The film is set in 1943 where two sailors, David Herdeg and Jim Parker, are stationed on a ship used for an experiment to make it invisible to radar. However, the experiment goes horribly wrong and the ship completely disappears and Herdeg and Parker find themselves in the Nevada desert in the year 1984. They find out the program has been revived in 1984, unexpectedly interacting with the experiment in 1943 and putting the entire world in danger.

References:
https://en.wikipedia.org/wiki/The_Philadelphia_Experiment_(film)