Empty promises: Invisible Labyrinth Hayward Gallery

Empty promises: Invisible Labyrinth (2005) by Jeppe Hein at the Hayward Gallery. Photograph: Tony Kyriacou / Rex Features

Invisible, the Hayward Gallery's new exhibition, has a theme so novel and provocative one cannot help rising to the challenge. What kind of art would be sufficiently invisible (as it were) to appear in this show? Perhaps there will be glowing after-images, or mirages conjured out of nothing by the American light artist James Turrell. Perhaps there will be sound works by Bruce Nauman or the Turner prize-winner Susan Philipsz; or maps to buried treasure such as Robert Smithson's greatSpiral Jetty, long since vanished beneath the waters of Lake Utah.

1. Invisible: Art About the Unseen
2. Hayward Gallery,
3. London
4. SE1 8XX

1. Starts 12 June
2. Until 5 August
3. Details:
   020 7960 4200
4. southbankcentre.co.uk

Perhaps the show will concern itself with lost art, destroyed art, or art that was never made in the first place, such as Leonardo's colossal bronze horse or Vladimir Tatlin's stupendousMonument to the Third International, which would have dwarfed the Eiffel Tower had his dreams been achieved. Perhaps the Hayward Gallery will be showing Marcel Duchamp's nostalgic vial of Paris air, or an evocation of Yves Klein's 1958 Paris exhibition, empty of everything except (he claimed) the artist's own spirit.

Once you start, a romantic anthology soon springs to mind. But Invisible only alludes to the Klein. A show of surprising range, touching on faith, philosophy and even love while remaining fully alive to the comic potential of its theme, it's nonetheless strictly concerned with non-visibility and what was known in the 60s as the dematerialisation of the art object.

What is there to see? Quite a lot, as it turns out, otherwise there wouldn't be much to add to Ralph Rugoff's excellent catalogue. The paradox is, of course, that an artist can only be represented here through something visible: a film, a photographic record, typed instructions about leaving a blank canvas outside overnight until it's suffused with pink dawn light. By the time you've read Yoko Ono's prose-poem, the image is in your head.

There is a blacked-out gallery (supposedly haunted by The Ghost ofJames Lee Byars, to use its title) that makes darkness visible. Visitors to Jeppe Hein's wall-less labyrinth collide as if their regulation headsets made them blind to the existence of others. The Taiwanese artist Lai Chih-Sheng has made an immense chalk drawing (the largest in the world, he claims) for those who have eyes to see it; which might be the crux of this show.

Even the nod to Klein involves a vivid archive film of the artist striding about his empty gallery contemplating the bare (but curiously glowing) walls as if there really was something to see. Which there was at this stage, of course: namely the artist filling the room with his artistic sensibility, parodying the Romantic tradition, displaying his aura.

Even when Klein wasn't there, visitors insisted they could still feel his presence. This was a proposition tested by Chris Burden in a 1975 performance. Burden lay on a concealed platform in a New York gallery for 22 days during which he saw nobody, and nobody saw him. Yet visitors became palpably infuriated by the lurking sense of his presence; or so it is claimed.

Invisible is a show replete with claims and assertions – that the artist was present; that this white canvas was primed with mountain snow; that these stones were once inscribed with water: they sound like confidence tricks, and certainly turn upon trust of a sort. You have to believe that the Chinese artist Song Dong was too poor to afford ink and wrote his diary in water instead, otherwise those stones are meaningless, aren't they? In fact, the stones are irrelevant as visible objects. As soon as the idea of that poignant act begins to grow in one's mind, it is only the thought that counts.

Some assertions can be tested. I could see no sign of Chih-Sheng's immense drawing in the central gallery until I ran a finger beneath a balustrade and found the chalk line transferred to me. But there is no way of knowing whether Maurizio Cattelan's hilarious police report concerning the theft of an invisible artwork from his car is genuine or not. What is the difference between fiction and not-fiction in art? This is art as unreliable evidence.

One room of the Hayward is empty except for an eavesdropping device (according to the wall text). But it's nowhere to be seen. Uneasiness sets in, which is apt since this is the work of Roman Ondák, born in former communist Czechoslovakia.

Another gallery is devoted to all-white canvases including a sharp send-up of the genre by Tom Friedman entitled 1000 Hours of Staring. But Bruno Jakob's works are a challenge to cynics, made as they are with not much more than canvas or paper exposed to the elements. There are no images but each bears faint traces of its making that inspire unexpected landscapes in the imagination.

With all this emphasis on invisibility, there is a cognitive bias towards spotting what's visible – the green temperature dial on the air conditioning machines in Art & Language's unrelievedly boring work of 70s conceptualism (nothing to see = nothing to buy). Or the unusual beauty of some of the actors hired by Bethan Huws to wander about distracting us from the show, thus rendering it supposedly invisible. The art is invisible because we're not looking at it? Try telling that to the children.

Invisible is a surprisingly various show, but oddly conventional in one way. It has stronger and weaker works, more or less imaginative, more or less involving; it is in this respect like any other group show.

There is, for instance, an immense gap between Jay Chung's project – a movie entirely shot without telling cast and crew that there was no film in the camera and thus no record of their mutual labour – and Claes Oldenburg's buried monument to John F Kennedy. Neither work is visible, indeed neither was fully realised. But Oldenburg's idea was to evoke the sense of loss through a hollow colossus: the space Kennedy occupied in life now sealed beneath the ground. Even the drawing for the proposal is poignant. Chung, by comparison, is working at the dead end of conceptualism.

This show puts its faith in the audience, in our willingness to think and our openness to ideas. But it cannot quite escape the trap of its own theme for not one of these works achieves total invisibility. Even in the black room there are discernible figures, pinpricks of light and visible forms. As long as our eyes are open, we continue to make pictures of the world.