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.

A major social obstacle is privacy. The record of our electronic lives is a convenience, except when it’s an annoyance or worse. In the popular imagination, the black market is buttressed by large metal cases of cash. But many underground transactions are more modest. New Yorkers frequently hire babysitters and housecleaners in cash and do not file the required tax forms; waiters may pocket tips without keeping a tally for the I.R.S. Cash’s fungibility enables slushy bookkeeping. Our willingness to put up with this reflects a sense we have that most people, in life, end up with certain records they would rather not keep.

After checking into my hotel in Stockholm, I went for a stroll to shake off jet lag. The city did not hide its appetite for plastic. Farmers’ stalls in the Hötorget, an old hay-market square, sold Swedish chanterelles and summer berries alongside mangoes shipped from Pakistan. They took cards. The flower-stall guys nearby hawked bouquets of late-summer roses and trimmed bracken. They took American Express.

Later, I wandered into a bar, in the Scandic Grand Central Hotel, and ordered coffee. The bartender had slicked hair and wore a mysteriously tropical shirt. I extracted my wad. “This is a cash-free bar!” he said, alarmed. He pointed to a sign atop the register that said “Cash Free Zone” and featured a picture of some coins and bills overlaid with an enormous “X.”

“Is that a new thing?” I asked, feeling like a smoker who’s had a cigarette plucked from his lips.

“It’s a new thing—two, three months ago,” he said.

“Oh, interesting,” I said. “Why?”

“More security for the people,” he said, handing me a credit-card receipt to sign. “Now write the total amount.”

Sweden seems nearest to stamping out paper currency, but Denmark and Norway are trailing close behind. Ninety-three per cent of consumer transactions in Belgium are now cashless—partly because, like other European countries, it has capped the amount that can legally be paid in cash—and cash use in Australia has fallen by a third in a period of six years. India, whose underground economy is thought to swallow up four hundred and sixty billion dollars annually, has considered capping cash transactions and cash holdings; in a recent radio address, Prime Minister Modi exhorted citizens to turn their backs on cash. Throughout sub-Saharan Africa, where only about a third of the population have bank accounts but at least sixty per cent have cell phones, mobile payments have begun to leapfrog over paper currency. (About a quarter of Kenya’s gross national product runs through its payment app, M-Pesa.) China, never keen to fall behind, has embraced mobile payments, with mixed success. Having spent two and a half millennia accumulating money, we now find that it weighs us down; we want to sail it through the ether.

Sweden’s bellwether case, though, is distinct, and borne by three overriding causes. A flurry of high-profile robberies, not limited to the Västberga heist, married paper money to security vulnerabilities in the public imagination, and led entities such as the Swedish bank tellers’ union to lobby against cash-handling. (Bank robberies and street muggings have declined notably since the cashless trend began.) The Swedish financial industry realized that fee-inclusive transaction technologies could turn a more handsome profit than cash handovers. And Sweden, a small country with an eye to the digital vanguard, has been a leader in developing new transaction apps and other tools. The appeal has started to sway small, urban businesses. “It’s efficiency, simplicity—we can work with a more modern system, and it’s easier for our staff,” Gül Heper, the former brand director at HTL, a chain of sleek, youth-oriented cash-free hotels, told me. “And security. Because the lounge is open twenty-four hours, and we have a lot of traffic.” In a cashless enterprise, you never have to worry about someone dipping into the till. “You always have to have someone counting cash,” David Zetterström, the co-founder of the boutique bakery chain Fabrique, cashless since February, says. When Zetterström and his wife started the bakery, eight years ago, thirty or forty per cent of all transactions were in cash, and the costs of cash-handling seemed unavoidable. More recently, that figure dropped to less than ten per cent, and credit-card-transaction fees for merchants came down, too. Last year, after Fabrique had four break-ins, Zetterström decided it was time to give the cashless thing a shot.

The security argument for cashlessness has been helped along by support both popular and pop. ABBA the Museum—an interactive athenaeum for the art and artistry of Sweden’s superfamous quartet—does not take cash, mostly owing to the deeply held beliefs of Björn Ulvaeus, the smaller and less bearded of the “B”s.

