At a military facility, staff members watch Professor Putnam go through a routine of taking care of an invisible girl. The staff members explain to an Air Force pilot, Tom Burke, that Putnam lost his daughter Jenny in a hit-and-run accident six months ago, and the driver was never identified. Since then, he has been acting strangely. Colonel Hawes, the man in charge, explains that Putnam has sympathy for the afflicted, and figures that he’ll sympathize with Burke, who has an aluminum leg due to an ejection seat accident. Putnam doesn’t trust anyone on the staff. Burke demands to know what he's doing, and the colonel explains that Putnam was working on a top-secret project involving the safety of the country. Since Jenny died, Putnam has stopped working and insists he doesn't want to work at the base because it's the wrong place to raise a young girl. They want Burke to not only protect Putnam, but become his friend and keep him happy.
Later, Burke reviews the information on Jenny and rehearses. When Putnam comes in with Jenny, Burke plays along as the professor says that he'll be taking his daughter to the beach to get some sun. They go to the beach and Burke takes her on the rides. Later he visits Putnam, who is brushing his daughter's hair, and assures her that he watched over her while she was swimming. Burke then offers to brush Jenny's hair, staging his own conversation with her. Putnam seems taken aback but allows it, and Burke takes her to her bedroom and tells her a bedtime story, while Putnam watches him. Once Putnam leaves, Burke is overwhelmed by memories of his personal grief and starts to cry.
Later, Burke meets with the staff psychiatrist, Dr. Cottrell. Cottrell is worried that they are maintaining Putnam's delusion, and his patient can't forget enough to escape his grief, despite his best efforts. The military won't allow Putnam time for proper therapy, and will maintain his dream until he finishes their work. Cottrell suspects that once Putnam is finished, the military will let him lapse into complete insanity to safeguard the project's secrecy.
Later, Putnam and Burke take Jenny to a restaurant. An irate man comes over and tries to take the empty chair, pointing out there's no plate. The waiter directs him away, but Putnam starts to notice something is wrong. Burke tries to take his mind off of it by asking about the work, and Putnam says that he's completed the final equations. He angrily says that they have what they need to make cheap fission bombs. Burke suggests that they leave and take Jenny for a walk, but Putnam walks away on his own.
The next day, Putnam meets with the top military staff and turns over his research. As he drives back with Burke and Jenny, he starts to rant about the murdering fools and drives erratically across the road. The car finally goes off the road and Burke says that he could have killed them "both" without mentioning Jenny. Later, Burke meets with Cottrell and tells him what happened, including his slip of the tongue. Cottrell wonders why Putnam wanted to kill himself, and says that the papers have arrived and they have started the tests. Cottrell checks on Putnam in the next room, and finds him talking to Jenny, saying he and everyone else will be with her soon. He tells his daughter that the world is bad and they're better off dead.
Cottrell closes the door and tells Burke that Putnam subconsciously knows that Jenny is dead. When Burke points out that Putnam was talking to Jenny as if he'd soon see her, Cottrell explains that Putnam is driven by conflicting desires, and has found a way to get around them. Burke asks what he means, and Cottrell explains that Putnam has found a way to get revenge on the hit-and-run driver and be reunited with his daughter. They look on in horror as a fission explosion sweeps across the planet.
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