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 $ \beta c $ 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-\beta^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 on 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.

翻译：我们重新审视涉及两个相对运动观察者的经典场景：爱丽丝保持静止，而鲍勃以速度$ \beta c $沿任意轨迹旅行，并在一定时间后与爱丽丝重逢。根据狭义相对论，两人重逢时各自经历的时间不同，鲍勃参考系中的时间缩短了$ \sqrt{1-\beta^2} $倍。我们从信息论角度研究这种不对称性如何体现。假设爱丽丝和鲍勃在整个旅程中以相等平均功率互相传输信号，且两侧均存在加性高斯白噪声，我们证明：爱丽丝能可靠传输给鲍勃的最大比特率始终高于鲍勃能传输给爱丽丝的比特率。等价地，爱丽丝每比特消耗的能量低于鲍勃，这意味着从通信效率角度看旅行者更低效——这与Jarett和Cover的猜想一致。