Issue |
EPL
Volume 146, Number 4, May 2024
|
|
---|---|---|
Article Number | 42002 | |
Number of page(s) | 6 | |
Section | Mathematical and interdisciplinary physics | |
DOI | https://doi.org/10.1209/0295-5075/ad3eae | |
Published online | 28 May 2024 |
An information-theoretic analog of the twin paradox
1 Faculty of Technical Sciences, University of Novi Sad - Novi Sad, Serbia
2 Department of Mathematical Sciences, Michigan Technological University - Houghton, MI, USA
3 Department of Communication Systems, EURECOM - Biot Sophia Antipolis, France
4 Department of Computer Science and Artificial Intelligence, University of Granada - Granada, Spain
Received: 29 September 2023
Accepted: 15 April 2024
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 . We investigate how this asymmetry manifests itself 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.
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