The Enterprise is ferrying Commodore Robert April, the first commander of the U.S.S. Enterprise NCC-1701, and his wife, Dr. Sarah April (the ship's first chief medical officer), to the planetoid Babel, where the ceremony for Commodore April's mandatory retirement is to be held. Suddenly an alien ship appears, traveling at the unheard-of speed of warp 36. Kirk hails the ship via subspace radio, only to discover that the alien pilot speaks English, only in reverse. Because the alien vessel is on a dangerous trajectory toward the Beta Niobe nova — the star exploded only a few months earlier, and remains highly dangerous — Kirk tries to use the Enterprise's tractor beam to stop it. This results in the Enterprise being dragged behind the alien ship straight through the nova remnant, only to emerge with the other vessel in a bizarre alternate universe in which empty space is white, speckled with black stars.
Kirk, his crew, and the Aprils quickly discover that they have entered an antimatter universe, in which ships fly backward and time itself moves in reverse, as demonstrated by Dr. April's Capellan flower; although this bloom is supposed to live for only a few hours, its wilting form begins "aging? in reverse, once again becoming a healthy bloom before reverting back to a seed pod. The other ship's occupant, now speaking in intelligible English thanks to the reversed nature of time in this universe, identifies herself as Karla Five, an explorer who passed into our "positive matter? universe by accident, and was using the Beta Niobe nova as a means of returning home. Karla explains that if a star goes nova in one universe at the same time as its counterpart in the other universe does, then the paired stars can be used as a means of crossing between universes. Unfortunately, the "window? Karla used to cross back into her home universe is now closed, preventing the Enterprise from returning home by simply retracing her steps.
Karla leads the Enterprise to her universe's version of Earth, her homeworld of Arret — "Terra? spelled backward — where she devotes all the resources of her laboratory to helping Kirk find another interdimensional pair of novas capable of returning the Enterprise to her original universe. On Arret, Kirk and his crew discover that people age in reverse in this universe when they meet an old man who is Karla Five's son, and an infant who is her father. Despite her society's progressive loss of knowledge as the individuals in it regress in age, Karla contrives a way to coordinate two stellar novae — one in the matter universe, the other in the antimatter universe — in order to create a gateway for the Enterprise. Karla sacrifices her own ship, using it to tow Kirk's vessel through the portal at a sufficiently high speed to prevent the passage from destroying it. But before the journey home can commence, the effects of reversed time begin having noticeable effects on Kirk and his entire crew; everyone aboard is losing experience and expertise because they are growing younger by the moment.
While the captain and crew regress to toddlerhood and infancy, the Aprils — who are much older than everyone else aboard — have been restored to full adult vigor. Commodore April takes command, safely piloting the Enterprise through the interdimensional portal. Once the starship is back in normal space, the Aprils use the transporter — which retains a molecular memory of every crewmember at his or her correct ages — to restore everyone to normal. The Aprils briefly consider hanging onto their newly acquired youth, but ultimately decide that living one's life over again makes sense only if one has regrets; like the Enterprise crew, they enter the transporter, which restores them to their real ages. Once back en route to the commodore's retirement ceremony on Babel, the Aprils are gratified to learn that their decisive actions in the antimatter universe have caused Starfleet to review its mandatory retirement policy; Robert and Sarah April may indeed receive a second chance at life, without actually turning back the hands of time to get it.