Newton on Space and Time (and Motion)

Transcription

1 Newton on Space and Time (and Motion) In De Grav. Newton begins by briefly stating his notion of space (primitive and indefinable), place ( a part of space that something fills evenly ), body ( what fills place ) and motion ( change of place ). Newton wishes to consider bodies as impenetrable, and so they fill place, rather than merely spread through it. It is clear already that in Newtonʼs view (1) body and space are distinct, and (2) the motion of a body is in respect to or relative to space, not to other bodies.

2 This sort of relative motion (relative to space itself) has come to be called absolute motion. Motion defined in relation to another body or other bodies (rather than space itself) is what is meant by relative motion. In 3 Newton summarizes Descartesʼ view of motion: Motion is the translation of one body away from the bodies that immediately touch it (which are regarded as being at rest) and into contact with other bodies. ( 3 of De Grav.) Huggett and Hoefer call this ʻmotion properly speakingʼ or ʻtrue motionʼ in 3.1 of their Stanford Encyclopedia article. This is in accord with Descartesʼ view (1) that as a matter of objective truth, there is only one way a body can be said to move at a given time. According to Descartes, there is only one touching set of surroundings of a given body. However, according to Descartes there is a colloquial, non-scientific, folk use of ʻmotionʼ which, while not objectively or scientifically correct, is also acceptable. A part of a thing that is really or truly moving can be said to move (in a derivative way), even though it may maintain its relation to the surrounding parts, and so may not be properly or truly moving. 2

3 We can, for example, say that a part of a comet moves, since the comet moves, even if that part does not change its relations with the parts of the comet that immediately touch or surround it. Huggett and Hoefer also point out that Descartes also recognized motion with respect to any arbitrarily chosen reference body, which they call change of place. This seems an odd term for this sort of motion. In this sense, they say, no motion is privileged (or special, distinguished in some way, unique). This kind of motion is Newtonʼs final (b) in 3. So Newton seems to have a four-fold classification of Cartesian motion: Motion is either (rn) relative to the immediately surrounding bodies or (rb) relative to any other body at all. And this motion may be spoken of in either a (sn) strict or scientific sense or (sb) a broader, colloquial or folk sense. But (sn) seems to apply only to (rn). And, as far as I can see, (sb) can be used only with (rb). So in the end we have two kinds of motion--the strict and scientific, relative to surrounding bodies, and the broad and relative to any arbitrarily selected reference point or object. Huggett and Hoefer, however, point out that Descartes discriminated amongst relative motions, that there is a (third) intermediate but relative sense of motion that 3

4 Descartes called motion in the ordinary sense (in Principles, II.24). If I am walking down the street, one might say that I am moving with respect to the stationary sidewalk or the sidewalk is moving relative to (stationary) me. But intuitively there is a cause of motion or action in me, whereas there is no such cause or action in the sidewalk. We say, therefore, that I am moving and the sidewalk is not. This might be even clearer for an automobile on the road. This observation can lead one to discriminate amongst relative motions. I move, not the sidewalk. The car moves, not the highway. Here is how Descartes puts it: 24. What the ordinary sense of ʻmotionʼ is. Motion, in the ordinary sense of that word, is simply the action by which a body travels from one place to another.... As I pointed out in section 13, a thing can be said to be changing and not changing its place at the same time; so a thing can be said to be moving and not moving at the same time. For example, a man sitting on a ship that is leaving port thinks he is moving relative to the shore which he regards as fixed; but he doesnʼt think of himself as moving relative to the ship, because his relations to its parts remain 4

