In particular, consider a pair of Rindler observers with coordinates and respectively. (Note that the first of these, the trailing observer, is accelerating a bit harder, in order to keep up with the leading observer). Setting in the Rindler line element, we readily obtain the equation of null geodesics moving in the direction of acceleration: Therefore, the radar distance between these two observers is given by This is a bit smaller than the ruler distance, but for nearby observers the discrepancy is negligible. A third possible notion of distance is this: our observer measures the angle subtended by a unit disk placed on some object (not a point object), as it appears from his location. We call this the optical diameter distance. Because of the simple character of null geodesics in Minkowski spacetime, we can readily determine the optical distance between our pair of Rindler observers (aligned with the direction of acceleration). From a sketch it should be plausible that the optical diameter distance scales like . Therefore, in the case of a trailing observer estimating distance to a leading observer (the case ), the optical distance is a bit larger than the ruler distance, which is a bit larger than the radar distance. The reader should now take a moment to consider the case of a leading observer estimating distance to a trailing observer. There are other notions of distance, but the main point is clear: while the values of these various notions will in general disagree for a given pair of Rindler observers, they all agree that every pair of Rindler observers maintains constant distance. The fact that very nearby Rindler observers are mutually stationary follows from the fact, noted above, that the expansion tensor of the Rindler congruence vanishes identically. However, we have shown here that in various senses, this rigidity property holds at larger scales. This is truly a remarkable rigidity property, given the well-known fact that in relativistic physics, no rod can be accelerated rigidly (and no disk can be spun up rigidly) — at least, not without sustaining inhomogeneous stresses. The easiest way to see this is to observe that in Newtonian physics, if we "kick" a rigid body, all elements of matter in the body will immediately change their state of motion. This is of course incompatible with the relativistic principle that no information having any physical effect can be transmitted faster than