A Commentary on NEWTON'S SCHOLIUM
Newton, Mathematical Principles of Natural Philosophy,
translated by A. Motte and F. Cajori, 1729
[6]
SCHOLIUM
Hitherto I have laid down the definitions of such words as are less known, and explained the sense in which I would have them to be understood in the following discourse. I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.
[Uchii's comment] Newton says that "the common people conceive those quantities under no other notions but from the relation they bear to sensible objects", and that this produces certain prejudices. As many people point out, Newton may well have Descartes' prejudices or confusions (place and motion may be defined by the immediately contiguous bodies) in mind. And Newton not only distinguishes absolute from relative space (time, motion), but also adopts the former. That's what he is going to say. But then, how does he relate absolute notions to relative notions (adopted by practicing scientists in most contexts, as well as by common people)? This is the question we have to keep in mind. In terms of Earman's commentary (1989, 7) that the common terms "are being given special technical meanings", that is correct, but these technical meanings must be related to scientific practice.
I. Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.
[Uchii's comment] It is one thing to define absolute time this way; it is quite another thing to establish that we do in fact have such absolute time in our experience, or in the world. How does he establish this? Why does he need absolute time? Relative time is related to motion, but absolute time "flows equably", independently, of itself; "flows equably" means, in modern terminology, that the time metric is uniform, not warped anywhere. And here I agree with Earman's rendering that this phrase "refers not to the ontology of time but to its structure" (Earman, 1989,8). But, given such structure, how do we know that this structure is applicable to the phenomena in our world? How do astronomers and physicists, in practice, measure time?
II. Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our sense determine by its position to bodies; and which is commonly taken for immovable space; such is the dimension of a subterraneous, an aerial, or celestial space, determined by its position in respect of the earth. Absolute and relative space are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth remains always the same, will at one time be one part of the absolute space into which the air passes; at another time it will be another part of the same, and so, absolutely understood, it will be continually changed.
[Uchii's comment] We have to notice some disparity between absolute time and absolute space. Relative space changes within absolute space; it is a changing part of absolute space; and since "magnitude" is mentioned, absolute space has its own metric, presumably intrinsic metric. Absolute space does not move, does not change. In contrast to this, absolute time does not contain relative time as its part; rather, it provides the standard for relative time. But again, assuming that Newton is saying that space metric as well as time metric is intrinsic, this assertion appears a priori, with no connection with the methods of measurement. Thus the question remains: how can we establish this intrinsicality?
III. Place is a part of space which a body takes up, and is according to the space, either absolute or relative. I say, a part of space; not the situation, nor the external surface of the body. For the places of equal solids are always [6/7] equal but their surfaces, by reason of their dissimilar figures, are often unequal. Positions properly have no quantity, nor are they so much the places themselves, as the properties of places. The motion of the whole is the same with the sum of the motions of the parts; that is, the translation of the whole, out of its place, is the same thing with the sum of the translations of the parts out of their places; and therefore the place of the whole is the same as the sum of the places as the parts, and for that reason, it is internal, and in the whole body.
[Uchii's comment] Newton means by "place" a position in space; thus an absolute place is a position in absolute space, determined and fixed once for all. In absolute space, place one is distinct from place two, however they may look similar. Place is quite different from the body which happens to occupy it; thus, whether occupied or not, place has its own individuality (Leibniz is to object against this later).