5 unchanged. We ordinarily think of motion as involving action, and of rest as the stopping of action, and by that standard the man sitting on deck is more properly said to be at rest than in motion because he isnʼt aware of any action in himself. [And the ship is more properly said to be moving, one might add]. If one keeps straight this polysemy in the term ʻmotionʼ and its cognates, then to say, for example, that something is still (in the strict sense) but moves (in the broad sense)-- or vice versa, of course--is not a contradiction, though it may be confusing. Keeping that in mind, letʼs look at Newtonʼs critical discussion of Descartes. Newton thinks that Descartesʼ definition of motion leads to absurdities ( 4): 1)The earth is supposed to be truly at rest, yet have a tendency to recede from the Sun. [In this case, Descartes isnʼt quite contradicting himself, but his kinematics of motion doesnʼt align properly with his dynamics, his account of forces. If the earth were truly and scientifically at rest, from whence would come a tendency to recede from the Sun? If it were moving about the sun, then both Newton and Descartes could 5

6 have an account of such a tendency--newtonʼs being the one we still accept. ] 1) There seems to be something subjective in Descartesʼ account of true motion. Consider a boat steaming (to be anachronistic) up a river at just the rate the current runs downriver. We think the boat is not moving (relative to the river banks, of course), but Descartes must say that it is truly moving (relative to the water immediately surrounding it). Is there, as we say now, a fact of the matter, or is it just that the river banks are more salient for us or more convenient to use as a reference point? [Where we say There is no fact of the matter, Newton would say instead: Even God could not say whether the boat truly moves or not. ] 2) It seems that we can say that the parts of the comet (above) really and truly do not move (in respect to their immediate surroundings) or really and truly do move (with the comet, in respect to its surroundings). This is inconsistent. In 5 Newton presents eight other problems with Descartesʼ account of motion. 1. In the strict and scientific sense, only the surfaces of bodies can be said to move, if its interior parts donʼt change positions with respect to each other. Itʼs odd to say that the exterior surface of a body moves, but the rest of it does not. 6

7 2. But it gets even worse, according to Newton, if the interior parts of an object (or system of any sort) do move! Here is a brief extract from 2.25 of Descartesʼ Principles of Philosophy: A piece of matter or body moves if it goes from being in immediate contact with some bodies that are regarded as being at rest to being in immediate contact with other bodies. I count as ʻone bodyʼ or ʻone piece of matterʼ anything that is transferred all together, even if it has many parts that are moving relative to one another. Then look at Newtonʼs example: the springs or gears moving in watch in the pocket of a man moving on a ship which is moving on the surface of the earth which is whirling around the sun in the ether (and which we would now think is moving in the galaxy). We have a choice. Perhaps objects have all these motions (2), but then how can this be reconciled with dynamics? [That, I believe, is the point of his pointing out that the Earth 7

8 tends to recede from the centre of the Sun because of a motion relative to the fixed stars, tends less strongly to recede because of lesser motion relative to Saturn There has to be (1) one unique tendency to recede from the centre of the Sun because there is one unique net force acting on the Earth at any instant, but Descartes is stuck with too many. What principle can he use to choose which whole the springs of the watch are part of? Descartes isnʼt entitled to pick any one motion as the true, absolute and proper one in preference to the rest Newton concludes that the Earth has just one natural and absolute motion, namely the motion that causes the Earth to tend to recede from the Sun In point 8 he claims that according to Descartesʼ system a moving body has no determinate speed and no definite line along which it moves. 3. If God stopped the vortex, but not the Earth, from spinning, Descartes would then be committed to saying that the Earth began to move (truly, properly and scientifically) without any force being applied to it. 4. What emerges at the end of this obscure (at least to me) argument is that Newton thinks that real absolute 8

9 motion is indicated by a (unique) tendency to recede (from a centre) rather than by translation (inertial motion, as we will call it). There can be only one real, absolute motion. 5. The planets are all, like the earth, motionless (in the scientific and true sense). Yet they constantly change their relative positions. This, says Newton, is contrary to reason. 6. Conversely, suppose that God stopped a planet in its tracks (so that it kept its relative position to the sun), but let the vortex continue to whirl around the sun. Then Descartes would have to say that the earth was truly moving while the sun was still, while they do not change relative positions. This, again, is contrary to reason. 7. In some cases, we may have no way to judge whether the matter surrounding a body moves or is at rest. In such cases, we canʼt judge true motion. 8. Descartes' definition implies that a moving body has no determinate speed and no definite line [trajectory?] along which it moves. This will be demonstrated in Amplification of point 8 just above. Where exactly, asks Newton, was the planet Jupiter a year ago? 9

