You don't need to have been alive in 1973 to appreciate the cultural gap that existed between the United States and these islands (far greater than the current gulf). But it does help. Paul Thomas Anderson's propulsive, evocative new film really is set in a whole other country. Returning to the San Fernando Valley he explored in Boogie Nights, he reminds us just how much stuff Americans then had. And the possibilities.

Based on the early life of Gary Goetzman, a child actor who grew up to become Tom Hanks's business partner, Licorice Pizza follows Gary Valentine (Cooper Hoffman), a precocious 15 year old, as he moves on from juvenile leads to selling waterbeds in the suburbs that abut Los Angeles. He meets an older girl. He rubs up against Hollywood producers. He actually makes money. None of this would have been remotely conceivable on the other side of the Atlantic in the same year. "The business of America is business," Calvin Coolidge didn't quite say. And sex. And fame. And movies. (At least in California.)

Yet Licorice Pizza does not take place in any sort of idyll. There is an obvious parallel here with Cameron Crowe's less interesting Almost Famous. Unlike the hero of that film, Gary is told off by no distraught parent, but there is a sense of unease throughout this agreeably meandering picture. We begin with a fabulous lengthy single take – less flashy than the Boogie Nights opening – that has Gary meeting up with Alana Kane (Alana Haim), assistant to a photographer, at school and moving into the gym to have his snap taken. Even at this early stage, we are aware that this is hostile territory for 21st century humans. The English photographer (where else would he then be from?) slaps her arse as she passes and she barely registers the assault. Should we be worrying that a romance seems to be brewing between a teenage boy and a grown woman? It may as well be Sweden in the 15th century.

There has been some criticism of a scene in which John Michael Higgins, playing a loud-mouthed restaurateur, speaks in an absurd Japanese accent to two successive wives from that country. But this feels too specific not to have been culled from real life. Also, the humour clearly depends on both the absurdity and the inappropriateness of his choice. We are everywhere exposed to a world that doesn't know what to do with the cultural rearrangements left over from the 1960s.

Sean Penn has a superb turn as an appalling, faded movie star – he is neither William Holden nor Steve McQueen, but nods are made in those directions – who spends his evening reliving old glories in the area's cocktail bars. Bradley Cooper is even better as Jon Peters, producer and then-boyfriend of Barbra Streisand, who leers at Alana and dismisses Gary. Everywhere we get the feeling that, though there is much fun to be had, jarring personal and societal corrections are on the way.

For now, we can sink into a partial celebration of the cliff-edge mayhem from the most reliable American director of his generation. Cut to contemporaneous needle-drops that always zing and only rarely give into the obvious (Life on Mars is a more obscure track in the US than here), the picture alternates easy ambles with an unprecedented amount of frantic running. That is how it was before mobile phones. Anderson and Michael Bauman shoot on 35mm with vintage lenses to further immerse us in the late-Nixon ambience.

Haim, whose sisters from the pop group of the same name appear with their parents, and Hoffman, son of Philip Seymour Hoffman, could hardly be in more satisfactory harmony. Hoffman gives us a kid mere nanometres into his comfort zone. Haim's character knows she is living through madness, but can't help but allow herself to be dragged along.

One can scarcely imagine a more enjoyably chaotic way of welcoming in the new year. What a blast.

Opens on January 1st