17a

Newton

(Matthews 139-146)

[I]n philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them.

– Newton, Principia, Scholium on space and time

In 1748 the great Swiss mathematician and physicist, Leonhard Euler, published a paper in the Mémoires de l’académie des sciences de Berlin entitled, “Réflexions sur l’espace et le tems,” (Reflexions on space and time). In it he observed that the principles of Newtonian mechanics had proven to be so useful for explaining the phenomena of nature as to be beyond doubt, and he cited two principles in particular that had achieved that status: that a body once at rest will remain at rest forever unless acted upon by some outside force, and that a body once set in motion in a certain direction will continue in that same direction with that same speed unless acted upon by some outside force. In effect, bodies will resist efforts to change their state of motion and rest.

Having made this observation Euler proceeded to ask a question: what is it with reference to which a body acts to resist efforts to change its state of motion? Alternatively, what is it with respect to which a body preserves in its state of motion? Or, yet again, what is it that governs the inertial behaviour of bodies?

Is it something real that does this? Or is it something merely imaginary — something that human beings have cooked up merely as a way of organizing and classifying things and that they could have made in any of a number of different ways, like our varying ways of classifying things into groups?

The answer to this question may seem so obvious that it would be absurd even to have bothered to ask it. Obviously, something merely imaginary could not be what bodies move with reference to or what causes them to resist certain kinds of motion while persisting in others.

But sometimes obvious answers to obvious questions can have disquieting results.

Euler was writing at a time when a significant proportion of the natural philosophers of continental Europe, a group Euler referred to collectively as the “metaphysicians,” had gathered behind Leibniz in opposition to the English “mathematical philosophy” of Newton. The metaphysicians had rejected action at a distance, and hence Newton’s account of gravity, as an abomination, and they were no friendlier to Newton’s claim that space is distinct from the extension of body and exists independently of it. All space is just the extension of some body, they had claimed, and all motion is relative to bodies, with it being simply a matter of choice or stipulation which bodies are taken to be at rest and which bodies are accordingly taken to be in motion relative to those stipulated to be at rest.

But then what about the inertial properties of bodies? If we say that a body resists changes in motion, do we merely mean to say that it resists being moved away from those bodies that immediately surround it? That can’t be right. Consider a ship in still water. The ship is at rest relative to the water particles that surround it. Now consider what happens if the water starts to move. At first the ship stays where it is and it is only gradually, as the water particles continue to hit it, that it begins to move with the stream and it takes some time for it to take on the full speed of the water particles. Why? We think it is because of the ship’s inertia. The ship, once at rest (or once moving in a certain direction at a certain speed) resists any changes to that state of motion so that it takes some force from the continually impacting water particles to make it move.

But if that is what is going on then it means that the ship’s inertial state cannot be determined with reference to the immediately surrounding bodies. If it were, then as soon as the immediately surrounding bodies started to move, the ship would move along with them, since the principle of inertia says that it strives to say in its state of motion, and if its state of motion is defined relative to the immediately surrounding bodies, then when they move it must strive to move along with them. Far from it taking a force to speed the ship up to the speed of the water, it ought to take a force to hold it back. But just the opposite occurs.

So let’s return to our question. What determines the inertial behaviour of bodies? If it is not the immediately contiguous bodies might it be some more remote ones, considered as being at rest? But which ones would those be? If all motion is ultimately relative and we merely stipulate which bodies we are going to treat as the landmarks relative to which others are moving, then we make the inertial behaviour of bodies depend on something merely imaginary, because we can imagine any bodies we want to be the fixed ones relative to which others are moving. And, manifestly, that is an incorrect way of looking at things, because we can pick certain bodies as the ones we want to consider to be at rest and then discover that the inertial behaviour of bodies does not follow in accord with our stipulations. Sitting by the window of a train I see another train pass by, and I stipulate that I must therefore be at rest and it in motion. But then I look down at the floor and see a bottle rolling down the aisle towards me at the same speed the train is passing by outside — even though the bottle was lying there motionless a moment ago. I am not going to say that some occult cause gave the bottle a push. I am going to say that the fact that I stipulated that my train car is at rest is merely the way I was imagining things and if I want to get the facts right I had better start to imagine that I and the train car have started to move in the opposite direction and that bottle and the outside train are preserving in their inertial state.

