The ontology of space and time has been controversial since the Greek philosophical traditions or even earlier in the eastern mystical tradition. Whereas the Eastern mystics considered space as an immutable platform of the universe in which things "arise", the Greeks including Plato and Aristotle used the concept of 'space' synonymous with 'place'. In the Timeaus, Plato wrote of space as a 'receptacle' of material being . Space, according to Aristotle was a limit of a piece of matter and motion is simply a change of place. The nature of time was also equally problematic because although 'space' is not immediately obvious, unless something occurs in it, time seems to flow and has directionality about it. If it is difficult for us to conceive of space as some 'thing' as an ordinary table or mug, it is even more difficult to think of time as a separate entity.
In this essay we try to examine this endlessly contentious issue. The two viewpoints that feature in the debates on the ontology of space-time are Substantivalism and Relationism, and the debate heated up especially after Newton's laws of gravitation and claims for absolute space and absolute acceleration. After a brief trip down history, we would discuss the philosophical approaches of the nature of space and time and then turn to the debates in detail. In trying to show the different approaches of space-time philosophy, we would examine whether it is possible to define space-time in terms of an approach in between the two traditional ones.
There are knotty issues relating the concept of space and existence - as Sklar asks, 'where do thoughts occur in space?'(1992, p.17). Even if ordinary matter can be posited in space, certain objects like thoughts cannot be assigned a location, suggesting that everything cannot be 'located' in space giving a sort of indefiniteness to space itself. Time always has definiteness about it, as our thoughts 'occur in a moment of time'. Aristotle thought time was distinct from the motion of material objects just as space was distinct from the objects in it. Yet Aristotle claimed that without a change of motion of objects, it is impossible to be aware of time's passage. Thus both space and time have similar problems. They were both defined in terms of things that they contained. They were both defined in terms of other parameters time as change of motion, space as change of place. Space is distance between two points. Time is the interval between two events. But does time and space themselves have a separate existence - is there something like empty space or empty time?
Historical Background
For Democritus, space was an empty extension that contained the motion of matter (as atoms) but did not interact with matter itself. This was then taken up by Lucretius who argued for an infinite extent of space and the subsequent infinite extent of the universe. And to Lucretius, just as Plato, space was a receptacle, where matter was posited. However, with Plato, matter and space became explanatorily linked. He considered the physical objects as categorized into geometric forms and empty space as identical to matter. Aristotle took this further as according to him, space determined the motions of bodies, and thus, space and matter were causally linked. Aristotle also postulated the impossibility of the existence of a void since a void will not have properties of direction or change of motion, so there is nothing like 'empty space'. Thus, there were three viewpoints on space - the atomistic view (Democritus and Lucretius where space contained motion of material particles), the Platonic view (stressing space as represented in geometric forms and connections between matter, form and space) and the Aristotelian view of space as causing motions (Cushing 1998).
The Aristotelian viewpoint was questioned when Copernicus, Galileo and Kepler started suggesting an infinite, structureless space independent of matter which in turn influenced Newton. However, in the 16th century, Descartes identified matter with geometrical extension . According to Descartes, the nature of a body is only understood in its extension and as extension is a basic entity of the universe and a void is impossibility, it followed that both space and universe have to be infinite. Matter and space were thus continually linked in spite of Newton's firm belief in space as a substance independent of ordinary material objects. At this point of time, even ether was considered as the material 'stuff' of the universe that pervades ordinary objects so ether and space were intricately connected. So it seems that post-Aristotelian viewpoints on space and time included the Newtonian view of an absolute, independent space and time, and a Cartesian view of space, as extension described by matter.
Substantivalism
Substantival views claim that space exists independently and have features independent of material objects. Thus space is a sort of 'container' where objects occur or events take place in time. According to Newton, who was a substantivalist, even if there is no matter in the universe, there would still be space in its Euclidean form and there would be time instants forming a temporal order. There would be space and time even if there are no events. So space and material objects are both objects in a similar way, only unlike material objects space and time are unchanging and immutable. Yet, material objects can be used to measure features of space and time. Space is thus distance between two points and two events have a temporal interval between them.
