The Enterprise is taking two Federation dignitaries to Babel: Commodore Robert April, the first captain of the Enterprise, and his wife Sarah, who served as chief medical officer. Since retiring as captain, Robert has served as ambassador-at-large for the Federation. He has reached the mandatory retirement age of 75 and is traveling to Babel to be honored. McCoy gives Sarah a tour of Sickbay and then brings her to the bridge where her husband is with Kirk. Sarah is carrying a Capellan flower that grows, blooms, and dies within a single day.
Spock informs them that they are passing the Beta Niobe supernova, one of the spectacles of the universe. As they watch the exploding star, Spock detects an unidentified ship on a collision course with the Enterprise, traveling at Warp 36, a speed believed to be impossible to achieve. They switch to a different heading and the mystery ship goes past them, and Spock realizes that they were in its way and it's only trying to get to the supernova. Kirk tries to contact the ship without success and has Sulu put a tractor beam on it to slow it down. They're able to slow it to Warp 32 but are unable to divert it. The ship's captain, a female, contacts them but speaks in a language that no one present understands. The universal translator determines that she is speaking in English... only reversed. When they play it backward, the captain tells them that she is on a priority mission and orders them to release the tractor beam or risk dooming her.
The captain ignores all hails and signs off, and Scotty calls to warn them that the Enterprise engines are buckling as they accelerate to Warp 11. They continue accelerating and Kirk has no choice but to order Sulu to release the tractor beam. However, the helmsman is unable to free the controls and the alien ship continues towing them into the supernova. Kirk apologizes to the Aprils, who assure them that they long ago came to accept that they would die in service to Starfleet trying to help others. The captain suggests that they break off as soon as the lead ship is destroyed, in the few seconds they have once they're drawn in. Spock concedes that the plan is feasible, but warns that they will only have 42 seconds to correct course.
The alien ship enters the heart of the supernova but remains intact. The Enterprise is helplessly towed in behind it and passes through. Instead of being destroyed, they find themselves in a white void filled with black stars. The starship is traveling backwards at warp speed. Scotty call to report that all of the controls now work in reverse, while Sarah's Capellan flower is aging backward, reblooming. Spock points out that the ship's chronometers are running backward and notes that they are all now aging backward.
The other ship's captain, Karla Five, contacts them and introduces herself. They are now able to understand her since their brains are working in reverse. Karla Five explains that she is an explorer who was mapping Amphion, a dead star in her universe that abruptly ignited, coming to life. She was pulled and found herself emerging from the Beta Niobe supernova in the Enterprise universe. From that Karla Five has concluded that when two stars in the same location go supernova at the same time, they form a gateway between universes. Amphion is no long a supernova, since in her universe dead stars come to life. Karla Five offers to escort the Enterprise to her homeworld of Arret so that her scientists can try and find another way for the Enterprise to return.
The two ships travel to Arret and the command crew gathers for a short briefing. Robert points out that if they remain long enough, he and Sarah will no longer face mandatory retirement. Spock suggests that their only hope of return is to recreate the conditions that caused the transfer in the first place.
When they arrive at Arret, Kirk, Spock, and Robert beam down to the lab of Karla's father, Karl Four. He is an elderly man, and a toddler is in a playboy. Karla explains that the toddler is her father, Karl Six. Spock realizes that in this reverse universe, people are born old and deage to infancy.
Karl Four brings up a starmap of his universe and the Enterprise compares it to their own. Earth corresponds to Arret and Beta Niobe is in the same location as Amphion. However, they find no stars that are supernovas in both universe that occupy the same space. Robert suggests that since dead stars ignite to become supernovas in the reverse universe, they find one that corresponds to a supernova in theirs and then ignite it. Karla explains that they would have to pass through at Warp 30+ as she did, and Kirk admits that the Enterprise isn't capable of such a speed. Spock proposes that they use Karla's ship, unmanned, and they send it through with the Enterprise riding it on a tractor beam. Realizing that they're out of alternatives, Kirk agrees and Karla willingly volunteers her ship.
Once they find a suitable star that corresponds to the Minara supernova, Karla loads her ship with positive-matter explosives. As they make preparations, Robert admits that he's looking forward to going home, but admits that he has no desire to retire. Karla
As they accelerate toward the star, Spock warns that the high warp speed will accelerate the deaging process, and that the youngest crewmember will reach the moment of birth within 18 minutes. However, the crew will lose all knowledge of how to man the ship long before that. Uhura and Sulu quickly learn their knowledge of how to run their consoles and Kirk becomes a teenager as well. Spock points out that as a Vulcan he ages slower so that he can maintain his knowledge a little longer, but he will not make it to the transition point either.
Spock finally takes command but he hesitates as well. Robert, now a healthy young male, steps forward and tells Spock that as ranking officer, he is taking command. Spock agrees and mans the helm, maintaining enough knowledge to initiate Robert's commands. He activates the explosives aboard Karla's ship, setting off the supernova, and Robert guides the Enterprise through the gateway back to their universe.
Robert and Sarah confirm that the deaging process has stopped. However, all of the crew is now babies. The couple realizes that they can send the crew through the transporter, which retains the memory of their original patterns. Sarah suggests that they avoid transporters and remain at their younger ages. Robert admits that it's tempting, but says that he would only do it if he had something to do over. He's satisfied with his life and doesn't see the need to do something over, and Sarah feels the same.
Once the crew is restored to their original ages, the Federation contacts Kirk and tells him that due to Robert's heroic actions, they will let him continue as ambassador-at-large. Sarah shows everyone her Capellan flower, which is blooming a third time as it ages normally, and says that she's glad that they've all received a second life.