SOURCE: "Newton's Arguments for Absolute Space," in Archiv fur Geschichte de Philosophie, Walter de Gruyter, 1985, pp. 80-91.

[In the following essay, Winterbourne offers a reading of Newton's "proofs" of absolute space that supports the claim that Newton's argument has been misrepresented by modern critics. Furthermore, Winterbourne suggests that Newton's argument may be interpreted more literally than has previously been the case.]

In this paper I shall examine Newton's 'proofs' of absolute space, and try to justify the claim that the argument has been misrepresented by recent commentators, and that it can be given a rather more literal rendering than has been the case.'

It is usually accepted that since Newtonian mechanics requires an absolute reference frame, Newton must defend that conception from within the framework of natural philosophy, or be compelled to present this reference frame as an epistemologically unjustified, but metaphysically necessary presupposition.² The orthodox view is that Newton uses the arguments of the spinning bucket, and the cord-connected spheres as evidence that 'empirically' verifies the existence of absolute space. In fact, it is not explicitly stated by Newton that these arguments prove the existence of absolute space: this conclusion is nonetheless said to follow directly from the fact that they demonstrate absolute motion³. The orthodox reading of Newton's argument is illustrated by Max Jammer, who cites this passage from Principia:

The causes by which true and relative motions are distinguished one from the other, are the forces impressed upon bodies to generate motion.⁴

(I shall refer to this passage as NI, i.e. 'Newton's first thesis'.) What Jammer calls Newton's first argument is based on the idea that only real forces generate real motion. According to Jammer, this argument is constituted by three significant passages. The first is the one I have called NI; the second is this:

The effects which distinguish absolute from relative motion are the forces of receding from the axis of circular motion. For there are no such forces in a circular motion purely relative, but in a true and absolute circular notion they are greater or less according to the quantity of the motion.⁵

(I shall refer to this passage as N2.) The third passage >cited by Jammer as constitutive of Newton's first argument—the argument from forces—is this:

It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent; because the parts of that immovable space, in which those motions are performed, do by no means come under the observations of our senses. Yet the thing is not altogether desperate; for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions.⁶

For reasons which will become apparent, I shall refer to this passage as N4.⁷

So much for what Jammer calls the first argument. The second argument for the existence of absolute motion is "that which proceeds , from the effects that such motion produces, in particular the appearance of centrifugal forces. So we have Newton's famous pail experiment."⁸ After discussing this 'experiment' Jammer says that "… the same inaccessibility to physical verification characterizes all the other attempts to enforce (Newton's) argument, as for example, his experiment with the two cord-connected spheres."⁹ Newton's final argument—based on the distinction between absolute and relative, or apparent motion—is not, in Jammer's opinion, developed further. On this interpretation, the logical status of both 'experiments' is the same. Both are attempts to move from the existence of forces, to the existence of absolute space, via absolute motion. It is this interpretation that I intend to question. There is, in addition a tendency to change the logic of the globes thought-experiment and attribute this changed logic to Newton.¹⁰

To support my thesis that the orthodox reading of the relevant Scholium passages is, if not strictly wrong, then at least not Newton's view, consider Jammer's discussion. What I have referred to as N1, N2 and N4, are run together by Jammer, as representative of a single argument. Perhaps the most often cited passage of the Scholium—referring to the introduction of the two thought-experiments—in fact introduces the argument of the globes. Most commentators present this as though the passage beginning "It is indeed a matter of great difficulty to discover … the true motions of particular bodies from the apparent …"; and which includes the significant assertion, "yet the thing is not altogether desperate …", preceded the bucket experiment. But it does not. It comes after this discussion, and immediately before the introduction of the globes thought-experiment. I hope to show that this is an important and neglected aspect of Newton's reasoning, and that the Scholium passages might be taken rather more literally than has been the case.¹¹

