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We investigate the time propagation of tachyonic (superluminal) and tardyonic(subluminal, ordinary) massive wave packets on cosmic scales. A normalizablewave packet cannot be monochromatic in momentum space and thus acquires apositional uncertainty (or packet width) that increases with travel distance.We investigate the question of how this positional uncertainty affects theuncertainty in the detection time for cosmic radiation on Earth. In theultrarelativistic 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, $m$ isthe mass parameter, $\delta p$ is the initial momentum spread of the wavefunction, and $p_0$ is the central momentum of the wave packet, which, in theultrarelativistic limit, is equal to its energy. This result is valid fortachyons and tardyons; its interpretation is being discussed.

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