“What happens to street crime when an advanced economy goes completely cashless?” Ulvaeus, who first registered the risks of cash after his son had a home robbery, wrote to me in an e-mail not long ago. “Why don’t politicians ask questions like that?”

However costly cash-handling is for businesses, it’s more so for the banks. Cash requires elaborate security for transportation and disbursement. It is a pain to track bill by bill. Financial institutions can make money from card transactions and account maintenance, but cash, for all its ubiquity, has questionable returns and a growing air of obsolescence. Sweden’s central bank, the Riksbank, has recently joined many of its peers in looking at blockchain technology. Björn Segendorf, a Riksbank economist, said it was an “open question” whether the central bank would be issuing digital currency in the future.

“We don’t add any value by handing over cash over the counter,” Mats Torstendahl, an executive vice-president at Skandinaviska Enskilda Banken, or S.E.B., one of Sweden’s Big Four, told me one afternoon. We were sitting in his office—big by American standards, bigger by Swedish—at a table opposite his desk. When we met, Torstendahl had leaned into my handshake as if into a rusting door handle. Now he settled in his chair in the authoritative lounge pose of a senior financier. He had neatly parted blond hair; round, tortoiseshell glasses; and the Swedish banker’s uniform—a well-cut, sober suit without a tie. There was a delicate orchid in every window of the room. “The banks have consciously been trying to transfer manual cash-handling in our system to automated cash-handling, to decrease risks in the environment for our co-workers,” Torstendahl said.

Per Långsved, a rising manager who is the head of retail banking products, chimed in: “Cash is actually one of the main carriers of diseases in the world!”

In Sweden, banks don’t run proprietary A.T.M.s, as in the U.S. Instead, the five largest jointly own an A.T.M. company, Bankomat. Insisting that every branch also have a vault and a cash-handling teller would be otiose, Torstendahl told me, especially given the sharp decline in cash transactions in the past decade. “Ask a Swedish customer, ‘Do you have cash on you?’ ‘I never have cash on me.’ ‘We are thinking of taking away cash.’ ‘No, you cannot take away cash!’ ‘But you don’t have any cash.’ ‘Yeah, but if I want to have cash you should have cash.’ ‘But you never have cash!’ ”

He leaned back and smiled. “You get into a kind of cash twenty-two situation.”

To the question of who’s left behind by low-cash life, the answer, in Sweden, rides on three numbers: latitude, age, and wealth. In the rural north, the de-cashing of bank branches changes daily life. Locals, especially those with cash-intensive businesses, like shops, now drive great distances to find a bank that serves their needs. “You have to go to one, two, three, four, five banks until you find one,” said Wiggo Lindgren, a plump, jovial pensioner who is the vice-president of the Småföretagarnas Riksförbund, or National Small Business Association, which represents thirty thousand firms. Today, fifty-three thousand people in Sweden must travel more than eighteen miles to withdraw cash. “One-fifth of them say it would be a disaster if cash went away—they’d have to close their shops,” Lindgren told me. “What we want is some kind of status quo.”

Stasis would suit the elderly, too. Some old people are undaunted by cashless ways of doing business. But many struggle to track debt, quail at smartphones, and forget the pin codes needed for their bank cards. Add to that matters of convenience (some toilets require digital payment, and the elderly are often urgent visitors) and the phasing out of cash seems, to at least one demographic, premature. Christina Tallberg, the chair of the Pensionärernas Riksorganisation, or National Pensioners Organization, told me that, after dues-collecting meetings of her organization, its elderly female treasurer has had to carry a big sack of money on two modes of public transportation in order to reach a bank branch that would accept the deposit.