I agree with Jammer's suggestion that the bucket experiment focusses attention on the special role of certain forces and their observable effects. According to Newton, these can only be explained by postulating an absolute reference frame.¹² Newton thinks this is accomplished by pointing out that in true circular motion such forces are greater or less, and are measurable. He is trying to establish that the endeavour to recede from the axis of circular motion is due to a force that is variable and measurable. What I have called NI is part of an argument from dynamics designed to show that true motion cannot be explained relationally. From the relational viewpoint, the translation of bodies can only be seen as a kinematic change, which means, for Newton, only by means of relative or 'sensible' measures. Since he is concerned to show that the confounding of these measures with the 'real' measures generates "vulgar prejudices" concerning space and time, Newton's task was to establish that though certain motions are kinematically equivalent, they are nonetheless dynamically distinguishable. This distinguishability is manifested by the measurable variations of certain forces. Hence the bucket experiment.¹³ A dynamic explanation must be relative to a frame of reference other than the "ambient bodies".¹⁴ Newton's argument is always from the existence of observable forces, or their effects, to absolute motion, and thence to absolute space. Although the latter cannot be observed, it can be inferred as a way of making these forces and effects intelligible.¹⁵

Newton advances the argument by repeating what he regards as the error of confusing sensible measures with real entities:

Wherefore relative quantities are not the quantities themselves … but those sensible measures of them (either accurate or inaccurate) which are commonly used instead of the measured quantities themselves. And if the meaning of words is to be determined by their use, then by the names time, space, place and motion, their (sensible) measures are to be properly understood; and the expression will be unusual and purely mathematical, if the measured quantities themselves are meant. On this account, those violate the accuracy of language, which ought to be kept precise, who interpret these words for the measured quantities. Nor do those less defile the purity of mathematical and philosophical truths, who cofound real quantities with their relations • and sensible measures.¹⁶

(I shall call this passage N3.) It is after this passage that Newton asserts that it is difficult to discover and distinguish true motion from apparent, yet reassures his reader that "the thing is not altogether desperate". If we accept the conventional reading, it would clearly be an inappropriate moment for Newton to say this: that is, after consideration of the bucket thought-experiment, which, on the orthodox reading, establishes all Newton's purposes in the Scholium arguments. The most plausible interpretation seems to be that Newton has tried to establish that a full explanation of certain phenomena must include reference to forces differentiating real and apparent motion. And "… the thing is not altogether desperate; for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions."¹⁷ Why should Newton, at this point, say that there are some arguments to guide us, if, as is commonly supposed, the bucket experiment constitutes the main argument? Immediately following the last quoted sentence, Newton introduces the globes thought-experiment. Perhaps Newton wishes to regard N4 as offering two separate arguments, which though related, do not aim to make precisely the same point. Suppose we assume that the bucket experiment is arguing for the special role of certain forces: we might then consider the possibility that the globes thought-experiment is the argument "… from the apparent motions, which are the differences of the true motions."¹⁸

The details of the bucket experiment are well known. It consists of suspending a bucket of water by a rope which is then twisted. A force is applied to the bucket in the direction of unwinding. 19 Newton's central point is that the resulting deformation of the water surface indicates the existence of forces acting.²⁰ The point is that certain kinds of forces, when applied to systems free to rotate, or to systems already rotating, give rise to centrifugal forces as their effects. The second law of motion associates accelerations with forces. With respect to what, then, is the water accelerating? Newton insists that it cannot be the bucket, since the water surface is successively plane and concave when there is relative acceleration, and since the surface may be plane or concave when there is no relative acceleration. He concludes not that the acceleration must be with respect to absolute space—this term nowhere appears in the relevant discussion in the Scholium—but that

this endeavour (of receding from the axis of rotation) does not depend upon any translation of the water in respect of the ambient bodies, nor can true circular motion be defined by such translation. There is only one real circular motion of any one revolving body, corresponding to only one power of endeavouring to recede from its axis of motion, as its proper and adequate effect.²¹

The fact that Newton is dealing here with a deformable body greatly complicates the issue.²² He says that when the relative motion of the water in the vessel is greatest, it produces no endeavour to recede from the axis. The 'it' here refers to the body of water considered as one body, and Newton is trying to show that "… there is only one real circular motion of any one revolving body, corresponding to only one power of endeavouring to recede from its axis of motion, as its proper and adequate effect." However, since the water is deformable, it is not strictly true that there was no endeavour to recede from the axis at the beginning of the experiment. The particles of water in immediate contact with the sides of the bucket would have received an immediate centripetal force, and would have started to rotate. The vessel, says Newton, "gradually communicates" its motion to the water; the endeavour shows that the real circular motion is continually increasing, and is at rest relatively to the bucket only when the whole body of water partakes of the motion, and thus acquires its greatest quantity. The concavity of the surface is a function of the combined circular motions of the particles constituting it. The 'true' circular motion Newton is trying to demonstrate is manifest only when the centripetal force has been communicated to the whole body of water. This takes time: when the circular motion of the water—considered as one body—is at a maximum, the water is at rest with respect to the sides of the bucket.

