The Philadelphia Experiment, also known as the "Philadelphia Incident," is a rumoured World War II event in which the United States Navy allegedly attempted to make the USS Eldridge (DE-173) invisible to radar. According to the story, the experiment took place on October 28, 1943, at the Philadelphia Naval Shipyard, and was witnessed by Carl M. Allen, an ex-merchant mariner.

In the 1950s, a man named Carl Allen (also known as Carlos Miguel Allende) wrote a series of letters to Morris K. Jessup, a writer and researcher who had published a book on UFOs and the possibility of advanced technology being used in the military. Allen claimed in his letters that he was a crew member on the USS Eldridge and that he witnessed the ship being rendered invisible by the use of a device known as the "Philadelphia Experiment Generator."

The experiment, according to Allen, was carried out by a team of scientists led by Dr. John von Neumann, a mathematician and computer scientist who had worked on the Manhattan Project. The experiment's goal was to make the USS Eldridge invisible to radar in order to protect it from enemy attack. The experiment, however, reportedly had unintended consequences, with the ship disappearing and reappearing in different locations.

According to one of the most widely circulated versions of the story, the ship's crew members were subjected to a variety of strange and terrifying experiences during the experiment, including hallucinations, disorientation, and even physical injuries. Some crew members were said to have vanished, never to be seen again, while others were said to have fused with the ship's metal structure, becoming a part of it.

Despite its many inconsistencies, the story of the Philadelphia Experiment has been widely circulated and has gained a significant following. Many people believe that the US Navy was working on advanced technology to make ships invisible to radar, and that the experiment failed, killing many crew members.

Numerous books and films have been made about the Philadelphia Experiment, including the 1984 film "The Philadelphia Experiment," starring Michael Paré and Nancy Allen. The story follows two sailors who are trapped on the USS Eldridge during the experiment and must find a way to escape.

Despite the numerous stories and theories about the Philadelphia Experiment, there is no credible evidence that such an event ever occurred. The US Navy has denied that any such experiment was ever carried out, and many experts believe that the story is a hoax.

The most likely explanation for the Philadelphia Experiment story is that it is a mash-up of various events that have been exaggerated or distorted over time. Some researchers believe the story was inspired by the real-life Operation Polaris, a secret Navy project to develop radar-cloaking technology. There is, however, no evidence that the project ever resulted in invisibility.

To summarise, the Philadelphia Experiment is a story that has circulated for decades but is not supported by any credible evidence. The US Navy has denied any such experiment ever occurred, and many experts believe the story is a hoax. Though the story is intriguing and has been popularised by books, movies, and other forms of media, it is important to remember that it is fiction.