Neutron Decay Length at 10^20 eV and the Question of Galactic Escape

A free neutron is unstable, but at ultra-high energy time dilation turns it into a long-range messenger. With a rest-frame lifetime of 879.4 seconds and a Lorentz factor of 1.064e+11 at 1e20 eV, the mean decay length is 9.093e-01 megaparsecs, or 9.093e+02 kiloparsecs: a neutron at this energy crosses the entire Milky Way, whose disk spans some twenty kiloparsecs, with a decay probability of only 2.175e-02 along the way, and typically survives into intergalactic space before decaying. At 1e19 eV the decay length falls to 9.093e+01 kiloparsecs, comparable to galactic scales, so the transition between neutrons as galactic prisoners and neutrons as intergalactic travellers sits inside the observed energy range. Neutrons produced in source interactions therefore constitute a neutral, undeflected component whose decay protons arrive from the source direction smeared only by the decay position. No density-bound effect alters the lifetime or the dilation. Simulated and computed; not a measurement.