Unified Field Theory: Newton + Maxwell + RealQM

Schrödinger created Quantum Mechanics by formulating in 1926 a mathematical model within classical continuum mechanics in terms of a wave function $\psi (x,t)$ depending on a 3d space coordinate $x$ and a time coordinate $t$ satisfying a wave equation named Schrödinger's Equation SE: 

• $i\frac{\partial\psi}{\partial t}+H\psi =0$     (SE)

with 

• $H=-\frac{1}{2}\Delta -\frac{1}{\vert x\vert}$ a Hamiltonian differential operator.

The eigenvalues of SE showed to exactly fit with the observed spectrum of a Hydrogen atom and so was the answer to a search begun by Bohr 15 years before. The success was complete: SE revealed the secret of the Hydrogen atom as an eigenvalue problem for a Hamiltonian with time-independent normalised real-valued eigenfunctions $\Psi (x)$ with energies as sum of kinetic and potential energies appearing as eigenvalues:

• $E = E_{kin}+E_{pot}=\frac{1}{2}\int\vert\nabla\Psi\vert^2dx-\int\frac{\Psi^2(x)}{\vert x\vert}dx.$ 

The ground state of a Hydrogen atom took the physical form of a charge density $\Psi^2(x)$ with minimal energy appearing as a compromise of negative $E_{pot}$ by concentration near $x=0$ balanced by a positive $E_{kin}=-\frac{1}{2}E_{pot}$ appearing as a form of "compression energy".

SE took the form of classical continuum mechanics with a clear physical interpretation as charge density and so represented a complete success of classical mathematical physics suddenly expanding its excellent service from macroscopics into atomic microscopics. 

SE combines perfectly with Newtonian gravitation giving $\Psi^2(x)$ a double role as both charge density and mass density, as well as with Maxwell's electro-magnetics. The resulting Newton-Maxwell Schrödinger NMS model was a Unified-Field-Theory covering all of Hydrogen physics from galactic to atomic scales. A tremendous success of mathematical modelling of real physics! Since Hydrogen accounts for 74% of the mass of the Universe NMS captured nearly everything.

But 25% is Helium and 1% all the other atoms, and so SE had to be extended to atoms with more than one electron like Helium with two electrons to qualify as UFT. But how?

A quick formal resolution lay on the table: Give each new electron a whole set of 3d coordinates and trivially extend (SE) to any atom with a stroke of a pen. That gave a wave function depending on $3N$ space coordinates for an atom $N$ electrons. Easy to do but without clear physical meaning. 

Schrödinger refused to take this step, but Bohr-Born-Heisenberg jumped on the band wagon of Standard Quantum Mechanics StdQM based on a multi-d Schrödinger equation forming the foundation of modern physics under heavy protests from Schrödinger because it replaced causality and physicality by non-physical probabilities of observer measurement outcomes. 

In short StdQM is viewed to be the result of a process of quantisation preventing unification with the classical continuum physics of Newton and Maxwell, which has grown out into the deep crisis of modern physics of today.

Since Maxwell and Newton represent perfect theories, without any need of quantification, the natural idea to form a UFT is to search for a form of QM without quantification. But this has been prevented for 100 years by the very strong domination of the Copenhagen Interpretation of Bohr-Born-Heisenberg. Efforts have been made of  "dequantisation" of StdQM bringing it back to classic continuum physics (e g Bohmian mechanics), but without success because quantification cannot be reversed. 

RealQM offers a generalisation of SE for Hydrogen to atoms with more than one electrons, which stays within the realm of classical continuum physics, and so combines perfectly with Newton and Maxwell into a UFT.  

 

Unified Field Model as Macro-Micro Continuum Model

It was Niels Bohr who in the 1920s implanted the idea into modern physics that the microscopic world of atoms cannot be understood/described using the concepts of classical physics, which had served so well to describe the macroscopic world we can directly experience. The new understanding/description took the form of Quantum Mechanics QM based on a multi-dimensional Schrödinger Equation SE of a non-classical form. 

