WASHINGTON >> At a lively Supreme Court argument today, the justices seemed troubled by the government’s ability to acquire troves of digital data without a warrant and puzzled about how to address it.

“New technology is raising very serious privacy concerns,” Justice Samuel Alito said.

Justice Elena Kagan expressed misgivings about a world in which “the government is getting 24/7 information.”

Justice Sonia Sotomayor said that “most Americans, I still think, want to avoid Big Brother.”

The argument lasted 20 minutes longer than the usual hour. But it ended without a clear consensus on whether or how the court might be prepared to revise long-standing constitutional doctrines that allow the government to obtain business records held by third parties.

The case concerns Timothy Ivory Carpenter, who was convicted of participating in a series of robberies, based in part on records provided by his cellular carrier showing his movements over several months. Nathan Freed Wessler, a lawyer for Carpenter, said that prosecutors had violated the Fourth Amendment, which bars unreasonable searches, by failing to get a warrant for the information.

A ruling in Carpenter’s favor could revise a fundamental Fourth Amendment principle: that people have no reasonable expectation of privacy when they voluntarily turn over information to a third party like a phone company.

The court’s decision will apply the Fourth Amendment, drafted in the 18th century, to a world in which people’s movements are continually recorded by devices in their pockets and cars, by toll plazas and by transit systems. The court’s reasoning may also apply to email and text messages and internet searches, as well as bank and credit card records.

Michael R. Dreeben, a lawyer for the federal government, urged the justices not to take drastic action.

“The technology here is new,” he said, “but the legal principles this court has articulated are not.”

Recent Supreme Court decisions have expressed uneasiness with allowing the government to have unfettered access to vast amounts of digital data. The court has limited the government’s ability to use GPS devices to track suspects’ movements, and it has required a warrant to search the cellphones of people placed under arrest.

Older cases, though, suggest that information turned over to third parties is fair game. In 1979, in Smith v. Maryland, for instance, the Supreme Court ruled that a robbery suspect had no reasonable expectation that his right to privacy extended to the numbers dialed from his landline telephone.

Relying on the Smith decision’s “third-party doctrine,” federal appeals courts have said that government investigators seeking data from cellphone companies showing users’ movements do not require a warrant.

A federal law, the Stored Communications Act, does require prosecutors to go to court to obtain tracking data, but the showing they must make under the law is not probable cause, the standard for a warrant. Instead, they must demonstrate only that there were “specific and articulable facts showing that there are reasonable grounds to believe” that the records sought “are relevant and material to an ongoing criminal investigation.”

Justice Anthony Kennedy said the balance struck by Congress was entitled to deference.

“Why shouldn’t we give very significant weight to the Congress’ determination?” he asked.

Several justices questioned whether people using cellphones know that they are leaving a digital trail of their whereabouts over time. Kennedy said it was common knowledge.

“If I know it,” he said, “everybody does.”

A decision in the case, Carpenter v. United States, No. 16-402, is expected by June.

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