10 How is a Cartesian to answer this question? The answer for Descartes cannot be in terms of the surrounding bodies, because the bodies that surrounded Jupiter a year ago have (presumably) moved, and so Jupiterʼs place no longer exists. Nor can it be in terms of the fixed stars (including the planets and the sun) since they all move too. If this place no longer exists, how can it be compared to Jupiterʼs present position? How can distance between the two be measured. If you canʼt determine the distance, then even if you know the time, you canʼt determine the speed (which is distance/time). [By way of contrast, Newton is thinking--must he not?--that space itself supplies a location for things. The place that Jupiter was a year ago, a spatial location, is changeless and eternal in Newtonʼs view. Distinguishing space or extension from matter is crucial even for kinematics, much less dynamics. Finding the place is the difficult job of astronomers.] Furthermore, what I have said about the starting-point of xʼs journey applies also to every point along the way So there is no trajectory, as well as no definite speed. This proves Newtonʼs claim in 5, point 8. 10

11 It turns out that a Cartesian must say that not even God himself could answer this because the place in question no longer exists. 7. What Extension (or Space) is. Space is neither a substance nor an accident, but it is not nothing either. [So even though the term substantivalism will be used for Newtonʼs position, itʼs clear that he had strong reservations about calling space a substance. Itʼs tempting to divide the contents of the world up into substances and the properties of substances (that is, accidents ), but then one faces a problem with the classification of space and time. They donʼt fit into these neat categories.] (i) There are two marks of substantiality--independence and ability to act. But space is dependent upon God [though independent of matter] and does not act--it does not move or think. So itʼs not (quite) substance. (ii) But extension is not had by something, doesnʼt inhere in something. These are the marks of properties or accidents. So extension is not a property or accident of anything. 11

12 In fact, we can imagine that there is space and nothing else at all, just empty space. (iii) Extension is not nothing, because nothing has no properties. But extension (or space) does have properties 8. The Properties of Extension (or Space) 1. Space can be everywhere divided into surfaces, surfaces into lines, lines into points. All these spaces are contiguous: spaces are everywhere right next to spaces. So there are spherical, cubical, etc. spaces everywhere (which is why a sphere can be put anywhere, can go anywhere, in space). The space is already there to contain [JBʼs emphasis, I assume] the spheres and cubes, etc. 2. Space extends infinitely in all directions. 10. The Properties of Space (Resumed) 3. The parts of space are motionless. The affirmation that they can (or do) move faces a dilemma: 12

13 Either (i) the motion is Descartesʼ proper motion (but that makes no sense since there is no surrounding body) or (ii) it is change of place (but that makes no sense, since a part of space is a place, or is what gives something a place. A place cannot change place.) Eventually, Newton makes this remarkable statement: The best way to understand the immobility of space is by comparing space in a certain way with time. The parts of time--e.g. individual days--get their individuality from their order: if yesterday could switch places with today, it would stop being yesterday and would become today. Similarly, the parts of space get their individuality from their positions, so that if any two of them x and y could switch positions, they would stop being the regions they are--x would become y, and y would become x, which is to say that there wouldnʼt be a switch after all! Our notion of what individual part of space (or time) we are thinking about comes from how it relates to the rest of space (or time); there is no way of identifying it except through its spatial (or temporal) location. That why nothing could count as changing the location of any part of space or time. 4. Everything that exists is related in some way to space. (So to affirm the existence of anything at all is to affirm the existence of space.) 13

14 [There may be a slide here from noting that everything that does exist has some spatial location to anything that can exist must have some spatial location. I donʼt think this follows. Must every possible world be spatio-temporal?] There is another interesting remark in this section: This very moment when I write this is the same in Rome and in London, on the earth and in the stars, and throughout all the heavens, because thatʼs the way times relate to space. Note that ʻspaceʼ here must be what I will call below space3d, assuming that ʻmomentʼ means something like instant. This idea seems to accord well with the way we do think of the relation of time (for instance, the present time) to space (space3d). To each moment or instant, there corresponds a space3d. 5. The positions, distances and movements of bodies are all to be understood in terms of the parts of space. 6.Space is eternal [sempiternal?] in its duration and unchangeable in its nature. 14

