Abstract

Mathematically, the fusion of space and time may be explained as follows. In pre-relativity physics, space was envisaged as a three-dimensional Euclidean continuum. Such a continuum is homogeneous and isotropic, and its metrical character can be specified by the definition of the distance between any two points in the continuum: s2 = 2 + 2 + 2. Now, while it is possible to speak of a four-dimensional continuum in pre-relativity physics by adding the time-coordinate to the three space-coordinates, there is no way, corresponding to the definition of s, to define the spatio-temporal "separation" or "interval" between any two points in this new four-dimensional continuum. Thus, while it makes sense from the classical point of view to ask for the distance between two points in space, it does not make sense to ask for the spatio-temporal interval between two events occurring in different places at different times. The spatio-temporal interval between non-simultaneous, spatially separated events is simply not defined in pre-relativity physics. Another way of putting it is that in classical physics space and time are measured in entirely disparate units and no method is provided for making these units comparable with one another. In relativity physics, on the other hand, light--or rather the velocity of light--provides the means for making the results of spatial and temporal measurement comparable quantities: one simply multiplies the time-like intervals by c, the fixed velocity of light, in order to obtain space-like intervals. The interval between any two events is defined as: s2 = 2 + 2 + 2 - c22. Interval, so defined, is an invariant, whereas spatial and temporal "separation" are now relative to the state of motion of the observer. The geometry of the four-dimensional continuum characterized by this formula is called "semi-Euclidean".