With the help of Heisenberg Bohr managed to let his idea take over modern physics into our days, on the way crushing Schrödinger asking for "Anschaulichkeit" or "possible to visualise" as understanding in terms of classical physics. The essence of the Bohr-Heisenberg dogma was:

• Only observation/measurement counts. Underlying ontology left out. Visualisation impossible.
• Complementarity: Contradicting physics allowed. Both particle and wave.
• Uncertainty Principle: Limit to what can be measured.
• Separation ontology (classic, what is) and epistemology (new, what we can say)

The result today is a science of physics in a state of crisis. The new concepts required by Bohr could never be clarified resulting in a QM which "nobody can understand" in the words of Richard Feynman. The basic form of a classical mathematical model of the physics of a solid, fluid or gasses is a partial differential equation involving functions $u(x,t)$ depending on a real variable/spatial coordinate $x$ ranging over some domain in 3d space and a time coordinate $t$. This is a continuum mechanics model with the set of real numbers offering space as a continuum without preset smallest spatial scale. The function $u(x,t)$ could represent the density at time $t$ of a fluid with $x$ ranging over the 3d domain occupied by the fluid.

Continuum mechanics as classical physics is described by a mathematical model covering all physical scales from micro to macro and thus does not single out micro-scopics as conceptually different from macro-scopics, which could be the case if macro-scopics is "continuous" and microscopics "discrete".

In continuum mechanics both micro- and macro-scopics are "continuous". Nothing is "discrete". No "particles". The continuum of real numbers can represent a continuum mechanics without smallest scale.

The multi-d SE depends on continuous spatial variables, and in this sense is a continuum model, but not a classical continuum model since the continuum is not 3d (for system with more than one electrons). 

RealQM offers a different Schrödinger equation as a non-linear system of non-overlapping charge densities in 3d thus in the form of classical continuum mechanics with a seamless connection to macro-scopics. 

It is thus possible to formulate a Unified Field Model combining classical Newtonian continuum models like Navier-Stokes and Maxwell's equations with a Schrödinger equation of the same principal form. This was what Einstein tried to accomplish, but did not succeed with because he was stuck with a perceived incompatibility between General Relativity and QM.  

 

Physical Laws without Physics vs Unified Field Theory

Standard Quantum Mechanics StdQM as one of the two pillars of modern physics, is based on concepts of formal rather than physical nature decribing the microscopic world of atoms: 

• Hilbert space
• observable as Hermitian operator
• Pauli Exclusion Principle
• antisymmetric and symmetric wave functions, fermions
• indistinguishable electrons 
• Heisenberg Uncertainty Principle
• wave-particle duality
• complementarity
• wave function as probability
• unitary transformation
• collapse of the wave function
• kinetic energy without motion
• exchange integral
• Slater determinant
• Gaussian.

We may compare with classical (macroscopic) physics with basic concepts: 

• force
• mass 
• kinetic energy 
• potential energy
• work
• position, displacement
• velocity
• acceleration
• physical extension
• volume
• density
• temperature.

We see that StdQM appears to be fundamentally different from classical physics as if the atomic world cannot be described and understood in terms of the same concepts as the macroscopic world. 

Real Quantum Mechanics RealQM offers a different picture with the microscopic world described and made understandable in terms of the same concepts as the macroscopic world, just on a smaller scale, both as forms of continuum mechanics with the continuum carrying all scales. 

If RealQM indeed shows to give a description of the world of atoms of the same form as the classical continuum models of mechanics and electromagnetics, Einstein's dream of a Unified Field Theory maybe can be realised, at least if Newton is allowed to take care of gravitation. 

Why No Unified Atom-Nucleus Model?

The previous post presented RealQM = RealAtom + RealNucleus appearing to be the first computable unified model of an atom including nucleus with full quantum mechanical representation in the form of non-overlapping charge densities of both electrons and protons interacting by Coulomb potentials. 

Is this really the first full quantum mechanical model of an atom + nucleus? What have theoretical physicists been doing during the 100 years since the advent of quantum mechanics in 1925? 

