The Supreme Court will hear oral arguments on Tuesday in the case of a Washington nightclub owner convicted of dealing cocaine in part based on evidence from a GPS device attached to his SUV without a warrant.

Both sides see high stakes in United States v. Antoine Jones, a case examining the line between security and privacy, which is increasingly obscured by new technologies. Depending on which side is arguing, the case could seriously hamper investigations of criminals and terrorists alike, or it could lead to police using your own cell phone to track your every move.

Seven years ago, nightclub owner Antoine Jones came under police and FBI suspicion of drug dealing.

Investigators attached a GPS device to his Jeep Grand Cherokee and collected data about where he drove for four weeks, according to court filings. But they didn’t comply with the terms of their warrant, allowing it to lapse and violating geographical restrictions.

Nonetheless, prosecutors used GPS data—which showed Jones visiting a stash house—to prove their case, along with other evidence. Jones was sentenced to life in prison for conspiracy to distribute nearly 100 kilograms—200 pounds—of cocaine...