John Giorno craved sleep. He would rise in the morning with a hangover, struggle through his day job as a stockbroker, come home, crash out, then go out on the town with the only person who made things worthwhile – his lover, Andy Warhol. It became a running joke, because Andy liked to do quite the opposite, and had even started taking amphetamines to stay awake. So, during a typical night, Giorno would drink, Warhol would pop pills, Giorno would pass out, and Warhol would be left wide awake – gazing, sometimes, at his lover.

Thus goes the story of how Warhol chanced upon the idea for his first film, Sleep, the five-and-a-half-hour epic that Tate Modern is screening this weekend in an extended 18-hour loop, along with a continuous live performance of Eric Satie’s Vexations. It’s a film that might be about many things – time in art, captured stillness and movement, the proximity of sleep to death – but the story of its inspiration seems, like a lot of the official explanations of Warhol’s artworks, rather too neatly anecdotal. It says that if we want to find depths in his work that’s up to us, but Warhol’s all surface and simplicity, and hunting for deeper motives is a fruitless task.

Warhol had been looking for a subject for a film ever since he bought his first movie camera, a Bolex 8mm, in July 1963. Even before that he had talked about an idea for a film of Brigitte Bardot sleeping. But one wonders if the idea goes back further than that. In particular, one wonders whether Warhol ever woke up to find his mother staring at him.

Not when he was a child – that might have seemed insignificant – but when he was in his twenties and had invited the eccentric Polish matriarch to live with him in New York. He loved her, and she looked after him, but she was an encumbrance. She drank, and sometimes, perhaps, he might have worried that she was losing the sense of herself. “Did you sleep well, Ju-lia?” somebody asked her one morning.

“Oh no," she replied. “I stayed up all night watching Andy sleep.”

If Julia Warhol really did watch her son sleeping, and he woke up and caught her, what thoughts might have passed through his mind as he sat there watching Giorno fall asleep night after night? Looking at Sleep, one must conclude that Warhol gave it some thought, as it’s a much more complex film than its simple concept suggests. The camera moves about often as the naked man slumbers, closing in on the texture of his skin, or the pattern of the bed sheets, leaping away as he turns in the night and threatens to wake. It’s not the simple real-time film it’s often presumed to be.

The primitive Bolex camera could shoot only four minutes of footage at a time, so Warhol had to assemble the film from a sequence of takes, and he decided to use the multiple takes to create a fragmented and repetitive montage after being inspired by John Cage’s 1963 performance of Vexations (at the film’s premiere in New York in 1964, however, it played to the accompaniment of a pop radio station).

Moreover, in projection, the film is slowed down from the conventional film speed of 24 feet per second to a time-stretching 16 fps. So, as you sit there watching, you have plenty of time to sort through the feelings you might have if you sat up watching someone sleep: maybe loving and protective, maybe aroused, maybe disgusted, quite possibly bored, or maybe, as Warhol surely thought as he looked at Giorno, sad, angry and jealous.

Warhol and Giorno had started dating in April 1962, and although they were always seen out together in public, in private they were incompatible. Giorno was good-looking and promiscuous, but he found Warhol unattractive (“gross and disgusting”, in fact), and was reluctant to have sex with him. Warhol always had a conflicted attitude to sex, being inclined to voyeurism and fetishism, but he was undoubtedly frustrated by Giorno’s refusals and, with time, probably came to regard him as just a distant object of desire.

Some have spoken of Warhol sublimating his desire into his art, and given Giorno’s account of the night the filming began at his New York apartment one can almost believe it. When the moment of creation was upon him, Warhol fell into a frenzy. Giorno was sitting in a chair, Warhol was checking where to put the camera and the lights, then all of a sudden the artist was on the floor kissing and licking Giorno’s shoes.

Soon enough, however, Giorno was asleep, and Warhol was left looking at him and thinking that even when you are close to a lover, you can feel very far away.

Sleep is part of UBS Openings: The Long Weekend at Tate Modern, London SE1, May 27 (7.30pm) to May 28 (3.45pm) (www.tate.org.uk/modern 020-7887 8888). Food and drink will be available.

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