Substantivalism led to absolutism , Newton wrote 'Absolute space, in its own nature, without relation to anything external remains always similar and immovable'. Horwich (1978) explicates the absolutist position, saying, Newton's view was that space is an all-pervasive medium, made up of qualitatively indistinguishable spatial points, and each such point continues to exist throughout all time (p.398). Newton is thus asserting that the structure of space is absolute and remains the same in any physically possible world. Relative space according to Newton is some movable dimension or measure of the absolute spaces - Newton further asserts that Place is part of space which a body takes up, and is according to the space, either absolute or relative (Newton, 1729). Absolute motion is the translation of a body from absolute place into another and relative motion is the translation from one relative place to another. Thus space according to Newton can be both absolute and relative - so, as Earman (1989) analyzes there are two meanings to space. Space means instantaneous space; space-time terminology can be applied to an instantaneous slice of space-time and a second meaning of space is as a reference frame or a means of identifying locations through time.
In special relativity, the propositions look a little different. Sklar suggests, in the special theory, Minkowski space-time is the appropriate structure of space and time representation and there is no definite spatial and temporal separation since these exist relative to a particular state of motion chosen as a reference frame (1974). Yet in relativity, space-time seems to have an independent structure as it can be defined only in terms of the geometry.
In general relativity, space-time is explicated using Riemannian geometry, it is four dimensional and 'curved'. So space-time has a different structure here and is connected with the non gravitational mass energy in it. Sklar writes, general relativity brings with it the possibility of different space-time structures. The substantivalist has a position compatible with commonsense thinking - when accepting the possibility of empty spaces in a room or in ordinary language an object is said to be 'in space'. Yet, as we have seen in case of general relativity and in scientific terms, one speaks of structures of space-time. One thing common to both science and ordinary discourse is, we talk of space-time as real and existent independent of the objects. Thus material objects and spacetime are similar so much so that matter is considered as 'pieces' of space-time. Plato took space as 'matter' of the world and Descartes' view of space suggests space as the 'stuff' of the world (Sklar, 1992). So there are two distinct substantival positions - space as a type of matter or substance, containing other types of matter or the objects and space and matter of the world as identical, so all matter is just space.
Relationism
This view claims that all there is in the universe are objects and space and time can only exist as relations between these objects. Thus space and time are not separate material entities and not objects, but 'relations' between these entities. Relationists do not talk of the structure of space itself but of the spatial relations of the points of locations of the objects. Time is also defined in terms of temporal 'relations' that events bear to one another. Sklar writes, 'the relata occupy the appropriate space-times only in the sense that they bear spatiotemporal relations to one another' (1974). An occupation in the sense of material objects is not conceivable in the relationist view as there is no independent space-time that exists by itself and which can be occupied. The occupation is nothing but the relations. Spatial relations are different from the temporal relations in that spatial relations are relations among things at one instant, whereas temporal relations are relations among events not occurring at the same time.
As Torretti writes of Michael Freidman's interpretation of space-time (1984) 'Relationism, is the doctrine, initiated by Leibniz, according to which the physical reality of space and time (and space-time) supposing they have any - must be fully accounted for by reality of material substances (bodies?) and their mutual relations.'(p. 287). Relationism, according to Torretti must thus deconstruct the space and time definitions from events extended in space and time to point events in space-time and from physically occupied points to empty ones. The difference between the absolutist understanding of space-time with that of the relationist is the interpretation of the relationship between space-time manifold and physically real point events. For the absolutist, the relation between occupied point events is one of inclusion; for the relationist, it is one of embeddability . This means that if space-time is absolute, the relations are over and above the events, so they might be included in our explanations of space-time, but for the relationist, since it is the relation that defines space-time, these relations are already embedded in the events.
