The panic gripping markets this week could destroy the euro, and with it the European Union in its current form. With any luck, Germany and other solvent countries will rally round to save tottering debtors such as Italy, but that is far from certain.
And even if the euro is saved, Europe's underlying weakness will persist. For it is not just a question of vacillating leaders and bad policies. It is something more basic than that - Europeans have stopped having babies.
A century ago it was common for a European couple to have half a dozen children. Now the fertility rate in Greece and Italy is a puny 1.4. That is a recipe for demographic collapse: for a population that ages, shrinks and loses its vitality at astonishing speed.
Many people expect a world with fewer people in it to be a better one - there would be fewer mouths to feed and lighter strains on the environment. But fewer people also means fewer hands and fewer brains.
Why are so many southern European governments so deeply in debt? Put differently, why have they so consistently spent far more than they raise in taxes? One important reason is that there aren't enough young and gainfully employed workers to pay the pensions and healthcare bills of the elderly.
We are living longer and longer, and we have stopped having large families to care for us in our old age. We assume that the state will look after us. But the state has no money of its own. It has only the taxes it can raise from working people, and the money it can borrow.
The money it borrows must be paid back by taxing the next generation of workers. But if we don't have children, there won't be a next generation of workers. That's why the bond markets are hyperventilating. They worry that European governments will not be able to honour their debts because - ultimately - they will run out of people to tax.
As I argue in my new book, immigration can help address this problem. When an aging rich nation allows a steady influx of young, energetic hands and brains, that nation will age more slowly and remain dynamic for longer.
To see how immigration affects a country's mojo, consider the differences between Japan, America and southern Europe.
Japan has an even lower fertility rate than Italy or Greece. Each Japanese woman can expect to have on average only 1.2 children. So the population is falling off a cliff: it will shrink from 127 million today to 90 million in 2050.
At the same time, Japan is remorselessly hostile to immigration. You can visit, and you will be treated as an honoured guest. But it is almost impossible to become Japanese, so few visitors stay for ever.
I went back to Tokyo a few weeks ago, having lived there in the 1990s. It was striking how much the country had aged. The streets are full of 70-year-old women going shopping with their mothers. The typeface on menus has visibly grown larger.
As Japan ages, it is losing its vigour. The government's debt is the highest in the world - a whopping 230% of GDP. The country is fading rapidly as an economic power - China recently overtook it, and others will follow.
America has a nasty debt problem, too. And as nearly every headline emanating from Washington reminds us, American politicians can be every bit as blinkered and short-termist as their European peers. But America's problems will in the long run be easier to manage, because of the country's benign demographics.
America has, by rich country standards, a reasonably high birth rate: about two children per woman. And its population continues steadily to rise, because of immigration. Under the UN's higher projections, America's population could grow from 310 million today to 500 million by 2050, and perhaps a billion by 2100.
America has vast tracts of empty space into which its cities could expand to accommodate such an influx. Were the US population to double, it would still be only one quarter as crowded as Britain.
Immigrants bring youth, ideas and global connections to America. And they assimilate because they work. An able-bodied immigrant cannot subsist on the dole in America. So he toils and pays taxes. And in the workplace, he learns to rub along with his new compatriots. When you work together, you have to.
Under Europe's more generous welfare states, immigrants are sometimes paid not to work, and lose their benefits if they find a job. Inflexible labour rules also make it expensive for companies to hire new people.
That is one reason why the French suburbs where North African immigrants live are so full of jobless youths, and so angry. American immigrants are more upwardly mobile, despite the current recession.
Whatever the bond markets do this week, Europe will not regain its mojo unless it addresses its demographic ills. We can't all retire early and expect the children we never had to pay for it.
Either we must work longer. Or we must have more children. Or we must allow in more immigrants. Or all three.
Robert Guest is the Business Editor of The Economist and the author of Borderless Economics: Chinese Sea Turtles, Indian Fridges and the New Fruits of Global Capitalism, which will be published by Palgrave Macmillan on 1 December, priced £18.99