Newton's Mechanics Does Not Require Absolute Space and Time

                                                          Local time. 

Newton expressed in the beginning of his monumental Principia Mathematica (Book I p 81-82) a direct warning to not view measured quantities of space and time as the quantities themselves:

• Wherefore relative quantities are not the quantities themselves, whose names they bear, but those sensible measures of them (either accurate or inaccurate), which are commonly used instead of the measured quantities themselves.
• And if the meaning of words is to vie determined by their use, then by names time, space, place, motion, their measures are properly to be understood; 
• and the expression will be unusual, and purely mathematical, if the measured quantities themselves are meant.
• Upon which account, they do strain the sacred writings, who there interpret  those words for the measured quantities.
• Nor do those less defile the purity of mathematical and philosophical truths, who confound real quantities themselves with their relations and vulgar measures.  

But this is exactly what Einstein did in his Special Theory of Relativity with its measuring apparatus of rigid rods and clocks, which in modern physics has replaced Newton's mechanics as being based on concepts of absolute space and time which cannot be identified and so have no meaning.

But interpreting Newton's concept of space and time as "quantities themselves" as "absolute time and space" is not what Newton had in mind understanding of course very well that position and time are both relative and not absolute.  

What Newton said was that if a clock stops, it does not mean that time itself stops. Nothing strange. 

The period of a pendulum clock scales with the square root of length divided by gravitational strength, and so in particular will run slow at higher altitude. But this does not mean that time stops in a space station with effectively zero gravitation. Normal processes of ageing of a human body continue even in weightless state. 

The caesium atomic clock is the most precise clock use to measure time. The rate of such a clock does not change much with changing environment but a dependence on e.g. temperature can be expected. 

In any case the World outside human influence somehow goes around without the help of Swiss clocks and then with local rates of change geared by local physical conditions somehow expressing the rate of local time itself, which is the time entering into Newton's 2nd Law as a law of local acceleration subject to local force. 

The ruling idea of modern physics is that Newton's inverse square law of gravitation requires instant action at distance, which requires global simultaneity and thus universal absolute time, which is viewed to be absurd, and so Newton's time itself must be replaced by Einstein's relative time. 

But as discussed in recent posts and under the tag New View on Gravitation, it is possible to view Newton's law of gravitation as an expression of local instant action, which only involves local time. 

It is thus possible to return to Newton taking advantage of all the marvellous simplicity and accuracy of Newtonian mechanics, and so not continue clinging to Einstein's relativity theory with all mysteries and difficulties it brings along. 

Newton's warning was directly addressed to coming generations, but it did not reach Einstein who apparently did not read even the introduction to Principia and so was free to question Newton's mechanics on loose grounds, and so be elevated to be the portal figure of modern physics whose wisdom cannot be questioned.  

So what do you say? Was Newton's warning well founded?

More from Principia Book I showing that Newton did not ask for any absolute space and time:

• But because the parts of space cannot be seen, or distinguished from one another by our senses, therefore in their stead we use sensible measures of them. 
• For from the positions and distances of things from any body considered as immovable, we define all places ; and then with respect to such places, we estimate all motions, considering bodies as transferred from some of those places into others. 
• And so, instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; 
• but in philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them. 
• For it may be that there is no body really at rest, to which the places and motions of others may be referred.

It is a common tactic in a debate to assign an idea to your opponent, which is not really carried by the opponent, so as to forcefully distance yourself from this idea (straw man argument). This is what modern physicists do when the claim Newton's mechanics requires absolute space and time, and then distance themselves from such a stupid idea.