The synth line was written circa 1981 by Eddie Van Halen, but it was rejected by the other members of the band. In 1983, producer Ted Templeman asked Roth to listen to the unused song idea. Riding around in the back of his 1951 Mercury, with band roadie Larry Hostler driving, Roth listened repeatedly to the tune. To come up with a lyric for it, he remembered seeing a TV news report the night before about a suicidal jumper. Roth thought that one of the onlookers at such an event would inevitably yell “go ahead and jump”. Roth bounced this suggestion off Hostler who agreed it was good; however, instead of describing a potential suicide, the lyrics were written as an ontological invitation to action, life and love. Roth later told Musician magazine that Hostler was “probably the most responsible for how it came out.”[4]

[in 2011] Angelus discussed the video [that he directed]. “‘Jump’ really was just about personality, really. It was a very simple video. We shot it for nothing. David wanted to incorporate his karate-flipping - that he loved so much - into the whole thing. The initial concept was just to film them in a very simple live setting, and let the personalities show through. We did it very quickly. Seriously, I think that we probably spent more money on pizza delivery than we did on the video itself. But that was the intention - make it a very intimate, personal feeling, with a very big band.”[20]

https://en.wikipedia.org/wiki/Jump_(Van_Halen_song)