The Philadelphia Experiment is the name given to a naval military experiment which was supposedly carried out at the Philadelphia Naval Shipyard in Philadelphia, Pennsylvania, USA, sometime around October 28, 1943. It is alleged that the U.S. Navy destroyer escort USS Eldridge was to be rendered invisible (or "cloaked") to enemy devices. The experiment is also referred to as Project Rainbow.
First of all I know this experiment existed because they have the USS Eldrige's barometer in warehouse 13 and they only use real artifacts for that show not some made up ones based upon wanton speculation and fantasy. for shame!
This entire scenario is filled with questions that will never be answered as the people involved have their own version on the events.