Alone in an art gallery, looking at a small, empty space – a patch of air above a plinth – I am daring myself to wave my hand through it. A little voice in my head hectors me, in the peer-pressuring tones of the teenage bully to "go on, just do it". But I won't, because I am too frightened. And that's the honest truth. The reason for my fear is that there is a text near the plinth which states that the artist, Tom Friedman, has asked a practising witch to curse a spherical area of air above it, and in the showdown between me and that piece of supposedly accursed air, I'm ashamed to admit that the air wins. I just don't want to be cursed – I would rather not take the risk. And so, rather pathetically, I walk away and leave those creepy molecules undisturbed.
The mental gymnastics of the type that accompany this work are experienced in several different forms in the Hayward's new exhibition, Invisible: Art about the Unseen, which explores the role that unseen and invisible elements can play in art. It's an incredibly refreshing and timely exhibition – a meditative oasis away from the endless stream of images, colours and lights constantly dancing before our eyes.
Friedman also presents a piece of paper he claims to have stared at for 1,000 hours, while elsewhere are paintings by Bruno Jakob that claim to use "unseen colours" as materials, as well as "brainwaves, energy, light and worries collecting and releasing". There is a bay meant for a car, taken from a line-up of vehicles created by the artist Carsten Höller for New World Race, which presented a futuristic Wacky Races-style set of propositional vehicles that could achieve unprecedented feats of speed or travel. Bay 4 is the home for The Invisible, and as we stand in front of it in the Hayward, we imagine its presence. The magical invisible car – surely the winner of any such race, is a pure fantasy.
This historical exhibition opens, unusually, in the Hayward's lower, smaller galleries, and takes Yves Klein's experiments as its starting point. The audacious artist opened an exhibition in 1957 which presented an empty white room that he claimed to have filled with "pictorial sensibility in the raw state". He spent years experimenting with ideas of invisible architectures, including buildings constructed with compressed air. Coupled with Marcel Duchamp's conception that a crucial part of the artwork happens in the mind of the viewer, his ideas, the exhibition points out, have led to a rich legacy of exploration into the invisible.
Yoko Ono's propositional instruction pieces are included here as wall texts, including the chilling Hide and Seek Piece (1964) that reads: "Hide until everybody goes home. Hide until everybody forgets about you. Hide until everybody dies." The act of imagining such events is enough to turn something in your mind – to ask the question: "Why hide except to have someone come looking for you?"
It's a rich history, and, although it seems rather radical for a public gallery, it has been explored before: the Pompidou hosted Voids, a Retrospective in 2009, while Hayward director Ralph Rugoff curated a similar show at the Wattis Institute in San Francisco. It's an exhibition which would once have enraged and delighted Britain's tabloids ("£8 to stare at nothing!", "Emperor's new clothes!" and so on) and yet I suspect they aren't so bothered any more. Perhaps I'm wrong, but a large swathe of the public and press seem inured to those elements of art that used to shock. Now what really makes jaws drop is the fact that, even in the midst of recession, prices for art reach ionospheric heights, art fairs become circuses and pleasure-grounds and multimillion pound museums and galleries take the form of architectural extravaganzas. Rugoff, in an essay in the exhibition's guide, wonders if this sort of climate is truly the thing that makes art invisible when he writes that "under these conditions, art disappears as a mere backdrop for flamboyant displays of social capital".
There are several serious points to be made by artists about the act of not showing as a way to tackle trauma or the unrepresentable. Claes Oldenburg's proposition for a monument to John F Kennedy (1965) was to dig a hole in the ground that would house a hollow brass casting – as big as the Statue of Liberty – of the assassinated president upside down, so that one could only peer into a dark cavernous space through a golf course hole.
Teresa Margolles uses humidifiers to pump moisture into the air, which, after it has covered us in a dewy, filmy coating, we realise from an accompanying text is water previously used to wash dead bodies of murder victims before autopsy in Margolles's native Mexico.
It's a relief to see the Hayward do a show like this, which is historical, yet contemporary. The gallery's recent programme of group shows has been typified by large-scale, immersive installations that promised much yet didn't deliver a huge amount of insight.
This exhibition is a refresher course in art well worth taking. Perhaps its most important message is that the magic and fear of art, as well as its intellectual and transformative capacity, comes from our mental or emotional engagement with it. When it really gets down to it, there is an awful lot of art that doesn't really need space-age buildings or luxe art fairs – just a sensitive audience willing to engage in a mental dance with the artist. And your partners are waiting.
'Invisible: Art about the Unseen', 1957-2012, Hayward Gallery, London SE1 (0844 875 0073; southbankcentre.co.uk) to 5 August