But if the inertial state of bodies is not governed by their motion or rest relative to the immediately surrounding bodies and not governed by what bodies I choose to imagine them to be moving or resting with respect to, then what is it governed by? Very remote bodies like the fixed stars? It would be a strange thing, however, if bodies that are so many trillions of miles away from us should govern the inertial behaviour of bodies here on Earth. — And a particularly strange thing for “metaphysical” natural philosophers to maintain, given their otherwise adamant rejection of action at a distance! Moreover, the problem simply recurs when we ask about the inertial state of bodies in close proximity to the fixed stars. Is it reciprocally governed by motion relative to the Earth?

For Euler there was only one sensible answer to the question. The inertia of bodies — whether or not they exhibit effects of inertial force — is not governed by whether or not bodies are moving relative to other bodies, be those other bodies near or remote. It is governed by whether or not they are accelerating relative to space itself.

Space must accordingly be a thing in its own right, even if a radically different kind of thing from body. The principles of inertia cannot be sustained in concert with a purely relativistic account of space and motion. There must be an absolute space existing independently of body as the ultimate reference frame for inertial motion.

Newton had been of the same opinion. His reasons for believing that space exists apart from body are similar to Euler’s and were stated in the Scholium to the 8^th definition of the first book of the Principles.

QUESTIONS ON THE READING

1. Under what notions do common people conceive space and time?

2. Does it make sense to say that an hour could take more or less time to pass?

3. List the properties of absolute space.

4. How is relative space determined?

5. How can absolute and relative space be the same in figure and magnitude, but different numerically?

6. How does absolute motion differ from relative motion?

7. Why is it absurd that the parts of absolute space should move or change position relative to one another?

8. Why do we consider relative places and motions instead of absolute ones?

9. Why should we not rest content with relative places and motions in philosophical disquisitions?

10. How can we distinguish absolute rest and motion from relative rest and motion?

11. Why can true and absolute motion not be determined by motion relative to surrounding bodies taken to be at rest?

12. What are the causes by which true motions are distinguished from relative motions?

13. How can a true motion be preserved when the relative remains unaltered, and the relative preserved when the true alters?

14. What are the effects that distinguish relative from absolute motion?

15. What does the ascent of the water up the sides of the spinning bucket prove?

16. Why can true circular motion not be determined by rotation relative to any ambient bodies?

17. What is wrong with Descartes claim that the planets are at rest in their vortices even though the vortices are in motion around the Sun?

18. Why is it a matter of great difficulty to tell true motions apart from apparent?

NOTES ON THE READING

However compelling the reasons for recognizing that pure space is a thing that exists in its own right, independently of anything else, there are equally compelling reasons for denying that there could be any such thing. People have long thought that whatever exists must either be a thing, or a property or relation of a thing, and they accordingly have treated space as either a property of things (their extension) or at least a relation between things (a relation of distance between bodies presumed to be at rest and taken as defining positions). Newton and Euler denied this. But if space is not a property or a relation of things, it does not seem that it could be a thing either. After all, two things cannot be in the same place at the same time. But space, if it exists, is perfectly penetrable. It allows bodies to occupy its own extension without moving to the side or putting up any resistance so that it coexists in the same place with bodies. How could a real thing do that? Moreover, if space were a thing, it ought to have properties of its own. But space doesn’t seem to have any properties — or if it does, then such properties as it has don’t amount to anything. Space is said to be undifferentiated, unbounded, immobile, immutable, indivisible (in the sense that one of its parts cannot be separated from the others and moved somewhere else), unresisting, and so on. As George Berkeley was later to put it,

And so let us suppose that all bodies were destroyed and brought to nothing. What is left they call absolute space, all relation arising from the situation and distances of bodies being removed together with the bodies. Again, that space is infinite, immoveable, indivisible, insensible, without relation and without distinction. That is, all its attributes are privative or negative. It seems therefore to be mere nothing. The only slight difficulty arising is that it is extended, and extension is a positive quality. But what sort of extension, I ask, is that which cannot be divided nor measured, no part of which can be perceived by sense or pictured by the imagination? … From absolute space then let us take away now the words of the name, and nothing will remain in sense, imagination, or intellect. Nothing else then is denoted by those words than pure privation or negation, i.e. mere nothing. [de Motu, art. 53]

