Bucket argument

Newton advanced his so-called "bucket argument" in support of the belief that space is a substance existing independently of the matter it contains. He thought of space as a container - of which we can have no direct experience - holding the objects of physics (matter and energy). The contrasting view, held notably by Leibniz, saw space simply as the system of relations between those objects: no container, no unknowable metaphysical substance, just a part of the experience we have of separated and extended objects.

The bucket argument is a thought experiment describing a universe containing nothing but a pail of water suspended from a rope. (We assume there is a force comparable to gravity, but no mass below the bucket; the rope is likewise attached to a tree that isn't there, keeping the bucket from falling.) Now suppose the bucket and the water inside it are both at rest: the surface of the water will be level. If, however, the bucket and water are both spinning at the same speed in the same direction, the water's surface will become concave. The problem for the relationalistic idea of space arises from the fact that in both cases, the water and bucket are at rest with respect to one another. Since there is nothing else in the universe (ignoring the rope, since we're good sports), there is nothing else with respect to which the water is spinning; therefore, since the water is behaving as though it is spinning, there must be something absolute with respect to which it is spinning: absolute space.

A variant of this argument which leaves out the troublesome rope has a universe composed of two rods lying separated in the z-direction, with their respective centres on the z-axis, and each perpendicular to the z-axis; one rod is at rest, and the other is rotating in the xy plane about its centre. An observer standing on the rotating rod will feel a centripetal force which is not present on the other rod; however, a relationalistic account of space gives no way to distinguish between the rods, since each could be described as rotating relative to the other.