  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.