Newton was undaunted by these metaphysical objections. If we have no place for space in our ontology, then so much the worse for our ontology, because our physics requires it. His own preferred metaphysical opinion on the matter was that space is what he called the “sensorium” of God. In early modern terminology, when you play a game of chess in your head, and picture the board with the pieces on it, the place where that picture exists is your “sensorium.” The sensorium is like the stage of a theatre: an empty mental space waiting to be populated with imaginary objects. God has a sensorium, too. Except that whereas our sensoriums are occupied with the creatures of our own imaginations, God’s sensorium is occupied with real things. In projecting things onto his sensorium God as it were imagines them into existence (his imagination being powerful in that way). However, even apart from that activity, the sensorium exists as a permanent part of God, apart from any created things.

However, none of these wilder speculations make it into Newton’s scholium on absolute space and time. Instead, we are confronted with what has turned out to be an enduringly challenging and perplexing set of arguments for the independent reality of space.

Opening definitions. Newton’s scholium opens with four definitions — offered, so he said to remove common prejudices arising from conceiving space and time relative to sensible objects. (There is an interesting denigration of sensory experience here. It is not the only one in the scholium and more will be said about this presently.) The definitions should be understood as simply laying out what he meant to talk about over the remainder of the section.

I. First, Newton claimed that we ought to understand “absolute, true, mathematical” time to be distinct from any sensible motion used to measure time. Sensible motions used to measure time may speed up or slow down; whereas what he meant to refer to by absolute time is something that passes uniformly, and would pass even if there were nothing in motion.

II. Second, Newton claimed that we ought to understand “absolute, true, and mathematical” space to be something that exists independently of the extension of any sensible object and apart from reference to any sensible object that is taken to serve as a landmark. Just as absolute time flows with perfect uniformity, never speeding up or slowing down, so absolute space is everywhere the same (undifferentiated or homogeneous) and immobile.

Absolute space is to be distinguished from relative space, which is space defined relative to sensible objects considered to serve as landmarks. “Relative spaces” can be numerically identical with a portion of absolute space, but they can also be in motion through absolute space, if the landmark objects are in motion.

III. Third, Newton defined absolute place is the part of absolute space a body takes up. The size and shape of an absolute space is determined by the size and shape of the body in question; however, its position is determined relative to the other parts of absolute space.

Relative place, in contrast, is the part of relative space a body takes up and its position is determined relative to sensible landmark objects.

IV. Finally, Newton defined absolute motion is the “translation” of a body from one absolute place to another. Absolute motion is again to be contrasted with relative motion. Bodies in relative or apparent motion may have no absolute motion (they may not change place in absolute space) or they may have a motion or variously compounded motions depending on how the sensible landmark objects with which they are compared are moving with reference to yet more remote landmarks, how those landmarks moving with reference to yet more remote landmarks, and so on.

Conceptual arguments for the existence of absolute space and time. Having laid down these definitions, Newton proceeded to offer two arguments for the existence of absolute space and time. The arguments are “conceptual” arguments in the sense that they depend, not on appeal to experience, but simply on analysis of common notions.

First, turning to absolute time, Newton claimed that astronomers have discovered that the various sensible motion used to measure time are not perfectly uniform. The motion of the Earth about its axis, for instance, is sometimes faster and sometimes slower. And while we have discovered this by comparing the motion of the Earth to other motions that we take to be more regular, such as that of pendulums, we realize that whatever moves is subject to moving forces that can accelerate or retard its motion. Anything we fix upon as a measure of motion could conceivably be sped up or slowed down by moving forces.

But a motion could hardly speed up or slow down over time if time just is what is measured by that motion. In our very way of thinking and speaking, therefore, we recognize the existence of something else: an ultimate time that passes uniformly independently of any sensible process.

Turning to space, Newton proceeded to argue that any merely relative space may be conceived to move in a larger, containing space. Given any set of objects considered to be immobile landmarks, we can imagine some more remote landmarks with reference to which the first objects move.

But it is conceptually impossible that any part of space itself could move. That is because motion just is change of place. If a part of space changed its place, there would have to be some place that stays behind and is immobile so that the part can be conceived as moving out of it. If that can’t be then no place can move. On the other hand, if we think it could be, then a place would have to move out of itself and come to be in two places at once. But one place cannot be two places. So, either way no place can move. There must be absolute places. And so there must be absolute space, which is just the sum of the collection of absolute places.

