The speed of transmission of phase modulated signals through a plasma medium

TL;DR

This paper demonstrates that phase modulated signals can propagate through plasma at superluminal phase velocities, enabling faster-than-light message transmission with minimal distortion under certain conditions.

Contribution

It provides a concrete scenario showing superluminal phase velocity transmission of phase modulated signals through plasma, highlighting the fundamental difference from pulse propagation.

Findings

Superluminal phase velocity allows earlier message arrival compared to vacuum.

Minimal signal distortion occurs when bandwidth is a small fraction of carrier frequency.

Phase modulation enables faster-than-light communication without violating causality.

Abstract

The impossibility of sending pulses of radio waves (Morse codes) through an ionized medium, despite the superluminal phase velocity of the constituent modes, has been demonstrated in many and various ways; essentially the reason is because each pulse, or wave packet, propagate through the plasma at the group velocity, which is subluminal. Nevertheless, messages can also be encoded as {\it phase} modulations of a monochromatic carrier wave, with more than one constituent modes (which may mathematically be extracted by Fourier transform). These modes propagate at their respective phase velocities and, upon reassembling them on the receiver's side, can become the original signal with the original message it bore having propagated at the phase velocity of the carrier wave, \ie~superluminally. We provide a concrete working scenario of transmitting a message for arrival with a time lead (compared to vacuum propagation) which is an order magnitude more than the duration of the message itself. It is also shown that the distortion of the signal due to the multiplicity of modes induced by the phase modulation is minimal if the bandwidth of the signal, including the duration of its onset and offset, is a small fraction of the carrier wave frequency. Thus phase and pulse modulations are fundamentally different phenomena in terms of their propagation speeds.