IV. Absolute motion is the translation of a body from one absolute place into another; and relative motion, the translation from one relative place into another. Thus in a ship under sail, the relative place of a body is that part of the ship which the body possesses; or that part of the cavity which the body fills, and which therefore moves together with the ship: and relative rest is the continuance of the body in the same part of the ship, or of its cavity. But real, absolute rest, is the continuance of the body in the same part of that immovable space, in which the ship itself, its cavity, and all that it contains, is moved. Wherefore, if the earth is really at rest, the body, which relatively rests in the ship, will really and absolutely move with the same velocity which the ship has on the earth. 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 imovable space, partly from the relative motion of the ship on the earth; and if the body moves also relatively in the ship, its true motion will arise, partly from the true motion of the earth, in immovable space, and partly from the relative motions as well of the ship on the earth, as of the body in the ship; and from these relative motions will arise the relative motion of the body on the earth. As if that part of the earth, where the ship is, was truely moved towards the east, with a velocity of 10010 parts; which the ship itself, with a fresh gale, and full sails, is carried towards the west, with a velocity expressed by 10 of those parts; but a sailor walks in the ship towards the east, with 1 part of the said velocity; then the sailor will be moved truely in immovable space towards the east, with a velocity of 10001 parts, and relatively on the earth towards the west, with a velocity of 9 of those parts.
[Uchii's comment] With relative motions alone, one seems to be driven to an infinite regress: the motion of a body is referred to the ship, that of ship referred to the earth, etc., etc.; but absolute, immovable space assumed, this can be prevented. Through the two paragraphs III and IV, Earman sees three meanings of space: (1) instantaneous space (freeze the time, and we obtain the 3-dimensional space at that instant), (2) reference frame (locations of events in space and time identified by choosing a reference frame--a coordinate system), and (3) substance or substratum of points underlying physical events (for space points are identifiable independently from events). See Earman (1989), 9-10. But in any of these meanings, absolute space cannot be discerned by our senses, or by physical means of measurement. Newton himself is well aware of this.
Absolute time, in astronomy, is distinguished from relative, by the equation or correction of the apparent time. For the natural days are truly un- [7/8] equal, though they are commonly considered as equal, and used for a measure of time; astronomers correct this inequality that they may measure the celestial motions by a more accurate time. It may be, that there is no such thing as an equable motion, whereby time may be accurately measured. All motions may be accelerated and retarded, but the flowing of absolute time is not liable to any change. The duration or perseverance of the existence of things remains the same, whether the motions are swift or slow, or none at all: and therefore this duration ought to be distinguished from what are only sensible measures thereof; and from which we deduce it, by means of the astronomical equation. The necessity of this equation, for determining the times of a phenomenon, is evinced as well from the experiments of the pendulum clock, as by eclipses of the satellites of Jupiter.
[Uchii's comment] Here, Newton for the first time touches on the means for ascertaining absolute time; that's what astronomers do, and the result, corrected time, is called ephemeris time (Barbour 1989, 181). But if this works, why do we need, in addition, absolute time? Newton seems to be in a curious dilemma: if we have empirical means for correcting relative time and it works, then absolute time is redundant; whereas if we do not have any such means, we have no means to know absolute time.
As the order of the parts of time is immutable, so also is the order of the parts of space. Suppose those parts to be moved out of their places, and they will be moved (if the expression may be allowed) out of themselves. For times and spaces are, as it were, the places as well of themselves as of all other things. All things are placed in time as to order of succession; and in space as to order of situation. It is from their essence or nature that they are places; and that the primary places of things should be movable, is absurd. These are therefore the absolute places; and translations out of those places, are the only absolute motions.
[Uchii's comment] Newton here repeats the character of absolute space, absolute time, and absolute motion.
But because the parts of space cannot be seen, or distinguished from one another by our senses, therefore in their stead we use sensible measures of them. For from the positions and distances of things from any body considered as immovable, we define all places; and then with respect to such places, we estimate all motions, considering bodies as transferred from some of those places into others. And so, instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them. For it may be that there is no body really at rest, to which the places and motions of others may be referred.
[Uchii's comment] Newton admits the indispensability of sensible means, of relative motions, for ascertaining absolutte motions; but he emphasizes the need for abstraction, for philosophical inquiries; and then proceeds to the essential argument for absolute motion.
But we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes, and effects. It is a property of rest, that bodies really at rest do rest in respect to one another. And therefore as it is [8/9] possible, that in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest; but impossible to know, from the position of bodies to one another in our regions, whether any of these do keep the same position to that remote body; it follows that absolute rest cannot be determined from the position of bodies in our regions.