We have failed to appreciate these conceptual points, Newton charged, because the parts of space cannot be seen or distinguished by our senses. Consequently, we have used sensible marks in their stead. While this has served us well enough for all practical purposes, Newton claimed that, “in philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them.”

Counterarguments. There are counterarguments to these two arguments. In response to Newton’s claim that our idea that any motion could speed up and slow down presupposes a reference to an absolute time the relativist could reply that the idea involves no such commitment. We never do any more than consider one motion to speed up or slow down relative to some other motion (perhaps some other motion that we conceive to be less subject to any special forces causing it to be unnaturally accelerated or retarded). Ultimately, the choice of which motion to pick as most uniform is stipulative, and once the stipulation is made it is impossible by definition for that motion to speed up or slow down. All other motions speed up or slow down with regard to it. If this means that the inertial properties of bodies are taken to depend on our arbitrary will and choice in making a stipulation, we can always choose to let our stipulation be guided by background theories about what moving forces are operating on bodies.

In response to Newton’s further claim that there must be an immobile and hence absolute space because motion is change of place and it is absurd that any place could move out of itself the relativist could reply that motion is not change of place. It is change of place relative to certain sensible landmark objects. So where there are no bodies there can be no motion just for that reason. And where it is not obvious which bodies to take to be the landmarks, we can make various stipulations and then the places determined by those stipulations will likewise be immobile, even though under other stipulations those same places would move. Again, if we are worried about making the inertial properties of bodies depend on our arbitrary will and choice in making a stipulation, we can always let our choice be guided by background theories about what moving forces are operating on bodies and pick those that our science tells us are not being accelerated by any known forces.

Finally, Newton’s claim that “in philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them,” bears particular notice. Seen in the light of what was said in the previous lecture this can only appear as a very odd claim — if not a strikingly inconsistent one. As noted in the previous lecture, it was Descartes who had sought to uncover “metaphysical first principles” that could serve as the foundations for natural philosophy, and he had sought to do so by “looking within” and engaging in a kind of conceptual analysis of body and mind and God. Newton, who had so strongly condemned that procedure and proposed to lop the metaphysical head off of the Cartesian scheme and just proceed by induction from experience, seems, in the scholium on space and time, to have entirely abandoned that Baconian project and taken up precisely the sort of a priori conceptual theorizing he had condemned in Descartes. The claim that we ought to abstract from what our senses tell us and consider things in themselves apart from sensible measures is the kind of claim that Descartes would have made in the second Meditation rather than the kind of claim made by the person who had sought to appeal to experience to justify appeal to forces and action at a distance.

Properties, causes, and effects. However, while the relativists would not have been silenced by Newton’s conceptual arguments it is far from clear that their responses do any more than preserve their positions from refutation. Newton’s conceptual appeals remain compelling and it is not obvious who has the stronger case. And Newton’s arguments for his position did not end here. The strongest argument is yet to come.

Newton proceed to observe that while absolute space and time cannot be seen or distinguished by our senses, the same is not the case with absolute rest and motion. Absolute rest and motion may be distinguished from relative rest and motion, he claimed, by their properties, causes, and effects. If this is true, it would pose an even more serious challenge to the relativist position. If there is absolute motion and rest, there must be an absolute space and time in which the motion and rest takes place. Sensible evidence for absolute motion and rest would accordingly give us more than a merely conceptual argument for the existence of absolute space and time.

Properties. Beginning with properties, Newton claimed that it is a characteristic of absolutely resting bodies that they rest with respect to one another. Contrapositively, where bodies are not observably at rest with reference to one another, there must be some sort of absolute motion going on. Even merely relative motion of one body towards another proves that something must be really moving somehow. One body can’t change its distance from another without something changing its place in absolute space, whether the one body, or the other, or some a combination of the two.

However, Newton went on to allow that it is difficult to determine from the differently moving bodies in the visible world which are the absolutely resting ones, if any. Just because a body is in motion or at rest relative to some surrounding bodies, such as the fixed stars, it does not follow that the body must be in absolute motion or rest. If the shell moves, the kernel moves with it, so rest relative to the fixed stars, considered as shell, does not prove absolute rest, since the fixed stars could be in motion. Conversely, if the kernel moves the shell may be moving in the opposite fashion so motion of a body, considered as kernel, relative to the shell of the fixed stars, does not prove absolute motion, either.

