Others say there must be a different standard because of the sheer amount of data on and available through cellphones. In February, for instance, the Texas Court of Criminal Appeals suppressed evidence found on the phone of a high school student who was arrested on charges of causing a disturbance on a school bus. "Searching a person's cellphone," the court said, "is like searching his home desk, computer, bank vault and medicine cabinet all at once."
The justices are not always savvy about technology. At last week's argument over whether an Internet streaming service is lawful, Justice Antonin Scalia seemed to think HBO is a broadcast rather than a cable channel.
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But the justices can be sensitive to the implications of new technology for privacy rights, especially their own. Things did not go well for the Justice Department after one of its lawyers said at a 2011 argument that the F.B.I. was free to place GPS devices on the justices' cars. The government lost the case, against a drug dealer it had tracked for a month, by a 9-to-0 vote.
Similarly, in 2001, the court limited the use of thermal-imaging devices to peer into homes. Justice Scalia, writing for the majority, said, "It would be foolish to contend that the degree of privacy secured to citizens by the Fourth Amendment has been entirely unaffected by the advance of technology."
The problem in the thermal-imaging case, he wrote, was that the devices could detect not only heat lamps used to grow marijuana but also "at what hour each night the lady of the house takes her daily sauna and bath."
Searches of phones may give rise to a similar protective reaction. "It's a technology that all the justices will understand," Professor Kerr said. "They all have cellphones."
But they may not know how much information such phones can contain, including call records, messages, Internet browsing records, calendars, books, diaries, photographs and videos, to say nothing of applications that connect to financial, medical and travel records.
Adam M. Gershowitz, a professor at William & Mary Law School, noted that his iPhone tracked and stored his movements. "I just looked," he said, "and my phone shows that I arrived at work yesterday at 8:56 a.m." It also showed where and when he had lunch.
The first case to be argued Tuesday, Riley v. California, No. 13-132, arose from the arrest of David L. Riley, who was pulled over in 2009 in San Diego for having an expired registration. The police found loaded guns in his car and, on inspecting Mr. Riley's smartphone, entries they associated with a street gang.
A more comprehensive search of the phone led to information that linked Mr. Riley to a shooting. He was later convicted of attempted murder and sentenced to 15 years to life in prison. A California appeals court said neither search had required a warrant.
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In its Supreme Court brief, California said information on phones "is not different in kind from wallets, address books, personal papers and other items that have long been subject to examination."