In January, the European Commission's information commissioner criticized the scanners' "privacy-invasive potential" and their unproven effectiveness. And tests have shown that the machines are not good at detecting low-density powder explosives: A member of Britain's Parliament who evaluated the scanners in his former capacity as a defense technology company director concluded that they wouldn't have stopped the bomber who concealed the chemical powder PETN in his underwear last Christmas.

So there's good reason to believe that the machines are not effective in detecting the weapons they're purportedly designed to identify. For U.S. courts, that's yet another consideration that could make them constitutionally unreasonable.

Broadly, U.S. courts have held that "routine" searches of all travelers can be conducted at airports as long as they don't threaten serious invasions of privacy. By contrast, "non-routine" searches, such as strip-searches or body-cavity searches, require some individualized suspicion - that is, some cause to suspect a particular traveler of wrongdoing. Neither virtual strip-searches nor intrusive pat-downs should be considered "routine," and therefore courts should rule that neither can be used for primary screening.

Will the Supreme Court recognize the unconstitutionality of body-scanning machines? It might have ruled against them five years ago, when the balance of power was controlled by Justice Sandra Day O'Connor.

O'Connor was an eloquent opponent of intrusive group searches that threatened privacy without increasing security. In a 1983 opinion upholding searches by drug-sniffing dogs, she recognized that a search is most likely to be considered constitutionally reasonable if it is very effective at discovering contraband without revealing innocent but embarrassing information. The backscatter machines seem, in O'Connor's view, to be the antithesis of a reasonable search: They reveal a great deal of innocent but embarrassing information and are remarkably ineffective at revealing low-density contraband.

The Supreme Court might not view the matter differently today, now that O'Connor has been replaced by Alito, who wrote the lower-court opinion insisting that screening technologies had to be both effective and "minimally intrusive." Last year, the court struck down strip-searches in schools by a vote of 8 to 1.

In many cases, furthermore, Supreme Court justices are influenced by public opinion, consciously or unconsciously, and some polls suggest that opposition to these screening measures has grown in recent months. That reflects a basic truth of the politics of privacy: People are most likely to be outraged over a particular privacy invasion when their own privacy has actually been violated.

By Sunday evening, a projected 24 million U.S. travelers will have flown over the Thanksgiving holiday, and although less than 3 percent of them will have received intrusive pat-downs, many more will have gone through the scanners, holding their hands up in surrender as detailed images of their bodies flashed across a government screen.

It's possible, of course, that the TSA will respond to the backlash by rethinking its screening policies or that Congress will step in with regulations. But if not, the Supreme Court may be asked to hear a constitutional challenge to the body scanners before long. If the justices take the case, they should strike down the use of "naked" machines and intrusive pat-downs as an unreasonable search and a violation of what Justice Louis Brandeis called "the most comprehensive of rights" - namely, "the right to be let alone."

Jeffrey Rosen, a law professor at George Washington University, is the author of "The Naked Crowd: Reclaiming Security and Freedom in an Anxious Age."