Yes, at least according to chatGPT, telling that there is QED for atoms = electrons+point-wise nuclei and QCD for nuclei = quarks and gluons, but QED and QCD represent different "sectors" and cannot be unified:

• There is currently no fully computable, unified quantum mechanical model of an , "atom that includes both the electrons and the atomic nucleus in full quantum detail and that is tractable for general-purpose computation.

How can this be? Is this the concrete meaning of the "crisis of modern physics" proclaimed by leading theoretical physicists? Is it a consequence of all the unresolved contradictions present in the mathematical foundations of quantum mechanics including "wave-particle duality", "complementary principle", "collapse of the wave function", "measurement problem", "statistical interpretation", "uncertainty principle", "exclusion principle", "anti-symmetry", "Born rule", "exchange energy", "indistinguishability of identical particles", "electron orbitals", "superposition", "entanglement", "decoherence", "spin-orbit coupling" + all the wonders of QCD…? 

When I ask if the lack of a unified atom-nucleus model is a sign of failure/crisis of modern physics, chatGPT explains:

• The lack of a unified, computable atomic-nuclear theory is not a failure — it's a reflection of the extraordinary success and specialization of the theories we already have (QED and QCD).  

This is the tragedy of modern physics: Too successful to fail. Like a Big Bank or Great Empire. If you find chatGPT's argument convincing, you have a position at a department of fundamental physics (about to collapse from missing unified theory).

RealQM: Unified Field Theory/Model

If you (like Einstein) have been looking for a unified field theory including both quantum mechanics and gravitation in a single mathematical framework, here is something to inspect to see if it meets your criteria of a unified theory in its form of RealQM.

RealQM offers a mathematical model of atoms and atomic nuclei in a form of classical continuum mechanics as systems of non-overlapping charge densities interacting by Coulomb potentials/forces. RealQM directly extends to Newtonian gravitation in its form of classical continuum mechanics. 

The previous post gave the last piece to this puzzle in the form of a model of atomic nuclei as composed of protons and electrons interacting by Coulomb potentials without need of the strong/weak force of the Standard Model. 

Recall that the search for a unified model has been going on for a long time and physicists of today still repeat a 100 year old mantra that quantum mechanics and Einstein's general theory of relativity/gravitation as the pillars of the immense success of modern physics, are incompatible and so pulls the carpet under the success. So physicists have desperately been searching to squeeze one theory into the other as quantum gravity or quantum relativity, but without notable success. 

It is agreed that Newtonian gravitation covers all situations but some very extreme cases. RealQM with Newtonian gravitation thus offers a unified model covering all scales from atomic to cosmic scales. I am searching for at least one physicist open to discussion of such a possibility. Maybe this is all fiction, but maybe it has a connection to reality...maybe fundamental physics is not infinitely complex...

RealQM is presented in series of short easy to digest articles here.

The World = Differentiation + Integration

The mathematics of the Calculus of Leibniz and Newton allows a description of the World as the result of competing actions between differentiation and integration expressed as the Fundamental Theorem of Calculus as follows in non-technical terms: 

• differentiation followed by integration = no change
• integration followed by differentiation = no change 

thus with differentiation the inverse of integration and vice versa. In other words, the World can be seen as a competition/combination between 

• increasing difference: separation: differentiation as local process: destabilising
• decreasing difference: mixing: integration/summation as global process: stabilising.

In the previous posts we saw that small scale mass density and charge density can be "created" by differentiation seemingly "out of nothing" followed by integration to create large scale order over time. The kinetic energy driving this process comes from concentration of matter with decreasing gravitational potential energy. Details of this process is given in the books listed on the blog including in particular Computational Thermodynamics and The Clock and the Arrow decoding the direction of time, together with Real Quantum Mechanics decoding atom physics.

Calculus describes a World with positive mass and charge of variable sign, generated by the Laplacian differential operator, geared by gravitational force on large scale and arising from integration electrostatic force on small scale.

