Prosperity is the sound of jackhammers and pile drivers in the morning.

Across San Francisco, cranes loom and the noise from construction sites can sound “like the city is being bombed,” as one manager of a senior center near downtown put it recently, or like the amplified cork-popping of a decade-long party.

Since 2000, median home prices in the city have nearly quadrupled; city coffers have doubled. Tech workers from the likes of Google, Facebook and Twitter line up at high-end restaurants and seek out trendy ice cream shops for a scoop of Balsamic Caramel.

And the cherry on top? That would be a giant sports and entertainment complex, surrounded by public parks and plazas, on 12 acres of abandoned port land. It is a proposal that has city officials salivating partly because, unlike most such arenas, taxpayers are not funding it. San Francisco did not plead with stadium developers by offering public lands or yearslong tax abatements. Some rich people were willing to take all the risk.

Namely, the owners of the Golden State Warriors, a team currently based in Oakland and fresh off an N.B.A. championship. They have purchased the land rights, plan to privately finance the arena and two adjoining office towers — an estimated $1.4 billion investment — and bring San Francisco one of the few things it lacks: a major indoor entertainment complex.

What’s not to like?

Well, this is San Francisco. So plenty.

At least to a hard-core group of well-financed opponents. The stadium, they say, wastes a chunk of one of the last stretches of undeveloped land in the city. They have loftier aims than mere entertainment: They would like the land used for biotechnology, a health care company or another enterprise consistent with the Mission Bay neighborhood, which already has a health care hub at the University of California, San Francisco.

Just across the street from the proposed 18,000-seat arena is a new children’s hospital, which is invoked by opponents in their more agitated moments. Arena traffic, could lead to “deaths of people stuck in ambulances,” said Bruce Spaulding, a former senior vice chancellor of the University of California, San Francisco, who helped create the medical hub and now leads the opposition. “Entertainment doesn’t trump health care and patient lives,” he said.

To stop the project, opponents have hired David Boies, the superstar litigator who brought the government’s antitrust case against Microsoft in 1998, represented Vice President Al Gore at the Supreme Court in the 2000 presidential election, and with Theodore B. Olson, brought an important same-sex-marriage case to the courts.

A basketball arena’s rising in San Francisco is no constitutional crisis, but the dispute taps into a growing anxiety that the city’s increasing affluence is displacing enterprises more consistent with its heritage.

Recent local newspaper articles have chronicled, for instance, how medical research groups, arts groups and working-class families have been priced out of the city by exorbitant rents. More generally, there is the constant tension over gentrification — for example, the protests over Google buses.

“San Francisco has always been that other city with a different set of values,” said Jeff Sheehy, a governing board member of the California Institute for Regenerative Medicine, the largest stem cell funding agency in the world. The institute is moving to Oakland after the expiration of a free-rent deal on its space near the proposed complex; it discovered that office rents in San Francisco were prohibitively high. He sees the arena, which he opposes (he would like affordable housing on the land), as suggestive that San Francisco secretly wanted mainstream credibility all along.

“We should have an arena because New York has Madison Square Garden. We should compete for the Olympics and the Super Bowl,” he says, mocking the pro-arena attitude. He describes the new San Francisco as “just another capitalist, consumerist, profit-driven, money-motivated Disneyland.”

To which opponents might say, “Give me a break. Why can’t we have a little fun?”

That is the point of Marc Benioff, the founder of Salesforce, a software giant and San Francisco mainstay. He sold the rights to buy the land to the Warriors, but is also a major hospital benefactor (he and his wife gave $100 million to the U.C.S.F. Benioff Children’s Hospital).

“If I want to see U2, I have to go to San Jose,” he lamented, adding, “without great sports franchises, we can’t be a great city.”

“This is about the future of San Francisco,” he said. “What is San Francisco going to be?”

Looking to Buy

One August morning, I met with Joe Lacob, a venture capitalist, and Peter Guber, a Hollywood producer, in Mr. Lacob’s corner office in downtown Oakland. As the majority owners of the Warriors, they are the arena’s boosters, and Mr. Guber became particularly animated while trying to explain its allure with what seemed like a tangential point: our obsession with cellphones.

“Have you ever seen a bunch of young people sitting together at a table and they’re all texting?” he said, leaning forward. “They’re texting each other!”

His point was that people crave interactive stimulation but also the intimacy of togetherness and that live events — sports, concerts — provide both. That, he said, is the future of entertainment.

Mr. Guber, the chairman of Mandalay Entertainment, has credibility in the entertainment realm, having made a fortune in movies as executive producer of hits like “The Color Purple” and “Rain Man.” Mr. Lacob made his money as a venture capitalist with Kleiner Perkins Caufield & Byers, all the while chasing his childhood dream of owning a sports franchise.

The men teamed up in 2010 (with around 30 minority partners) and paid $450 million for the Warriors, at the time the largest price commanded for an N.B.A. team.

