The Philadelphia Experiment & The Montauk Project
A pair of linked legends spanning four decades: the alleged 1943 attempt to render the USS Eldridge invisible — and, in some tellings, teleport it — through unified field theory experiments, and its rumored sequel at a Montauk, Long Island radar station, where displaced Eldridge crewmen and abducted local teenagers were said to be used in mind control, time travel, and psychic research into the 1980s.
Why it was classified
Nothing was: the Office of Naval Research has answered inquiries for decades by stating no such experiment occurred. What is documented is degaussing work at the Philadelphia Navy Yard to hide ships from magnetic mines — invisible to a fuze, not to the eye.
Why it matters
It is the clearest case of a real, mundane classified program mutating into a mythology no denial can close. Camp Hero's radar tower still stands, and the absence of a paper trail is treated by believers as the strongest evidence of one.