Creating the Universe by Plucking a String 2

The previous post outlined a possible mechanism to create a large scale Universe $U$ of non-negative mass density $\rho$ from a small scale small amplitude perturbation of a zero gravitational potential with mass density "created" from a gravitational potential $\phi$ by the instant action of the Laplacian differential operator $\Delta$ acting in a Euclidean space with coordinate $x$ according to the assignment   

•  $\rho (x,t)= \Delta\phi (x,t)$ for all $x$ and $t>0$,               (G)

where $t$ is a time coordinate starting at time $0$. The only force in $U$ so far is gravitational force $-\rho\nabla\phi$ which together with Newton's 2nd Law describes the dynamics in $U$, which is large scale.

The physics of $U$ is in a second step expanded with an electric potential $V$ with electric field $E=\nabla V$ as a small scale small amplitude perturbation of a zero electric potential with small scale large scale amplitude electric charge $q$ of variable sign created by an assignment analogous to (G):

• $q(x,t)=\Delta V(x,t)$ for all $x$ and $t>0$,                          (E)                 

with $q=q_++q_-$ split into $q_+\ge 0$ and $q_-\le 0$. A further contribution is given by connecting $E$ to a magnetic field $B$ through Maxwell's equations into electro-magnetics.

The result is a Universe including large scale large amplitude physics of gravitation and small scale large amplitude electro-magnetics created from small amplitude perturbations according to (G) and (E) through the action of $\Delta$, as a Universe created by plucking two strings. 

Note the fundamental difference: 

• Gravitational force is attractive/repulsive between masses of same/opposite sign. 
• Universe of positive mass density separated from Universe of negative mass density. 
• Electric force is repulsive/attractive between charges of same/opposite sign. 
• Gravitational potential strong on large scale because mass density is non-negative and so add without cancellation, but weak on small scale.
• Electric potential is strong on small scale short range but weak on medium/large scale because charge density has variable sign with cancellation.
• Electro-magnetics of light on small/large scale. 
• Laplacian differential operator fundamental as instant local action. 
• No need of instant action at distance.  
• The relative strength of electrostatic and gravitational force between a proton and an electron is nearly $10^{40}$.  

The effect is a toy Universe of large scale non-negative mass density + small scale charge density of variable sign + large/small electro-magnetics of light captured by Newton + Maxwell + Schrödinger as a unified theory. Einstein has no role to play.

Unification of Light Propagation and Mechanics

Summary of recent posts:

In modern physics Maxwell's electromagnetics including propagation of light and classical Newton's mechanics are viewed to be fundamentally different because Maxwell's equations are Lorentz invariant (take the same form under Lorentz transformation of Euclidean coordinates), while Newton's equations are Galilean invariant (take the same form under Galilean transformation). This has prevented the formation of a unified theory, which is a major element of the crisis of modern physics.

Einstein formed the Special Theory of Relativity SR in 1905 by declaring that laws of physics have to be Lorentz invariant, thus declaring Maxwell's equations to represent laws of physics, while dismissing Newton's equations as being Galilean but not Lorentz invariant. Einstein then replaced Newton's mechanics by a new form of relativistic mechanics as SR exhibiting new strange physics of space contraction and time dilation, which today is viewed to be a fundamental part of modern physics. 

But Einstein's frank declaration that laws of physics must be Lorentz invariant appears as an ad hoc requirement without any real physical basis, and so it may be reasonable to seek to give Newton's mechanics under Galilean invariance a new chance. 

Doing so, we then face the fact that Maxwell's equations are not Galilean invariant, which means that the choice of Euclidean coordinate system for the expression of the equations comes into play.

Maxwell's equations in particular describe propagation of light as wave between a light emitter A and a receiver B as two points in Euclidean coordinate system E. It is natural to assume that the receiver does not move in E, while the emitter A is allowed to move (creating Doppler effect). 

We thus consider propagation of light from A to B described by Maxwell's wave equations expressed in a spatial Euclidean coordinate system in which the receiver B is stationary. Maxwell's wave equations contain a coefficient $c$ representing the speed of light as speed of wave propagation. 