Both Lindgren’s and Tallberg’s organizations have joined Kontantupproret, “Cash Uprising,” a loose coalition for the preservation of cash. The founder is Björn Eriksson, a former president of Interpol and, it must be noted, chair of the Association of Swedish Private Security Companies, which represents armored trucks and the like. Cash Uprising holds that everybody should be able to get and deposit cash anywhere—the view that Torstendahl and others find so obtrusive. (“History has many sad examples of people who have tried to stand in the way of science, technology and capitalism,” Björn Ulvaeus, of ABBA, wrote me about the group.) Yet Cash Uprising is not quite fringe. “When I speak today with an organization, this is actually one of the key topics, the key frustrations, that they’re very angry about,” says Jan Bertoft, the secretary-general of the Swedish Consumers’ Association, a federation of twenty-four groups, including retirement, disability, and immigrant organizations. The Uprising publishes editorials that are critical of what Eriksson calls “this abnormal way of making it as difficult as possible to use cash out of the pocket.” At first, it tried appealing to the banks, but they wouldn’t engage. So the Uprising and its surrogates moved on to politicians.

One subject of their attention has been Sweden’s deputy minister of finance, Per Bolund. In late June, Christina Tallberg handed him a petition, signed by 139,064 pensioners, asking the government to safeguard the use of cash. Bolund had won some political points recently by attending to the cash concerns of asylum seekers. (He pushed for a plan that would give them quick access to banking services.)

I went to visit Bolund one morning, in a governmental office building. He is a tall man, with the wide, concerned grin of a Boy Scout who has finished tying his ropes but worries about whether he’s done it right. He led me to a conference table at one end of his office and poured piping-hot black coffee from a carafe. He wore a dark suit with a crimson tie of ribbon thinness, tugged into the smallest knot I had ever seen. Bolund’s attitude toward Sweden’s cashless tendencies is both upbeat and circumspect—which is to say, fairly political.

“This is not something that’s been thought out by the government—‘We’re going to be a cashless society’—but, rather, a development from the bottom up, so to speak,” he said. “I will have a dialogue with the private sector, trying to point out that they have a responsibility for giving payment services for all citizens.”

One model, he said, could be Sweden’s alcohol-provision system, which allows Swedes in remote locations to order booze to be delivered, and held, at the nearest store. (Similar systems exist for medication and parcels.) Bolund wants the banks to consider such an arrangement for cash. “If there is not a solution that has been provided by the private actors, there will come a time when we are faced with no other option but to regulate this,” he said—but he preferred to let demand, innovation, and time run their course.

“We have generations of young people now entering the economy who have never used cash, and see no reason whatsoever to start using cash at all,” he went on. “And, of course, for natural reasons the elderly citizen will”—he came to a terrified stop, as if racking his processors for an apt euphemism—“move out of private society, and that will, of course, bring a move toward electronic payments. For natural reasons!”

No passage of time is likely to help the unregistered poor. At some point, I started chatting with panhandlers in Stockholm, all of whom were foreigners, off the Swedish books and social programs. A cheery, gray-bearded Bulgarian man named Atanas told me, through a few words of English and some artful hand gestures, that a miscreant had absconded with eighty thousand kronor (about ninety-three hundred dollars), leaving him penniless. An Austrian woman, Sigrid, who was perched on a street corner, knitting, said that her Austrian pension had been locked. She’d been bouncing around various cities in Europe. Fortunately, she did not find the Swedes less liberal with their cash on the street than any other nationality she’d encountered, and she had managed to save money that she would use to buy a bus ticket elsewhere. “You won’t need a bank card?” I asked. Sigrid laughed. “No, no!” she said brightly. She was old and poor, and just the sort of person no one thinks of when imagining a thriving future, so I hoped that she was right.

In every European city, there are cafés, bars, and restaurants that stand as totems to a youthful cosmopolitan dream. They are tavernlike and multipurpose places. Usually, their customers are under forty-five. The language of first resort is Global English, which extends the present into the continuous and makes bathrooms “toilets”: language that belongs to nobody, and so to all. These are the places where expatriates gather to feel less foreign, and where locals go to avoid losing touch. To visit is to feel lost, but also on the verge of being found.

One of the newest of these spots in Stockholm is Nomad, halfway up a hilly stretch of road, just past the central station. On a Monday evening, I stopped by for a plate of meatballs. Some American guys on the back patio were playing poker. I sat inside, beside three young women clustered around a table over drinks. One, dark-haired and with a nose stud, clutched a packet of tobacco and distractedly rolled a cigarette. Another was a visiting Berliner; the third, a freckled Californian.

