Tuesday's US supreme court arguments involved a seemingly basic legal question about the future of the Fourth Amendment: do police officers need a warrant to search the cellphone of a person they arrest? But the two privacy cases pit against each other two very different conceptions of what it means to be a supreme court in the first place – and what it means to do constitutional law in the 21st century.

"With computers, it's a new world," several justices reportedly said in the chamber. Are they ready to be the kinds of justices who make sense of it?

Cellphones expose so much of our most personal data that the decision should be a 9-0 no-brainer. The basic problem that makes it a harder call is that lawyers and judges are by training and habit incrementalists, while information and communications technology moves too fast for incrementalism to keep up.

Judges wear legal professionalism and precedent as a mantel that secures legitimacy for their decisions. It's how they distinguish themselves from politicians or administrative agencies, while wielding power that is sometimes much greater than those democratically accountable actors. But this kind of narrow legalism simply cannot do when the world is changing as rapidly as it is today: all narrow analogies will systematically fail to preserve the values they did five or ten years ago, especially when we're walking around with all the metadata coming out of the bank/medical monitor/full-on GPS trackers in our pockets.

One of Tuesday's cases, United States v Wurie, stems from an arrest in 2007, the same year the first iPhone was launched and changed handheld computing forever. In the second case, Riley v California, the arrest and search happened only two years later. So the future of the Fourth Amendment will therefore depend not on the particular doctrines of the case, but on whether the formalistic justices – the ones with a line of reasoning that lacks agility to deal with a radically changing world – prevail over those who take a broader constitutional vision. If they do, we are in for a dramatic erosion of constitutional privacy protections in the coming years – all thanks to the same kind of old-school legal approach that allowed National Security Agency lawyers to justify mass telephony meta-data surveillance.

Should spy-level sway continue to hold when it comes to getting pulled over on the side of the highway?

Police in Tuesday's cases have argued that they don't need a warrant to search the cellphone of people whom they arrest, at least when the cellphone is on the person arrested. This is a country in which between 30-40% of young people will have been arrested by the time they reach age 23. That's an age group with practically universal cellphone use. Connectivity is the foundation of sociality, and the practical implications of the court's decisions to the privacy of Americans simply cannot be reduced to saying "the case raises grave constitutional questions". A wrong turn by the justices will give every federal, state and local police officer discretion to search the most ubiquitous and invasive surveillance device we have ever seen without a warrant or probable cause.

The briefs in the case are, as you might imagine, full of carefully crafted legal arguments on both sides. But the decision ultimately will be decided by a much more basic choice that was presented in the most important recent supreme court case pitting constitutional method against technological change.

In 2011, in United States v Jones, the justices exhibited two opposing visions of what a constitutional court should be – a technical legalistic court, and a broad constitutional-vision court. In Jones, the government had attached a GPS tracker to a suspect's car for a month, and all nine justices held that such tracking went too far. Justice Scalia, writing for four conservatives and joined by Justice Sotomayor, held on narrow technical grounds – the tracker had been a physical invasion of the suspect's property, he wrote, and so it fell within a narrow technical category of "trespass" that the government could not violate without a warrant.

Justice Alito wrote a combative Jones dissent for himself and three liberal justices, which would have provided a broader vision, recognized the rapid change of technological change and set as the court's goal the achievement of a stable level of substantive privacy in the face of innovation. Justice Sotomayor voted with the majority on the narrow technical grounds, but wrote an opinion that was even more assertive than Alito's opinion: what the court needs, she wrote, is a constitutional vision sensitive to radical change.

If Tuesday's cases are resolved under Justice Scalia's specific rule, there simply is no trespass, because we own the phone – we carry it of our own accord. More importantly, if Scalia's technical approach carries the day, our level of privacy in the coming decades will rise and fall more or less randomly, based on whether a particular new technology can or cannot be shoehorned into this antiquated doctrine.

But the world is changing, and that narrow view of constitutional adjudication will not offer us meaningful protection. We have already seen how technical legalism allowed well-intentioned NSA lawyers and conscientious judges of the Foreign Intelligence Surveillance Court to approve pervasive telephony surveillance because it involved "metadata". They were professionally blinded from seeing that metadata – in our current big-data universe, is simply not the same thing as call records were during a court decision in 1979. In the Patriot Act telephony metadata fiasco, legal formalism completely disabled both lawyers and judges: they were blessing a program that had become unrecognizable as consistent with constitutional protection of privacy – anyone who read Edward Snowden's documents soon knew that, and the legal world should have known it sooner.

But we have a way out. In that 2011 decision in US v Jones, five of the justices showed that they understood we needed something more than just technicalities. What we need in these news cellphone cases is for those five justices to join together and show that constitutional vision is more than just the workmanlike competence of lawyers. Otherwise, the coming decades will become a series of lurches from one formally defensible but substantively implausible invasion to another, with no end in sight – as long as there's another iPhone in the works.

Questions from Justice Kennedy – and perhaps Kagan and Sotomayor, though maybe not Alito – appear to suggest that the court may finally be ready to embrace that broader, more substantive view of its own role. It's about time.