The main plot-line is a project by aliens who inhabit a parallel universe (the para-Universe) with different physical laws from this one. By exchanging matter with Earth, they seek to exploit these differences in physical laws. The exchange of matter provides an alternative source of energy in their dying Universe. However, the exchange of physical laws will have the ultimate result of turning the Earth's Sun into a supernova, and possibly even turning a large part of the Milky Way into a quasar. This is the alien's ultimate goal, as it would provide more energy for the para-Universe.
The exact time when the novel occurs isn't specified, but it is stated to be approximately two and a half centuries since the Opening of Japan and a century and a half since the discovery of quasars, suggesting early 22nd Century.
The first part takes place on Earth, almost a century after the "Great Crisis", where ecological and economic collapse reduced the world's population from six billion to two billion. Radiochemist Frederick Hallam discovers that a container's contents have been altered. He initially accuses a colleague of tampering with his sample, but eventually finds that the sample, originally tungsten, has been transformed into plutonium 186—an isotope that cannot occur naturally in our universe. As this is investigated, Hallam gets the credit for suggesting that the matter has been exchanged by beings in a parallel universe; this leads to the development of a cheap, clean, and apparently endless source of energy: the "Electron Pump", which transfers matter between our universe (where plutonium 186 decays into tungsten 186) and a parallel one governed by different physical laws (where tungsten 186 turns into plutonium 186), yielding a nuclear reaction in the process. The development process grants Hallam high position in publicopinion; winning him power, position, and a Nobel Prize. Despite his success Hallam is a mediocre scientist who is inclined to take punitive action against anyone who threatens his legacy.
Physicist Peter Lamont, while writing a history of the Pump about thirty years later, comes to believe that the impetus of the Pump was the effort of the extraterrestrial "para-men"; but Hallam is infuriated by the suggestion that his role is secondary, and destroys Lamont's career. Lamont enlists the help of Myron "Mike" Bronowski, an archeologist and linguist known for translating ancient writings in the Etruscan language, to prove his claim by communicating with the parallel world. They inscribe symbols on strips of tungsten to establish a common written language as the strips are exchanged for ones made of plutonium-186. As Bronowski works, Lamont discovers that the Pump increases the strong nuclear force inside the sun, and thus threatens both universes by the explosion of Earth's sun and the cooling of that in the parallel universe. Bronowski receives an acknowledgment from the parallel universe that the Pump may be dangerous. Lamont attempts to demonstrate this to a politician and several members of the scientific community, but they refuse his request. Lamont decides to tell the para-men to stop the use of the Pump, but Bronowski reveals that they have been in contact not with the other side's authorities, but with dissidents unable to stop the Pump on their side. The last message was them begging Earth to stop.
The second part is set in the parallel universe where, because the nuclear force is stronger, stars are smaller and burn out faster than in our universe. It takes place on a world orbiting a sun that is dying. Because atoms behave differently in this universe, substances can move through each other and appear to occupy the same space. This gives the intelligent beings unique abilities. Time itself appears to flow differently in this universe: the events take place in an apparently short space of time in the lives of the inhabitants, while more than twenty years pass in our universe, and a long feeding break of one of the characters translates into a two-week gap on Lamont's side.
Like the first part of the novel, this section has an unusual chapter numbering. Each chapter except the last is in three parts, named "1a", "1b", and "1c". Each reflects the viewpoint of one of the three members of the "triad" central to the story's theme.
The inhabitants are divided into dominant "hard ones" and subject "soft ones". The latter have three sexes with fixed roles for each sex:
All three 'genders' are embedded in sexual and social norms of expected and acceptable behavior. All three live by photosynthesis; whereas sexual intercourse is accomplished by bodily collapse into a single pool (known as 'melting'). Rationals and Parentals can do this independently; but in the presence of an Emotional, the "melt" becomes total, which causes orgasm but also results in unconsciousness and memory loss. Only during such a total "melt" can the Rational "impregnate" the Parental, with the Emotional providing the energy. "Stone-rubbing" is a practice of partially melting with solid objects like rocks, possible for Emotionals, but the other genders are only capable of it in a very limited form. It is an analogue of human masturbation and generally frowned upon. Dua appears to be the only one who practices it while married.
The hard ones regulate much of soft one society, allocating one of each sex to a mating group, called a "triad", and acting as mentors to the Rationals. Little is shown of "hard one" society; wherefore the Emotional Dua, the protagonist of this section of the book, suspects that the "hard ones" are a dying race, retaining the "soft ones" as a replacement for their absent children. This is dismissed by Odeen, the Rational of Dua's triad. Having the most contact with the "hard ones", Odeen has heard them speak of a new "hard one" called "Estwald", accounted of exceptional intelligence and the creator of the Pump.
