To define a time everywhere, it actually takes an infinite number of observers, none of which are co-located. We call such a infinite number of observers a family of observers. With such a family we have the ability to define a coordinate system. (Yes, in physics a coordinate system implicitly assumes you have a family of observers with clocks and rods through the region of space you are interested in.) We'll deal with how to measure distance between the observers and get \(x,y,z\) coordinates in the next set, but for now it should be clear that at least we have a notion of time that is well defined everywhere: the value of the observer's clock at each point in space.
Nothing that we've done so far involves Newtonian mechanics. We'll now move into the realm of Newtonian mechanics by making the additional assumption, which has a physical significance, that light travels infinitely fast.
Question 4: If we synchronize our clocks according to our rule, with infinitely fast light, how are \(A_r,F_1,F_f\) related?