|Some dare call it|
The Philadelphia Experiment (also referred to as Project Rainbow) was an alleged naval experiment in October 1943 in which the destroyer escort USS Eldridge was briefly rendered invisible, with disastrous side effects. It is universally considered a hoax.
Legend has it that the experiment was based on a Unified Field Theory, which parts of it describe how light can be bent around something via electromagnetism to render it invisible. They then got a bunch of powerful magnets. When they powered up, a green fog appeared around the ship. Then things got ugly. Some of the crew were found embedded in the ship itself. Others developed mental problems, and still others simply vanished. The ship also teleported to a port over 200 miles away and back, and went back in time for about 10 seconds. So in effect, they invented a 3-in-1 megadevice: invisibility cloak, teleporter, and time machine.
Despite the woo, none of this is true. First off, even today, we still don't have a Unified Field Theory. Second, there's no documentation of any such experiment occurring; in fact, the crew themselves said that they never left port.
 Likely beginnings
The most likely explanation for this story's origin is in the degaussing procedures used on the USS Eldridge. Degaussing would render it undetectable to certain types of torpedoes and underwater mines; however, it has no effect on visible light or radar. Likewise, accounts of this degaussing were garbled and exaggerated, and voilà, the Philadelphia Experiment was born.