I want to suggest three ways to analyse the globes thought-experiment. The first is the modern interpretation; the second is more firmly based on Newton, and concerns what might be called 'Clarke's embellishment'; and the third is the argument I take it that Newton offered in the Scholium itself.

The modern version, which I shall briefly outline, starts with the assumption of a universe empty except for the globes. In this case, the question of whether the globes rotate presents the problem as a matter of semantics. If one asks a relationist why we may not affirm that the globes rotate, his reply will be that the idea of circular, or any other kind of motion, is intelligible only when some other body is given as reference standard. He may simply offer a challenge to the Newtonian to say, without question-begging, what is meant by rotation in an empty universe. The relationist presupposes that motion is intelligible only relationally; the Newtonian, in trying to make sense of the globes rotation, presupposes that the relational explanation is incomplete by neglecting the facts relating forces and tension. Of course the Newtonian admits the intelligibility of relational theories of motion: for a Newtonian it is both meaningful and true—though not, of course, the whole truth.²³ This first version of the argument has the merit of recognizing that the problem can be reconstructed in terms of what it makes sense for us to affirm in certain well-understood cases of dynamics. It errs in attributing to Newton a too metaphysical cast of mind in this important argument.

The second version is, though not found in the Scholium, a recognizably Newtonian move. Consider the possibility that all objects, apart from the globes, are annihilated from the actual, non-empty universe. Does it make sense to talk about rotation and direction of motion of the globes? Newton, and Clarke (in the correspondence with Leibniz) have no hesitation in saying that it does.

(And) yet no way is shown to avoid this absurd consequence, that the parts of a circulating body would lose the vis centrifuga arising from their circular motion, if all the extrinsic matter around them were annihilated.²⁴

There is no doubt I think that this way of stating the problem caused Leibniz some embarrassment. It seems that he cannot agree with Newton without undermining his concept of phenomenal motion—partly because of the uneasy traffic in his system between metaphysical and phenomenal levels of reality.²⁵ If Leibniz denied that in the circumstances obtaining in Clarke's embellishment of Newton, there would be tension or rotation, he would commit himself to the view that an occurrence transcending the globes could have an immediate effect on the globes; he is committed, in other words, to action-at-a-distance of a quite radical kind—a thoroughly un-Leibnizian notion.

As I have said, the globes thought-experiment is not described by Newton in terms of which Sklar's account, for example, is typical. This brings me to third interpretation of the argument.²⁶

If two globes, kept at a given distance one from the other by means of a cord which connects them, were revolved about their common centre of gravity, we might, from the tension of cord, discover the endeavour of the globes to recede from the axis of their motion, and from thence we might compute the quantity of their circular motions.²⁷

Evidently, at the point where Newton explains the purpose of the experiment and the results that might accrue, there is no suggestion that we should consider the globes in an otherwise empty universe. Newton is claiming only that by 'testing' the cord for tension, we could compute the amount of circular motion. He argues that variations in the application of forces to alternate faces of the globes would either add to the quantity of circular motion or diminish it.²⁸ It is at this point in the argument that Newton suggests for the first time that such computations would be possible "… even in an immense vacuum, where there was nothing external or sensible with which the globes could be compared." This extension of the conditions of the argument would not be intelligible to the relationist. The differences in the conditions given to us in various (Galilean) frames—exemplified in the argument from forces and accelerations—may be regarded either as intrinsic or as due to external influences.²⁹ This is Newton's only direct reference to such a possible, nonactual universe. From this point, Newton extends his reasoning by adding the fixed stars to this hypothetical universe. Even then we could not tell by means of the relative translations of the stars and the bodies, which of them was really in motion: we have to accept the kinematic equivalence of hypotheses. However,

