Space, Rotation, Relativity

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Submitted by Stephen Boydstun on Sun, 2007-06-10 14:47

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.

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More Newton, More Leibniz

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Concerning Newton’s conceptions of space, see also this other Objectivity essay:

“On Newtonian Relative Space” by Fred Seddon 


The International Society for the History of the Philosophy of Science

Presentations from History of the Philosophy of Science 2008


Abstracts of session The Seventeenth Century Origins of Absolute Space and Time


Analogical Reasoning in Precursors of Absolute Time: Gassendi and Barrow 

Geoffrey Gorham (St. Olaf College and Minnesota Ctr. for Phil. of Sci.)

"In a recent overview of early modern metaphysics, Nicholas Jolley observes in passing that 'philosophical theories that seem primarily tailored to space are often said to apply mutatis mutandis to the case of time'.[1] I examine this tendency to argue by analogy from space to time in two likely influences on Newton: Pierre Gassendi and Isaac Barrow. In the Aristotelian tradition, space implies body and time implies motion. However this symmetry is broken by the end of the sixteenth century: void space is widely entertained but time remains wedded to motion or change. There are many reasons for this asymmetry; but here I emphasize a factor that has been little discussed.

"Practically every early modern natural philosopher who treats space and time invokes – even if only to refute – traditional metaphysical arguments for endowing space with intrinsic dimensionality apart from body. For example, it is argued that God could annihilate a certain part of the world leaving a vacated space with the same dimensions as the part destroyed. However, as Leibniz recognized, such arguments simply do not extend to time: 'If there were a vacuum in space one could establish its size. But if there were a vacuum in time, i.e. duration without change, it would be impossible to establish its length. . . . It follows from this that we cannot refute someone who says that two successive worlds are contiguous in time. . . with no possible interval between them'.[2] The relative paucity of empirical investigations of changeless time, as compared with local spatial vacua, is unsurprising given the inherent conceptual barrier to gauging such duration. It is in this precisely this context that analogical arguments from space to time come to the fore.

"Drawing on recent philosophical discussions of analogical reasoning in science, I show how time is endowed with an intrinsic dimensionality and measure isomorphic to an already articulated absolute space. This kind of reasoning is pervasive in the seventeenth century but Gassendi and Barrow are especially influential and instructive instances. The former develops an elaborate version of the traditional thought experiment for absolute space, but his case for changeless time rests primarily on the otherwise strong analogy between time and his geometrical space: both are extended, continuous, neither substance nor accident, and composed of parts. Given these similarities, Gassendi concludes, time is simply the successive counterpart of absolute space: 'there exist two diffusions, extensions, or quantities, one permanent, namely place or space, and one successive, namely time or duration'.[3] Similarly, in Barrow absolute time emerges parasitic on absolute space and inherits spatial features: the 'space of motion' (spatium motas), as he refers to time, is conceived as successive existence stretched out along a single spatial dimension.[4] Finally, I will argue that the Gassendi-Barrow methodology is assimilated by Newton in his early accounts of absolute space and time (e.g. De Gravitatione). From this point of view, I suggest, we can make better sense of certain otherwise puzzling features of Newton’s famous Scholium, especially his comparatively limp defense of absolute time vs. absolute space and motion."

[1] Metaphyiscs, Cambridge Companion to Early Modern Philosophy, 128-9. [2] New Essays, II, xv. [3] Syntagma, I, ii. [4] Geometrical Lectures, I. 


Cambridge Platonism and Newton's Ontology of Absolute Space

Edward Slowik (Winona State and Pittsburgh Ctr for Phil. of Sci.)

"This presentation will investigate the influence of Cambridge neo-Platonic concepts and arguments on Newton’s natural philosophy of space, matter, and motion, with special emphasis placed on the manner by which both Henry More and Walter Charleton may have prompted or informed Newton’s ontology of space. A number of important questions, much discussed in the recent literature on Newton, will be addressed. (1) Did Newton accept a form of 'substantivalism', which (among other things) regards space as a form of substance or entity? (2) Did Newton ground the existence of space upon an incorporeal being (i.e., God or World Spirit), as did his neo-Platonic predecessors and contemporaries? (3) What is the status of the parts or points of space in Newton’s scheme, and does his pronouncement on the identity of the points of space (in his tract, De Gravitatione) undermine his alleged substantivalism?

"As regards (1), A number of important reappraisals by Howard Stein and Robert DiSalle have concluded that the content and function of Newton’s concept of 'absolute' space should be kept separate from the question of Newton’s commitment to substantivalism. In Stein’s contribution to The Cambridge Companion to Newton, he further contends, more controversially, that Newton does not sanction substantivalism, a view that may also be evident in various early articles by J. E. McGuire.

"Concerning (2), Stein rejects any significant neo-Platonic content, as did McGuire’s early work. Finally, the problem of the points of space, raised by an enigmatic discussion in the De Gravitatione, has brought about several recent reappraisals by Nerlich and Huggett concerning the viability of Newton’s espoused substantivalism.