It is assumed that $c$ is a constant which does not change with choice of Euclidean coordinate system. This conforms with the 2019 SI Standard where the length scale in any Euclidean coordinate system is determined by travel time of light with a preset value of the speed of light  $c$ equal to 299792458 meter/second and time measured by a caesium atomic clock. 

The propagation of light from A to B is thus described by Maxwell's equations expressed in a Euclidean coordinate system E fixed to the receiver with a preset speed of light. 

We now compare with propagation of sound in still air represented by E described by a wave equation similar to Maxwell's. Alternatively, we may compare with elastic waves in an elastic bar. 

The fundamental aspect here is that fixing E to the receiver makes propagation of light fully analogous to propagation of sound in still air or elastic waves in an elastic bar represented by E, as if E in both cases serves as a medium for wave propagation. In the case of sound waves/elastic waves the medium is material in the form of still air/elastic bar represented by E, while in the case of light the medium/aether is immaterial in the form of E. 

We thus face a situation where the medium/aether for wave propagation in the form of a Euclidean coordinate system is tied to the spatial configuration, more precisely to the receiver as if the medium/aether is "dragged along" with motion of the receiver, just like the medium of an elastic bar in motion will be moving.

We reach so a unification of immaterial light propagation and material mechanics by always connecting the coordinate system for Maxwell's equations to the receiver. This is fully compatible with Newtonian mechanics and the 2019 SI Standard and there is no place for SR since no Lorentz transformation is involved. 

There are still issues if several receivers are involved moving with different velocities, which is the subject of Many-Minds Relativity.

  

Einstein's Happiest Thought made him Unhappy

Why was the later Einstein so unhappy?

It started with a young Einstein expressing that "his happiest thought" was the following:

• The gravitational field has only a relative existence... Because for an observer freely falling from the roof of a house – at least in his immediate surroundings – there exists no gravitational field.

It was the pivotal thought to allow Einstein to take the step from his 1905 Special Theory of Relativity SR without gravitation, to his 1916 General Theory of Relativity GR including gravitation. 

Einstein's happy thought was to view free fall of a (small) object as a state without internal forces (stress free) with all parts of the body accelerating the same way subject to a gravitational force being constant over the body, and then draw the conclusion in the absence of internal forces that the body was not subject to any force at all. This brought GR with gravitation back to SR without gravitation. 

Recall that a body in free fall is subject to gravitational force, which is constant for an infinitesimally small body, but for a body with extension gives rise to internal tidal forces, like the gravitational force from the Moon creating tidal waves in the oceans of the Earth. To view free fall as inertial motion without gravitational force lacks reason. 

In any case, Einstein considered a (small) observer O1 with closed eyes under 

• inertial motion (SR)
• free fall (GR)

Einstein noted that in both cases O1 would feel to be stress free without internal forces, and so it would be impossible for O1 to distinguish between inertial motion and free fall from the presence of internal forces, since they would be zero in both cases. But to a stationary observer O2 in a Euclidean coordinate system following the motion of O1, there would be a clear difference between inertial motion as motion with zero acceleration and free fall as accelerated motion. This would also be clear to O1 when opening the eyes.

But Einstein did not take the position of O2 or O1 with open eyes, but instead made a distinction between inertial motion as motion in flat space-time and free fall as motion in curved space-time, which led him to GR. 

So far so good, but Einstein's goal was to form a unified field theory including both gravitation and electromagnetics, which required electromagnetics to also be expressed in curved space-time. Einstein worked on this problem incessantly since 1916 to his death in 1955, however without any success. 

This was the reason Einstein was so unhappy during his later life. 

Is it also the destiny of a modern physicist in quest for a unified field theory including GR, to be unhappy?

Not necessarily, since it is possible to form a unified field theory including Newtonian mechanics and electromagnetics because this possibility was opened with the 2019 SI meter Standard, as exposed in recent posts. Would you be interested in exploring this possibility, and get happy? Then send me a note and I will help to get started, to the best of my knowledge. Ok?

Einstein, the loneliest man in town as smart as a man can be but: He ain't got rythm.

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.