The Californian was discussing work and money. “When you’re dying in bed, are you going to think, I wish I had worked those extra twenty hours?” she asked. “Or are you going to think, I wish I’d gone to that place? Right now, we are young. No matter, we’re going to be broke. Yeah?”

“You’re going to spend it,” the woman with the cigarette said. “You’re going to spend it—on the concert ticket, on clothes, on the apartment, whatever. You’re going to spend it. So, like, make sure you’re happy what you spend it on.”

“Travel is definitely the solution,” the Californian said.

A willowy woman from Bonn wandered in, trailing a guy from Peru who wore a fedora. “My roommate!” the Bonn woman called out to the Californian. “You are still here!” Everyone was introduced. The Bonn and Berlin women started speaking German, and the guy in the fedora asked if he could grab a chair from my table. He sat across from the Californian, who began to tell him that she’d love to travel to Peru but that, as a woman, she was worried about going alone. “You are very beautiful, so you would be fine there,” the Peruvian said. They discussed his nation’s landscape.

On the other side of my table, a pair of women, Swedish and Serbian, were playing rummy with two decks of cards, one pale red and the other blue. They got a round of cocktails in coupe glasses and invited me to join them, but it was getting late, and I was almost finished with my meatballs. I asked them whether they often used cash. Usually plastic cards, they said, or else mobile apps. “Even at farmers’ markets and things, people don’t need cash,” the Swede said. The Swedish central bank’s recent release of a new line of bills and coins struck her as foolish. “It’s trying to be more like the E.U.—two-kronor coins and things like that,” she said. “But it’s, like, why? What’s the point? No one uses it anymore.”

To get a clearer sense of forms of money people do use, I went to visit Peter Fredell, whose company runs a mobile wallet called SEQR (“secure”). SEQR launched in 2012, before Apple Pay, and reflects the kind of thinking that drives Sweden’s cashless thrall. Fredell is a garrulous bald man with glasses and a predilection for snus, the tea-bag-like sachets of tobacco that Swedes place underneath their upper lip to buzz their gums. On his wall, he had mounted the bleached skull of a bear, which he’d shot, and a giant swatch of animal fur, which he kept framed—an allusion to the calming “furry wall” in the broad comedy “Get Him to the Greek.”

SEQR, which now carries out tens of millions of transactions globally each year, purports to do most of the things that can be done with cash. When you download the app on your phone, you link it directly to your bank account, not to an existing card number, as with Apple Pay. Retailers key the transactions with designated QR codes (those pixellated, radarlike bar codes) at their registers. SEQR also has a peer-to-peer function, which allows money to be sent to another user, and a “touchless” interface at some registers. Many people have visceral anxieties about doing business with their cell phones, but Fredell insists that it’s the safest money-carrying medium there is.

“When you want to do a payment, we check: Is it the sim card? Yes. Is it the hardware, the same phone? Yes. And do you have the pin code?” He waved his own smartphone. “You can’t really hack that, because this number is unique to this telephone.” Even if somebody broke through all the interlocking keys on one phone, they would have to start all over again on the next. “That means it’s not scalable fraud,” Fredell told me. The flip side of this elaborate security is lost privacy: Big Brother can’t protect you from what he doesn’t see. But Fredell thinks that concern is passing. “Eventually, everyone will pay with their mobile,” he said. “When they will do it is written in the stars.”

Fredell pulled a soggy snus bag from under his lip, swapped it for a new sachet, and suggested that we go shopping. It had rained lightly through the lunch hour, but it was dry now. We walked to one of the big Swedish supermarkets, Hemköp, and toward the sweets section, where Fredell plucked a small bag of Ahlgrens Bilar gummy candies. He took it to the cashier and snapped the QR code on his phone. “I’m waiting for the cashier to put in the amount—there it comes!” he chirped. “I do my pin code, and it’s done.” The cashier offered him a receipt. “I don’t need that,” he said proudly, raising his phone. “I have a total receipt here.”

