We consider a Neo-Newtonian cosmological model in the form of Euler's equations for a compressible gas subject to Newtonian gravitation: Find $(\phi ,m, e,p)$ depending on a Euclidean space coordinate $x$ and time $t$, such that for all $(x,t)$:
- $\Delta\dot\phi + \nabla\cdot m =0$ (1)
- $\dot m +\nabla\cdot (mu) +\nabla p + \rho\nabla\phi =0$ (2)
- $\dot e +\nabla\cdot (eu) +p\nabla\cdot u +\rho\nabla\cdot m=0$, (3)
The primary variables in this model are the gravitational potential $\phi$ and the momentum $m$ connected through (2) expressing conservation of momentum or Newton's 2nd law. We view matter density $\rho =\Delta\phi$ as being derived by local action of the differential operator $\Delta$. The model is complemented by a constitutive equation for the pressure.
The essential components of this model are:
- Newton's law of gravitation $\rho =\Delta\phi$ connecting mass to gravitational potential
- $\nabla\phi$ as gravitational force
- Newton's 2nd law (2) connecting motion to force,
- (1) expressing conservation of mass and (3) conservation of energy,
- no action at distance with $\phi$ primordial and $\rho =\Delta\phi$ derived quantity
- global clock synchronisation not needed because all action is local
- equivalence of inertial and gravitational mass by (2)
- $\Delta\phi$ of variable sign opens to positive and negative matter
- no limit on matter speed
- no electro-magnetics or nuclear physics so far included in the model.
Some form of starting values are needed for simulations using the model, but like in weather prediction initial values at a given global time are not known, but have to be constructed from observations over time possibly involving synchronisation of nearby clocks.
Recall that nobody understands what "curved space-time" is, while everybody can understand what a Euclidean coordinate system is and how to measure local time. If we follow Einstein's device of always seeking to "make things as simple as possible, but not simpler", then Newton would have to be preferred before Einstein, or what do you think?
The basic force of cosmology is gravitation, and thus it may appear from rationality point of view to be irrational to seek to eliminate gravitational force from the discussion altogether, which is what Einstein did and which maybe paradoxically gave him fame bigger than that of Newton.
PS1 What drove Einstein into his extremism? Well, the reception of the special theory of relativity Einstein presented in a short sketchy note in 1905, did not draw any attention the first years and when it did, the reaction was negative. The only thing left for Einstein before getting called and kicked out of academics, was to increase the bet by generalising the special theory, which did not cover gravitation, into a general theory of relativity including gravitation. The only thing Einstein had in his scientific toolbox was the Lorentz transformation between non-accelerating inertial systems and the only way to bring that in contact with gravitation was to introduce coordinate systems in free fall, which in the presence of gravitation required strange transformations of space and time coordinates.
Einstein's "happiest thought" was when he realised that sitting in a freely falling elevator cannot be distinguished from sitting in an elevator at rest assuming no gravitation... until the freely falling elevator hits ground....It was this idea of free fall seemingly without gravitation, which allowed him to keep the Lorentz transformation with all its wonderful effects of the special theory without gravitation, when generalising to include gravitation...but the price was high...and the free fall is going on...Compare with Einstein's Pathway to General Relativity.
PS2 Another fact not to suppress is that the special theory of relativity was focussed on propagation of light with the same speed in all inertial coordinate systems if connected by the Lorentz transformation, which gave strange effects for the mechanics of matter (without gravitation) including dilation in time and contraction in space. But the Lorentz transformation was shaped for light propagation and not for mechanics of matter and so it was no wonder that strange effects came out. Since the Lorentz transformation also underlies the general theory of relativity, it is even less wonder that strange effects come out when adding gravitation to the picture.
The lack of scientific logic is clear: If you apply a theory designed to describe a a certain phenomenon (light propagation) to a different type of phenomenon (mechanics of matter), then you must be prepared to get in trouble, even if your name is Einstein...