Brilliant but irresponsible scientist Tony Nelson (James Congdon) develops an electronic amplifier that he hopes will allow any object to achieve a 4th dimensional (4D) state. While in this state any object can pass freely through any other object. Tony, however, fails to pay attention to the overload, which sparks an electrical fire that burns down his lab. This results in the university terminating his contract. Now unemployed, Tony seeks out his brother Scott (Robert Lansing) to help him with his experiment. Scott is a researcher working on a material called Cargonite that is so dense that it is impenetrable.
Scott is underpaid and unappreciated at his new job. He does not have the necessary drive to ask his employer, Mr. Carson, for greater recognition. Scott has become the driving force behind the development of Cargonite (named after Carson, who is now taking much of the credit for Scott's work). When his girlfriend (Lee Meriwether) falls for Tony, an enraged Scott steals Tony's experiment and starts playing around with it, eventually transforming himself into a 4D state. When demonstrating this to Tony, Scott leaves the amplifier power turned off, yet he successfully passes his hand through a block of steel. Scott can now enter a 4D state via his own will. Tony is amazed, but warns Scott not to reveal this ability until he can further test for possible side effects.
While in the 4D state, Scott can pass through any solid object, but he ages at a greatly accelerated rate. The aged Scott soon learns how to survive, when he visits the company doctor, who, while examining him, suddenly drops dead. Simply by touching others, Scott can drain anyone's lifeforce, thereby rejuvenating himself. He experiments with his new abilities by shoplifting a piece of fruit through a grocery store's solid window. Scott also notices a diamond necklace on display in a nearby jewelry store window, but decides against stealing it. When he sees a bank, however, his face breaks into a sly grin.
The police wonder about a bizarre crime. More than $50,000 was stolen from the bank with no sign of forced entry, nor any video footage of the crime. Strangely, a $1000 bill was found protruding from a solid piece of tempered steel. Tony realizes that Scott is abusing his power and tries to convince the police.
Scott starts using his newly-found power to acquire all the things he felt he was denied: money, recognition, power, and women. Scott confronts Carson, revealing the experiment, then taking his revenge "for the life drained from me" by literally draining Carson's life force. Scott then proceeds to a sleazy bar, where he gets some street toughs to back down. With his new found bravado, combined with his ill-gotten money, he tries to impress a bar girl. When they later kiss, Scott does not kill her, but drains her life force to the point where she has aged badly.
The police have to find a way to stop a man who is unstoppable. Looking very old now, Tony returns to the lab, but they are unable to stop him. Scott's former girlfriend catches him in solid form and shoots and wounds him. Bleeding and feeling betrayed, Scott maniacally proclaims his invincibility and defiantly phase-shifts his body with difficulty through a wall embedded with supposedly impenetrable Cargonite. "The End" appears on screen, followed a moment later by a question mark. This interrogative statement leaves in question whether the aged Scott died or survived.
Jack H. Harris was able to begin production of the film with the money he had received from distributing The Blob (1958). This was the film debut of Lee Meriwether and Robert Lansing. Young Patty Duke also makes a small cameo appearance in the film.
The film was released in the United-States on October 7, 1959.