Monday, March 05, 2007

What is Space, Stephen Tiley

The Reality of Space

Two questions immediately arise:

1) what is space? [metaphysical question]

2) how can we know space? [epistemological question].

Needless to say, both questions are intricately connected: in order to ask what space is we must ask how, if at all, we can know acquire knowledge of it.

The two main historical positions concerning the nature of space are absolutism [or substantivalism] and relationalism.

Absolutism, most prominently expressed by Newton , argues that space has an existence over and above the objects contained within it.

Relationalism, most prominently expressed by Leibniz, argues that space has no existence over and above the relations between objects contained within it.

Both offered intricate arguments to support their respective positions.

According to Newton , as space is ontologically prior to the objects contained within it, viz., space can exist even when there are no objects contained within it, his view entails that objects in space can have absolute positions and velocities.

For Leibniz, on the other hand, space exists only as a relation between objects, and therefore has no existence apart from the existence of those objects; motion exists only as a relation between those objects.

Leibniz believes that such notions as absolute position and velocity, as espoused by Newton ’s absolutism, are meaningless and lead to contradictions.

The two arguments he offers us rely on his principle of sufficient reason and the identity of indiscernibles.

Leibniz thought-experiment:
He asks us to imagine two universes situated in absolute space. The only difference between them is that the second is placed five feet to the left of the first, a possibility available if such a thing as absolute space exists. Such a situation, however, is not possible according to Leibniz, for if it were:
a) where a universe was positioned in absolute space would have no sufficient reason, as it might very well have been anywhere else, hence contradicting the principle of sufficient reason, and
b) there could exist two distinct universes that were in all ways indiscernible, hence contradicting the Identity of Indiscernibles.

In defence against Leibniz, Newton offered us his famous ‘Bucket’ thought-experiment.

Newton’s Bucket:

The rotating bucket argument attempts to show that true rotational motion cannot be defined as the relative rotation of the body with respect to the immediately surrounding bodies. It is one of five arguments from the "properties, causes, and effects" of true motion and rest that support his contention that, in general, true motion and rest cannot be defined as special instances of motion or rest relative to other bodies, but instead can be defined only by reference to absolute space.

Water in a bucket, hung from a rope and set to spin, will start with a flat surface. As the water begins to spin in the bucket, the surface of the water will become concave. If the bucket is stopped, the water will continue to spin, and while the spin continues the surface will remain concave. The concave surface is apparently not the result of the interaction of the bucket and the water, since the water is flat when the bucket first starts to spin, becomes concave as the water starts to spin, and remains concave as the bucket stops.

This argument attempted to demonstrate the necessity of the existence of absolute space to account for phenomena like rotation and acceleration that cannot be accounted for on a purely relationalist account. Clarke argues that since the curvature of the water occurs in the rotating bucket as well as in the stationary bucket containing spinning water, it can only be explained by stating that the water is rotating in relation to some third thing, namely absolute space.

According to Newton , absolute space has the following properties:

1) Space has an ontologically prior existence to the objects contained within it.
2) Space can affect the objects/matter contained within it, but these objects cannot affect/influence space itself.

On a first reading absolute space seems to be endowed with a rather bizarre ontological status: it can exert an influence on objects contained in it but cannot itself be affected. It is immutable, eternal and unchanging.

Furthermore, if we cannot exert and influence of space itself, how can we possibly acquire knowledge of its existence?

As all we can really interact with are the objects contained within space, surely it follows that only these objects can be said to exist….?

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Blogger bloggin the Question said...

First reation is to side with Leibniz and say that with the spinning bucket the motion is relative to itself and the arm of the spinner. If there were two buckets in an infinite void with the same energy they would be the same. The water is accelerating in the spinning case.

6:58 PM  
Blogger Anatole said...

Mmm, interesting point.

However, if there's nothing else in the universe, how could it be established that the bucket was genuinely spinning...?

Surely it's equally possible that the water surface in the bucket would stay flat.

As such an experiment would be impossible to actually carry out, admittedly,this is all completely speculative.

Ernst Mach argued that the water in such a bucket in an empty universe [well, empty except for the bucket!] would remain flat.

But why, Mach asks, should the bucket be rotating relative to Newton's absolute space?

Why should it be rotating relative to something which is metaphysically dubious and epistemologically inaccessible...?

Why not simply argue that, if the bucket has to be rotating relative to something, why not simply argue that it's rotating relative something that could be regarded as 'fixed' relative to the bucket?

But what could be regarded as being the relatively 'fixed' object the bucket's rotating relative to?

Mach's answer: the distant stars...

7:49 PM  
Anonymous Anonymous said...

