An Information-Theoretic Analog of the Twin Paradox

Abstract

We revisit the familiar scenario involving two parties in relative motion, in which Alice stays at rest while Bob goes on a journey at speed $βc$ along an arbitrary trajectory and reunites with Alice after a certain period of time. It is a well-known consequence of special relativity that the time that passes until they meet again is different for the two parties and is shorter in Bob's frame by a factor of $\sqrt{1-β^2}$. We investigate how this asymmetry manifests from an information-theoretic viewpoint. Assuming that Alice and Bob transmit signals of equal average power to each other during the whole journey, and that additive white Gaussian noise is present at both sides, we show that the maximum number of bits per second that Alice can transmit reliably to Bob is always higher than the one Bob can transmit to Alice. Equivalently, the energy per bit invested by Alice is lower than that invested by Bob, meaning that the traveler is less efficient from the communication perspective, as conjectured by Jarett and Cover.