Corruption of Modern Physics 11: Gravitation vs Mass

In the common rubber sheet gravitational model the ball is instantly reacting to the gradient of the deflection field (no action at distance). 

Gravitation is the great unresolved problem of physics. When Newton presented his law of gravitation stating that the gravitational force $F$ between two point masses $M_1$ and $M_2$ at distance $R$ is given by the Law of Gravitation:

• $F=G\frac{M_1M_2}{R^2}$  

where $G$ is a universal gravitation constant, his adversary Leibniz did not question the Law itself, but was not at all happy with the fact that the physics of the creation of the gravitational force from the presence of mass was not addressed by Newton. This question has still no answer as the main conundrum of modern physics. The idea of force carrying particles as gravitons has been tried but no such thing has been discovered. 

The mathematician Laplace gave the Law of Gravitation another form of Poisson's equation involving the Laplacian differential operator $\Delta$:

• $\Delta \phi = \rho$    (1)

where $\rho (x,t)$ is mass density at position $x$ at time $t$ and $\phi (x,t)$ is the corresponding gravitational field with $\nabla \phi (x,t)$ the gravitational force, with the standard view that 

• Gravitational field/force is created by the presence of mass.  

Leibniz asked about the physics of this process of creation of gravitational field/force from presence of mass, but got no answer. If there are no gravitons, then what?  Why is it so difficult to answer? Is the question incorrectly posed? 

In Many-Minds Relativity the question is turned around to ask if it may be so that mass is created from the presence of gravitational field? The equation (1) connecting gravitational field $\phi (x,t)$ to mass density $\rho (x,t)$, can be viewed in two ways: (see also previous posts):

• The standard way viewing $\rho$ as given an $\phi$ the resulting gravitational obtained by solving Poisson's equation, which is a global process as integration requiring instant action at distance.
• The new alternative way is to view $\phi$ as given and $\rho =\Delta\phi$ is obtained by a local process of differentiation thus without action at distance.    

The main difficulty in the standard view is the instant action at distance. That action is instant follows from the observed fact that the Earth is attracted by the gravitational force in the direction of the present (as measured by $t$) position  of the Sun, and not the position 8 minutes before seen in the sky, which would be the case if gravitational force traveled by the speed of light. In the alternative way action is local and the unresolved problem of instant action at distance does not come up. 

The reason a problem cannot be solved can be that the problem is incorrectly formulated. Would Leibniz have been less unhappy with the new formulation without instant action at distance? Maybe he would have said that it connects to an idea of Best Possible of Worlds or Perfect Harmony of gravitational force and mass distribution.

In the setting of Einstein's General Theory of Relativity (if it makes sense) the alternative would take the form of curvature of space-time as creating mass by differentiation as a local operation.