Physics Illusion 14: Gravitational Motion by Instant Action at Distance

Newton envisioning a trajectory of free fall by watching an apple fall and contemplating about a possible New View of gravitational motion without instant action at distance.

In the New View of Gravitational Motion the gravitational potential $\phi (x,t)$ is primordial with mass density $\rho (x,t)$ derived as $\rho (x,t) =\Delta\phi (x,t)$, formally by differentiation as instant local action in space with Euclidean coordinate $x$ and with $t$ a time coordinate.

In the Standard View instead the mass density $\rho (x,t)$ is primordial and the gravitational potential $\phi (x,t)$ is formally generated as solution to Poisson's equation  $\Delta\phi (x,t)=\rho (x,t)$ as instant global action in space.

The basic mystery in the Standard View is the instant action at distance acknowledged by the inventor Newton himself:

• That gravity should be innate, inherent and essential to matter, so that one body may act upon another at-a-distance, through a vacuum, without the mediation of anything else by and through which their action may be conveyed from one to another, is to me so great an absurdity that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it. 
• So far I have explained the phenomena by the force of gravity, but I have not yet ascertained the cause of gravity itself. ... and I do not arbitrarily invent hypotheses. (Newton. Letter to Richard Bentley 25 Feb. 1693)

There is no progress towards a resolution of the absurdity of instant action at distance. The New View offers a way to get around this basic difficulty instead of running head-on into it. 

The New View presents gravitational motion by an evolution equation for the gravitational potential expressing mass conservation (with the dot indicating differentiation with respect to time):

• $\Delta\dot\phi +\nabla\cdot (u\Delta\phi ) = 0$,

combined with an equation defining free fall trajectories $x(t)$ as the motion of immaterial pointwise particles according to Newton's 2nd law:  

• $\ddot x(t) +\nabla\phi (x(t),t) = 0$,

which define the immaterial velocity $u(x(t),t) =\dot x(t)$ in the evolution equation for $\phi$. 

Motion under gravitation is thus according to the New View described by the following set of equations in terms of the gravitational potential $\phi (x,t)$ and immaterial free fall trajectories $x(t)$;

1. $\Delta\dot\phi +\nabla\cdot (u\Delta\phi ) = 0$,
2. $u(x(t),t)=\dot x(t)$,
3. $\ddot x(t) +\nabla\phi (x(t),t) = 0$,

where the mass density $\rho (x,t)$ does not appear, but is instead tied to $\phi (x,t)$ by the relation $\rho (x,t)=\Delta\phi (x,t)$ by differentiation as instant local action in space.  Notice that the immaterial trajectories cover space even where $\Delta\phi (x,t)=0$ expressing absence of matter. The differential equations 1-3 are complemented by initial conditions $\phi (x,0)$ and $x(0)$ and $\dot x(0)$.  

The New View would be the view of an observer who is blind to real matter, but can envision immaterial free fall trajectories $x(t)$ and instant local action. In the New View the gravitational potential changes and as result moves matter.  Watching an apple fall is envisioning a free fall trajectory and corresponding change of gravitational potential.

The Standard View is natural to an observer who can envision real matter and instant action at distance, but is blind to immaterial free fall trajectories.  In the Standard View matter moves and as a result changes the gravitational potential. 

The New View and Standard View describe the same physics, for example the Earth moving around the Sun or a falling apple. The Standard View requires instant action at distance, which is unthinkable physics. The New View involves instant local action, which is thinkable physics. 

Which view do you prefer?