[Uchii's comment] Newton now says, "we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes, and effects". Still, "absolute rest cannot be determined from the poisitin of bodies in our regions". And Newton's argument against predecessors (Descartes, in particular) continues two more paragraphs; for more on this, see Barbour (1989), 628-637.
It is a property of motion, that the parts, which retain given positions to their wholes, do partake of the motions of those wholes. For all the parts of revolving bodies endeavor to recede from the axis of motion; and the impetus of bodies moving forwards arises from the joint impetus of all the parts. Therefore, if surrounding bodies are moved, those that are relatively at rest within them will partake of their motion. Upon which account, the true and absolute motion of a body cannot be determined by the translation of it from those which only seem to rest; for the external bodies ought not only to appear at rest, but to be really at rest. For otherwise, all included bodies besides their translation from near the surrounding ones, partake likewise of their true motions; and though that translation were not made, they would not be really at rest, but only seem to be so. For the surrounding bodies stand in the like relation to the surrounded as the exterior part of a whole does to the interior, or as the shell does to the kernel; but if the shell moves, the kernel will also move, as being part of the whole, without removal from near the shell.
A property, near akin to the preceding, is this, that if a place is moved, whatever is placed therein moves along with it; and therfore a body, which is moved from a place in motion, partakes also of the motion of its place. Upon which account, all motions, from places in motion, are no other than parts of entire and absolute motions; and every entire motion is composed of the motion of the body out of its first place, and the motion of this place out its place; and so on, until we come to some immovable place, as in the before-mentioned example of the sailor. Wherefore, entire and absolute motions can be no otherwise determined than by immovable places; and for that reason I did before refer those absolute motions to immovable places, but relative one to movable places. Now no other places are immovable but those that, from infinity to infinity, do all retain the same given position one to another; and upon this account must ever remain unmoved; and do thereby constitute immovable space. [9/10]
The causes by which true and relative motions are distinguished, one from the other, are the forces impressed upon bodies to generate motion. True motion is neither generated nor altered, but by some force impressed upon the body moved; but relative motion may be generated or altered without any force impressed upon the body. For it is sufficient only to impress some force on other bodies with which the former is compared, that by their giving way, that relation may be changed, in which the relative rest or motion of this other body did consist. Again, true motion suffers always some change from any force impressed upon the moving body; but relative motion does not necessarily undergo any change by such forces. For if the same forces are likewise impressed on those other bodies, with which the comparison is made, that the relative position may be preserved, then that condition will be preserved in which the relative motion consists. And therefore any relative motion may be changed when the true motion remains unaltered, and the relative may be preserved when the true suffers some change. Thus, true motion by no means consists in such relations.
[Uchii's comment] Newton now explicitly refers to "the forces impressed upon bodies" as the causes which distinguishes absolute from relative motions. Since this discrepancy exists between absolute and relative motions, absolute motion cannot be reduced to relative motion. And now follows the famous "bucket" experiment, where this general argument is illustrated by a specific physical process.
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 motion, they are greater or less, according to the quantity of the motion. If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then filled with water, and held at rest together with the water; thereupon, by the sudden action of another force, it is whirled about the contrary way, and 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, 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 ascent to the sides of the vessel, forming itself into a concave figure (as I have experienced), 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. This ascent of the water shows its endeavor to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, becomes known, and may be measured by this endeavor. At first, when the relative [10/11] motion of the water in the vessel was greatest, it produced no endeavor to recede from the axis; the water showed no tendency to the circumference, nor any ascent towards the sides of the vessel, but remained on a plain surface, and therefore its true circular motion had not yet begun. But afterwards, when the relative motion of the water had decreased, the ascent thereof towards the sides of the vessel proved its endeavor to recede from the axis; and this endeavor showed the real circular motion of the water continutally increasing, till it had acquired its greatest quantity, when the water rested relatively in the vessel. And therefore this endeavor 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 endeavoring to recede from its axis of motion, as its proper and adequate effect; but relative motions, in one and the same body, are innumerable, according to the various relations it bears to external bodies, and like other relations, are altogether destitute of any real effect, any otherwise than they may perhaps partake of that one only true motion. And therefore in their system who suppose that our heavens, revolving below the sphere of the fixed stars, carry the planets along with them; the several parts of those heavens, and the planets, which are indeed relatively at rest in their heavens, do yet really move. For they change their position one to another (which never happens to bodies truely at rest), and being carried together with their heavens, partake of their motions, and as parts of revolving wholes, endeavor to recede from the axis of their motions.