This may seem perplexing. Having claimed that absolute motion may be distinguished from relative motion by its properties, causes, and effects, Newton seems to have ended up by saying that it may not be distinguished from relative motion by its properties after all. But we have not reached the end of the scholium. Newton has at least established that where there is relative motion there must be some sort of absolute motion. A difficulty remains over just how the bodies are to be supposed to be moving in absolute space. He will later propose a solution to this difficulty.

Causes. Turning to causes, Newton proceeded to observe that whatever has a moving force impressed upon it is truly moved, and so is in absolute motion.

But here again there is a problem because it is a question how to determine what the moving forces are, and where they are acting. We can’t turn around and take merely apparent motions as proof of the existence of impressed forces. A body can seem to move, not because some force is acting on it, but rather because some force is acting on its surroundings to push them in the opposite direction. Likewise, a body can seem to be at rest even though both it and its surroundings are mutually being moved by some impressed force. We might think that we might ourselves be in something of a privileged position in this regard because we can at least sense when we are putting out an effort to move something and so ought to be able to tell what forces we are impressing on bodies to make them really move. But we are ourselves often carried around by other forces that make our best efforts produce the opposite of any motion. Think of trying to paddle a canoe upstream. Our efforts would only be a guide to determining which bodies have forces acting on them if we only ever acted on bodies that did not already have other forces acting on them, and that is not the case.

Again we seem to have drawn a blank. But again it would be premature to infer that causes can never be used to distinguish true from apparent motions.

Effects. Finally Newton turned to the effects of absolute motion, and it is at this point that the principal argument for absolute motion, and hence for absolute space, is expressed.

In any revolving body, Newton claimed, a real circular motion of the body — arising from the body really changing place in absolute space — can be distinguished from a merely relative circular motion — arising from its surroundings changing position with regard to it — by the effect of the parts of the body endeavouring to recede from the axis of rotation.

Here we do not draw a blank. Where we see a spinning body throwing off parts in all directions, we can be sure it is really spinning. On the other hand, if the body has no rigidity or cohesion, like a merry-go-round piled high with old, discarded boots, and we see it spinning around with none of its contents flying out of it even though they are the sorts of things that are not stuck together, then we can be sure that the motion is merely apparent and it is rather the surroundings that are turning.

Newton proceeded to illustrate this point with the example of a rotating bucket of water. According to this famous experiment, we are to fill a bucket part way with water, hang it from a long cord, spin it around to twist the cord tight, and then release it so that the unwinding cord causes the bucket and its contents to start to spin. The ensuing experiment proceeds through three stages, at which we make the following observations:

Stage 1: The bucket cord is wound up and the bucket held. We see the water in the bucket to have a flat surface. The water is at rest relative to the sides of the bucket.

Stage 2: The bucket is released and the cord unwinds, spinning the bucket. Though the bucket spins, its motion is not immediately communicated to the water. At this stage, the surface of the water is still flat. However, the water is in high motion relative to the sides of the bucket.

Stage 3: As time passes, the spinning bucket communicates its motion to the water. As this happens, the water comes to rest relative to the sides of the bucket. However, something else happens as well. The surface of the water is no longer flat, but concave. Because the water is spinning, its parts are trying to recede from the axis of rotation and the water is heaving up the sides of the bucket as it tries to do so. So though we have rest relative to the sides of the bucket, as we did at stage one, everything is not the same as before. There is a force effect present that shows the true circular motion of the water, notwithstanding its rest relative to the sides of the bucket.

Stage 4. Though Newton did not go any further, we can imagine a fourth stage at which someone grabs the spinning bucket and holds it stationary. At this stage the water in the bucket continues to spin, and its surface continues to be concave as its parts mount up the sides of the bucket to recede from the axis of rotation. Now, once again, there is high relative motion of the water to the sides of the bucket. But unlike at stage 2, at this stage there is a force effect, indicating that the motion of the water is not just relative, but real.

Taken in sum the four stages of the experiment show that there can be true motion or true rest irrespective of whether there is relative motion or rest. The latter does not determine the former. Instead, the former is indicated by the presence of force effects. High relative motion can be due to the motion of the surroundings rather than the contents (as at stage 2), in which case the contents do not really move, and high absolute motion can occur even when there is zero relative motion, as at stage 3 where both the contents and the surroundings are in absolute motion.

