I didn't really intend for this to be my FIRST entry but, oh well... its kind of fun to think about I think.
In 1944, pilots began reporting unusual lights sometimes about six feet in diameter that would tag along and 'observe' their actions but never interact directly. The pilots also reported that the mysterious objects could not be shot down, so they were shooting at them. They were seen in both the Pacific and European theaters of operation and not only by pilots but also by ship borne sailors. At first only really seen at night, they began to be reported during daylight hours also. The threat was taken very seriously by Command.
It was believed at first that they were some German super weapon, but was later denied by the Axis powers and they thought it was an Allied weapon... The truth is out there!