The Enterprise is en route to some much-needed shore leave, when suddenly the crew experiences a small loop in time. Shortly thereafter, they intercept an emergency automatic transmission from Dr. Paul Manheim, a scientist who's been working on some odd theories concerning nonlinear time. Upon hearing his name, Picard reacts strangely, but orders the ship to the coordinates specified in the message.

With several hours remaining before arrival, Picard goes to Holodeck 3 and programs it for Paris as it was twenty-two years ago, where he sits at a table where he once had a rendezvous, but never showed up. He quickly tires of "this self-indulgence" and leaves.

As the Enterprise arrives at the coordinates given, they find a relay signal, sending them to Vandor Four, a small planetoid orbiting a double star: one a red giant, the other a pulsar. As they arrive, Manheim's wife answers, and Picard freezes for an instant. She turns off the force- field blocking their transporters, and both Manheims are beamed aboard. When Picard arrives in sickbay, he gets Jenice's attention, and she instantly recognizes him.

She explains that the rest of the scientific crew was killed several weeks earlier in the other lab, and that Manheim's recent experiments have been looking for windows to other dimensions that can be opened by changing the nature of time. After another experience of the Manheim effect (this time, Riker, Data and Picard meet themselves in the turbolift), Riker leads an away team and attempts to beam down to get Dr. Manheim's notes. The beam, however, bounces, and they are lucky to make it back to the Enterprise at all.

After Dr. Manheim awakens, he claims to be partially trapped in another dimension. When he hears what has happened, he insists that his experiment must have a controlled shutdown, to close the rift he has opened. He gives the security codes to get down to the lab, and Picard sends Data down alone, as Data seems the least affected by the time distortion. Despite one security precaution that Dr. Manheim forgot to mention, Data makes it into the lab.

He prepares to drop a specific amount of antimatter into the rift precisely 27 seconds after the next effect begins. However, when it does begin, he finds that there are three Datas, each holding some antimatter. The middle Data successfully realizes that he is the one in the correct time continuum, and manages to close the hole (or at least patch it). The closure completely restores Manheim, and Picard says one last goodbye to Jenice on the holodeck before the Enterprise departs.