Lorentz transformation it is evident that there exists a less than for which (in particular, ). In other words, given two events that are timelike separated, it is possible to find a frame in which the two events happen at the same place. In this frame, the separation in time, is called the proper time. Δs2 < 0: In this case, the two events are separated by more space than time, and they are hence said to be spacelike separated. This implies that and given the Lorentz transformation there exists a less than for which (in particular, ). In other words, given two events that are spacelike separated, it is possible to find a frame in which the two events happen at the same time. In this frame, the separation in space, is called the proper distance, or proper length. For values of greater than and less than the sign of changes, meaning that the temporal order of spacelike-separated events changes depending on the frame in which the events are viewed. The temporal order of timelike-separated events, however, is absolute, since the only way that could be greater than would be if Δs2 = 0: In this case, the two events are said to be lightlike separated. This implies that and this relationship is frame independent due to the invariance of From this, we observe that the speed of light is in every inertial frame. In other words, starting from the assumption of universal Lorentz covariance, the constant speed of light is a derived result, rather than a postulate as in the two-postulates formulation of the special theory. Relativity of simultaneity Consider two events happening in two different locations that occur simultaneously in the reference frame of one inertial observer. They may occur non-simultaneously in the reference frame of another inertial observer (lack of absolute simultaneity). From (the forward Lorentz transformation in terms of coordinate differences) It is clear that the two events that are simultaneous in frame S (satisfying ), are not necessarily simultaneous in another inertial frame S (satisfying ). Only if these events are additionally co-local in frame S (satisfying ), will they be simultaneous in another frame S. The Sagnac effect can be considered a manifestation of the relativity of simultaneity. Since relativity of simultaneity is a first order effect in , instruments based on the Sagnac effect for their operation, such as ring laser gyroscopes