The full original text of this essay is available at Objectivity Archive.
The following is an abstract of

“Space, Rotation, Relativity” by Stephen Boydstun

 Part 1 – Descartes and Huygens
Volume 2, Number 2, Pages 17–31

This is a study of philosophic and scientific arguments concerning the nature of space and motion from Descartes to Einstein. Part 1 surveys the thought of Descartes and Huygens.

Treated here are Descartes’ views on the relativity of space to bodies and his arguments for the relativity of the motion of spaces and bodies to choice of material reference frame. His novel and equivocal definition of motion is dissected. The philosophical and theological setting of his theory of motion, his principle of conservation of quantity of motion, and his mechanics of the solar system are charted.

Descartes’ celebrated formulation of the principle of inertia is discussed along with the conceptual hurdles that remained before the principle could become Newton’s First Law. Descartes’ erroneous analysis of circular motion is displayed.

The author then conveys Huygens’ formulation of correct, quantitative principles of mechanics. Huygens introduced the requirement that correct principles of mechanics must be invariant under transformation between frames in uniform relative motion. Included in this conceptual history is the argument by which Huygens arrived at the correct formula for the centrifugal tendency of a body in circular motion. Huygens’ arguments contra Newton for the frame-relativity of all motion—not only uniform linear motion, but rotary motion—are also detailed in this study.

Part 2 – Newton and Leibniz
Volume 2, Number 3, Pages 49–75

Here is Newton in his student years, to 1666. He deviates from Descartes concerning the proper perspective and constituents for mechanics. Newton sets down his definition of bodies and their relation to space, which latter he takes as a primitive that is coeternal with God. Adopting doctrines from Aristotle, Epicurus, and Gassendi, young Newton sheds Cartesian views on the definition of motion, the relativity of planetary orbital motions, the existence of vacuum, and the infinite extent of space. The author shows the way in which Newton deduced in this period, independently of Huygens, the correct expression for centrifugal force. At this stage, there were lingering ambiguities in Newton’s conception of force still clouding the causal analysis of rotary motion. Nevertheless, conservation of angular momentum was discovered by Newton at this time.

Here is Newton of Principia. By the 1680’s, he had gotten the dynamics of rotary motion entirely right, ready for its part in his analysis of planetary and lunar orbital dynamics. In support of the view that rotary motions are not wholly relative motions, Newton adduces two arguments. These are his famous arguments based on the behavior of the surface of water in a rotating bucket and on the possible centrifugal tension in a cord connecting two globes in outer space. The author examines these arguments closely, relying on his own performance of the bucket experiment. Newton’s conclusion is that rotary motion is not only motion relative to this or that body, but motion relative to some absolute fixed places in space. Then an occasion of rotary motion is always motion, never rest, regardless of the frame of reference from which it is measured.

For Leibniz extended space is not an ontological primitive. It is an attribute of something more primitive. The truly primitive elements are quasi-spiritual, not material. However, these immaterial primitive elements founding extended space require matter for their existence. Space is an ideal, not a real, though space is founded on a real that requires matter. The author examines Leibniz’s arguments for all those conclusions.

Leibniz contended against Newton that identical translations of all the points of space make no physical difference and that reflections of all the points of space through a plane dividing space make no physical difference. These contentions are assessed in light of modern physics. An internal conflict is exposed between Leibniz’s conception of force and his affirmation of the relativity of uniform straight-line motion. Faults in Leibniz’s arguments for the relativity of rotary motion are also exposed.

Part 3 - Kant
Volume 2, Number 5, Pages 1–31

This Part is devoted entirely to Kant’s new conceptions of space, motion, causality, and mechanics. Kant’s development of these topics is traced through his Precritical period, which begins with his efforts to modify the received Leibnizian-Wolffian metaphysics so as to bring it into harmony with Newton’s physics. Kant’s failed effort to outdo Newton by deducing the three-dimensionality of space from the inverse-square law of gravitational force is one strand followed within this study. The influence and stimulus from Euler and Lambert on Kant during the 1750’s and 60’s are not neglected. This Precritical section includes English translations, by the author, from Kant’s previously untranslated 1758 treatise “New Theory of Motion and Rest.”

Kant’s disquisitions on space in the “Inaugural Dissertation,” Critique of Pure Reason, Prolegomena, and Metaphysical Foundations of Natural Science are intensely examined. Contrary to both Newton and Leibniz, Kant concludes that even the deepest features of space knowable by us must be features wrought by our cognitive faculties, not by mind-independent reality. The three-dimensionality of space is a feature of our cognizing the world. The author criticizes Kant’s view of the ontology of space as well as Kant’s attempt to graft Newton’s mechanics into his system of Transcendental Idealism. The author argues against Kant’s account of how mathematics is so powerfully employed in physics and Kant’s treatment of principles of kinematics and the principle of inertia as knowable by a priori derivation.

Kant’s 1786 proposal of a new notion of absolute space to replace Newton’s notion of absolute space is roundly criticized for its making relative to mere fiat the question of whether a particular frame of reference is an inertial frame. Newton’s arguments for an absolute spatial frame with respect to which rotary motion occurs are defended against Kant’s counters.

Part 4 – Invariance, Electrodynamics, and the Special Theory
Volume 2, Number 6, Pages 131–89

Not that Newton’s thesis was entirely correct. Consistent with his mechanics, Newton’s arguments could only establish that rotary motion remains rotary motion relative to all inertial reference frames, not that there is one inertial frame objectively singled out as at rest. An inertial frame of reference is one at rest or traveling in a straight line at a constant speed. Part 4 introduces the modern requirement, descended from Huygens, that basic physical laws be invariant in their mathematical form when transformed from coordinates set on one inertial frame to coordinates set on any other inertial frame.

This invariance property under the transformations appropriate to the kinematics of Galileo is reported from authoritative sources (or demonstrated by the author in the endnotes) for a wide range of basic laws from classical physics. Highlighted too are the specific failures of invariance under these transformations for phenomena abiding by the wave equation, for a generalized version of Ampere’s Law, and for Faraday’s Law. It is then shown how Einstein’s theory of Special Relativity remedied those specific failures of invariance by a new and improved kinematics to replace the kinematics that had been used since Galileo. All of the basic laws of physics could then be shown to be invariant in form when transformed from coordinates set in one inertial frame to coordinates set in another inertial frame.

The revisions implied for our concepts of space and time, for Newton’s mechanics, for the distinction of kinematics and dynamics in electromagnetic phenomena, and for the equivalence of mass and energy are then laid before the reader. Experimental results are integrated all along the theoretical road.