CHRONOTOPE. - This word, which modern physics has taken from Gioberti, denotes the union of space and time, conceived together as a single environment in which all material entities are localized.
These are then conceived as having four dimensions, namely: length, width, thickness (spatial dimension) and duration (temporal dimension). Every elementary occurrence or event is localized at a certain point (in space) at a certain instant (in time).
The fusion of the two traditional and intuitive concepts of space and time into the single concept of the chronotope (or space-time, as it is also called) would have only a purely conventional value, had the experiments of physics, which later led to the so-called theory of special relativity, not given this function a real meaning. And indeed it has been seen that the ordinary spatial distance and the interval of time between two events, measured by a certain observer, have no real meaning in themselves, inasmuch as another observer, under suitable circumstances, detects between the same events a spatial distance and an interval of time different from the previous ones.
It is demonstrated, however, that from these measurements of distance and time it is possible to arrive at a single length δ, which depends on both and which is called the interval or universal distance between the two events, and which on the other hand is always the same, even if the measurements of space and time detected by different observers are very different. More precisely, if we denote by l and t the spatial distance and the interval of time between two events detected by a certain observer, and by l' and t' those detected instead by another observer, it always follows that
δ = √{c² t² - l²} = √{c² t^{1/2} - l^{1/2}}
if we denote by c the speed of light. It is therefore this universal distance δ between the two events that is the only entity having a real, objective meaning, that is, independent of individual observers and of the circumstances of observation. But the reality that it represents is not only spatial or only temporal, but at once spatial and temporal, that is, to be referred to the chronotope, which is therefore the only true environment in which such reality has a sense.
The introduction of the chronotope into modern science is due substantially to Minkowski, who thereby adapted a previous mathematical theory, namely the abstract theory of a four-dimensional space, into a logical instrument more adequate for the understanding of the physical universe than the previous intuitive categories of space and time. This is an important stage in the current evolution of science, inasmuch as for the first time the categories of thought suggested by sensory intuition are replaced by new categories, new logical schemas chosen from the far broader mathematical universe of entities of pure reason. And then, taking from this latter the idea of an even broader space, of five or more, or infinite, dimensions, in which the chronotope is immersed — a four-dimensional space containing the totality of the physical universe past, present and future — it becomes easy to conceive how at a point of such a broader space, which is external to the chronotope, that is, outside space and time, the chronotope itself (and therefore the whole physical universe past, present and future) can appear all together present.
Luigi Fantappiè