If the world still thought about power the way the Victorians did, yesterday would have been a black day for the American empire. For at a stroke, the accession of 10 new members to the European Union significantly increases its size in territorial and demographic terms. As of this weekend, there are more than one-and-a-half times as many EU citizens as US citizens. The growth of the EU has been, until now, a gradual affair, with new members quietly joining the original six in groups of two or three per decade — beginning in 1973, when we were admitted with Ireland and Denmark. This is more spectacular. At a stroke, the EU’s area and population will increase by a fifth. Its new neighbors will be Russia, Belarus and Ukraine.

Euroskeptics used to delight in pointing out how little of Europe was actually represented by the EU — no Switzerland, no Norway and a great territorial hole between Austria and Greece, in the heart of which terrible wars raged during the 1990s. Such skepticism becomes harder now. What is more, this enlargement is by no means the last. Romania and Bulgaria are next in line. Turkey’s long-standing bid for membership suddenly looks like a serious proposition. That would take the EU as far as the frontier of Iraq.

No one should be in any doubt that this is one of history’s undisputed “good things”. It is not just a question of making a reality of the rhetoric about European reunification that was heard so often after the collapse of the Iron Curtain in 1989. Western Europe also has some large moral debts to countries such as the Czech Republic, Slovakia and Poland that go back further than the Cold War — to the dark years of 1938 and 1939.

Moreover, the world has reason to celebrate the integration of such countries into an institution that explicitly stands for democracy. As independent states between the wars, many of the new member states failed to make a success of democracy. Now we can regard them as permanently democratized. EU membership is a powerful incentive for political good behavior.

Why then does the US seem unworried by European enlargement? Why do so few American analysts share the anxiety of Charles Kupchan of Georgetown University that the EU is “an emerging pole, dividing the West into American and European halves”? After all, any other political entity that trebled in size in just over three decades would surely set the alarm bells ringing in Washington. The answer is simple. Americans do not measure power in terms of territory or demography. They measure it in terms of economics and technology — especially military technology. And by those measures, it is far from clear that enlargement will significantly help the EU.

Because the new member states are relatively poor, enlargement has only a minor impact on aggregate EU output, raising it by little more than 4 percent. Depending on how you measure total output — particularly how you adjust for changing exchange rates — that keeps EU and US gross domestic product within sight of one another. But many Americans are confident that the gap between their economy and the European economy can only widen in the years ahead. Here’s why.

First, European productivity growth has, for the first time in the postwar, period, been below that of the US since the mid-1990s. Second, Europeans are, for a variety of reasons, working a lot less than Americans. Unemployment is higher; the labor participation rate is lower; above all, working hours are shorter. In the early 1970s, the Germans and French worked about as many hours per year as their US counterparts. Since then, Americans have grown more industrious — working nearly 2,000 hours per year — while Europeans have taken longer holidays and had shorter working days. Today the average Frenchman aged between 15 and 64 works around 35 percent less, in hours, than the average American. That explains why in only one year of the past 10, EU GDP growth has been higher than that of the US.

But the third, and biggest, problem facing the EU is that it is a union of senescent societies. By 2050, according to the United Nations, the median age will be above 40 in all pre-enlargement EU members countries and above 50 in Austria, Greece, Italy and Spain. In these countries, about one in three citizens will be 65 or over. When Donald Rumsfeld spoke scathingly about “Old Europe” last year, he didn’t know how right he was.