When I spoke to Meylan, he was even more direct. Making smartwatches is a mistake, he argued, particularly for elite brands. To be sure, he said — as many of his peers did — the Apple Watch will probably be successful. “With the right battery, eventually it’ll become something very useful that I will probably wear myself,” he said. But he considers putting smartwatch technology inside a mechanical Swiss timepiece to be brand suicide. “It shouldn’t be a gimmick,” he said. “Especially in our range.” His company, like Montblanc and Ateliers deMonaco, sells watches that cost tens of thousands of dollars. They shouldn’t be creating “some kind of monsters that are a merger of a mobile phone and an actually beautiful mechanical watch.”

Once a timepiece becomes a computer, what should it not do? Should there be limits? Does watchness become only a trivial part of a smartwatch’s function? “That’s a little bit the scary thing,” says Pim Koeslag of his work at Frédérique Constant. “Once you get into it, you see that this is only the beginning of the beginning.” There’s no GPS in his smartwatch now, but he could imagine putting it in. “You could put in cameras or weather stations or whatever. The only limit is imagination.”

TAG Heuer is one high-end brand that plans to produce what Silicon Valley might recognize as a smartwatch: a digital version of the TAG Heuer Carrera. TAG Heuer’s engineers will design the physical case, but everything else will come from technology partners. Intel will make the touch screen and the electronics; Google will provide Android Wear software. The goal is to release something by the end of this year that can compete with Apple on the apps front while also being unmistakably Swiss.

“At two meters distance, you will not know, ‘Is this guy wearing a TAG Heuer Carrera connected or is this guy wearing a chronograph Carrera normal?’ ” said Biver, the chief executive of TAG Heuer, when I visited his office in Nyon. “That will give us the watchmaking appeal, which the computer guys at Apple, Samsung don’t have.”

Biver is a famously voluble, opinionated figure, prone to grand statements and poetic riffs on the beauty of timepieces. He wears, and occasionally caresses, a chunky watch from Hublot (another luxury brand that he oversees). He says the design of the Apple Watch is “not very sexy.”

“There is not enough emotion,” he said. “It’s just a reduction of the phone for the wrist.”

Yet it’s fair to ask how “Swiss” his prospective watch will really be. As several observers told me, it’s just as much an Intel-and-Google watch. “Where is your value-add?” asks Amy Glasmeier, an M.I.T. professor who has written about the watch industry. Swiss watchmakers, she adds, will need to create their own high-tech intellectual property in smartwatches. “Otherwise,” she says, “what they’ve got is just the use of their name. It’s not the use of their human capital.” Raffaelli, the Harvard professor, is a bit more sanguine. He says that the Swiss watchmakers may promote their preindustrial history, but they’ve long been experts at innovating. All those mechanical features — perpetual calendars, self-winding mechanisms — were the transformative high tech of their day. The clock itself was a first step toward the “quantified self,” making visible information that was previously hidden, your precise progress through the day.

Even if the Swiss smartwatch never takes off, many of the watch executives I spoke with said that the Apple Watch might be good for sales of high-end mechanical watches. Why? Because a generation of Americans has grown up without the habit of wearing a watch. Apple is now spending millions to convince younger consumers — those who coordinate their lives not by looking at a wristwatch, but with “I’m on my way!” text messages and shared Google Calendar events — that a watch can be useful and fashionable again. “Many young people who would never wear something on their wrist, they will start wearing something on their wrist, which is the connected watch,” Biver said. Having acquired the habit of glancing down, maybe they’ll eventually decide they want to look at an older sort of device instead — a machine that, in a sense, is outside time.