Despite many claims about not being able to use contractions, Data famously reveals that he is the correct version of himself in the time loop sequence by claiming "It's me!"
At the end of the episode Mannheim declares that he must go back and resume his experiments, and Picard comments that the Federation will likely want to help. Um, what? It's just been demonstrated that 1) This technology has the capacity to shatter time across a region thousands of light years across, minimum, and 2) Mannheim has an imperfect understanding of it and an imperfect ability to contain it. In what universe is anybody going to let him go back and restart his experiments? The fact that he even wants to means that he should be locked up somewhere for the good of the galaxy!
The title is a quote from the movie "Casablanca"
An automatic distress call is picked up, from Paul Manheim - a Federation scientist who has experimented with non-linear time. Manheim left Earth years ago with a group of scientists after his ideas failed to find acceptance from the scientific community there. Picard knew of him as he was a teacher at the University of Paris when Picard went there, but the two never met. The Captain sets off to the co-ordinates given in the message.
Troi approaches Picard, telling him that she sensed a strong emotional reaction in him when Manheim's name was mentioned. She advises him to try and work through his feelings before the ship arrives at its destination. Picard goes to the holodeck and recreates the Café des Artistes, a place he had planned to meet a woman 22 years ago. He explains to a young woman there that he had failed to show up, perhaps because he was afraid. As he talks Picard stops, chiding himself for his "self indulgence" and heading back to the bridge.
Subsequent investigation has revealed that the time loop was experienced far beyond the Enterprise; the USS Lalo and the Coltar IV both report feeling it. As the ship reaches the co-ordinates given in the distress calls, it finds nothing there; a new set of co-ordinates arrive and the ship heads for the Vandor system, a binary system consisting of a red giant star and a pulsar. On arrival they detect a small forcefield on Vandor IV, a planet in the system. Picard hails the planet and a woman answers, saying Manheim is having convulsions. She lowers the forcefield the two are beamed to sickbay.
The woman turns out to be Jenice, Manheim's wife and an old flame of Picard's - the woman he was to meet in Paris all those years ago. She reveals that some sort of accident in the lab killed Manheim's team. His theory was that there were infinite dimensions and that these could be accessed by changing the linearity of time. However, the experiments were very dangerous; hence the elaborate security measures Manheim instituted, including a "safe room" that Jenice stayed in whilst the experiments were being carried out, and various security systems around the laboratory. Crusher reveals that manheim is dying, though she can't work out why. As Picard heads back to the bridge with Riker and Data time loops again, and they find themselves facing duplicates of themselves. The looping effect is becoming more pronounced. Riker wants to take an Away Team down to the laboratory, but the transporter is unable to function as the beam is reflected back.
Manheim wakes and informs Picard that his experiment succeeded and he has been on the other side - but his mind is still floating between two dimensions. He gives the crew the access codes and transporter coordinates to beam down and an Away Mission is planned. Data has calculated that the closing of the dimensional window must be precisely calculated to match the looping effect. As the mission is planned Picard talks to Jenice again about the past; he tells her he was afraid of staying behind, and she wonders if he was afraid of having an ordinary life. Meanwhile Troi visits Beverly and they talk about Jenice and how Crusher feels about having to compete with "a ghost from the past".
Picard decides to send Data down alone, since he is unlikely to be as badly affected by the time distortions as everybody else. Data agrees and is able to beam down. he makes his way to the lab, avoiding the surviving security systems on the way. He finds the distortion and determines that it can be sealed with some antimatter. As he prepares to deposit some in it the loop effect occurrs again and three Datas find themselves preparing to seal the distortion. They manage to work out which is the "real" Data and he deposits the antimatter into the distortion, successfully sealing it.
With the time distortions eliminated, Manheim returns to normal. He vows to complete his experiments as a memorial to his co-workers, and Jenice agrees to remain with him while he works. Before they leave Troi brings Jenice to the holodeck where Picard waits at the recreation of the Café des Artistes, finally fulfilling their date. Afterwards he returns to the bridge and orders the ship on to its next mission.
The time thing also doesn't work as well as it should. Some of it is good; the idea of time being linked to gravity is not only reasonable, it's perfectly true even in modern day physics. Putting Manheim's lab near a pulsar to take advantage of the high gravity is a clever idea in this respect, and it provides a good way to introduce an unconventional solar system to the plot. Though it might have been nice to make more of that, perhaps by having the planetoid so close to the pulsar that it was difficult or dangerous for the ship to approach or something.
The time effect itself makes little sense, though. The idea seems to be that time wound back a few seconds so that a moment replayed itself. But if that happened, it would be impossible to perceive it; your memories would rewind with everything else, so the second time through the loop would be experienced just as if it were the first. This is a problem that is more pronounced in the later "Cause and Effect"; here it's more of a minor niggle than anything, but it is annoying nevertheless.
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