An unsophisticated alien probe assumes a relative position, holding steady with the U.S.S. Enterprise, and releases a nucleonic particle stream that penetrates the ship's shields. Focusing solely on Picard, the beam knocks him unconscious. When he wakes up, Picard finds himself in unfamiliar surroundings, being cared for by an attractive woman. The woman, Eline, tells him his name is "Kamin," and he is her husband of three years. She also tells him that he has been sick and must be experiencing a memory loss. Picard soon learns that he lives on the planet Kataan, where he works as a simple iron weaver. His confusion is compounded when he notices that Eline wears an exact replica of the alien probe as jewelry. She tells Picard he gave her the necklace as a gift.
On the Enterprise, the crew is unable to revive Picard. Realizing the particle emission that has attached itself to him may control his life, they are afraid to destroy the beam. Only a few moments have passed, but on Kataan, it is already five years later, and Picard is settling into his life. He comes up with a solution to the drought that is destroying the planet, but his advanced ideas are laughed at by leaders of the primitive society. However, his life is not without its pleasures. Picard kisses Eline, an act that causes his pulse to rise back on the Enterprise. Worf insists they must destroy the beam since their Captain is under attack.
They do so, and Picard's pulse drops dramatically. On Kataan, where seven more years have passed, he falls to the floor. Acting quickly, the crew restores the beam. Back on Kataan, another 12 years have passed, and Picard has two children. The drought continues to worsen, and Picard's teenage daughter, Meribor, realizes their planet is doomed. At the same time, Geordi and Data are able to chart the probe's radiation to Kataan, a planet that was destroyed in a supernova explosion over a thousand years ago.
On Kataan, the years continue to fly by. Picard continues his quest to get something done about the drought, but his suggestions fall on deaf ears. Later, Eline dies, as does Picard's best friend Batai, and his first grandchild is born.
The elapsed time on the Enterprise is still only a few minutes. However, Dr. Crusher becomes alarmed when she realizes that Picard's metabolic rates match those of an 80-year-old man. In fact, Picard is actually 85 years old on Kataan, where the drought has almost completely destroyed the planet. His children and grandchild convince the unwilling old man to accompany them to a missile launching — an event they are all very excited about. Picard doesn't understand the point, knowing the missile will do nothing to save the planet or its people. However, as the missile takes off, his family, with the help of Eline's spirit, explain to Picard that they are launching a probe into the future to find a person who will bring them immortality by telling others about their planet after it is destroyed. Picard realizes the missile is actually the probe that brought him to Kataan over 30 years ago. As this happens, he wakes up aboard the Enterprise and is amazed to learn he has only been unconscious for 25 minutes, in which time he lived a third of a lifetime.