0, see W. Hurewicz, Dimension Theory, 1941.) The philosophical and physics literatures contain speculations about a discrete time built of ‘chronons’ or temporal atoms, but thus far such hypothetical entities have not been incorporated into a satisfactory theory.
Absolute versus relative and relational time. In a scholium to the Principia, Newton declared that ‘Absolute, true and mathematical time, of itself and from its own nature, flows equably without relation to anything external.’ There are at least five interrelated senses in which time was absolute for Newton. First, he thought that there was a frame-independent relation of simultaneity for events. Second, he thought that there was a frame-independent measure of duration for non-simultaneous events. He used ‘flows equably’ not to refer to the above sort of mysterious ‘temporal becoming,’ but instead to connote the second sense of absoluteness and partly to indicate two further kinds of absoluteness. To appreciate the latter, note that ‘flows equably’ is modified by ‘without relation to anything external’. Here Newton was asserting (third sense of ‘absolute’) that the lapse of time between two events would be what it is even if the distribution and motions of material bodies were different. He was also presupposing a related form of absoluteness (fourth sense) according to which the metric of time is intrinsic to the temporal interval.
Leibniz’s philosophy of time placed him in agreement with Newton as regards the first two senses of ‘absolute’, which assert the non-relative or frame-independent nature of time. However, Leibniz was very much opposed to Newton on the fourth sense of ‘absolute’. According to Leibniz’s relational conception of time, any talk about the length of a temporal interval must be unpacked in terms of talk about the relation of the interval to an extrinsic metric standard. Furthermore, Leibniz used his principles of sufficient reason and identity of indiscernibles to argue against a fifth sense of ‘absolute’, implicit in Newton’s philosophy of time, according to which time is a substratum in which physical events are situated. On the contrary, the relational view holds that time is nothing over and above the structure of relations of events.
Einstein’s special and general theories of relativity have direct bearing on parts of these controversies. The special theory necessitates the abandonment of frame-independent notions of simultaneity and duration. For any pair of spacelike related events in Minkowski space-time there is an inertial frame in which the events are simultaneous, another frame in which the first event is temporally prior, and still a third in which the second event is temporally prior. And the temporal interval between two timelike related events depends on the worldline connecting them. In fact, for any e ( 0, no matter how small, there is a worldline connecting the events whose proper length is less than e. (This is the essence of the so-called twin paradox.) The general theory of relativity abandons the third sense of absoluteness since it entails that the metrical structure of space-time covaries with the distribution of mass-energy in a manner specified by Einstein’s field equations. But the heart of the absolute–relational controversy – as focused by the fourth and fifth senses of ‘absolute’ – is not settled by relativistic considerations. Indeed, opponents from both sides of the debate claim to find support for their positions in the special and general theories. See also EINSTEIN , METAPHYSICS , RELATIV- ITY , SPACE , SPACE -TIM. J.Ea. & R.M.Ga.