CRONOTOPO. — This word denotes the union of space and time, conceived together as a single environment in which all material entities are located; modern physics borrowed the term from Gioberti.
These entities are then conceived as having four dimensions, namely: length, width, thickness (the spatial dimension), and duration (the temporal dimension). Every elementary occurrence or event is located 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 experiments of physics, which subsequently led to the so-called theory of special relativity, had not given this fusion a real significance. Indeed, it has been seen that the ordinary spatial distance and the time interval between two events, measured by a certain observer, have no real significance in themselves, since another observer, under suitable circumstances, finds between the same events a spatial distance and a time interval different from the preceding ones.
It can nevertheless be demonstrated 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 world interval or world distance between the two events; this, on the other hand, is always the same, even if the measurements of space and time recorded by the 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 certain observer, and by l' and t' those recorded 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. This world distance δ between the two events is therefore the only entity having a real, objective significance, that is, independent of the individual observers and of the circumstances of observation. But the reality it represents is neither solely spatial nor solely temporal; rather, it is spatial and temporal together, and thus must be referred to c., which is consequently the only true environment in which such reality has meaning.
The introduction of c. into modern science is due essentially to Minkowski, who thereby adapted a previous mathematical theory—namely, the abstract theory of a space of four dimensions—into a logical instrument more suited to the understanding of the physical universe than were the preceding intuitive categories of space and time. This is an important stage in the present development of science, since 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 belonging to pure reason. And then, taking from the latter the idea of an even broader space, of five or more, or infinitely many, dimensions, in which c. is immersed—the four-dimensional space containing the totality of the physical universe, past, present, and future—it becomes easy to conceive how, from a point in this broader space that lies outside c., that is, beyond space and time, c. itself (and therefore the entire physical universe, past, present, and future) might appear as wholly present all at once.