Space
Space commonly refers to any region of the universe that contains a very low density of dust and gas particles, such as interstellar space. Space is also defined as the three-dimensional extent of the physical universe. In relativistic terms however, the volume of the universe is associated with a fourth dimension, i.e. that of time, thus defining a four-dimensional space-time.
Classical representations of space are based on Euclidean geometry, which describes objects in three-dimensional space using the Cartesian coordinate system and following a series of postulates and axioms. The Euclidean model of space is built from systems of parallel lines and objects in space are described as points using equations defining variables representing distances from real or imaginary parallel lines. The Pythagorean theorem provides an illustration of Euclidean space by providing a means to calculate the distance between any two points or objects. Some of the Euclidean postulates were shown to be non valid and other types of geometries were developed to represent space, such as hyperbolic geometry, which rejected the Euclidean postulate stating that only one parallel line can be drawn through a point located next to a line, and elliptic geometry, which modified other Euclidean axioms, such as the one stating that two parallel lines are taken to be everywhere equidistant.
It was, however, the work of Herman Minkowski that had by far the most significant impact on the classical 3-D concept of space. He realized that the geometry of space had to introduce a time dimension element and he described space as a flat, four-dimensional space-time continuum in which the time coordinate of one coordinate system depends on both the time and space coordinates of another system moving relative to the first. This concept was incorporated in the relativity theory, formulated by Albert Einstein. In the Special theory, space representation uses points to describe events, which are both moments in time and locations in space and straight lines represent particles moving through space as a function of time. In the General theory, the Minkowski concept is modified to introduce space-time curvature and mass points, which allow the formulation of the equivalence principle stating that gravitational mass is identical to inertial mass.
If we consider a region of interstellar space relatively near some stars, and assume the only force felt in this region is the gravitational pull of these stars, then all bodies accessing this region will accelerate in precisely the same way. This is equivalent to stating that space has a property responsible for this acceleration due to gravity. The important conclusion then is that gravity alters the properties of space, which implies that space is a dynamical quantity along with time and they are affected by matter and energy, i.e. by the bodies present in space. These deformations of space and time in turn determine the subsequent motion of the bodies in space-time: matter tells space-time how to curve and space-time tells matter how to move.
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