Does Einstein's Generalization of Newton's Gravitation Survive Ockham's Razor?

In a recent sequence of post we are exploring Newton's theory of gravitation based on Poisson's equation:

1. $\rho (x,t)=\Delta\phi (x,t)$  for all $(x,t)$,                    

where $\rho (x,t)$ is mass density at space-time coordinate $(x,t)$ and $\phi (x,t)$ is the corresponding gravitational potential connected through the Laplace differential operator $\Delta$.

The idea is to view the connection $\rho =\Delta\phi$ as an expression of "perfect harmony", instead of viewing matter with mass density $\rho$ as the cause and the gravitational force $\nabla\phi$ as the effect in a cause-effect relation. Or with $\phi$ the cause and $\rho =\Delta\phi$ the effect created by the local process of differentiation, without any action at distance.

Newton's equation $\Delta\phi =\rho$ is nothing but Einstein's equation in flat Minkowski space-time, which appears to be the space-time we are living in, assuming infinite speed of propagation of light or gravitational effects.

Viewing 1 as a cause-effect relation with matter the cause and gravitational force as the effect, Einstein's equation emerges as a generalization of Newton's equation from infinite to finite speed of propagation of the gravitational force. 

On the other hand, if we do not view $\rho =\Delta\phi$ this way, then the question of speed of propagation of gravitational effects does not arise, and so the motivation to generalize Newton's equation into Einstein's equation suddenly disappears. General relativity would then be cut off from the tree of science under Ockham's Razor.

No evidence of finite speed of propagation of gravitational force has been found despite serious efforts  in the LIGO project to detect associated postulated "ripples in curved space-time". The search now continues in the Advanced LIGO project from the zero result of LIGO. The hope is that increasing the sensitivity by a factor 100, it will be possible to detect some miniscule gravitational effect from a massive gigantic galactic collision of supernovas or black holes. This amounts to detecting a smallest possible effect of a biggest possible cause, which has become the trade-mark of modern super-collider experimental physics, described in the Aesop fable about the mountain that gave birth to a mouse:

But if no evidence can found indicating that it is matter which generates gravitational potential/force, irrespective of infinite or finite speed of propagation, then we will have to give up this idea at least if we decide to follow the device of Richard Feynman:

• If the fact will not fit the theory---let the theory go.

So we have search a new theory and what comes up is then to give up a matter-gravitational potential  cause-effect relation with $\rho$ given and $\phi$ the solution of the equation $\Delta\phi =\rho$, and either view the connection as somehow established in "perfect harmony" without cause-effect, or to search for some physical mechanism allowing a gravitational potential as cause to "generate" matter as the effect through a procedure of local differentiation according to $\rho =\Delta\phi$.

Regularizing the relation $\rho =\Delta\phi$ by adding terms depending on derivatives of $\phi$ can bring out different cause-effect relations depending on the regularization. For example, the wave equation

• $- \frac{1}{c^2}\frac{\partial^2\phi}{\partial t^2}+\Delta\phi = \rho$, 

emerges as Einstein's equations in flat Minkowski space with speed of light equal to $c$, reducing to
$\Delta\phi =\rho$ with $c=\infty$. Experimental measurement of speed of propagation of gravity are inconclusive but there is some evidence pointing to a speed larger than the speed of light.

It may be that all we need to know about gravitation is expressed in the relation $\rho =\Delta\phi$, while the true physics behind the relation is hidden to us, because we cannot see the gravitational potential itself, because it does not emit/reflect light, yet is there as a "dark source" of the gravitational force we can feel.

Of course, discussing this possibility with a physicist will lead nowhere,  because even if gravitational waves or ripples in space-time can never be detected, they must exist because Einstein said so (but did not believe himself), or if he did not say so he must have meant so (he suffered from senility already in early middle-age, as we all know...). This is one of the reasons for the deep crisis of physics today, driving physicist into increasing absurdities away from rationality and reality.