Dispersion of Ultra-Relativistic Tardyonic and Tachyonic Wave Packets on Cosmic Scales

TL;DR

This paper analyzes how wave packets of superluminal and subluminal particles spread over cosmic distances, affecting the timing uncertainty in their detection on Earth, with a unified formula in the ultrarelativistic limit.

Contribution

It derives a unified expression for the positional uncertainty of tachyonic and tardyonic wave packets over cosmic scales in the ultrarelativistic limit.

Findings

Positional uncertainty increases with travel distance.

Unified formula applies to both tachyons and tardyons in the ultrarelativistic limit.

The uncertainty in detection time depends on mass, initial momentum spread, and travel time.

Abstract

We investigate the time propagation of tachyonic (superluminal) and tardyonic (subluminal, ordinary) massive wave packets on cosmic scales. A normalizable wave packet cannot be monochromatic in momentum space and thus acquires a positional uncertainty (or packet width) that increases with travel distance. We investigate the question of how this positional uncertainty affects the uncertainty in the detection time for cosmic radiation on Earth. In the ultrarelativistic limit, we find a unified result, $\delta x(t)/c^3 = m^2 \delta p t /p_0^3$, where $\delta x(t)$ is the positional uncertainty, $m$ is the mass parameter, $\delta p$ is the initial momentum spread of the wave function, and $p_0$ is the central momentum of the wave packet, which, in the ultrarelativistic limit, is equal to its energy. This result is valid for tachyons and tardyons; its interpretation is being discussed.