Colonel Hawes and Dr. Charles Cottrell call in Tom Burke, a retired Air Force Pilot, to show him Professor Putnam. Putnam is in an isolation room, miming taking care of a young girl. The men explain that Putnam lost his daughter Jenny in a hit-and-run accident, and the driver was never found. Putnam still believes that his daughter is alive, and refuses to work unless she is taken care of. Hawes explains that they need Putnam to finish his work on a top-secret project, and he hates everyone on staff. They want Burke because he lost a leg in an ejector-suit accident, and they figure he'll win Putnam's sympathy. Burke says he needs to know what Putnam is working on to do the job, and Hawes explains that Putnam is working on a project to ensure the safety of the United States. He wants Burke to work with Putnam, maintain his illusion that Jenny is alive, and keep him happy.
Burke agrees to the plan and rehearses all of Jenny's personal information. Putnam brings in "Jenny," and Burke plays along. The professor wants to take his daughter to the amusement park at the beach, and Burke goes with them. He takes Jenny out for the day while Putnam works. Afterward they go to Putnam's hotel room and the professor starts brushing his daughter's hair. Burke offers to do it, while explaining that he took good care of Jenny throughout the day. Putnam seems surprised that Burke can see his daughter. When he snarls Jenny's hair, Burke offers to tell her a bedtime story. He carries her into the bedroom and briefly breaks the charade to relax. When Putnam sticks his head in, Burke goes back to reading Jenny a bedtime story, breaking into tears.
Later, Burke meets with Cottrell, the military's psychologist. He warns Burke that they're helping Putnam maintain his delusion instead of taking steps to cure him, and that Putnam will never overcome his grief no matter how much he tries to forget by pretending that Jenny is alive. Cottrell insists that the military will only help Putnam maintain his delusion until he completes his work, and then they'll let him lapse into insanity to maintain the project's secrecy.
Burke continues to visit with Putnam and Jenny. They go to a restaurant and pretend she's eating, but a man comes over and asks for the empty chair. When Putnam insists that Jenny is sitting there, the man points out that there's no plate. Burke and the waiter hastily usher the man away, but Putnam is clearly stricken. Burke asks Putnam about his work and the professor says that it's almost done, and it's a project to make cheap fission bombs. He snaps at the military, insisting that they're abusing his work, and walks away.
The next day, Burke and Putnam drive to the base and Putnam turns over his work to the authorities. As they drive back, Putnam rants about the military perverting his work and starts to lose control of the car. Burke manages to grab the wheel and stop the car just in time, saying that Putnam could have killed them "both."
Burke reports to Cottrell, who says that his slip is the least of their problems. Cottrell wonders why Putnam is now trying to kill himself, and checks on Putnam in his room. The professor is sitting in the dark, rambling about how he'll be with her soon and that the word is bad and they're all better off dead. Cottrell realizes what is happening and explains to Burke that Putnam subconsciously realizes that his daughter is dead. The professor is driven by conflicting desires, and he has finally found a way around him. Burke wonders if Putnam gave them false equations, and Cottrell says that a world-wide nuclear detonation would kill the hit-and-run-driver and reunite Putnam and Jenny. As they look on in horror, the military test goes out of control and a nuclear holocaust sweeps across the planet, killing everyone and everything.