From Wikipedia:
The video was directed by British director Phil Griffin. McCartney enters an elegant hall, where a group of black-dressed and very similar female dancers walk around. He meets his doppelgänger, who starts dancing with the others while singing the song. The two McCartneys meet up two more times. At the end, McCartney is left alone in the middle of the room, bends on his knee and fades away slowly. This and the presence of the doppelgänger have been interpreted as contemporary references to the Paul is dead urban legend.
