Counterintuitive properties of relativistic relative motion for accelerated observers

TL;DR

This paper explores two counter-intuitive properties of relativistic relative motion involving accelerated observers, revealing phenomena where relative speeds and approaches differ depending on the observer's frame, with implications for understanding gravity and horizons.

Contribution

It introduces two lesser-known relativistic effects for accelerated observers, enhancing understanding of relative motion and its implications in general relativity.

Findings

Constant radar distance does not imply zero relative speed.

Observers can disagree on whether objects approach or recede.

These properties aid in understanding gravitational fields and horizons.

Abstract

A challenge in teaching about special relativity is that a number of the theory's effects are at odds with the intuition of classical physics, as well as student's everyday experience. The relativity of simultaneity, time dilation and length contraction are prominent examples. This article describes two additional, less well-known counter-intuitive properties, both of which follow from the relativistic definition of relative motion, in situations with accelerated observers: (a) when two objects have a constant radar distance and are by that standard ``at relative rest,'' their relative speed is not necessarily zero, and (b) for two observers A and B, a situation is possible where A considers the two to be approaching each other, while B considers them to be moving away from each other. In general relativity, the generalisations of these two properties prove helpful for understanding static gravitational fields, and they also provide some insight into the nature of horizons.