Neo-Newtonian Cosmology 3

Recent posts 1+2 in this series with further details in Time to Welcome Newton Back outlines a possible Neo-Newtonian Cosmology based on an expanded form of Newton's Theory of Gravitation with mass of both positive and negative sign with a corresponding gravitational force which is attractive/repulsive for mass of equal/opposite sign, where we happen to live in a visible region of positive mass with only gravitational attraction. 

Invisible regions of negative mass would then supply the mysterious dark energy estimated to contribute 70% of the total energy of the visible Universe filling the very large observed voids apparently without positive mass possibly driving the observed expansion of the visible Universe. 

The idea of an Anti-Universe to our Universe with all signs switched, with negative mass and anti-protons/electrons et cet, was suggested by Hannes Alfvén, Swedish Nobel Laureate in Physics 1970, in his book Worlds-Anti Worlds: Antimatter in Cosmology 1966. 

The possibility of dark energy in the form of negative mass has been proposed by Massimo Melli:

• Most of the substance of the Universe appears to consist of dark energy and dark matter, but until now scientists don't have the faintest idea about their origin and ignore what they are. 
• I believe that dark energy and dark matter could consist of tachyons formed during the inflationary phase of the early Big Bang, when time was slow or zero due to the extremely high density of the Universe. 

Melli refers to Big Bang, but one can equally well speculate about creation of mass of variable sign from a perturbation of gravitational potential as suggested in NNC 1+2 as a physically more possible little big-bang, with electro-magnetics similarly resulting from a perturbation of an electric potential creating charges of variable sign.  

It remains to explain why we can see presence of positive mass through interaction with electro-magnetics but not the negative mass supposedly filling the voids, then apparently without interacting with the electro-magnetics of our universe.  

Key Question: Why does negative mass not interact with visible light? 

We recall that atomic electrons (of positive mass) oscillating between two energy levels in an atom radiate electro-magnetic waves in the form of light, which can be absorbed into oscillating electrons in our eyes and so make a star visible to us. This gives a connection between positive mass and visible light.

In any case large voids are present, which does not fit with a universe of only positive mass. 

It is conceivable that large voids of negative mass can explain the observed expansion of the visible Universe. 

We recall the basic model of Neo-Newtonian Cosmology of immense simplicity and generality expressing the interplay between gravitational potential $\phi$ as primordial, mass density $\rho$ and $u$ material velocity all depending on a Euclidean space coordinate $x$ and time coordinate $t$ with the dot on top representing differentiation with respect to time:

• $\rho = \Delta\phi$                    (inverse square law in differential form)
• $\Delta\dot\phi =-\nabla\cdot (\rho u)$    (conservation of mass)
• $\vert\rho\vert\dot u=-\rho\nabla\phi$            (Newton's 2nd Law)  

Here $\rho$ is created from $\Delta\phi$ by fast-local-action, changes of $\phi$ in time are created  from changes of $\rho u$ in space by slow-global-action (see previous post) and changes of $u$ from gravitational force $-\nabla\phi$ by fast-local-action. We see three concise simple equations in three variables $\phi$, $\rho$ and $u$ describing all of celestial mechanics. Amazing! How can you ever imagine to throw away this mathematical model? Compare this post: Unthinkable that the inverse square law is incorrect.

Answer to Key Question: Dark matter as mass $\rho =\Delta\phi$ with $\vert\rho\vert$ too small to carry electro-magnetics, can by presence as negative mass in large voids drive observed expansion and as positive mass in spiral galaxies drive observed rotation.