When first I came upon Newtons absolute time, I took it to mean that non relative time which rests with his God. But now I must examine his use of this word, it’s etymology at least from the Latin if not the Greek prior philosophy , to the translators use in the English version of his great Natural Philosophy of Astrological Principles!
The occasion of this research has been the reading of Galileos Dilogo , in part, the apprehension of the Galilean fractal principle contained therein and Newtons use of the same in his triumvirate of Vis, under the heading of the Centrioetency of force, that is the Centripetal Force.
I hope , by these means to reveal the backwards structural arrangement of Newtons definitions, and why the measure that is the quantity of motion is placed as a foundational or initial definition.
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
late 14c., “unrestricted; complete, perfect;” also “not relative to something else” (mid-15c.), from Middle French absolut (14c., Old French asolu, Modern French absolu), from Latin absolutus, past participle of absolvere “to set free, make separate” (see absolve).
Most of the current senses also were in the Latin word. Sense evolution was “detached, disengaged,” thus “perfect, pure.” Meaning “despotic” (1610s) is from notion of “absolute in position.” Absolute monarchy is recorded from 1735 (absolute king is recorded from 1610s); scientific absolute magnitude (1902), absolute value (1907) are from early 20c. In metaphysics, the absolute “that which is absolute” is from 1809.
It may be seen that in this context and at the time Newton wrote that he meant to convey the idea of ” non relative” ” non dependant” and ” isolated” in regard to the observations and deductions Galileo had made of the Jovian system. Thus in this system the absolute vis was evident as a separate system from that of the earth moon system. In quantitative terms this had to be the whole or totality of that quantity of vis.
Through the telescope this sense of isolation is profound, and the sight of the moons of Jupiter and the realisation that they are ” independently ” rotating around Jupiter was the deepest possible shock to the system men and women of those days could experience!
It takes a mind that measures to see this system as an absolute quantity! In the sense that a triangle is a different absolute quantity o a hexagon, say. Only by seeing these as Arithmoi, pebbles or mosaic chips can the profound quantitative analogy be understood. For a picture may capture that which takes a thousand words to describe the extensive properties and propensities of, but that same picture cut into a mosaic gives a quantitative and relative encoding of each part in the Arithmos. Each Arithmos is as an absolute quantity, complete and entire to itself.
That such properties of vis, namely centripetal vis should be so evidently associated to this quantity or Arithmos is a revelation! However to use the quantitative apprehension with the vis some rule of relation must be observed. For example this absolute quantity of force might be divided uniformly though the isolated system. . However by this time, sufficient evidence and deduction had been gathered as to suggest that the rule of relationship was an inverse square law. So this quantity of vis was distributed so as to act differently at different distances from the centre. This notion was not absolute therefore as it depended on the absolute quantity of the system however it was measured by the accelerative effect this distribution of vis had throughout the system thus Newton called this measure the acclerative vis. It is a dependent subdividing of the isolated or indent quantity of vis in the system. Thus while encoding the same regional quantity, so that the total should be the same, the distribution of the summation should reflect the greater sum where the greater concentration of vis is and vice versa.
How might this be achieved quantitatively? This requires that there be another subdivision of the vis such that the greater acceleration is embodied in the greater part of the whole or if necessary the greater acceleration being in the smaller part, the force being small yet the time of application is longer. That being the requirement means that the accelerative vis must impinge a change in velocity of parts dependent on time! It is thus the measure of that velocity change over time. This is agin a definition of acceleration given by Galileo, but here the proportion of the system, ie it’s relative” bulk” or mass compared to he Abdolute, affects the quantity of vis in that part.
But then, should a part be moved centripetally as a whole then that part is a measure of motive vis in the following precise sense: if it is opposed by a spring or by the parts acting as moments to a balance! Thus a part or a summation of parts may now be given a motive as a multiple of some standard notive or weight, and balanced accordingly on a pair of scales.
Thus has Newton brought down from the starry heavens, by Alikening to a system of measures that quantify the absolute systems of planets by their motions over time and by their bulk in the heavens or yet within each absolute system.
I now turn to Abdolute time. This is not an observed property of the Jovian system, but rather an addiction by Newton, that if a system may be absolute, that is isolated and entire, that time might also be absolute. In fact it was necessary to use earth based times to discuss the changes in the Jovian system, yet it is evident that if Jupiter has moons then it has it’s own system for recording Tymes! That being the point explicitly made within the first chapter of genesis as regards the function of a moon!
Given then that each absolute system has its own absolute time, that makes time a relative concept! But that was unacceptable or that way lies confusion! Thus absolute that is independent time was the solution. Such a time may well exist with god, but it’s conception was more mathematically adduced than for any other reason. If such a time is not demanded how will 1 second be measured any where in the universe never mind on the planet earth.
Absolute time represents a simple knee jerk reaction to the difficulty of quantitatively measuring acceleration and velocity in these absolute systems. Later Einstein would point the way to how to relate all these relative measures together in a system based exactly on Galileos principle of uniform motion of reference frames.
Returning now to the motive, it is clearly a quantity that is proportional to the bulk or mass of a part and the velocity of a part under accelerative vis. It is exactly a quantity of motion. What we find is that Newton defines such a measure almost as the first of his definitions before defining vis or acceleration or velocity. These are assumed to be known from Galileo’s work.
The quantity of motion is thus his final definition of motive, placed first to emphasise it as a fundamental unit within a centripetally acting absolute vis system, with an accelerative bis rule.
This is. Newtons exposition of the Galilean principle in a form amenable to quantitative measures.