مرکز منطقه ای اطلاع رساني علوم و فناوري - Asymmetries in relativistic information flow

Abstract :

In the so-called "twin paradox" of relativity theory, one spaceship leaves another at velocity v = ftc and returns to find that the other ship has aged more by a factor $\\gamma =(1- \\beta ^{2})^{-1/2}$ . The asymmetry is first isolated in order to resolve the paradox. Then the principle of relativity is used to derive the relative aging factor $\\gamma$ and the relativistic Doppler shift. Using the Doppler factor, asymmetries in information transmission between moving spaceships are investigated. An additive white Gaussian noise channel with Shannon capacity $C = W \\log (l+P/NW)$ is considered. After accounting for the effect of the relativistic Doppler shift on signal power and bandwidth, it is found that for a given transmission rate and bandwidth, the traveler needs $\\gamma$ times the energy of the stationary spaceship to transmit $1/ \\gamma$ times as much information. The asymmetry in efficiency is thus $\\gamma ^{2}$ . A simple proof is given that the round trip asymmetry in efficiency for constant-rate transmission is always the square of the relative aging factor for all trajectories regardless of accelerations and the presence of gravitational fields.