Killtech said:
I have not brought up the concept of proper time in terms of Newtons theory. I was pretty clear on highlighting that his original work is based on a concept of time that aligns with coordinate time.
In Newton's theory, coordinate time and proper time are
the same--the time elapsed along
any clock's worldline is the coordinate time. And of course that coordinate time is the same in all inertial frames, because Galilean transformations do not change coordinate time at all. That's why Newton sometimes used the term "absolute time" to describe the time in his theory. Newton didn't bother to distinguish a distinct concept of "proper time"--time elapsed along a particular clock's worldline--because he didn't think there
was a distinct concept. We now know that he was wrong about that.
Killtech said:
Newtown who takes a lot of effort to make the distinction between absolute and relative time
I have already explained why the "relative time" that Newton described has nothing to do with proper time; it was due to a lack of understanding in general of the variability of the phenomena that were then used as standards of timekeeping. As far as this discussion is concerned, Newton's "relative time" is off topic (and indeed it plays no role whatever in modern applications of Newtonian mechanics).
Killtech said:
Newton put quite a lot of effort to find a time suitable to describe the movement of celestial bodies and his reasoning is not too different from IAU conceptions of fundamental position (ICRF) and time (TDB) systems - obviously, since those are a further refinement of the very same astronomical origins Newton refers to.
Sort of. Modern definitions of, for example, the Earth-Centered Inertial frame and the solar system barycentric frame take into account relativistic corrections, which Newton of course did not and could not. These corrections do not just involve proper time, btw; there are also simultaneity differences between the two frames.
Killtech said:
the prescribed corrections needed to arrive at the specified ideal
Yes, I understand that Newton allowed for the possibility of having to apply corrections to a particular timekeeping method because of non-idealities in that particular method. But his "ideal" was absolute time (or "coordinate time in any Newtonian inertial frame"--as above, all of those are the same), and, as I have already said, he believed that the ideal "elapsed time" along any clock's worldline was the absolute time. And, as I have pointed out multiple times now, he was wrong about that. We know that from many experimental tests, for example the Hafele Keating experiment--if Newton were correct about absolute time, the clocks in that experiment would all have shown the same elapsed time from start to finish, but they didn't.
Killtech said:
If you really want to challenge that please consider reading this section of the Principa and point out text passages that support your claims.
I don't think you understand the point I have been making. The fact that Newtonian mechanics has an absolute time, as I described above, has been a well known feature of Newtonian mechanics ever since it was published. Do you really need me to point out specific passages in the Principia that illustrate that fact?
If you mean that you don't understand how Newtonian mechanics predicts that the elapsed time along any clock's worldline is the same as absolute time as I described above, again, do you really need me to point out specific passages in the Principia that illustrate that fact? Every single equation that has time in it does. In terms of our earlier formalism with models and interpretations, part of Newton's interpretation ##I## of his model was that the time ##t## that appears in his equations directly reflects the elapsed time on ideal clocks. (His comments about "relative time" then allow for non-ideal clocks to be corrected appropriately--but the ideal they are correcting to is as I have just said.) Do you really need me to point out specific passages in the Principia to back that up? Isn't it obvious from the entire book?
What you don't appear to grasp is the simple fact that Newton was
wrong in his belief about absolute time. We know that now; it was one of the key things we learned from relativity. But that doesn't change what Newtonian theory says. It just makes the theory wrong, at least in this respect.