“The Master,” a new film by writer-director Paul Thomas Anderson, follows shattered World War II veteran Freddie Quell (Joaquin Phoenix) as he is drawn into to The Cause, a fictional cult, in 1950s America.

The film’s title refers to Lancaster Dodd, the cult’s leader, played by Philip Seymour Hoffman, who bears a remarkable resemblance to L. Ron Hubbard, the science fiction writer and founder of the Church of Scientology. Many have noted that Anderson has written a commentary on Hollywood’s favorite controversial religion. But his goals are darker, and more far reaching, than providing fodder for Tom Cruise jokes.

Shot in sumptuous 65mm and edited over a percussive pizzicato score by Jonny Greenwood (of Radiohead fame), “The Master” plays like an epic stuck on two characters, Freddie and Dodd. Though some of his conclusions, or lack thereof, may be undeserved, Anderson’s film represents a remarkable attempt to fill an entire universe with the friction between binary opposites — master and initiate, impulse and control, rebellion and authority.

Freddie is an animal. He drinks whatever he’s given, assaults anything that looks remotely like a woman and is fired from whatever job he can find. Of course, it isn’t his fault. Freddie has a tortured backstory, a bland “Game of Thrones”-like cocktail of PTSD, incest and unrequited pedophilia, but the details are seen through Phoenix, who wisely plays everything from ape-like aggression to shamed-puppy guilt with his arms, hunched back and the twisted corners of his mouth.

Lancaster Dodd, who Freddie encounters after sneaking onto a cruise ship run by The Cause, provides the necessary counterpoint to the troubled veteran’s indeterminate violence. Dodd, as he likes to tell people, is a man of the mind. The leader of The Cause barely moves; his body is weighed down under sweat and three-piece suits.

His voice, however, is enthralling. The best scenes in “The Master” are the “processing” sessions between Freddie and Dodd, in which the cult leader does all he can to crack the initiate. Dodd’s questions deal with afterlife mumbo-jumbo, but the weight of his presence is enough to accomplish his goal, as if a charlatan could will himself into performing magic.

The rest of “The Master” is concerned with what that magic is. Do the members of The Cause buy into Dodd’s thrall? His son, played by Jesse Plemons (Landry from “Friday Night Lights”) readily admits that his father is making it up, but stays on for the money. His young wife, played by Amy Adams (a necessary addition to any Oscar-bait), however, is a true believer.

Adams’s interruptions allow the film to occasionally split its themes across three, rather than two parts. Always concerned with the bottom line, she takes an immediate dislike to Freddie, whom she views as a threat, and strives to turn Dodd against him. She is also pregnant for most of the movie. The resulting id, ego, superego dynamic provides more than enough fodder for section assholes everywhere to interpret the film as a sort of Freudian nightmare.

If only “The Master” was more complicated than that. Anderson’s films are famous for their ferocity. In “There Will Be Blood,” Daniel-Day Lewis takes increasingly vindictive measures to secure a supply of oil and, in “Punch-Drunk Love,” Adam Sandler deals with the adult world through bursts of infantilized violence (unlike every other Adam Sandler movie, it isn’t played for laughs). But “The Master” fails to break out from an exhausting, beautifully coordinated fizzle.

Much of this is due to Anderson’s insistence on avoiding specificity in favor of allegory. Both Freddie’s brutality and Dodd’s power are causeless and all-consuming, definitions of actors in a fable rather than aspects of characters a film. Anderson sets the film in the ’50s, a time filled with nuclear-age stress, but he is more interested in the era’s affects, obtuse references to the war and girls in floral-print dresses, than its details.

“The Master,” like Dodd’s cult, is a test of the power of suggestion. How much can be said by showing little? Inevitably, devotees of Anderson will be able to invent an interpretation for every moment in the film — what exactly is meant by the shot where Joaquin Phoenix arches his back over the rigging of a ship at sea (I say he was tired) — and claim that the character’s true motivations are hidden in corners.

But how much of that is invented? The audience knows that Dodd is a charlatan because he substitutes charisma for evidence, but Anderson either fails or refuses to offer the level of detail that The Cause lacks to his own film. “The Master” lacks the authority it subverts; like any good cult, it answers the mysteries of the universe, but only if you are willing to buy in.