Primordial Gravitational and Electric/Magnetic Potentials

Dialog between the Two Greatest World Systems with primordial potentials vs densities.  

This is a further remark to previous posts on New Newtonian Cosmology with a gravitational potential $\phi_m (x,t)$ and electric potential $\phi_c(x,t)$ with $x$ a Euclidean space coordinate and $t$ a time coordinate, viewed as primordial with mass density $\rho_m (x,t)$ and electric charge density $\rho_c(x,t)$ given by 

• $\rho_m=\Delta\phi_m$      (1)
• $\rho_c=\Delta\phi_c$      (2)

Here $\rho_m \ge 0$ while $\rho_c$ can be both positive and negative, and $\Delta$ is the second order Laplacian differential operator. 

The corresponding gravitational force $f_m\sim -\nabla\phi$ is attractive between positive mass densities and the corresponding Coulomb force $f_c\sim \nabla\phi_c$ is attractive between charge densities of opposite sign and repulsive for charge densities of the same sign. 

In principle $\rho_m<0$ is possible in (1), with then repulsion between mass densities of different sign which would separate large scales into Universa with positive and negative mass, where we happen to live in one with mass positive. It is thinkable that presence of negative mass density shows up as dark energy. It is thinkable that a very smooth $\Delta\phi_m$ corresponds to dark matter.  

The gravitational force $f_m$ acts on large masses at large distances. The electric Coulomb force $f_c$ acts on small small charges at small distances, which requires physics preventing charges of different sign to come too close, which is represented by the presence of the Laplacian in Schrödinger's equation. 

Including also a magnetic potential connected to the electric potential by Maxwell's equations and Newton's 2nd Law for mass motion subject to force, gives a model including Newton's mechanics, electromagnetics and gravitation, with potentials as primordial quantities from which mass and charge densities and forces are derived. Here Real Quantum Mechanics naturally fits in as a classical 3d continuum mechanics model. 

An important aspect of (1) and (2) is that $\rho_m$ and $\rho_c$ are derived by differentiation as an operation acting locally in space, which can be perceived to act instantly in time,  thus avoiding the hard-to-explain instant-action-at-distance coming with the standard view with mass and charge densities as primordial. 

The absence of magnetic monopoles corresponding to point charges makes magnetics different from electrics in the formation of electromagnetics.