A Stage for Big Bang as Separation: $0 =\Delta\phi$

The previous post presented a stage for the creation of gravitational mass and electric charge as the fundamental components of the World, in the form of the Laplacian differential operator $\Delta$ with respect to a Euclidean space coordinate $x$ acting on a potential $\Phi (x)$ satisfying the equation 

• $\Delta\Phi (x) = 0$ for all $x$.     (1)

With $\Phi (x)$ vanishing for large $x$ the potential $\Phi (x) = 0$ for all $x$ and so represents a null state like a guitar string at rest before plucking or a stage prepared for a play.   

Suppose now the null state $\Phi$ is subject to a highly oscillating perturbation $\phi (x)$ and consider the  assignment:

• $\rho (x) =\Delta\phi (x)$ for all $x$,    (2)

where $\rho (x)$ can be large even if $\phi (x)$ is small because differentiation makes small oscillations big, and so a substantial $\rho (x)$ can emerge from a small perturbation. 

It is possible to view this as a form of Big Bang with creation seemingly out of nothing.  Here (1) sets a stage of possibilities and (2) represents realisation of possibilities as creation of $\rho (x)$ representing  mass or charge density. 

Note that (2) amounts to a "separation" into positive and negative mass/charge out of a zero state, and so the "creation" of $\rho (x)$ is the result of a process of separation, maybe easier to understand than direct creation out of nothing: God separated the light from the darkness.

Also recall that Hesiod's Chaos has been interpreted as the gaping void above the Earth created when Earth and Sky are separated from their primordial unity. The prerequisite for creation is a Euclidean space with a Laplacian differential operator prepared for separation.  

Even if this model "explains" creation of mass and charge, the question remains of how the geometry of Euclidean space with Laplacian as the stage (1) is prepared. Maybe Euclide knew but didn't tell.  

Note if the "creation" happened once it may happen again. Separation does not require massive input of energy and the required energy to form create matter/radiation can come from gravitational collapse in a net zero game, once positive and negative mass have been separated into new Universa.  

For a more detailed specification see the previous post New Newtonian Cosmology and chap 32 in Computational Thermodynamics. In particular, notice conservation of total energy as kinetic energy plus heat energy minus gravitational energy, where gravitational energy thus can feed kinetic and heat energy. This gives an answer to the question from where the energy comes in a conventional Big Bang scenario. 

A notable aspect in the case of separation into positive and negative charges connecting to Real Quantum Mechanics, is that of charge conservation as a result of the conservation law of electromagnetics: 

• $\frac{\partial\rho}{\partial t}+\nabla\cdot J =0$

where $J=\rho v$ current with $v$ charge velocity, from which follows that 

• $\int_{\Omega}\rho dx = constant$, 

where $\Omega$ is the domain where $\rho (x)>0$ or where $\rho (x)<0$ separated by a boundary where $\rho (x)=0$. In particular this motivates why in Real Quantum Mechanics a proton meets an electron with vanishing charge densities, answering a question raised in this post. The number of protons which is equal to the number of electrons does not change over time.