Newton's De Gravitatione
Newton's notions of absolute space and of absolute time did not appear abruptly in 1687 with the publication of Principia. We now have his manuscripts on gravitation, entitled De Gravitatione et Aequipondio Fluidorum (On the Gravity and Equilibrium of Fluids), presumably written when he was young, around 1670, and from this we can infer that he already had basically the same idea in this period, although the word "absolute" does not appear yet. This is quite interesting in that we can know Newton propounded his doctrine of absolute space and time in order to refute Descartes' strange theory of motion which may be named as a radical relativism (in Principia Philosophiae). Moreover, we can find many explicit statements on the nature of absolute space and time, which are often omitted in his later and published version in Principia. After a brief introduction, Newton presents the following definitions.
The terms quantity, duration, and space are too well known to be susceptible of definition by other words.
Def. 1. Place is a part of space which something fills evenly.Def. 2. Body is that which fills place.Def. 3. Rest is remaining in the same place.Def. 4. Motion is change of place. (Hall, A. R. and N.B. Hall, eds., Unpublished Scientific Papers of Isaac Newton, Cambridge University Press, 1962, 122)Here, it is clear that for Newton (at this period), the crucial notions of quantity, of duration (of time), and of space looked already evident and secure. In Principia, of course, he became more cautious and he carefully chose the words for describing space and time. But the essential content is here stated straightforwardly. And in particular, he explicitly mentions Euclid when speaking of motions in space; that is, space is Euclidean 3-dimensional space (together with, in modern terminology, the metric characterizing it). And the essential point is that (1) space is distinct from the bodies in it, and (2) motion is determined with respect to space, not to any other bodies. And, in particular, Newton has the Cartesian notion of motion in mind, and (3) he wishes to dispose of it. He summarizes Descartes' doctrine as follows:
(1) That from the truth of things only one particular motion fits each body (Principia, Part II, Art. 28, 31, 32) , which is defined as being the translation of one part of matter or of one body from the neighbourhood of those bodies that immediately touch it, and which are regarded as being at rest, to the neighbourhood of others (Principia, Part II, Art. 25; Part III, Art. 28).
(2) That by a body transferred in its particular motion according to this definition may be understood not only any particle of matter, or a body composed of parts relatively at rest, but all that is transferred at once, although this may, of course, consist of many parts which have different relative motions. (Principia, Part II, Art. 25.)
(3) That besides this motion particular to each body there can arise in it innumerable other motions, through participation ( or in so far as it is part of other bodies having other motions). (Principia, Part II, Art. 31.) Which however are not motions in the philosophical sense and rationally speaking (Part III, Art. 29), and according to the truth of things (Part II, Art. 25 and Part III, Art 28), but only improperly and according to common sense (Part II, Art. 24, 25, 28, 31; Part III, Art. 29). That kind of motion he seems to describe (Part II, Art II; Part III, Art. 28) as the action by which any body migrates from one place to another. (Hall and Hall 1962, 123)
Even the general reader can suspect that something funny going on here. A body's motion is defined by reference to its contiguous environment, but the latter may be in any of various motions relative to something else! Thus it is rather easy for Newton to point out absurdities such as this:
For he [Descartes] says that speaking properly and according to philosophical sense the Earth and the other Planets do not move, and that he who declares it to be moved because of its translation with respect to the fixed stars speaks without reason and only in the vulgar fashion (Part III, Art. 26, 27, 28, 29). Yet later he attributes to the Earth and Planets a tendency to recede from the Sun as from a center about which they are revolved, ... (Hall and Hall, 124)
And a lot more follows. But at this point, a thought may occur to a charitable reader: why on earth did Descartes propose such a doctrine, which leads to many such absurdities? According to Julian Barbour (2001, 435-50), the famous incident of Galileo's condemnation by the Inquisition (1633) came in, for Descartes who was in the final stage of preparing The World (a book on cosmology, posthumously published in 1664, where Descartes's earlier theory of motion was also propounded). In this work, Descartes had the notion of space as the "container of things", independent of the things; thus he was able to say that the Earth moves, for instance. Descartes was forced to revise the definition of motion, so that he was able to say that "the Earth does not move", and at the same time he was able to advance a theory of motion; thus this revision was incorporated in the later Principia Philosophiae (1644). Be that as it may, Descartes' radical relativism set the stage for the later development of relativistic mechanics, as well as for the Newtonian doctrine of absolute space and time. The problems for any relativistic mechanics are far harder than you may imagine, since it must be able to treat on a par any frame which is in any state of motion. Thus, at least in this stage, Newton's choice (maybe intuitive) of introducing external frame (space and time) was quite reasonable, since it can dispense with infinite possibilities of motion and enables us to concentrate on far simpler motions with respect to the supposed frame of space and time, without regard to any other bodies in the world!
It must be noted that in his argument against Descartes, Newton considers the possibility of defining a body's motion by reference to remote objects, such as fixed stars (later mentioned by Ernst Mach in the 19th century), but he quickly dismisses any such attempt as insufficient for determining the "natural and absolute motion" of a body, such as the Earth (Hall and Hall, 127). For any further analysis of De Gravitatione, Barbour's discussion is recommended.
References
Barbour, J. (2001), The Discovery of Dynamics, paperback ed., Oxford Univ. Press.
Last modified, July 9, 2005. (c) Soshichi Uchii