It's worth bearing in mind that the relativist theory of space and motion that Newton's own theory was set up in opposition against was not that of Leibniz but rather that of Descartes. (An aside: if one looks at the original title page of Newton's Principia, the words of the title are disproportionately sized: it reads 'PRINCIPIA mathematica PHILOSOPHIAE naturalis', a pretty blatant allusion to Descartes's own 'Principia philosophiae', the chief work of Cartesian physics and, indeed, the most authoritative and best-supported work of any kind of physics around at the time when Newton was writing).

This is probably why Newton was content to limit his attention in the bucket discussion to the relative motion between the water and the bucket that contained it. Descartes, following Aristotelian tradition, had indeed defined (external) place in terms of the boundary between an object and its immediate surroundings, and he had defined motion as "the transference of one part of matter or of one body, from the vicinity of those bodies immediately contiguous to it and considered as at rest, into the vicinity of others" (Principia philosophiae, pt. 2, sect. 25).

Descartes also wrote: "the transference is reciprocal; and we cannot conceive of the body AB being transported from the vicinity of the body CD without also understanding that the body CD is transported from the vicinity of the body AB, and that exactly the same force and action is required for the one transference as for the other." (pt. 2, sect. 29). It is this concept of force that really gets to the heart of the difference between Newton and Descartes. Newton, let's not forget, was exceptionally keen on real forces -- even to the point of leaving open the possibility that his gravitational force might operate by non-mechanical means. In the case of the bucket, the fact that the water could be either flat or concave, regardless of whether or not it was in relative motion with the bucket, surely showed that there had to be some real force that was sometimes acting and sometimes not; and, when acting, then acting on it.

Even if a relativist did take objects outside the system into account -- the distant stars, or whatever -- it was only by opting to regard these as at rest that he could support an ascription of motion to the water. But what if they weren't really at rest? What if the water was in fact the stationary thing, and the whole of the rest of the universe was rotating around it? Now, Leibniz (and probably Descartes too) would say that there could be no fact of the matter about which of these scenarios was really the case. The two situations would be indiscernible, and hence identical. But surely (and here, admittedly, Newton does have to indulge in a bit of hand-waving) there is a fact of the matter about whether it's the water or the rest of the universe that's moving. And, even more surely, it can't possibly be right to say, as Descartes did in fact suggest, that "exactly the same force" is required, either to swirl a couple of kilograms of water gently about, or to shift the whole of the rest of the universe, and, what's more, to move the more distant portions thereof at a truly colossal speed!

Descartes's theory of place and motion is actually riddled with difficulties, far more than it's worth getting into here (and more, as it happens, than Leibniz's version). There's a very intriguing paper by Thomas Lennon in the latest Journal of the History of Philosophy, which argues that these problems were in fact just illusory, on the grounds that Descartes didn't think that motion was real at all, or even that bodies were real. For Descartes, Lennon suggests, body (extended substance) was real, but bodies (extended substances) were not. I'm not sure Lennon has done quite enough yet to establish so surprising a conclusion, but it would certainly clear up myriad problems for Descartes if it could be made to stick. As for Leibniz, we certainly know that he regarded body, and physics in general, as belonging to a phenomenal realm, albeit a realm of 'well-founded' phenomena. Berkeley too, another relativist, also drew bodies into the phenomenal realm. But Newton was convinced that bodies, motions and forces were real. More precisely, he felt that there had to be some way to define a difference between real and merely relative motions, in order to be in a position to defend the claim that there were such things as real forces that could have effects on such real motions. (Every schoolchild knows the law I have in mind: F=ma). Hence, the appeal to absolute space (and also time).

It is certainly ironic that, in order to preserve the reality of the objects of empirical knowledge, Newton had to resort to a metaphysical thesis about an underlying structure that was wholly unobservable. But then, I suppose the same is true of forces themselves -- they're not observable either. That didn't stop Newton from believing in them. Anyway, I could go on, but I'm tired, so I shall leave it there.

10:25 PM  
Anonymous Enigman said...

Well, physical objects might affect space, by curving the space-time, if the space exists, of course. And if we are primarily mental beings then we interact primarily with sensations and ideas and such like; so we would be positing the physical objects much as we posit the space they occupy. But it makes sense to posit physical objects, and so similarly to posit space. The idea of spatial relations between objects without any actual space between them seems (according to my everyday experiences) no better than the idea of objectual relations between my perceptual sensations without there being any actual objects there. So, why have no space but have objects?

11:26 AM  
Anonymous Anonymous said...

I think all this leads us to deeper questions - about matter and space (abs. or rel. -whatever)

12:32 AM  

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