Their plan assumes that the arena will host roughly 220 events each year, only about 50 of them being basketball games. The rest will range from pop concerts and opera performances to political conventions and theater, enabled by a space in which seats and walls could be reconfigured for different audiences. The average crowd might be 9,000, half the size of the crowd for a Warriors game.

This revolving use is the only way to justify the $1 billion investment, Mr. Lacob said. “We do have to fill the building to make it work.”

Rodney Fort, co-director of the Center for Sport Management at the University of Michigan, said the vision fit the new national model of arenas (such as stadiums in Brooklyn, Detroit and Minneapolis). “All of these places are 24/7,” Mr. Fort said. “Switch in hours from fine art to rock to a TED talk.” The arena owners get the spoils of shared ticket revenue, concessions and parking.

The Warriors’ owners are only leasing their current home, the Oakland-Alameda County Coliseum, so they cannot fully cash in on current entertainment trends. They do not control concessions, manage nonbasketball events or sell naming rights. So, with their lease deal running out in 2017, they went looking for new digs.

The team first tried to relocate to San Francisco in 2012, at a spot on the pier south of the Bay Bridge (more than a mile north of the Mission Bay site). The city embraced the idea, but a grass-roots campaign fought back, saying it would ruin the waterfront.

Then, last year, Mr. Lacob got a call from Mr. Benioff. Salesforce spent $278 million in 2010 for 14 acres in Mission Bay with the intention of building a headquarters across from the hospital. But then the company found another space downtown. Mr. Benioff invited Mr. Lacob and Mr. Guber to his Presidio Heights home to propose a sale.

“You could own your own land, control your destiny,” Mr. Benioff recalled telling Mr. Lacob.

They reached a deal in which, Mr. Benioff said, the Warriors agreed to pay a $30 million nonrefundable deposit for the rights to buy the land. The eventual price will be about $150 million, Mr. Benioff said, if the proposal goes forward.

A poll commissioned by the Warriors this summer showed strong support for the arena. Those who want the stadium say it would bring pleasures and benefits — a murky concept that economists have started to try to quantify in recent years.

For instance, Brad Humphreys, an associate professor of economics at West Virginia University, used an economic technique called contingent value economics to study whether Canada was getting its money’s worth after investing $110 million to train athletes for the 2010 Winter Olympics in Vancouver. Based on his research, the answer was yes. Canadians valued their athletes’ performance at $300 million to $700 million, a veritable happiness profit.

On the other hand, a separate study using more traditional quantifiable metrics, also by Dr. Humphreys, found that when the Seattle SuperSonics left for Oklahoma City in 2008, condo prices rose in the immediate Seattle neighborhood, suggesting that noise and traffic from the arena had been having a “downward pressure on housing prices.”

No such analyses have been done in San Francisco — after all, the city is not paying for the arena, thus lowering the bar for skeptics. But Dr. Humphreys said it would be fair to assume that San Franciscans could enjoy intangible emotional benefits valued over the years at several hundred million dollars (along with a relatively paltry $14 million in annual tax revenue the city estimates the arena will generate).

“This is the place to put an arena,” Mr. Lacob said. “It’s a world-class city without a world-class entertainment venue.”

From Mess to Success

“Mud, weeds, broken glass and decrepit buildings” is how a recent article in The San Francisco Business Times described the state of Mission Bay in the late 1980s. Once a rail yard and port, it had been abandoned as the shipping business moved elsewhere, notably Oakland, and the need for rail fell sharply.

Then Mr. Spaulding got involved.

Formerly a municipal executive in Fresno and Las Vegas, he became the senior vice chancellor of U.C.S.F. in 1988 and was charged with finding a second campus for the teaching hospital and research center. He homed in on Mission Bay, then about 303 decrepit acres designated for redevelopment.

From that mess has risen a municipal success story: a sprawling life sciences center with 3.1 million square feet of labs and offices in six research buildings; a 289-bed medical center, surrounded by 1.7 million square feet of biotech commercial space, including the offices of Bayer and Pfizer; and at least nine venture capital firms specializing in life sciences, according to U.C.S.F.

The development provides the surprising answer to a trivia question: What industry employs more people than any other in San Francisco? It is not finance or tech, but life sciences and health care.

“Scientists run into other scientists. Students run into professors,” Mr. Spaulding said recently as he walked through the campus. By his own admission, he is loquacious to a fault, a walking filibuster, and as he toured, he waxed about the “ambience”: broad walkways with views to the water, pleasant quads between buildings and open staircases inside buildings so that, even there, “scientists could bump into each other.”

Putting an entertainment complex in this neighborhood, he said, would not only poison the existing atmosphere but also discourage other life science enterprises from filling the handful of still-vacant lots. “That’s what this place is all about.”

Mr. Spaulding clearly feels strongly about the Warriors’ arena. He is also being paid to make the point by the Mission Bay Alliance, a nonprofit group. The way it is incorporated keeps its membership private. Seizing on this mystery, the Warriors and their allies have called the alliance a “shadow” group of billionaires. The Warriors and their allies suggest this group may even want the land to itself.

