Counterintuitive properties of relativistic relative motion for accelerated observers

A challenge in teaching special relativity is that a number of the theory's effects are at odds with the intuition of classical physics as well as students' everyday experience. The relativity of simultaneity, time dilation, and length contraction are prominent examples. This article describes two other counterintuitive properties of relative motion with accelerated observers: (a) when two objects have a constant radar distance and are by that standard “at rest,” their relative speed is not necessarily zero, and (b) for two observers A and B, it is possible for A to observe the two to be approaching each other, while B considers them to be moving away from each other. The two effects provide insight into static gravitational fields and horizons in general relativity.