Sweden’s anti-cash movement must now contend with the Cash Uprising alliance. Illustration by Nishant Choksi

A fantastic heist (we like our crimes as smart and magical as dreams) took place some years back, when a stolen helicopter landed on the roof of a cash depot in Stockholm and three masked men smashed a skylight to climb inside. It was September 23, 2009. The depot was freshly stocked in expectation of a coming Swedish payday. Armed with a Kalashnikov, the invaders held employees at bay while their accomplices outside positioned road spikes to keep cop cars from swarming the building. Fake bombs had been set among the police helicopters to delay an aerial chase. The thieves loaded bag after bag of bills into their aircraft, then departed. Seven men were later caught and sentenced, but nearly all of the stolen cash—reportedly some $6.5 million—still has not been found.

The robbery is known as the Västberga heist, and, like many capers, it became a source of public fascination. (It is the subject of Evan Ratliff’s e-book “Lifted.”) But it also earned astringent notice from some economic theorists, who saw in it a parable about the risks of paper money. Cash is the squirmy ferret of societal wealth—tricky to secure physically and, once liberated in the wild, almost impossible to get back—and money, as technology, has changed a lot in half a century. A day’s errands once called for bulging pockets. Now it’s possible to shop for groceries, pay rent, buy lunch, summon a taxi, and repay your sister for a movie without handling a checkbook, let alone fumbling with bills and coins. Most people think of card and electronic payments as conveniences, stand-ins for exchanging cold, hard cash. Yet a growing group of theorists, led in the United States by Kenneth S. Rogoff, a former chief economist at the International Monetary Fund, are embracing the idea that physical currency should be the exception rather than the rule.

In a new book, “The Curse of Cash,” Rogoff, now a professor at Harvard, argues for phasing out paper money in the U.S., starting with big bills and slowly letting small denominations fall toward disuse. “Paper currency has become a major impediment to the smooth functioning of the global financial system,” he writes. His cause dates to the late nineteen-nineties, when he found that sixty per cent of the value of the country’s currency supply was in hundred-dollar bills—an astonishing proportion, considering how rarely C-notes show up in ordinary life. Since then, the percentage has risen (it’s now about eighty per cent), with $1.34 trillion outside banks at any moment. That’s nearly forty-two hundred dollars carried by every man, woman, and child in the U.S. Under whose mattress has all this cash vanished?

Rogoff argues that the invisible large notes must be paying off-the-book wages. They are sitting in Zurich safe-deposit boxes, probably, crossing borders with cartels and traffickers, and doing other awful things. The U.S. dollar is an unofficial currency in both unstable economies (such as the Philippines) and under-the-table oligarchies (China, Russia). Phasing out big bills would make it harder for domestic currency to support corruption abroad. A million dollars in hundred-dollar bills is easy to tote in a shopping bag, but a million in ten-dollar bills weighs an ungainly two hundred and twenty pounds. Hobbling the underground market should also temper tax evasion, a costlier problem than many people realize. The most recent I.R.S. estimates indicate a tax-payment shortfall of four hundred and sixty billion dollars a year—a disparity that’s transferred to those who pay. Rogoff speculates that eliminating big bills would also be a more effective deterrent to illegal immigration than, say, a border wall, because the wages of undocumented workers are, necessarily, paid in cash.

Most important for many economists, low-cash life allows for negative interest rates, in which the lender pays the borrower interest. These are already in limited use in Europe and Japan, and they’ve become the subject of increasing attention in the U.S. (Paper money is an obstacle, because if interest rates went negative a lot of people would cash out and stuff money into sock drawers—that way, at least, they’d get a zero rate.) Some economists think a quick drop into negative rates during a global economic crisis, like the one in 2008, would have the effect of a defibrillator: there would be a brief jolt, but then the system would get pumping again, and both interest rates and inflation would return to healthy, growth-oriented zones. As things are, rates can’t drop below zero, but they struggle to climb. For these and other reasons, Rogoff told me, some formerly skeptical colleagues have warmed to the idea of phasing out cash. Seriously considering his sunset scenario in the U.S., however, would require looking to a country that has already started toward that horizon.

That country is Sweden, the site of the Västberga heist. Cash circulation, long on the decline, has plunged since the time of the robbery, from a hundred and six billion Swedish crowns, or kronor, to seventy-seven billion last year. In 2013, Sweden eliminated its largest-denomination bill, and demand for its second-largest bill, the five-hundred-krona note (about sixty dollars), surprisingly fell off soon afterward. By 2014, only a fifth of Swedish retail transactions were being conducted in cash. (In the U.S., it’s slightly less than half.) Swedish ticket machines for trains and buses usually take only cards; increasingly, cafés and bars and restaurants refuse cash, too. About half of the country’s bank branches don’t allow withdrawals or deposits in bills. As of a few years ago, “you could see the first signs of Sweden moving toward a true cashless society,” Jacob de Geer, who runs the pan-European, Square-like transaction service iZettle, told me recently. “Many of the smaller shops started putting signs up on their doors saying ‘We Don’t Accept Cash.’ ” In late summer, I flew to Sweden to see what life is like when no one wants the money in your hand.

On an immaculate train from Stockholm’s airport, a conductor in a yellow shirt said that if I’d forgotten to buy a ticket I could pay him the fare, but only with a bank card. “You can go to the ticket counter in our small waiting room, at the station, and pay with Swedish cash,” he said, as if conceding that it was possible, at certain backward rural pubs, to purchase beer with turnips. He brandished his card reader proudly. He was not allowed, he said, a little less proudly, to handle money.

During my walk from the baggage claim to the train platform, I had passed ten ticket machines, all fitted not with coin slots or cash trays but with delicate, recessed card slides. On the train, small, silent screens set at the front of the cabin shuffled between ads for MasterPass, by MasterCard, and English headlines from the morning’s news. “A 27-year-old PhD student has been charged with stealing poisonous substances from Uppsala University as part of an alleged plot to blackmail the Czech Republic into paying large sums of money in Bitcoin,” one item read. Even thieves seemed to have moved on to better things.

I had not. I had withdrawn a wad of Swedish bills, seven hundred kronor (about eighty-three dollars), with the very American goal of keeping myself entertained by trying to spend it around town. The sum was more than I am used to carrying. One thing encouraging the anti-cash crowd is the conduct of the young; a survey of about a thousand U.S. adults, in 2014, found that more than half of those younger than thirty preferred cards to cash even for transactions of less than five dollars. When I run a transaction through my credit card, I get fraud protection, airline miles, and a digital record that I can export into budgeting software and spreadsheets. When I use cash, I get nothing: the transaction disappears. A generation that already orders cabs and music on screens needs no introduction to the joys of a cashless life.