The show's organisers make some sweeping claims. "His archetypal views of America have assumed an unrivalled place in our collective consciousness," asserts a big panel at the entrance. "Perhaps no other painter has touched us so deeply or provided a more compelling model for other artists, film- makers and writers seeking to interpret the experience of American life in the 20th century."
The show sets out the main evidence for its claim in a multimedia exhibit planted squarely in the middle of the exhibition space. A half- hour presentation compares Hopper's work with film stills and clips, photographs and canvasses by other painters. Audiences gasp at some of the juxtapositions - for example, Nighthawks with Boulevard of Broken Dreams, Gottfried Helnwein's popular spoof poster, and the diner scene in Herbert Ross's Hollywood version of Pennies from Heaven. The visual rhymes are unmistakable.
Hopper himself was typically much more modest and doubting. "Who is to say from where influence comes?" he once said. "It's probably a reflection of my own loneliness. It could be, I don't know, a reflection of the human condition."
And only a few moments' reflection leaves you, too, wondering whether many of these echoes are more than superficial. Boulevard of Broken Dreams is a case in point: the composition is formally identical, of course, but the conception of the scene is all wrong, replacing Hopper's morose, silent nonentities with a clutch of glamorous (albeit doomed) celebrities. There's a mood of jollity to the joint: Elvis, as the short-order cook, looks almost as if he's rock 'n' rolling behind the counter.
Conversely, where there's a vague similarity of theme - solitude, melancholy, sense of yearning - the images often lack Hopper's distinctive visual mannerisms: the strong, geometric but asymmetrical composition, the foreshortened perspectives, the clean diagonal shafts of light and shadow. A scene isn't Hopperesque just because it has a gas pump in it.
Last year, in the BBC's Moving Pictures series, the case was made for Hopper's influence on film-makers. Hopper, an avid and eclectic movie- goer, was seen as one of the first 20th-century artists to be influenced by the cinema. The directors Alan Rudolph (Dorothy Parker and the Vicious Circle) and John Dahl (The Last Seduction) and designers Jack Fisk (Days of Heaven) and Ken Adam (Pennies From Heaven) all declared their debt to him.
This case is more convincing even if there still seems something incompatible between Hopper's paintings - their stillness, their silence - and the very idea of motion pictures. And it's notable that almost all the film- makers cited come from the art-house end of the spectrum.
His impact on US popular culture is harder to measure. Perhaps, for Americans, he does embody a kind of romantic national self-image. But a British visitor is just as likely to find his sensibility rather European; the show reluctantly acknowledges as much, noting the writers he liked: Goethe, Moliere, Tolstoy, Mann.
It's doubtless flattering for Americans to think that the national imagination is embodied by this distinguished artist but, for audiences abroad, it's more likely to be something different. Something not arty but popular, not timeless but ferociously modern, not quiet and still but manic and ever-moving, disseminated not by a lone artist but by the global media. Something like Mighty Morphin Power Rangers, Michael Jackson or Oprah Winfrey.
n Edward Hopper and the American Experience continues at the Whitney Museum of American Art until 15 October