Local Simultaneity Saves Newton's Mechanics

Local simultaneity of galley slaves.  

In modern physics Newton's mechanics is replaced by Einstein's theory of relativity based on an argument that Newton's mechanics requires notions of absolute space and absolute time, which have shown to be difficult to give reality. 

Newton's mechanics is together with Maxwell's electromagnetics the main achievement of classical mathematical physics and to throw it out carries a large cost. It is thus natural to ask if it is really true that Newton's mechanics requires notions of absolute space en time?

Recent posts argue that Newton's mechanics only requires notions of local space as local coexistence and local time as change of local coexistence. This is seen in explicit time-stepping of Newton's equations of motion where velocities and positions are updated from one local instant of time to a next using only local information in space. In other words, the World can very well go around without notions of absolute space and time, with only local coexistence or local simultaneity in the sense of shared time locally in space necessary for locally coordinated motion. 

Local coexistence involves time synchronisation locally in space as a natural element of local physical interaction within extended bodies.  

Recall that Einstein motivated the special theory of relativity by exhibiting the difficulty of establishing a system of absolute time with global simultaneity, but did not realise that such a thing is not needed, since local simultaneity is enough.  

It may thus be possible to save Newton's mechanics from Einstein's assault, and so avoid all the complications coming with Einstein's theory of relativity. This could help modern physics out of its present relativity theory paralysis.