Questions. Though the bucket experiment may seem to shatter the view that all motion is relative, commentators continue to be divided over exactly what it proves. Is the bucket experiment an experiment or just an illustration? If it is an experiment is it an empirical experiment, intended to produce an observation that confirms a theory, or a thought experiment — one that cannot actually be performed but that appeals to our intuitions about what would happen in some contrary to fact case? Newton claimed to have performed it, which suggests that he intended it as an empirical experiment.

But then, what exactly does the bucket experiment prove? It can’t plausibly prove that when we see the water move up the sides of the bucket we are seeing the true motion of the water in absolute space. It can’t prove this because we know that the Earth is moving relative to the fixed stars, and therefore that the whole Earth and everything on it, including the bucket and water are very likely in some state of absolute motion (granting that it is implausible that the Earth is the only body in the universe that is truly at rest). So the true or absolute motion of the water in the bucket could not only be its rotation about its axis in the bucket. It would have to be some combination of that rotary motion with other motions, not revealed by the experiment.

On standard interpretations, the point of the bucket experiment is not to fix the true, absolute state of motion of the water. The bucket experiment only suffices to establish a point of principle: that not all motions are merely relative; there are such things as real or true or absolute motions, even if we may not know in any given case exactly what they are. But, it is argued, we don’t need to know this for any given case. All we need to know is that for sure there are some components of observed motions that are unquestionably due to absolute motion. If there are absolute motions, there must be an absolute space. And thus, the bucket experiment constitutes a kind of empirical confirmation of the existence of absolute space.

On this understanding, Newton was not so Cartesian in his scholium after all. The claims about absolute space ultimately rest on appeal to experience and not on mere conceptual analysis.

But not everyone has been satisfied with the argument considered in these terms — or, consequently, willing to attribute precisely this version of it to Newton (being reluctant to suppose that he could have intended to give an argument that they consider to be bad).

A problem with this argument is that it does not actually prove that there is absolute space. It only proves that there are absolute motions (those indicated by force effects). It is a bit of a leap to say that because there are force effects that therefore there must be motion in absolute space, especially given that we don’t see motion in absolute space. What we do see is, ultimately, motion relative to the fixed stars. And perhaps that is all that the bucket experiment proves: that when bodies move relative to the fixed stars there are force effects that aren’t there when they are at rest relative to the fixed stars.

Newtonians like Euler claimed that it would be an odd thing if the fixed stars were to direct the inertial properties of bodies here on Earth. But Newton himself had declared it to be a “rule of reasoning in philosophy” that “we are to admit no more causes of natural things than such as are both true and sufficient to explain the appearances.” If we see that bodies gravitate towards one another over immense distances, then we are to pronounce it a law that bodies gravitate towards one another over great distances and not to formulate hypotheses about what intermediate mechanism might be responsible for this producing this effect via contact. Later natural philosophers have taken this to heart, and wondered why, by parity of example, we should not just take it to be a law that bodies attempt to persevere in their state of rest or motion relative to the fixed stars and not seek to formulate hypotheses about some absolute space that might be more immediately responsible for producing the effect as the body moves in and out of its places.

One response to this line of criticism on the part of defenders (or reinterpreters) of Newton has been to say that Newton never intended for the bucket experiment to be taken as empirical confirmation of absolute motion and hence a reason for inferring absolute space. Instead, it ought to be read as something more like a thought experiment. In the actual experiment, the water rotates or rests relative to the sides of the bucket while the fixed stars have the status of landmarks with reference to which the bucket is rotating. But what if we change the experiment and imagine the bucket and water rotating in an otherwise empty space, or if we imagine that instead of just the bucket turning the entire visible universe is caused to rotate with just the water in the bucket remaining in place. When we ask these questions we have entered the realm of thought experiment.

It is not implausible that Newton would have wanted us to think along these lines and reach the conclusion that even in an otherwise empty universe, the water would still rise up the sides of the bucket as it starts to rotate — or that even in our universe, it would remain flat if the heavens and all of the rest of the universe were rotating around it, rather than it rotating within them. That would certainly scuttle any attempt to argue that inertial forces might be determined by reference to the fixed stars. The point of the experiment would be to get us to see that this is not plausible because intuitively, even if there were no fixed stars there would still be inertial forces, and even if there were motion relative to the fixed stars, there might be no inertial forces.