… if we observed the cord and found that its tension was that very tension which the motions of the globes required, we might conclude the motions to be in the globes, and the bodies to be at rest.³⁰

What can Newton mean by "… that very tension which the motions of the globes required …"? The tension must be such as to guarantee that the globes rotate about their common centre of gravity, so we might read this as 'the tension required for orbital motion'. But what Newton seems to be referring to here is the preceding remark, where he thinks he has shown how one might come to the conclusion that variations in tension are caused by, and directly proportional to, forces variously applied to the alternate faces of the globes. This is achieved by measuring the variations of tension observed in the actual non-empty universe. Thus we could discover "… from the translation of the globes among the bodies" the determination of their motion. That is, once it is established that it is the globes, not the stars, that are in motion, we can compute the direction of their motion with respect to the stars considered as at rest.

Newton's last remarks in the Scholium effectively embarrass any relationist of a Leibnizian persuasion who rejects action-at-a-distance. Newton has tried to show that the addition of forces on alternate faces of the globes has a direct and measurable effect on the cord's tension, which is its "proper and adequate effect". It might be plausible to suggest that the connection between circular motion and centrifugal effects is sufficiently ambiguous, such that we could not tell if rotating the fixed stars around the globes would result in the generation of such forces on the globes: but it is a good deal less plausible to say that by addition of force on the body one effects the fixed stars.³¹ It is not the existence of centrifugal effects simpliciter that Newton believes refutes the relationist. In this case the bucket thought-experiment would have probably been sufficient. It is the law-like connection Newton thinks he has established between the variations in the amount of tension in the cord, and the variations. of applied forces. Having rejected kinematic relativity as explanations of these phenomena, the thesis must be developed mathematically and dynamically. What Newton has done thus far is indicate what is necessary to explain these causes and effects, and thus true and apparent motion. How this is to be done is the task of Principia as a whole.³²

To summarize: the globes argument postulates the cord-connected spheres in the actual universe. Here, we may refer to impressed forces, tension etc. without being open to the charge that these assertions have no clear sense. It is important to keep in mind that any such assertions are based upon our knowledge of the globes themselves, considered in a normally inhabited universe. From this we conclude that the impressed forces and variations of tension mutually imply one another in some law-like manner. It is this that Newton believes justifies the assertion that there would be such forces even in an otherwise empty universe. To deny this would be to deny, not some metaphysical/theological thesis about absolute space, but the putatively established connection between forces and tension. Newton is extrapolating from the known behaviour of bodies in the actual universe to the intelligibility of the idea of force in a possible world inhabited only by the globes. In other words, in such a universe, the science of dynamics would still apply—an assumption necessary for the laws of motion.³³ The analogical reasoning which leads to the acceptance of the intelligibility of forces in a universe empty except for the globes, helps us to grasp the logic of the laws of motion themselves. The assertion about the existence of forces and tension in the globes system holds, for Newton, also in the idealized case. The whole argument is epistemological, although for Newton, and especially his contemporaries, it has metaphysical/theological consequences.

The thought-experiments are thus analogical arguments, and are less abstract and metaphysical than they are sometimes taken to be. By treating both of Newton's arguments in much the same way, commentators have missed an interesting byway in the argumentation of the Scholium.³⁴

Notes

¹ I shall offer a less 'metaphysical' and more literal reading of the arguments for the existence of absolute space as given in the Scholium to Definition VIII of Principia. That there should be a more epistemological rendering of these famous discussions is suggested by Tamny: "… whereas all previous arguments drawn from Newton concerning this claim have been purely metaphysical and theological, we have seen that there may well have been epistemological considerations as well." It is my intention to take up this suggestion. See Martin Tamny, "Newton, Creation and Perception", Isis, 70, 1979, p. 57, footnote. I shall also suggest that Newton's original argument has been idealized, and that the logic of the globes experiment in particular has been changed. When this changed logic is attributed to Newton, important aspects of his reasoning are overlooked, and a more literal reading of these discussions obscured.