[Uchii's comment] Newton now mentions a circular motion, and the point of this can best be illustrated by the following figure. An external force is applied to the bucket, and this generates the rotation of the bucket; but initially only the bucket rotates. But then the rotation is transmitted to the water, and the water rotates with the bucket, with the same angular speed; but notice that the two are at rest to each other. However, there appears a conspicuous difference, due to the rotation of the water. This proves, Newton says, that no relative motion can explain this phenomenon; only absolute motion can.
Then Newton extends his argument to planetary motions; their revolution around the sun is just as real as the rotation of water in the bucket, since both are governed by centripetal force.
By this ingenious argument, based on experimental facts, Newton claims that we do in fact have a real connection between absolute motion and observations; absolute motion can be detected by forces acting in empirical phenomena.
Wherefore relative quantities are not the quantities themselves, whose names they bear, 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 properly to be 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 confound real quantities with their relations and sensible measures. [11/12]
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 observation 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. For instance, if two globes, kept at a given distance one from the other by means of a cord that connects them, were revolved about their common centre of gravity, we might, from the tension of the cord, discover the endeavor of the globes to recede from the axis of their motion, and from thence we might compute the quantity of their circular motions. And then if any equal forces should be impressed at once on the alternate faces of the globes to augment or diminish their circular motions, from the increase or decrease of the tension of the cord, we might infer the increment or decrement of their motions; and thence would be found on what faces those forces ought to be impressed, that the motions of the globes might be most augumented; that is, we might discover their hindmost faces, or those which, in the circular motion, do follow. But the faces which follow being known, and consequently the opposite ones that precede, we should likewise know the determination of their motions. And thus we might find both the quantity and the determination of this circular motion, even in an immense vacuum, where there was nothing external or sensible with which the globes could be compared. But now, if in that space some remote bodies were placed that kept always a given position one to another, as the fixed stars do in our regions, we could not indeed determine from the relative translation of the globes among those bodies, whether the motion did belong to the globes or the bodies. But 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 motion to be in the globes, and the bodies to be at rest; and then, lastly, from the translation of the globes among the bodies, we should find the determination of their motions. But how we are to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained more at large in the following treatise. For to this end it was that I composed it.
[Uchii's comment] After warning that we should not confuse relative quantities with absolute quantities, Newton adds another example for which we can determine absolute motion. See the following figure.
Newton argues that by measuring the tension (force) in the cord, we can tell the quantity of absolute rotation, even if there were no other bodies in the universe. And if there are other bodies, we can tell, by the same means, whether or not the two globes are moving, and hence other bodies are moving or at rest.
In the final two sentences, "But how we are to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained more at large in the following treatise. For to this end it was that I composed it", Newton gives us a promissory note. But Julian Barbour complains (1989, 639): "We read through the Principia with eager anticipation but have to put it down at the end virtually no wiser on this key question. Newton does not return to it specifically anywhere in the book."
References
Barbour, Julian (1989) Absolute or Relative Motion?, vol. 1, Cambridge Univ. Press, 1989. (Discovery of Dynamics, paperback reprint, Oxford Univ. Press, 2001)
Earman, John (1989) World enough and Space-Time, MIT Press, 1989.
Last modified March 27, 2003. (c) Soshichi Uchii