For more than a year, the badly deteriorating political relationship between the United States and Europe has provided rich fodder for analyses, dire predictions, threats, and appeals. Meanwhile, as politicians, diplomats, and generals have fretted over the geopolitical causes and consequences of the worsening trans-Atlantic relationship, the U.S. dollar has been sliding against the euro. Recently, the dollar hit a four-year low in its value against the euro; most experts believe the greenback will not regain its strength for some time. And that points to a truth that is not yet fully recognized on either side of the Atlantic: A U.S. dollar whose value relative to the euro has plummeted by about 40 percent since late 2000 will have a greater impact on the U.S.-European relationship than all the diplomatic maneuvers, speeches, and articles on the current state of trans-Atlantic affairs.

The most immediate consequence of a weaker dollar is that Europe will be flooded by U.S. exports, and the United States will see a surge of European tourists whose apprehensions about President George W. Bush’s unilateralism will be tempered by increasingly cheap opportunities to take the children to Walt Disney World. Americans will not switch to Californian wines because of France’s stance on Iraq but rather because French wines will become more expensive. Yes, the exchange rate is indeed a magic number.

The realignment of the U.S. dollar against the euro will make life more difficult for European industries, while making U.S. companies more competitive. The U.S. private sector has already been sharpened by its swift, ruthless, and profound restructuring in response to the bursting of the stock market bubble, a slow economy, corporate scandals, and the shock of terrorism and war. In contrast, Europe’s...