CRONOTOPE. — This term, 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 entities are then conceived as having four dimensions: length, width, thickness (spatial dimension) and duration (temporal dimension). Every elementary event or occurrence 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 c. (or space-time, as it is also called) would have only a purely conventional value if the findings of physics, which later led to the so-called theory of special relativity, had not given this concept real significance. Indeed, it has been shown that the common spatial distance and the time interval between two events, as measured by a given observer, do not in themselves have real significance, since another observer, under suitable circumstances, records between the same events a spatial distance and a time interval different from the previous ones.
It is demonstrated, however, that from these measurements of distance and time it is possible to derive a single length δ, which depends on both and is called the interval or world-distance between the two events; this is always the same, even if the measurements of space and time recorded by different observers are very different. More precisely, if we denote by l and t the spatial distance and the time interval between two events as recorded by a given observer, and by l' and t' those recorded by another observer, it always results that
\[\delta = l'^{2} - c^{2} t^{2} = l^{2} - c^{2} t'^{2}\]
if we denote by c the speed of light. It is therefore this world-distance δ between the two events that is the only entity possessing real, objective significance—that is, independent of individual observers and the circumstances of observation. Yet the reality it represents is not merely spatial or merely temporal, but both spatial and temporal; it refers to the c., which is thus the only true environment in which such reality has meaning.
The introduction of the c. into modern science is essentially due to Minkowski, who thereby adapted a previous mathematical theory—namely, the abstract theory of a four-dimensional space—to serve as a more adequate logical tool for understanding the physical universe than the earlier intuitive categories of space and time. This marks an important stage in the current evolution of science, in that for the first time categories of thought suggested by sensory intuition are replaced by new categories, new logical schemes drawn from the far broader mathematical universe of purely rational entities. And then, taking from this latter the idea of a space even more extensive—with five or more, or infinite, dimensions—in which the c. is immersed, a four-dimensional space containing the totality of the physical universe past, present, and future, it becomes easy to conceive how a point in such a more extensive space, external to the c. and thus outside space and time, the c. itself (and hence the entire physical universe past, present, and future) could appear all present at once.