# Do you collect Pokemon cards?

The universe has at least three spatial and one temporal (time) dimension. It was long thought that the spatial and temporal dimensions were different in nature and independent of one another. However, according to the special theory of relativity, spatial and temporal separations are interconvertible (within limits) by changing one's motion. To understand this interconversion, it is helpful to consider the analogous interconversion of spatial separations along the three spatial dimensions. Consider the two endpoints of a rod of length L. The length can be determined from the differences in the three coordinates Î”x, Î”y and Î”z of the two endpoints in a given reference frame L2 = Î”x2 + Î”y2 + Î”z2 using the Pythagorean theorem. In a rotated reference frame, the coordinate differences differ, but they give the same length L2 = Î”Î¾2 + Î”Î·2 + Î”Î¶2. Thus, the coordinates differences (Î”x, Î”y, Î”z) and (Î”Î¾, Î”Î·, Î”Î¶) are not intrinsic to the rod, but merely reflect the reference frame used to describe it; by contrast, the length L is an intrinsic property of the rod. The coordinate differences can be changed without affecting the rod, by rotating one's reference frame. The analogy in spacetime is called the interval between two events; an event is defined as a point in spacetime, a specific position in space and a specific moment in time. The spacetime interval between two events is given by s^{2} = L_{1}^{2} - c^{2} \Delta t_{1}^{2} = L_{2}^{2} - c^{2} \Delta t_{2}^{2} where c is the speed of light. According to special relativity, one can change a spatial and time separation (L1, Î”t1) into another (L2, Î”t2) by changing one's reference frame, as long as the change maintains the spacetime interval s. Such a change in reference frame corresponds to changing one's motion; in a moving frame, lengths and times are different from their counterparts in a stationary reference frame. The precise manner in which the coordinate and time differences change with motion is described by the Lorentz transformation.

Tnot intrinsic to the rod, but merely reflect the reference frame used to describe it; by contrast, the length L is an intrinsic property of the rod. The coordinate differences can be changed without affecting the rod, by rotating one's reference frame. The analogy in spacetime is called the interval between two events; an event is defined as a point in spacetime, a specific position in space and a specific moment in time. The spacetime interval between two events is given by s^{2} = L_{1}^{2} - c^{2} \Delta t_{1}^{2} = L_{2}^{2} - c^{2} \Delta t_{2}^{2} where c is the speed of light. According to special relativity, one can change a spatial and time separation (L1, Î”t1) into another (L2, Î”t2) by changing one's reference frame, as long as the change maintains the spacetime interval s. Such a change in reference frame corresponds to changing one's motion; in a moving frame, lengths and times are different from their counterparts in a stationary reference frame. The precise manner in which the coordinate and time differences change with motion is described by the Lorentz transformation.