He added: “A person who knows all of another’s travel can deduce whether he is a weekly churchgoer, a heavy drinker, a regular at the gym, an unfaithful husband, an outpatient receiving medical treatment, an associate of particular individuals or political groups — and not just one such fact about a person, but all such facts.”

Federal appeals courts in Chicago and San Francisco, on the other hand, have allowed the police to use GPS tracking devices without a warrant. The police are already allowed to tail cars and observe their movements without warrants, those courts said, and the devices merely allow them to do so more efficiently.

Judge Richard A. Posner, writing for a unanimous three-judge panel in the Chicago case, did caution that institutionalized mass surveillance might present a different issue.

Some judges say that world is fast approaching.

“Technology has progressed to the point where a person who wishes to partake in the social, cultural and political affairs of our society has no realistic choice but to expose to others, if not to the public as a whole, a broad range of conduct and communications that would previously have been deemed unquestionably private,” Magistrate Judge James Orenstein of the Federal District Court in Brooklyn wrote last year.

The case to be heard by the Supreme Court arose from the investigation of the owner of a Washington nightclub, Antoine Jones, who was suspected of being part of a cocaine-selling operation. Apparently out of caution, given the unsettled state of the law, prosecutors obtained a warrant allowing the police to place a tracking device on Mr. Jones’s Jeep Grand Cherokee. The warrant required them to do so within 10 days and within the District of Columbia. The police did not install the device until 11 days later, and they did it in Maryland. Now contending that no warrant was required, the authorities tracked Mr. Jones’s travels for a month and used the evidence they gathered to convict him of conspiring to sell cocaine. He was sentenced to life in prison.

The main Supreme Court precedent in the area, United States v. Knotts, is almost 30 years old. It allowed the use of a much more primitive technology, a beeper that sent a signal that grew stronger as the police drew closer and so helped them follow a car over a single 100-mile trip from Minnesota to Wisconsin.

The Supreme Court ruled that no warrant was required but warned that “twenty-four hour surveillance of any citizen of the country” using “dragnet-type law enforcement practices” may violate the Fourth Amendment.