Absolutism and relationism

Now we will consider the question of the ontological status of time itself, and its relation to the material world. The problem can be stated as follows: is time a fundamental substance, capable of independent existence, or is it ontically dependent on things/events? One particular way of cashing out this general question is to ask whether it is possible for time to exist without any change. Of course the possibility in question has to be considered as metaphysical (stronger than logical but weaker than physical). The situation in which time exists but there is no change can be described as follows: there is a non-zero interval (t, t’) such that for any two moments t1 and t2 from this interval, all objects have exactly the same properties at t1 and at t2 (we can call the world in the interval a “frozen universe”). But now it can be argued that because all situations within the interval are indistinguishable, the statement that the length of the interval is non-zero has no empirical meaning. We could also appeal to the Principle of the Identity of Indiscernibles to argue that the moments t and t’ should be identified. However, Sydney Shoemaker has proposed an argument showing that under certain circumstances the hypothesis of the frozen universe can offer some advantages even to an empiricist. Suppose that the universe consists of three parts A, B, and C, and that the data gathered shows that region A goes through the period of a freeze every three years, region B freezes every four years, and region C freezes every five years. From these, empirically confirmed hypotheses it follows that the entire universe will freeze every 60 years, but of course this consequence can never be empirically confirmed or disconfirmed. Facing the choice between two empirically equivalent hypotheses we should choose the simpler one, and this is the one which assumes that there are no gaps in the regular patterns of freezing for regions A, B, C. So methodological postulates accepted by empiricists favour the hypothesis that the entire universe can freeze.

The issue of the dependence between time and the material world can be considered in an even more radical way. We may ask whether it is possible for time to exist without any events taking place. Can there be a period of time consisting of “empty” moments? Notice that this would be a case of time without change, but not all cases of time without change are cases of empty time. The view that it is fundamentally, metaphysically possible for such a situation to occur is known as absolutism, or substantivalism, with respect to time. On the other hand, those who believe that moments cannot exist without participating events (whether they are changes or not) are called relationists. Relationists believe that only spatiotemporal objects (things, events) and their temporal and spatial relations exist in the fundamental sense. Temporal objects (moments) are derived from the fundamental temporal relations. We should notice that absolutism and relationism can be formulated with respect to space as well as time. Relationists with respect to space believe that spatial points and the relations between them are mere reflections of events and their spatial relations (in particular, the relation of co-location).

Leibniz gave a strong argument against absolutism and in favour of relationism. Suppose that absolutism with respect to space is right and that space and spatial points exist independently of the material objects occupying them. Then shifting the entire world 5 metres in one direction would produce a distinct state of affairs (different points would be occupied by different objects) which nevertheless is indiscernible from the original one. Leibniz points out that such a possibility violates the principle of the identity of indiscernibles, and the principle of sufficient reason. We may also add that this argument shows that absolutism violates the principle of ontological parsimony, because it postulates the existence of objects (spatial points) which are not necessary to explain observable phenomena. In addition to this argument, known as the static shift argument, Leibniz also produced another one, based on a dynamic shift. The absolutist should consider the following two states of affairs as distinct: one in which the entire universe is stationary, and the other, in which it moves at a constant speed in a particular direction. But again, there is no observable effect that could distinguish between the two.

Newton was a proponent of absolutism. In support of his view, he pointed out that it is possible to distinguish between being at rest and moving, but this possibility applies only to a certain category of motions, namely accelerated motions. One example of such motions is rotation, which produces observable effects in the form of the centrifugal forces. Newton used this fact in his famous bucket argument. Consider a bucket full of water, suspended on a rope. The rope is twisted, and then released. In the first stage the bucket will start rotating, but the water will for some time remain stationary. The surface of the water will be flat. In the second stage the water being dragged by the sides of the bucket begins its rotational motion. This stage is characterised by a concave surface of the water, due to the centrifugal forces. Finally, the bucket is stopped, but the water inside it will continue spinning for some time. The concavity of the surface is still visible. Newton compared the first and the third stages, arguing that they are perfectly symmetrical with respect to the relative motions of the bucket and water. And yet only in the third stage we observe the concave surface. This can be only explained by postulating the existence of absolute space, against which the water rotates in the third, but not the first stage. But later critics, including Ernest Mach, pointed out that the situation is not exactly symmetrical. In the first case the water is stationary with respect to the rest of the universe, whereas in the second the water moves with respect to the fixed stars. Mach observed that Newton’s argument would be valid if we somehow managed to make the entire universe spin around the water inside the bucket. But this is impossible to achieve. Mach’s position is sometimes interpreted as suggesting that the inertial effects (e.g. centrifugal forces) are a result of the influence of all the masses in the universe on a given system. But Mach himself was sceptical of such a hypothesis, due to its apparent unverifiability.

We can distinguish several variants of the relationist account of space and time. The most radical version of relationism claims that space and time do not exist – the only entities are events and things which enter spatial and temporal relations. More moderate version of relationism accepts that time and space can be defined by abstractions from events, using relations of simultaneity and co-location. Moderate relationism rejects the existence of empty points of time and space, but this fact gives rise to a conceptual problem. Suppose that the universe consists entirely of three equidistant things A, B and C. In spite of the fact that no physical thing exists between A and B, or A and C, we would like to be able to say that there are points of space on line joining A, B and C. One solution could be to assume that a point exists if it is possible for a physical object (an event) to exist at this point. Such a position can be called “modal relationism”. But we have to note that modal relationism comes dangerously close to absolutism. The key is of course the notion of possibility, which has to be defined in a way that saves the distinction between relationism and absolutism.

The historical development of the debate between absolutism and relationism in the context of physical theories has followed a rather twisted path. Newtonian mechanics was originally founded on the idea of absolute space and time, whose mere reflections are temporal and spatial relations given to us in experience. But soon it became clear that Newtonian mechanics can be formulated in a relationist-friendly way, in the so-called Galilean invariant form. In this formulation, spatial and temporal coordinates of objects are defined not as positions in absolute space and time, but rather relatively to some frame of reference of a particular type, known as an inertial frame. All laws of classical mechanics have the same form in all inertial frames of reference, so no particular frame is privileged. The only types of frames which are physically distinguishable from the inertial frames are the ones that accelerate. In the special theory of relativity the absolute character of acceleration is retained, therefore the theory is not fully relationistic. Einstein attempted to include the principle of relationism in his general theory of relativity. Thanks to the principle of equivalence, accelerating frames of reference are locally indistinguishable from inertial frames of reference in a gravitational field. Although the general theory of relativity has certain mathematical features that make it well suited for a physical expression of relationism (mostly its covariant character), it turns out that some consequences of its fundamental equations seem to support substantivalism. In particular, there are solutions to Einstein’s field equations which describe an empty space-time (with no distribution of masses and energy). Another possible solution describes a solitary and yet rotating object, which goes against the idea that all motions are relative.

Readings:

B. Garrett, "Time: Three Puzzles", pp. 87-94, What is this thing caled metaphysics?
E.J. Lowe, Chapter 14 "Absolutism versus relationism", pp. 253-270, A survey of metaphyics.