"This presentation will examine the ontology of Newton’s spatial theory in order to determine the adequacy of these interpretations and arguments. As will be demonstrated, Newton’s spatial theory is not only deeply imbued in neo-Platonic speculation, contra (2), but these neo-Platonic elements likewise compromise any strong non-substantivalist interpretation, contrary to (1). Throughout our investigation, however, the specific details and subtleties of Newton’s particular brand of neo-Platonism will be contrasted with the ontologies of his contemporaries and predecessors, especially More and Charleton, and by this means a more adequate grasp of the innovations and foreword-looking aspects of his theory of space can be obtained. In short, the spatial theory that Newton advances, especially in De Gravitatione, bears much in common with a property view of space, such that space is correlated and coextensive with the existence of an immaterial being, namely God (and where the details of this interpretation differ significantly from the conclusions reached by McGuire’s influential early work). Finally, the ontological implications associated with this picture of Newton’s spatial ontology also render his theory immune to some of the problems raised in the current literature, e.g. (3)."


Newton and Barrow on Sensible Measures of Absolute Space

Katherine Dunlop (Brown University)

"I show how the influence of Isaac Barrow accounts for asymmetries in Newton’s treatment of space and time. In the Scholium following the Principia’s Definitions, Newton contrasts the 'absolute' quantities space and time with their 'sensible measures'. He airs the possibility that no measure of time is 'exact'. Time is measured only by motion. Since the rate of a motion, unlike 'the flow of absolute time', can change, the quantity of absolute time marked out by a motion may vary according to when in time’s 'flow' the motion occurs. For Newton, measures of space are not subject to this kind of deviation. Absolute space is measured by 'relative spaces', which can move with respect to it. Newton asserts that the quantity of absolute space marked out by a relative space is the same no matter where (in absolute space) the relative space is located: though relative spaces and the parts of absolute space differ 'numerically', they remain 'the same in magnitude'.

"I argue that Newton’s asymmetrical treatment of the quantities reflects his conception of geometry. He intends to prove the need for and possibility of a science, 'rational mechanics', that measures time as accurately as geometry measures space. In conceiving geometry as the science of sensible measures of spatial quantity, Newton follows Isaac Barrow. Barrow subscribes to an Aristotelian view on which measurement, to count as science, must pertain to the natures of things and involve the senses. On this basis, he concludes that the most basic measurement, determination of equality, must involve comparison (e.g. juxtaposition) of objects in space. Yet Barrow holds that a measure’s magnitude can be compared only with that of objects in space, not regions of space. For on his view space exists, and thus has magnitude, only insofar as it can be filled by objects. Hence, a spatial region’s magnitude cannot deviate from that of its potential measures. Barrow’s ontology of space, as the potential for magnitude-bearing objects, thus guarantees the accuracy of spatial measures.

"For Newton as well, the possibility of geometry guarantees the accuracy of spatial measures, but not on the same epistemological and ontological grounds. Without accepting Barrow’s Aristotelian view of science, Newton agrees that measures must be sensible and thus ultimately spatial. So on his view, like Barrow’s, the accuracy of spatial measures is a condition of all measurement. Yet for Newton, its satisfaction is not ontologically guaranteed. Space, on Newton’s more robust conception, actually has magnitude prior to being filled by objects. So its magnitude can deviate from that of its measures. I suggest that the satisfaction of the condition is instead guaranteed by Newton’s conception of geometrical activity. On Newton’s view, geometry is a practice of measurement involving the movement of objects through space. This practice of comparison would not be possible if measures did not retain the same quantity through changes in spatial position."


Leibniz on Empty Space and Changeless Time

Michael Futch (University of Tulsa)

"Few disagreements are more central to the history of the philosophy of space and time than that between substantivalists and relationalists, and few figures are as central to this quarrel as Leibniz. It was in no small measure because of his relationalism that Hans Reichenbach lauded Leibniz for possessing “insights that were too sophisticated” to be understood by his Newtonian adversaries. Leibniz’s commitment to relationalism is beyond dispute, but less obvious is what he takes to be the consequences of this view, especially with respect to the possibility of empty space

"Though most are agreed that Leibniz denies that there is, as a contingent matter of fact, empty space, many scholars have concluded that he allows for the metaphysical and physical possibility of a spatial vacuum in a way that he does not allow for the possibility of time without change. This conclusion is reached on the basis of passages in Leibniz’s corpus where he points to a disanalogy between empty time (time without change) and empty space, averring that the former could not in principle be empirically detected, whereas the latter could.

"It therefore appears that Leibniz denies that space could exist in the absence of any matter whatsoever, but does not rule out the possibility of interstitial vacua between pieces of matter. This position is consistent with the demands of his relationalism since it holds that the existence of space in general is dependent upon the existence of at least some bodies – no bodies whatever, then no space – while also denying that every part of space must be filled with matter.

"In this paper, I argue against the above view, suggesting that Leibniz is no less committed to the impossibility of local regions of empty space than he is to changeless time. In particular, I try to show that (some of) the same reasons that lead Leibniz to opt for relationalism and to disavow the Newtonian view that space is ontologically prior to bodies also provide him with grounds for denying not only the actual existence but also the possibility of empty space. Here I focus on two tenets that are at the core of Leibniz’s philosophy of space and time, the Principle of the Identity of Indiscernibles and the Principle of Sufficient Reason. It is widely recognized that these principles are often employed by Leibniz against his Newtonian adversaries. My objective is to show how he similarly employs them to establish the conclusion, contra a prevalent view among Leibniz exegetes, that Leibniz does not countenance the possibility of unoccupied spatial positions."

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