Is Einstein > Newton?

Einstein: Newton, forgive me!

Modern physicists are trained to say that Newton's mechanics as the cornerstone of classical physics must be replaced by Einstein's mechanics to serve as a new cornerstone of modern physics. If you ask for reasons to give up the best we have, you get the answer that of course this would be stupid and that in fact Einstein differs from Newton only in very extreme cases with black holes as a key example, albeit beyond even Einstein's theory. 

To see what can be wrong with Newton's mechanics, let us follow the line of thought of New Newtonian Cosmology and extended Newtonian gravitation with labels to previous posts. Here all mechanics ultimately is rooted in gravitation from a primordial gravitational potential $\phi (x)$ depending on a Euclidean space variable $x$ with motion under gravitational force $-\nabla\phi (x)$. The motion of a body with position $x(t)$ at time $t$ is monitored by Newton's laws of motion with the dot denoting differentiation with respect to time:

•  $\dot v +\nabla\phi =0$                               (1)

with $\dot x = v$, which express conservation of energy as the sum of kinetic energy and potential energy:  

•  $\frac{v^2}{2} + \phi (x) = constant$.

Here $-\nabla\phi$ represents gravitational force per unit mass and (1) takes the following form for a body of gravitational mass $m$ as a collection of unit masses:

•  $m\dot v +m\nabla\phi =0$                          (2) 

Here $-m\nabla\phi$ offers a reference to measure other forces than gravitational and so (3) can be extended to Newton's 2nd Law for any force $F(x)$:

• $m\dot v = F(x)$.                                          (3)

From this relation inertial mass $m=\frac{F(x)}{\dot v}$ can be defined in terms of force $F(x)$ and acceleration $\dot v$ as a form of resistance to acceleration, with then inertial mass = gravitational mass.

The main idea is that all of motion/mechanics ultimately is governed by motion in a gravitational field given by a gravitational potential $\phi (x)$, which is connected to mass distribution $\rho (x)$ through Poisson's equation 

• $\Delta\phi =\rho$.                                     (4)

What can possibly be wrong with this model? Not with (1), nor (2), nor (3) or (4). It is a model of a mechanical universe with motion governed by gravitation according to (1) and then extended to any force according to (3) including definition of mass as resistance to motion. It is a mechanical universe without electromagnetics and light. There is here no limit to the speed a body can reach as long as the force of acceleration $F(x)$ in (3) is consistent.    

The only possibility is that adding electromagnetics to the picture, somehow will change the mechanics.

This was what Einstein did in his special theory of relativity SR stating that the mass $m$ of a body will increase with speed and so slow down acceleration under constant force to limit the speed to stay below the speed of light. But SR does not include gravitation and thus says nothing about Newton's mechanics, and then maybe nothing at all. So Einstein gave up SR and turned to General Relativity GR as a modification of Newton's theory of gravitation, but an observable modification only in some extreme case where even GR falls short.

Sum up: There does not seem to be any reason to question that Newton's mechanics does not describe a mechanical Universe. Both SR and GR are viewed as modifications of Newton's mechanics however so small that they do not seem to matter. Newton >> Einstein!

Physicists will tell you that GPS works because of SR and GR, but is not factually correct. GPS works because satellite clocks are synchronised with a master clock on Earth and their positions are surveyed. Simple Euclidean geometry as part of Newtonian mechanics. If you understand this, you will get a kick to a healthy scepticism as concerns SR and GR and maybe you get incentive to take a look at Many-Minds Relativity presenting both critical analysis and new perspectives. 

In addition, observations of redshift of far away galaxies show that they are receding from us with a speed larger than the speed of light, so Einstein's basic assumption of SR appears to be invalid. 

On large scale the Universe consists of a gravitational potential $\phi$ creating mass $m=\Delta\phi$ moving under gravitational force according to Newton's 2nd Law $\dot v+\nabla\phi =0$. Isn't that neat?

If thus Newton is ok, what is left to Einstein?