Unified Field Model of Gravitation and Electromagnetism

This is a continuation of the post New Newtonian Cosmology - Universe from Nothing. We know from experience that creation of material goods from nothing is not possible. To make a soup we need ingredients. So it is natural to ask from where the ingredients came to the Big Bang as the postulated incredibly hot primordial soup as the origin of the Universe we are part of. But we get no answers from physicists proclaiming Big Bang. 

Another possibility is that the Universe came out of virtually Nothing from the equation

• $\Delta (\phi + \psi ) = \rho + \epsilon$ 

where $\psi =-\phi$ and $\epsilon =-\rho$ as formally 

• $\Delta 0 = 0$ as Nothing out of Nothing,

where $\Delta$ is the Laplacian differential operator with respect to a Euclidean coordinate $x$, $\phi (x)$ is a gravitational potential with corresponding mass density $\rho (x)$, and $\psi (x)$ is an electric potential with corresponding charge density $\epsilon$. 

The potentials generate a gravitational force $F_g$ expressing Newton's Law of Gravitation and an electric force $F_e$ expressing Coulomb's Law:  

• $F_g=-\rho\nabla\phi$                            (1)
• $F_e =\epsilon\nabla\psi = \rho\nabla\phi$      (2)

with the force balance: 

• $F_g+F_e=0$. 

We consider an initial zero state as cancelling small-amplitude micro-scale fluctuations $\phi$ and $\psi =-\phi$ generating by the action of the Laplacian large-amplitude micro-scale cancelling fluctuations $\rho$ and $\epsilon =-\rho$ both of variable sign, while the corresponding forces have the following characteristics:

• $F_g$: attraction/repulsion between mass density of same/opposite sign.
• $F_e$: repulsion/attraction between charge density of same/opposite sign.

By the action of the gravitational force, macro-scale collections of large-amplitude positive and negative mass density can form by attraction, which by repulsion separates into widely separated supermacro-scale Universa with either positive or negative mass density, where our Universe has positive mass. 

The action of the electric force is opposite with the effect that large-amplitude micro-scale fluctuation into positive and negative charge will be maintained in the form of atoms, while macro-scale electric effects cancel to zero. It is natural to assume that the initial fluctuation has atomic scale. 

More precisely, atoms can form on micro-scale by attractive electric forces while microscope repulsive gravitational forces can cause an expansion in space separating electric and gravitational effects into short and long range.

We thus find that from a unified zero state split into balancing gravitational and electric potentials an evolution may follow by balancing gravitational and electric potentials/forces into a Universe with positive mass density subject to gravitation as a large-amplitude macro-scale force, combined with a variable-sign charge density subject large-amplitude micro-scale electric force.  

The basic ingredient to this soup is the Laplacian differential operator capable of generating balancing potentials with corresponding initially balancing mass/charge densities subject to initially balancing gravitational/electric forces. Gravitational force then comes out to act on macro-scale while Coulomb electric force acts on micro-scale. 

This can be seen as a unified field model including both gravitation and electrics generated from a common source balancing to zero. Magnetics is then to be added into electromagnetics with light/radiation as new phenomenon.

The micro-scale of Coulomb electric force connects to Schrödinger's equation for quantum mechanics and it remains to understand how the split into micro-scale of electrics and macro-scale of gravitation is formed.

We see that that Newtonian gravitational forces and electric Coulomb forces may have a common origin so that in particular there is no incompatibility between Newtonian gravity and electromagnetism/quantum mechanics.  On the other hand, Einstein's theory of gravitation is viewed to be incompatible with quantum mechanics, an idea which has traumatised modern physics. It appears to be possible to get out of the the trauma by returning to Newtonian gravity, but this not allowed since progress requires that Einstein has dethroned Newton.  

One-Stage of scenario

Mass density from gravitational potential with Newtonian gravitational force:

• Initial small-scale mass density $\rho (x)$ of variable sign expands by repulsion into macro-scale.
• Regions of positive and negative mass density form which reced by repulsion. 
• A Universe with positive mass density forms separated from negative counterpart.
• Gravitational collapse within Universe form galaxies of stars with planets. 

Charge density from electric potential with electric Coulomb force:

• Initial small-scale charge density $\epsilon (x)$ of variable sign representing protons and electrons contracts by attraction into micro-scale of Hydrogen atom as a proton kernel surrounded by electron cloud. 
• Gravitational collapse gives energy to fusion of electron and proton into neutron as electron kernel surrounded by proton cloud, and atomic kernels of protons and neutrons surrounded by electron cloud.
• Atomic kernels formed by attractive gravity force (strong force) stronger than repulsive Coulomb force on micro-micro scale.   

The main idea is thus

• variable sign mass and charge energy densities initially emerge from balancing gravitational and electric potential fluctuations with balancing gravitational and electric forces
• gravitational forces drive expansion of mass density into macro-scale
• electric forces drive contraction of charge densities into micro-scale
• altogether forming a Universe of positive mass density with gravitational attraction on macro-scale combined with electric forces acting on variable charge densities on micro-scale
• combined with attractive gravitational force on micro-micro-scale (strong force).     

Two-Stage Scenario

Instead of a initial one-stage scenario, it is possible to speculate about a two-stage scenario where first mass density of variable sign is created by a gravitational potential micro-scale fluctuation, which expands by repulsion between mass densities of different sign into a macro-scale Universe of positive mass density with its negative counterpart disappearing out of sight while keeping some gravitational connection.  

In a second stage charge density of variable sign in the form of protons with charge +1 and electrons with charge -1 which do not overlap, may be created by an electric potential micro-scale fluctuation, which is maintained by attraction between protons and electrons. Protons and electrons do not annihilate or disintegrate and so keep their unit charge expressed as charge conservation. The second stage then connects to the first stage by assigning positive mass density to both protons and electrons with ratio of 1836 to 1. The scene is then set for formation of atoms followed by gravitational collapse into stars and galaxies and heavier atoms. 

The spatial extension of both charge and mass density may vary and be different for both protons and electrons depending on circumstances, with a proton having less extension than an electron in an atom. Different charge and mass density extensions may explain why electric forces dominate on atomic and gravitational forces dominate on macro-scale. 

In a Hydrogen atom a point-like proton is surrounded by an electron density cloud. It is possible to think of a neutron as a point-like electron surrounded by a proton cloud. 

The strong nuclear force may possibly be seen as a micro-micro scale gravitational force resulting from a very small mass density extension of a proton and neutron. 

The micro-scale is in precise terms expressed in the form of Real Quantum Mechanics with atoms as non-overlapping clouds of positive and negative charge densities held together by attractive electric forces.  

Summary

1. Gravitational potential fluctuation $\phi (x)$ creates mass density $\rho (x)=\Delta\phi (x)$ of variable sign. Repulsion between mass densities of different sign drives expansion into large scale separation of a Universe with positive mass density or matter from a counterpart with negative mass density. 
2. Electric potential fluctuation $\psi (x)$ creates charge density $\epsilon (x)=\Delta\psi (x)$ of variable sign. Attraction between charge densities of different sign drives contraction into micro-scale of protons and electrons of unit charge emerging as gravitational matter and combining into Hydrogen atoms. 
3. Gravitational collapse of a minor part of the matter in Universe creates by fusion from Hydrogen visible galaxies of stars, while the remaining major part remains as invisible gravitational dark matter.