NASASpaceNews reports on Dr. Richard Lieu's groundbreaking theory that gravity could exist without mass which connects to posts on Neo-Newtonian Cosmology with a new view on the connection between mass density $\rho (x,t)$ and gravitational potential $\phi (x,t)$, which can take two different forms with $\Delta$ the Laplacian differential operator in 3d Euclidean x-coordinates and $t$ is time :
- Given $\rho(x,t)$, find $\phi (x,t)$ by integration: $\phi =\Delta^{-1}\rho$. (1)
- Given $\phi (x,t)$, find $\rho (x,t)$ by differentiation: $\rho =\Delta\phi$. (2)
Here (1) represents the standard view with mass creating gravitational potential, while (2) offers a new view with gravitational potential creating mass as the essence of Neo-Newtonian Cosmology.
(1) requires a mechanism for instant action at distance (global integration), which has not been found.
(2) involves instant local action (local differentiation), which is thinkable.
(1) starts out with positive mass, while (2) starts out with a gravitational potential for which $\rho (x) =\Delta\phi (x)$ can have variable sign as the main idea of Lieu. Negative mass repels positive mass and so acts like dark energy, while dark matter appears as small $\Delta\phi >0$ in regions where $\phi (x)$ is smooth.
In short, Neo-Newtonian Cosmology is in line with Lieu's theory by NASA presented as groundbreaking. But there is a basic difference, since Lieu adheres to (1) rather than (2).
The idea of particles carrying mass is fundamental in (1), but no dark matter particles have been identified, nor any particles with negative mass. But with (2) the focus is instead on the nature of the gravitational potential $\phi$, which does not have to be particle-like and so opens to forms of $\Delta\phi$ without particles including dark matter and dark energy.
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