But it does seem to be quite clear that the number of UFO sightings skyrocketed within a couple of years after the first nuke was detonated. Yeah they were either nearby, or they had a monitoring station nearby - those are the most logical explanations imo. Your math is way off here - remember that as radius increases linearly, volume increases by the cubed power. There are about 14,600 stars within 100 light-years of the Earth. But not if the signal were transmitted FTL in some manner, either via an FTL probe or a wormhole or something we haven't imagined yet. No the first atomic bomb test was detonated on July 16, 1945 - almost exactly 2 years before Roswell.