But then the “experiment” is not an empirical proof of the existence of absolute space, but a further conceptual argument in the grand old Cartesian style — or perhaps just an illustration of what it means to say that real motion is distinguished by force effects.

Perhaps that is all Newton ever intended it to be.

From effects to causes to properties. Earlier I alluded to the fact that while Newton said that absolute motions are distinguished from merely relative ones by their properties, causes, and effects, he seemed to give up on the idea that the properties and the causes of absolute motions are readily detectible. But I also suggested that this only seems to be the case. The scholium concludes by running through the cases in reverse to show how, starting from the effects, we can go back to use causes to determine absolute motions, and then go even further back to properties.

To show how this might be done, Newton asked us to consider two globes connected by a cord. In an otherwise empty universe, the true rotation of the globes about a common center would be distinguished by tension in the cord (as indeed it would be in a universe filled the way ours is). So this motion, at least could be picked out as an absolute one.

We could go a step further. We could take the amount of tension in the cord to be a measure of the degree of relative motion.

Now comes the second stage. From having determined what we can by reference to the effects of absolute motion, we turn to the causes: We deliberately apply a moving force to opposite faces of the two globes and see whether the tension in the cord increases or decreases. If it increases, we know that the globes were all along rotating in the direction of the forces we applied. If it decreases, we know they were moving in the opposite direction. (Keep in mind that we are in an otherwise empty universe, so this is the only way to determine the direction of rotation.)

At this point we have determined both the speed and the direction of rotation of the globes.

Now imagine the universe filled with bodies and look for some circumambient objects that appear to be preserving their distance from the globes and from one another while rotating in the opposite direction. These bodies can be considered to be at rest in absolute space (because where they rotating they would recede from one another), and their positions can define positions in absolute space, so that the absolute state of motion of all other bodies can be determined relative to them.

Thus we really do end up being, at least in principle, able to use causes and properties as well as effects in order to discriminate absolute motions.

Rejoinders. Two final objections are worth mentioning.

The first is that Newton’s final attempt to account for how we might distinguish between absolute and relative motions does not discriminate between the case where the landmark objects are really at rest in absolute space and the case where the entire visible universe, globes and all, is in uniform rectilinear motion. Force effects only arise with respect to accelerations (changes of speed or direction.) Where there is uniform motion there are no more force effects than there are when there is absolute rest.

Newton’s opponent, Gottfried Wilhelm Leibniz, made much of this fact, claiming that in this case, it would make no observable difference whether the landmark bodies are supposed to be in uniform motion or at absolute rest. But there can be no distinction without a difference. If there is no difference between the cases of uniform motion and absolute rest, there can be no distinction between them, either.

So we can’t tell what bodies are in absolute motion or at absolute rest after all. All we can do is say what bodies are in motion relative to what other bodies. The notion of absolute space is inapplicable and might as well be abandoned.

A final objection reiterates a point made earlier. If the arguments for the existence of absolute space are all purely conceptual, how does that fit with the inductivist scientific methodology Newton elsewhere advocated? Was he, in the end, more of a metaphysician than he let on?

ESSAY QUESTIONS AND RESEARCH PROJECTS

1. Newton’s supposition of the existence of absolute space brought its own metaphysical difficulties with it. One of the most brilliant statements of some of these difficulties is to be found in Notes F and G of the article on Zeno of Elea in Pierre Bayle’s Dictionnaire historique et critique (available in translation in Richard Popkin, ed., Historical and critical dictionary: selections [Indianapolis: Hackett, 1991]), 353-372. Recount and assess Bayle’s case against the possibility of the existence of a real space.

2. Leibniz engaged in a critical correspondence with Newton’s colleague, Samuel Clarke, that is widely available in various independent editions and collections of Leibniz’s works (usually under the title of “the Leibniz-Clarke Correspondence”). Study the correspondence and identify Leibniz’s main objections to Newton. Describe Leibniz’s alternative account of the nature of space and assess whether it is more plausible than Newton’s.

1. George Berkeley considered absolute space and time to be “abstract ideas” that have been invented by philosophers and that do not reflect anything that could possibly exist. He was unpersuaded by Newton’s bucket experiment and attempted to respond to it both in his Principles of Human Knowledge 101-117 and in his De Motu 52-66. Explain and assess Berkeley’s arguments.