Lorentz Transformations 7:7  The Twin Paradox 1:1 » 
Lorentz TransformationsSpaceTime and Minkowski Space 


In classical Newtonian mechanics space the threedimensional "world" is a place where all the events occur and time is absolute and the same for everybody. Space and time are separate and independent of each other and they cannot be mixed in any way. In special relativity, however, space and time are just different coordinates of the socalled spacetime, i.e., space and time merge together into a fourdimensional "world". The space coordinates and the time coordinate are mixed up together by the socalled Lorentz transformations. Every event corresponds to a point in spacetime. In the words of Minkowski: "Henceforth space by itself, and time by itself are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality." In classical Newtonian mechanics, we measure distances between two points by the formula ^{2} = (x_{1}  x_{2})^{2} + (y_{1}  y_{2})^{2} + (z_{1}  z_{2})^{2}, where (x_{1}, y_{1}, z_{1}) and (x_{2}, y_{2}, z_{2}) are the coordinates of the two points. This is possible, since we have an absolute concept of simultaneity. In special relativity, however, the interval between two events is defined by s^{2} = c^{2} (t_{1}  t_{2})^{2}  (x_{1}  x_{2})^{2}  (y_{1}  y_{2})^{2}  (z_{1}  z_{2})^{2}, where (t_{1}, x_{1}, y_{1}, z_{1}) and (t_{2}, x_{2}, y_{2}, z_{2}) are the coordinates of the two events. Note that s^{2} can in fact be negative! If we consider two events separated infinitesimally, (t, x, y, z) and (t + dt, x + dx, y + dy, z + dz), then the interval becomes ds^{2} = c^{2} dt^{2}  dx^{2}  dy^{2}  dz^{2}. This "distance" formula is called the Minkowski metric and the corresponding fourdimensional "world" is called the Minkowski spacetime or just the Minkowski space. 
Related Laureate 

The Nobel Prize in Physics 1902  Hendrik Antoon Lorentz »  