² For example, see A. d'Abro, The Evolution of Scientific Thought, Dover Books, New York, 1950, especially Ch. X, p. 106 ff., and Ch. XXXVII p. 412 ff. Also John Losee, A Historical Introduction to the Philosophy of Science, Oxford U.P. 1971, p. 84 ff.

³ This view that the space-time Scholium was not intended as a proof of absolute space, has been argued recently by Laymon: see R. Laymon, "Newton's Bucket Experiment", Journal of the History of Philosophy, October 1978.

⁴ Newton, Principia, p. 10. All references to Principia will be from the translation by Andrew Motte of 1729, revised by F. Cajori, and published as Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World; University of California Press, 1960; hereafter cited as Principia. See also M. Jammer, Concepts of Space, Harvard U.P. 1954.

⁵Principia, p. 10.

⁶Principia, p. 12.

⁷ Newton states quite clearly here that the problem is to distinguish true and relative motion, given the existence of absolute space. The function of the thought-experiments is to show that any relational mechanics leaves out something important in the description of certain kinds of motion, giving indirect support to the idea of an absolute reference frame.

⁸ Jammer, p. 104.

⁹ Jammer, p. 106.

¹⁰ For example, Sklar describes the globes experiment in what has become the accepted fashion, thus idealizing Newton's original case. The orthodox manner of considering the argument is based on what are taken as the initial conditions given in the Scholium, that is, something like: "… consider two globes, connected by a cord, in an otherwise empty universe." See L. Sklar, Space, Time and Space-time, California Press, 1974, p. 183. In fact, the implications of considering a universe empty except for the globes, concerns Newton's extensions of his argument: this particular case, as described by Sklar (and others) is what issues from the argument, rather than being an initial condition.

¹¹ Here I agree with Laymon's strategy, when he says that his interpretation of Newton "… has the advantage of being closer to the text and of avoiding the attribution of a mistake to Newton." Laymon, op. cit., p. 405.

¹² The notion of force is really what the Scholium passages are about, and it is this notion—as a fundamental reality on the phenomenal level—which most embarrasses Leibniz in the correspondence with Clarke. Once Leibniz has admitted that it is the attribution to a body of force that determines whether it is really in motion, he has made a major concession to Newton's position. Leibniz's problems are intimately related to the different levels on which force and motion are realities in his system. On the phenomenal level Leibniz adheres to a mechanical explanation: on the other hand, force is something that a body possesses as part of its intrinsic metaphysical nature.

¹³ Newton expresses no doubts about this example or its results: "There are no such forces in a circular motion purely relative, but in a true and absolute circular motion, they are greather or less, according to the quantity of the motion." See Principia, p. 10.

¹⁴ Laymon suggests that the proper reading of 'ambient' in this connection is one which expresses Newton's anti-Cartesianism. See Laymon, p. 404.

¹⁵ Newton regarded it as the simplest hypothesis to explain the observed facts of mechanics. Absolute motion is motion which cannot be regarded as relative to anything observable, such as the 'ambient bodies', or matter in general.

¹⁶Principia, p. 1. McGuire has pointed out the continuity in Newton's thinking on this, from the early treatise "De gravitatione" through Principia and beyond. See J. E. McGuire, "Newton on Place, Time and God: An Unpublished Source", The British Journal for the History of Science, Vol. 11, 38, 1978, p. 124ff.

¹⁷ This concept of "differences" is made somewhat more explicit by MacLaurin: "In general, the actions of bodies upon each other depend not upon their absolute but relative motion; which is the difference of their absolute motions when they have the same direction, but their sum when they are moved in opposite directions." See Colin MacLaurin, An Account of Sir Isaac Newton's Philosophical Discoveries: in Four Books, London, 1748, Book II, p. 128. This is what Newton seems to have in mind in the following: "But if the earth also moves, the true and absolute motion of the body will arise, partly from the true motion of the earth, in immovable space, partly from the relative motion of the ship on the earth." Principia, p. 7. McLaurin seems to use the term 'force' interchangeably with 'absolute motions of bodies'.