I thought we were done shopping, but Fredell remembered that he had to buy more snus—I had a hunch that he was always buying more snus—and so we walked to the tobacco counter, and he did the QR-code thing again, this time on a gigantic, ten-cannister column of General snus, which, with gold-foil wrappers, looked like something pillaged from the minibar of a Trump hotel. On the way to another supermarket, Fredell ate candy and sucked snus and talked about the mobile-payments drug market. He waved a slim card sheath under my nose. “This is my wallet—no cash here!” he said. “I made it from eel skin that I fished myself.”

For many people, cash signifies autonomy, but for the young or the technologically adventurous it’s an inhibition on the freedom of self-made exchange. The romance of this notion helps account for the success of Swish, the most popular mobile cash-transfer app in Sweden. Swish, a peer-to-peer service like Venmo, launched in December, 2012. Less than four years later, it is used by half the Swedish population and by ninety per cent of adults under thirty. The service moves money instantly; you need only a recipient’s phone number. Its interface is so simple that it is used for church collections and other basket-passing fare. (On the metro platform one night, I passed a busker with a sign: “If you don’t have Cash, pay with Swish!”) Last summer brought Sweden’s first Swish mugging, when two thugs beat up a man and forced him to Swish them. The criminals were rapidly identified by their account.

The success of the app is striking, because it wasn’t dreamed up by a Zeitgeist-attuned entrepreneur. Swish was conceived, driven, and funded by the Swedish banks. Settling on a Bankomat-type model, they sponsored development together and hired a marketer, Per Ekwall, who had a basic insight into how this new cashless technology would fit the population’s needs.

“I thought, This is about social payments,” Ekwall told me one morning, in the offices of his firm, The World Loves. “It was a big mental leap for banks to think about payments not as a technical thing, or a product, but as a social thing. The value of Swish is nothing unless my best friend has it.”

Ekwall focussed on two groups that he called Innovators and Administrators. The Innovators were early tech adopters. The Administrators were “class parents”—the sorts of people who organize school events and group gifts. Administrators were always arranging things, Ekwall reasoned, so people in their social circles constantly owed them money, and would download a simple app to repay them if requested to do so. In marketing Swish, he aggressively targeted those two groups, on the theory that almost everyone else would get pulled on board as well.

The theory held. Today, some Swedish banks have more Swish transactions than A.T.M. withdrawals. The app has also brought with it an element of cultural identity. “It’s important for Swedish society,” Anders Edlund, who is in charge of Swish at the bank Nordea, told me. “When Swish has production disturbances, it takes, like, one minute, and the big Swedish newspaper writes about it. It’s thatimportant.”

One Saturday night, I put on a jacket and walked through central Stockholm. Cafés on Sturegatan spilled late diners out onto the sidewalk. A group of women with a sign that read “kyssen 10 kr” (“Kiss 10 Kronor”) wandered by, chortling intermittently. Crowds had started to swell outside certain bars and clubs. On a whim, I talked my way past a gray-clad bouncer and climbed a grandiose flight of red-carpeted stairs.

The place was called Sturecompagniet, and it had a cover charge. I took out my wad, but the cashier wanted my American Express. The interior looked like a public spa, set under vaulted ceilings, with a mosaic floor. The music was a soundtrack of millennial nostalgia—Shakira, Snoop, “Ride wit Me”—and a smoke machine shot off sharp plumes of mist. After a while, the Kyssen 10 Kr women drifted in. A woman in a bridal veil danced wildly beneath the lights.

Someone grabbed my shoulder and shouted unintelligibly in my ear. The guy wore a black blazer and a white shirt with a matching pocket square; he had blond hair buzzed close to his scalp. He said his name was Henry, and that he was in town for the weekend to meet girls. In fact, he said, a Superhot Girl was on her way here—did I want to meet her? The smoke cannons fired triumphally behind him. I said that I was always happy to meet anyone. The only thing was, he said, I should pretend that I’d known him all his life. Although I’d said I was a journalist, he had decided that I was a lawyer. I had introduced myself as Nathan, but Henry preferred his own version: Manson.

Henry introduced me to his wingman, Sebastian. He had known Sebastian for years and years, he said, though I now had reason to suspect that claim. “Sebastian, this is Manson,” Henry said.