Debates on Space-time - From Nature to Structures
With the advent of general relativity, the substantivalist-relationist debate, lost its 'focused' direction and yet, got a new impetus, as from a debate on the nature of space-time, it turned to a controversy of space-time 'structures'. General Relativity proposes that space-time has mass-energy and mass-energy is in turn the basic aspect of matter. It may be thus meaningless (according to Sklar, 1992) to talk of 'relations among matter' as against 'space-time'. Thus following general relativity, the ontology of space time caught up further problems. The rise of electromagnetism and introduction of the 'field' in physics brought in the concept of matter as different from ordinary matter making up objects. Fields were thus problematic to substantivalists - although Sklar suggests, fields are closer to the substantival definition of space than the relationist definition which has to consider ordinary objects only, we would maintain that the field is not the matter of ordinary objects and fields are not even matter in the sense the substantivalists viewed it. Here Earman suggests manifold Substantivalism M or space-time manifold functions as a basic substance , so he writes 'Post-relativity, it seems that the electromagnetic field, and indeed all physical fields, must be construed as states of M' (1989, p.154).
Two problems encompassed this entire debate of spatio-temporal structure ? according to special relativity, a space-time event could only be relative to a frame of reference, so a general notion of space and time that the substantivalists believed is no longer tenable. The second problem is as we have mentioned the problem of mass-energy in space-time - here space becomes linked with matter in a way that cannot be compatible with Relationism. So, traditional space-time theories face double trouble. The problem also arises because classical Newtonian mechanics was deterministic, whereas general relativity is not completely so, as there are regions in space-time like black-holes, where the curvature becomes infinite and all determinism breaks down. It is not possible to predict anything further beyond these regions. From this follows the fact that space-time structures can vary within different regions and are not the same, although the universe appears homogeneous and isotropic.
The other aspect of the debate is about the relationship of space-time and causality. Some philosophers would claim that spatiotemporal structures could only be real only if they are causal structures and are causally related. Events in the world are believed to be caused by each other. In general relativity, simultaneity cannot be causally defined and events in the world do not have to be causal as in a relativistic context different space-time 'structures' are possible.
Now, in post-relativistic times, we see that the debates of space-time ontology have shifted from its nature to its structure. A structure of space-time is in turn defined by the kind of geometry that we consider, although due to problems of underdetermination, this is a controversial issue. We would now move on to our arguments on the ontology of space-time.
The Ontology of Space-time
The arguments on the nature of space-time have varied, as we have seen from space and time as an absolute unchanging material, a kind of substance containing ordinary objects which are also made up of substance but of a different kind, to space and time as relations between objects having no separate entity apart from these relations which depend on the existence of such objects. Space has been defined as extension, and also as structure. The theory of relativity has implications that 'space-time' is a bit of all of these. Whereas Leibniz's influence of relational philosophy might have permeated into special relativity, the Aristotelian space-matter link has entered general relativity. Space is measured in terms of relations and defined in terms of mass-energy.
But is the theory of relativity, the final chapter of space-time? Obviously, not. Although it might seem that space-time has apparently resolved the substantival-relational debates, as Einstein's theory is a theory of 'structures' and of geometry, and although it seems Einstein's theory has vindicated Leibniz's relationism, the implications of general relativity are not so obvious. General relativity explains the 'nature' of space-time but the explanation is dependent on space-times geometries and frames of reference, laying emphasis on the 'structures'. Thus, the theory of relativity is primarily a structural theory. Field theories and the quantum theory are theories about the 'nature' of things. Although, we can maintain that all these theories together help us to understand the ontology of space-time and of matter.
We finally take a brief look at the problems of the 'nature' of space-time as very well articulated by Torretti in the beginning of our essay. In our commonsense thinking, when we talk of space-time as existing, the manner of existence we imply is different from existence of tables and chairs. Tables and chairs are objects, just like we can say, even quantum particles are objects. But space-time is structure and that is why we have difficulties in explaining the existence of space-time in the same manner we describe real objects. But Torretti, claims it would be boorish to rush to the conclusion that the being of space-time is any weaker than the being of ordinary objects. Torretti suggests, the description of being, can be expanded to include not only the being of objects, but also the structures by which we seek to understand them. Thus, the structures seem to act as a means of understanding the real nature of space-time. Although Torretti has hit on the right point, we would like to suggest that equating the nature of objects with the structure of space-time (which we require as a context to understand the nature) has several problematic implications and remains as the main rub when we try to unite the theory of relativity with the theory of the quantum. So, in so far as the theory of relativity remains a theory of structures and in so far as we have to conceive of the 'nature' of space-time as structure, the ontology of space-time might remain elusive.
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