Dua is an oddball Emotional who exhibits traits normally associated with Rationals, resulting in the nickname "left-em". While being taught by Odeen, she also discovers the supernova problem that Lamont uncovered in the first section. Outraged that the Pump is allowed to operate, she attempts to halt it; but cannot persuade her own species to abandon the Pump. Given that their own sun and all the other stars in their universe can no longer provide the energy necessary for reproduction, they consider the possible destruction of Earth's sun worthwhile if it might provide a more reliable source of energy.
Driven by an innate desire to procreate, Tritt, the "Parental" of the triad, at first asks Odeen to persuade Dua to facilitate the production of their third child. When this fails, Tritt steals an energy-battery from the Pump and rigs it to feed Dua, which stimulates thee triad into a total melt, resulting in conception. Dua discovers this betrayal and escapes to the caves of the hard ones, where she transmits the messages received by Lamont. This effort nearly exhausts her mortally; whereupon she is found by her triad. Here, it is revealed that each melt, in addition to causing reproduction, briefly creates a hard one. Hard ones are not a separate species, but the fully mature form of the species. Odeen convinces Dua that the hard one they will become will have influence with the hard ones to stop the Pump; but during their final metamorphosis, Dua realizes (too late to prevent irreversible union) that 'Estwald', the Pump's creator, is her own triad's 'hard' form.
The third part of the novel takes place on the Moon. Lunar society is diverging radically from that of Earth. The lower gravity has produced people with a very different physique. Their food supply is manufactured from algae and distasteful to inhabitants of Earth. They enjoy low-gravity sports that would be impossible on Earth, such as an acrobatic game like "tag" performed in a huge cylinder (these sports are vital to them, since their metabolism is still that of Earthmen, and proper strenuous exercise must be maintained for it to function properly). Some Lunarites want to further adapt their bodies to life on the Moon, but Earth has outlawed genetic engineering decades ago. Lunarites are beginning to see themselves as a separate race, although procreation between them and Earth people is quite common. Sex, however, is problematic, since an Earthborn person is likely to injure his or her partner due to loss of control. Sexual morals are loose, and nudity is not taboo.
The plot centers on a cynical middle-aged ex-physicist named Denison, briefly introduced in Part 1 as the colleague and rival of Hallam whose snide remark drove Hallam to investigate the change in his sample of tungsten and, eventually, develop the Pump. Finding his career blocked by Hallam, Denison leaves science and enters the business world, becoming a success.
Denison, independently of Lamont, deduced the danger in the Electron Pump. He visits the Moon colony hoping to work outside of Hallam's influence using technology that the Lunarites have developed. He is helped by a Lunarite tourist guide named Selene Lindstrom. She is secretly an Intuitionist (a genetically engineered human with superhuman intuition), who is working with her lover, Barron Neville. They are both part of a group of political agitators who want independence from Earth. The group particularly wants to be allowed to research ways to use the Electron Pump on the Moon. Although solar energy is plentiful enough to power their underground habitats Neville wants to live entirely underground and never have to venture out on the surface. With the scientists' help, Denison gets access to the technology and proves that the strong force is indeed increasing, and will cause the Sun to explode.
Denison continues his work, tapping into a third parallel universe that is in a pre-big bang state (called 'cosmic egg' or 'cosmeg'), where physical laws are totally opposite to those of Dua's universe. Matter from the cosmeg starts with very weak nuclear force, and then spontaneously fuses as our universe's physical laws take over. The exchange with the second parallel universe both produces more energy at little or no cost, and balances the changes resulting of the Electron Pump, resulting in a return to equilibrium. However Selene clandestinely conducts another test showing that momentum can also be exchanged with the cosmeg. Denison catches her and forces her to admit her secret purpose: Neville thinks the momentum exchange can be used to move anything without using rockets, including the Moon itself. He wants to break away from Earth in the most complete way possible. Denison is appalled, although he sees the potential of the technology to make travel within the Solar System easier and to the stars possible.
When Selene discusses Neville's plan with the rest of the group, most of them agree that moving the entire Moon will be meaningless, and building self-sufficient sublight starships will be better. A later public vote goes against Neville as well. Hallam is ruined by Denison's revelations. Selene and Denison become a couple. Having received permission to produce a second child, Selene requests Denison to become its father. The novel ends with them deciding to try working around the sexual incompatibility problem.