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But more than 40 per cent of the works on display have not been shown in Tate Modern before. Major works have been brought out of storage. Roy Lichtenstein’s Wham!, for instance, now forms part of one of four “pairings” that introduce each of the principal sections. Juxtaposed with Boccioni’s striding bronze figure, marching heroically forward into a brave new technological world, it makes a powerful impression. Here are two divergent but echoing responses to the chaos of violence of their respective eras.

Historical precedents are examined from an emphatically contemporary perspective. Almost a quarter of the works on display are recent acquisitions. Here is a room devoted to a Minimalist-inspired, interactive installation by Cildo Meireles, for example, just one of the Latin American artists whom Tate Modern is now collecting as it seeks to extend its international range. There is a gallery devoted to the gang of Cubist-influenced agit-prop poster-producing feminist rebels the Guerrilla Girls. Here is a room of works by contemporary painters, Marlene Dumas and Luc Tuymans prominent among them, who return to the gestures of postwar American painting. There is a vast four-screen projection by Christian Marclay, who plays with Duchampian ideas. All find their roots in earlier ideas and techniques. Ideas ebb and flow across the years as single-theme rooms — such as that devoted to the “ready-made” — make clear immediately.

But the flow is not all one way. A huge Miró canvas and Matisse’s iconic Snail suddenly pop up in a gallery that leads on from Abstract Expressionists. These Modernist patriarchs continued their careers into the 1950s and explored contemporary experiments with scale.

Of course the Tate cannot cover up innate deficiencies. It cannot compete with MoMA, which owns not just works by all the great masters but among the greatest works they ever did. And nor can contemporaries compare with Modernists. How could they? Europe from the last couple of decades of the 19th century until well into the 1920s was swept into a creative whirlwind that whipped up masterpiece after masterpiece.

But what Tate Modern succeeds in doing in its confident new rehang is reanimating this incredible moment, reinvigorating it with life. Martin Creed — best known for his Turner prizewinning on-and-off light switch — installs a rude little intervention. It blows raspberries at bystanders.

Is it mere puerile impudence to blow raspberries at Jackson Pollock? Or does it remind us, accustomed as we are to this world of hallowed spaces and lofty plinths, that all these artists were seen as tasteless, provocative troublemakers in their day? Tate Modern makes plenty of suggestions but it doesn’t promise final answers. With a bit of luck, like all good family gatherings, this one will end in an almighty row.

Tate Modern’s rehang opens to the public today (020-7887 8888, www.tate.org.uk/modern)

TOP TREATS AND WHERE THEY ARE

Francis Bacon, Second version of triptych, 1944, 1988, Level 3, Poetry and Dream

Marcel Duchamp, The Bride Stripped Bare By Her Bachelors, Even, 1915-1923, Level 5, States of Flux

The Mark Rothko Room Level 3, Material Gestures

Donald Judd, Untitled, 1972, Level 5, Idea and Object

Anish Kapoor, Ishi’s Light, 2003, Level 3, Material Gestures