15 The latter claim, we will see, is denied in the general theory of relativity (GTR). The former claim introduces an important ambiguity in the term ʻspaceʼ. It can mean all of extension at one time. Let us call this space3d, since it is 3-dimensional. But space existing through all time is a 4-dimensional entity that I will call space4d. Let us keep watch to see which way(s) Newton uses the term space. It is possible, according to Newton, for there to be empty space. 11. Launching a Metaphysic of Body Hereʼs a possible account of body: God could cause regions of spacetime to be impenetrable and reflective in such a way that it [empty space, presumably] would have all the appearance of body. 12. Clarifications 1. This way of looking at body has no need for the notion of substance as substratum--as that in which properties or accidents inhere. 15

16 But this way of looking at body does presuppose two things: (1) space and (2) an act of Godʼs will. 2. If this is how body is, then it would be real body. They will be just as much substances as actual bodies are. 3. The relation between extension and impressed form is much like the relation between Aristotleʼs materia prima and substantial form. 4. But Aristotleʼs materia prima is officially indescribable. Newtonʼs space or extension has many properties. Therefore it has more reality than materia prima. 5. We have some idea of Godʼs power to endow space with materiality in our ability, through our wills, to move our bodies. 13. Metaphysical Benefits of this Account of Matter. On the positive side, this account of body confirms and explains three important truths (as Newton sees it) of metaphysics: (1) God exists. (2) He has created bodies in empty space out of nothing. (3) Bodies are distinct from created minds but able to form a union with minds. 16

17 On the negative side, the usual substance/attribute view of bodies leaves us with bare substances [or, as others put it, bare particulars], and bare substances are puzzling. If they have no properties or attributes at all, (a) how could they differ in essence, and (b) how can they differ at all? NB: if the parts of space could move about, as Descartes thinks, then parts of space [and space itself] would be corporeal substance. Newton lists again the properties of space. It is: eternal, infinite, uncreated [but dependent on God], uniform throughout [or homogeneous] immobile, unable to affect how bodies move. [He could have added that his space is isotropic--the same in every direction, Euclidean--the geometry of space3d, of course] 14. Against Descartesʼs Argument against the Existence of the Vacuum. 17

18 The argument of this section is complex. Whatʼs the bottom line? The thesis is that space is distinct from body. Space is only the place in which bodies exist and move. Descartes denied this difference when he identified matter with extension (that is, space or a region of space). And: Since matter and space are distinct, it is possible for a portion of this space to be lack body, to be empty, to be a vacuum. Descartes claimed that if you abstract from (or think away ) body or matter all the properties that you can--its weight, colour, hardness, or other sensible properties--you are left with its extension. That is its essence. Take away extension, and you have nothing; but you can take away everything else. But body has a certain dispositional property or faculty or power, call it P, to stimulate the perceptions of thinking [or sentient] beings [and to move other bodies, as he says at the end of this section]. [That is, a body can to be tangible, even if it need not be hard or soft; visible, even if it need not be any particular colour?] (2) Property P is essential to bodies. Nothing could count as a body that didnʼt have P, the power to cause perceptual states in minds. 18

19 (1) But property P is not essential to extension. According to Newton there is no necessary connection between extension and perception. [The text says ʻthoughtʼ, but perception seems to be the right capacity to invoke.] A given part of extension E that has P could lose it through natural causes. So P is accidental to E, not part of its essence. Newton claims that if one removes property P from bodies, then one also removes the power of that body to affect other bodies, e.g. in collision. That, says Newton, would be to turn the body into empty space. There may be various grades of resistance to passage (from liquid mercury to water to air to aether), but at the limit--no resistance at all--we donʼt have the finest matter, we have nothing, vacuum, empty space. 19