Nonsense, Mr. Spaulding countered. He said the alliance members wanted their privacy because some of them were associated with the university — as donors, doctors, nurses — and they did not want to run afoul of management. A handful of the alliance’s members have stepped forward, including the big-name San Franciscans William J. Rutter, a highly regarded U.C.S.F. researcher and biotech pioneer, and Jeanne Robertson, former chairwoman of the U.S.C.F. Foundation, a fund-raising group. (Her husband, Sandy Robertson, sits on the Salesforce board.)

The city expects to approve the project’s environmental review by November, which in theory paves the way for construction. But there will be a challenge. The Mission Bay Alliance said that the 800-page environmental impact report for the arena did not accurately account for the impact of noise, trash and traffic.

If their claim is rejected, the group may try to force a referendum or otherwise stall until the project dies. Mr. Boies said that he was “very dubious” that there could be sufficient mitigation to preserve the neighborhood. A lawsuit is not out of the question.

City officials say opponents have created a false dichotomy; not only can the hospital and arena coexist, but there also remains plenty of land within a mile or two of Mission Bay — as much as eight million square feet, noted Ken Rich, the city’s director of development — for other purposes. Besides, while the city wanted life science to be the “core idea” in the area, he said, we “never intended it to be exclusively life sciences.”

Somewhere in the middle lies the university itself, which manages the hospital and research campus. Its chancellor, Dr. Sam Hawgood, has offered qualified support for the Warriors, as long as the owners and the city address his big concerns about traffic, including creating dedicated lanes for health emergencies and increasing public transportation options and the number of parking lots.

Negotiations are continuing, but Dr. Hawgood said he was confident that the opposing sides would reach an agreement by the end of September. As to whether a Warriors arena will change the ambience, he said it undoubtedly would, and that’s O.K. “Injecting some variety I don’t think is necessarily a bad thing at all,” he said.

‘Into the Lion’s Den’

Scholars who study sports arenas say the Warriors’ opponents face long odds of winning. The land is private, and the Warriors plan to finance themselves, making the dispute one that the courts would be reluctant to enter into, said Mark Rosentraub, a professor of sports management at the University of Michigan.

It is “good news for San Francisco,” Mr. Rosentraub said. The city gets an arena without paying for it — an enviable position — and “tip your hat” to the entrepreneurs for knowing they have to pick up the bill, he said.

Sam Singer, a spokesman for the opponents, countered that there were tens of millions of dollars in “hidden” costs involving transportation, parking and police staffing.

The public relations battle rages on. And each side is well armed. The Warriors have retained a former spokesman for Willie Brown, the onetime mayor of San Francisco. The opponents have landed one of the city’s best-known operatives, a political consultant named Jack Davis, who successfully ran three San Francisco mayoral campaigns and was described by The San Francisco Chronicle as “one of the most feared and loathed political players” in the city.

Mr. Davis, 68, got involved in the fight not because he is antigrowth or outraged by gentrification, but as a personal favor to Mr. Spaulding. When Mr. Davis’s brother, who lived in Arizona, learned he had cancer, Mr. Davis told him to get on a plane to San Francisco and go to U.C.S.F. He told him, “I’ll call Bruce Spaulding and get you squared away with the best doctor you can find.”

Shortly after that, Mr. Davis, who now lives part time in Wales, came to San Francisco and told Mr. Spaulding: “I owe you big time. Is there anything I can do for you?” He said his longtime friend answered, “Yeah, there is,” and told him about the arena. And Mr. Davis said, “Oh, yeah, sure, count me in.”

Mr. Davis, who relayed this story via FaceTime from Wales, said his goal was to help the alliance — he called it “a group of billionaires” — get on the map. “So I decided the right way to do it was to go right into the lion’s den and start a brawl.”

He succeeded. On April 30, at a fairly standard informational meeting at the nearby Mission Creek Senior Community, Mr. Davis stood and gave what several meeting attendees described as an acerbic presentation that was out of character with what had been months of tame negotiations. He was “so combative that he drew boos and hisses,” read a piece in the next day’s San Francisco Chronicle. Mr. Davis said arena opponents would not stop until the Warriors project was undone, adding, “There will be litigation until the cows come home.”

He laughed when he recalled it. “They’re still talking about the cows coming home, aren’t they?”

Shortly after that meeting, the local nurses’ union, with support from the Mission Bay Alliance, announced its opposition to the project, saying it was “fundamentally incompatible” with the hospital.

Dr. Hawgood, the university chancellor, said he disagreed with the nurses who worked for him. At the same time, he said he understood where they were coming from. “There is a background anxiety, which is that it’s harder to get around than it was five or 10 years ago,” he said. “People are responding to a booming city.”

Every square foot of San Francisco has become a morsel for the prosperous. For this countercultural city, which long took pride in being different, it is a bit like having been an awkward adolescent who derided his parents’ status car, then later decided, after having grown up, that a BMW was a really smooth ride and not so stupid after all. He may well enjoy the fancy car but still feel the occasional heart tug when a Volkswagen bus rumbles by.