The term space time simple consider the space and time which are one quantity given by Physicist and Mathematician Albert Einstein. In Physics, space time is any mathematical model that combines space and time into a single continuum.Then we have “space time” instead of “space and time”. However, Space is something like a fabric which can be inflated so long distance but we cannot deny the bounded space where continuum has its end. But now space time both are not relative as they both are independent on each other not dependent.
(NOTE): Continuum theories explain variation as involving gradual quantitative transition without any change or we say discontinuities.
The space-time especially for our universe is usually represented from a Euclidean Space (that is three dimensional spaces) and time as the fourth dimension. Combination of space-time into single manifold called Minkowski’s space (four dimensional spaces).
1) In geometry, Euclidean space shows the two dimensional Euclidean space, the three dimensional space of Euclidean geometry. It is name after the death of Alexander (Mathematician of Euclid, c.300BC as philosopher Proclus (c.AD410-485) said in his reports).
2) Manifold is something like this which shows how other dimensions look rather than one, two, three and four and also known as Calabi You manifold.
(NOTE): Example of embedded: We have a group which subgroup is a part of a group. If some object say A is said to be embedded in another object B, the embedding is given the form of mapping f: A to B.
(NOTE): There exists String Theory which suggests that there may be 10 or 26 dimensions rather than four dimensions which are too small in size to see or notice these dimensions are difficult. As M-theory suggest only eleven dimensions (first termed by Edward Witten). Where (M) stands for magic, membrane, mystery as there is no suggestive name for this as research going on further.
AMAZING FACT: Edgar Allan Poe in his easy on cosmology titled Eureka (1848) that space and time are one. In 1895, The Time Machine by H.G Wells in his novel, there is no difference between Time and any of the three dimensions of space except that our consciousness moves along it.
(NOTE): Eureka (1848) is a non-fiction work by American Author Edgar Allan Poe (1809-1849). Time represented as duration in essay of Edgar Allan Poe.
However, in ancient (cosmos) ideas, there was mathematically description with differential equation, abstract Algebra. Space-Time was described as an affine space with quadratic form in Minkowski space in 1908. Space time is considered to be a part of geometric creation, is this or not? Space is in that kind of geometry whose mathematical laws confined its limit.
(REMEMBER): An affine space is a geometric structure and in affine space there is no distinguishes point that we say as its origin. There is no vector which has a fixed origin and no vector can be uniquely associated to a point in an affinity space. (Not to be confused with Affinity Space).
In non-relativistic classical mechanics, we use the Euclidean space which is appropriate. As we treat the time as a universal with a constant rate of passage which is independent of the state of motion of an observer. But for relativistic time cannot be separated from the three dimensions of space due to the observed rate at which the “time” passes for an object depend upon the “objects velocity” relative to the observer and also to the strength of the “gravitational field”.
In cosmology the concept of space-time combines the term space and time into a single abstract universe. Dimensions which we all know are independent components because we needed to locate a point in a certain “space”. We know that we have three and a one dimension means (3+1) dimensions such as length , width (height) and temporal dimension (time). As we notice in our daily life but the actual fact is that there does not exists only four dimensions. But one question arises, is there any need of space?