The Inner Light (Star Trek: The Next Generation, Season 5, Episode 25)
A mysterious probe blasts Picard with an energy beam, which knocks him unconscious. When he wakes up, he's Kamin, an iron weaver on the non-Federation planet Kataan. Picard lives for decades as Kamin, starting a family with his wife Eline (including a son played by Patrick Stewart's actual son, Daniel), spending time in nature, and learning to play the flute. He and his daughter investigate a drought on their planet that threatens all life there.
Back on the Enterprise, only a few minutes pass while the crew tries to revive Picard.
We don't want to spoil the ending of this one for people who haven't seen it. Patrick Stewart once said that this is his favorite episode.
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