¹⁸ I shall pursue this line of argument, in spite of the fact that Newton refers to the two experiments in the reverse order here. It is much harder to make sense of the Scholium argument if a distinction between the purposes of the two thought-experiments is not made. If Newton does, as I believe, intend such a distinction to be made, this seems the likeliest place in which to identify the beginning of his argument. The distinction between these two lines of argument has been confused partly by the running together of passages N1, N2 and N4, and using them as justification for the bucket experiment, without the mediation of N3.

¹⁹ "While the cord is untwisting itself, the vessel continues for some time in this motion; the surface of the water will at first be plain, and, as before the vessel began to move; but after that, the vessel, by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede by little and little from the middle, and ascend to the sides of the vessel, forming itself into a concave figure … and the swifter the motion becomes, the higher will the water rise, till at last, performing its revolutions in the same times with the vessel, it becomes relatively at rest in it." Principia, p. 10, italics mine.

²⁰ This is not surprising, since part of the experiment specifies the application of an external force to the bucket.

²¹Principia, p. 11. C. D. Broad suggested that since the term 'absolute space' nowhere appears in the premises of Newton's argument, it cannot occur in the conclusion. In fact, the term occurs neither as premise nor conclusion. The argument is about force, both as a cause of certain kinds of motion, and as an effect of such motions. See C. D. Broad, Scientific Thought, Kegan Paul, 1923, p. 100ff.

²² Cf. Laymon, op. cit., p. 408.

²³ If the problem is seen in this fashion—as a semantic dispute—it could be argued that Leibniz has the most consistent position. The initial conditions of the thought-experiment, viz. 'consider an empty universe …' would not pass unchallenged. This would, however, be for metaphysical rather than dynamic or 'semantic' reasons. Leibniz would appeal to his metaphysical principles of 'Perfection' and 'Sufficient Reason'.

²⁴Clarke's Fifth Reply, H. G. Alexander, The Leibniz-Clarke Correspondence, Manchester University Press, 1970, p. 101.

²⁵ This complicates Leibniz's own theory of space in turn: see my "On the Metaphysics of Leibnizian Space and Time", Studies in History and Philosophy of Science, 13, No. 3, 1982.

²⁶ Cf. also Ian Hacking: "In Principia we are to imagine a universe with nothing in it but a bucket of water that starts to spin. This hypothesis can make no sense to a relativist, yet we know what would happen if it were true. Although the "spin" would not be visible, the water would gradually start to rise up the side of the bucket. Hence, even if there were nothing else in the world, there would be a difference between spin and rest, and so, said Newton, relativism is refuted." In: "The Identity of Indiscemibles", The Journal of Philosophy, May 1975, p. 249-250. This is a considerable distortion of the argument of the Scholium: Newton nowhere suggests that we should consider the bucket in an empty universe.

²⁷Principia, p. 12.

²⁸ Such computations would enable us to establish the quantity of the motion, and its direction or determination, i.e. its vectorial value.

²⁹ Newton, in his 'postulate of isolation' opts for the former. Cf. D'Abro, op. cit., p. 106ff.

³⁰Principia, p. 12.

³¹ Newton anticipated this in the early treatise "De gravitatione": "… who will imagine that the parts of the earth endeavour to recede from its centre on account of a force impressed only upon the heavens? Or is it not more agreeable to reason that when a force imparted to the heavense makes them endeavour to recede from the centre of revolution thus caused, they are for that reason the sole bodies properly and absolutely moved." See "De gravitatione et Aequipondo Fluidorum", in Unpublished Scientific Papers of Isaac Newton, ed. by A. R. Hall and M. B. Hall, Cambridge University Press, 1962.

³² "But how we are to obtain the true motions from their causes, effects and apparent differences, and vice versa, how from their motions either true or apparent, we may come to the knowledge of their causes and effects, shall be explained more at large in the following treatise. For to this end it was that I composed it." Principia, p. 12.

³³ The Laws of Motion may be taken as idealizations of the motions of observable and measurable bodies. Such observations lead to the Laws of Motion, though the latter are not merely inductive generalizations from such observations of course.

³⁴I would like to thank Peter Alexander for some very helpful comments on an earlier draft of this paper. I have tried to incorporate as many of his suggestions as I felt was possible, although the responsibility for the ideas expressed here remains, of course, my own.