“Nathan,” I said.

“Manson, Sebastian,” Henry said, pointing a route. “Let’s go outside.”

We wandered out to the sidewalk, where a patio had been set up. The street was quieter. While Henry fussed with his phone, tracking down the Girl, I talked with Sebastian, a grad student from somewhere he described as “like Westeros from ‘Game of Thrones.’ ”

“He likes to make up these complicated stories to try to impress the girls,” Sebastian said. “For example, I am supposed to say that he’s a Russian spy.” Sebastian’s hero was Elon Musk, whom he had never met but whom he considered a model human being. “I really think I’d take a bullet for that guy,” he told me.

We spoke about the Hyperloop of Elon Musk, and the American election, and the awfulness of Swedish trains in winter. Henry periodically checked in with updates: the Girl was en route. At some point, he began to call me Nitch. He approached a guy on the patio, well dressed, with salt-and-pepper hair. “You look great!” Henry declared. The guy was a Canadian named Eric, and Henry urged him to stay and meet the Superhot Girl, too. “This is Nitch,” Henry said, pinching my shoulder. “I’ve known him forever.”

“Nathan,” I said.

“Nitch is an Italian lawyer,” Henry said. It occurred to me then that Henry was gathering a dream team of random strangers to hang out with him, the better to impress the Girl. I felt moved by his attention to her happiness.

Henry wandered off because it was the Superhot Girl’s birthday, or so he said, and he was trying to get her in for free. It struck me that, as much as cashless life enabled one kind of cosmopolitan fluidity—no more costly money-changing across borders, the breezy trust that comes with financial lucidity—it impeded another. With a pocket of cash, you could be anyone: a Russian spy, a birthday celebrant, an avvocato out for a night on the town. With a cashless trail, you were fated always to be what you had always been; you couldn’t flee far from your name, your purchases, even your network of friends. You were always, by your cards or cell phone, outed as yourself.

For Americans, who lack the institutional trust of the Swedes, cashlessness feeds paranoia. And, for the U.S. government, it might mean more unwanted chores. Rogoff believes that the prickliest details of a cashless transition would rise from the de-facto regulation it prompts. Suddenly, small-scale marijuana purchases and the like, mainly overlooked to spare an overburdened penal system, would become conspicuous. Negligible tax evasions of the babysitter variety, less rewarding for the I.R.S. to pursue, would emerge. Do Americans, fetishists of self-invention and self-interest, want that much clarity? “Sweden has been very fast at doing these things—they’re incredible,” Rogoff told me. “But they’re very determined. I don’t think we’d be as determined. It would take a while.”

On the patio, the three of us—Sebastian, Eric, and Nitch—began talking about money. Eric had been travelling a lot, and he had noticed something different in Sweden. “I have a routine when I arrive in a place,” he said. He’d go to the A.T.M. and take out cash. In Sweden, he’d been having trouble getting rid of it. Maybe, someone said, it really is all about precious metals. Sebastian looked across the busy street. “It’s so strange,” he said. “We need food. But do we need gold? Do we need silver? These are things we find.”

What do we want from money? As Henry finally connected with his Superhot Girl and—looking as charmed and uxorious as I have ever seen a person—led her up the carpeted stairs toward his bizarre, makeshift posse, I began to think that, beyond home and nurture, what we seek in most currency is a way to mete out dreams. So far, the U.S. still embraces cash, because our concept of wealth is material: we collect it, handle it, hoard it. American money is private. Sweden has embraced cashlessness more readily in part because it finds the value of currency in the transfer and velocity, the social path it follows, the bonds it traces. It’s social: a network conception of wealth. The two conceptions met on nights like this, when fantasies and friendships came together in a hideaway of space and time, remaking each other among fleeting opportunities. We weren’t thieves, and yet we lived as if we were.

Soon after that, I left and walked toward my hotel. It was crisp and fresh out, and I stopped in at a restaurant, to delay the end of a long night just a little while longer. “We don’t take cash,” the waitress said when the bill came. I was tired; the expense was small. I felt a small rush of acquittal as I paid.