes, 2018

7. Guansheng He, Exact Harmonic Metric for a Uniformly Moving Schwarzschild Black Hole
Article in Communications in Theoretical Physics · January 2014 261016243

8. Richard A. Hutchin, A Natural Combination of Gravity and Electromagnetism, Journal of Modern Physics, 2015, 6, 749-757
2015.66080

9. Bahram Mashhoon, Gravitoelectromagnetism: A Brief Review
0311030

10. Athanasios Bakopoulos, Gravitoelectromagnetism: Basic principles, novel approaches and their application to Electromagnetism
1610.08357

This equation was first digitally written and cryptographically signed on Sep-04-2022 09:46:26 PM +UTC as shown in "decoded input data" in the "more details" section of the following link:

E = Y*(m + i*Q/(4*pi*e0*G)^(1/2))*C^2

This document is licensed under CC BY: Creative Commons Attribution

Marcelo Villarreal Fasanelli - emq.guy@gmail.com

E = Y*(m + i*Q/(4*pi*e0*G)^(1/2))*C^2

This document is licensed under CC BY: Creative Commons Attribution

Marcelo Villarreal Fasanelli - emq.guy@gmail.com