The dollar's sharp drop over the past few weeks has led to considerable anxiety about the status of the United States as the dominant force in the global economy. Closely related to this fear is constant worry about the rise of China and the evermore complicated relationship between Beijing and Washington.

Most people are now aware that China is the largest creditor to a heavily indebted U.S. government. It holds close to a trillion dollars of U.S. Treasurys and has invested hundreds of billions more in private enterprises in America. Even though these facts are plainly acknowledged, policy makers and experts continue to underestimate the full ramifications of this relationship.

Consider what happened in 1946, when a cash-strapped Great Britain turned to the U.S. for a loan. For 30 years or more, the British had been consumed by the threat of a rising Germany. Two wars had been fought, millions of lives had been lost, and the British treasury was dramatically depleted in the process. Britain survived, but the costs were substantial.

In spite of its global empire, a powerful military, and an enviable position at the center of world-wide commerce, in early 1946 the British government faced a serious risk of defaulting on its financial obligations. So it did what it had done at various points over the previous decade and turned to its closest ally for assistance. It asked the U.S. for a loan of $5 billion at zero-interest repayable over 50 years. As generous as those terms seem today, such financing had been almost routine in years prior. To the surprise and shock of the British, Washington refused.

Unable to take no for answer, Britain explained that unless it received funds the government would be insolvent. The Americans came back with a series of conditions. They would lend Britain $3.7 billion at 2% interest, and the British government would have to abide by the 1944 Bretton Woods plan, which made the dollar rather than the pound sterling the reference point for global exchange rates and required Britain to make the pound freely convertible. Even more significantly, Britain had to end its system of imperial preferences, which meant no more tariffs and duties on goods to and from colonies such as India. These were not mere financial penalties: Taken together, they meant the end of the British Empire.

Within two years, Britain had left India and was on its way to decolonizing throughout Asia and Africa. Unable to compete with the United States economically and no longer able to reap the benefits of colonial trade, Britain's military shrank and its commerce contracted. It quickly receded from its dominant global position and entered several decades of economic malaise. In the 1980s, Britain finally emerged as a prosperous country, but it was a shadow of what it had been in its heyday.

The U.S. replaced Britain as the guardian of the West. As one British official, Evelyn Shuckburgh, remarked in the late 1940s, "it was impossible not to be conscious that we were playing second fiddle." And that was precisely what the U.S. desired. Having supported the British for decades and become its banker and manufacturer during two wars, at the end of World War II the U.S. fully intended to supplant the British Empire. The loan request provided the pretext, but by then the balance had already shifted and Britain could have done little to reverse the tide.

By 2030—if not sooner—China is likely to surpass the U.S. in the size of its economy, though it will remain on a per capita basis a much poorer society for many years after that. Trajectories can change, but the recent implosion of the American financial system has only accelerated China's rise.

Given the lesson of the British Empire's demise, it would be foolish to base current policy on the assumption that China will hit a fatal speed-bump before it is able to supplant the U.S. And while the level of current indebtedness is manageable for the U.S.—and in fact tethers the Chinese closely to the U.S. economy in ways that are arguably beneficial for both countries—the fact that these economies are currently bound together does not mean that their interests will always be in sync.

Here, too, the British analogy is sobering. For decades, the relationship between Britain and the U.S. was mutually beneficial, though the Americans resented being treated as junior partners. As tension festered, the British were consumed with the more immediate threat of Germany. But in the end it was the U.S. that delivered the knockout blow.

The Americans have not had to deal with a true economic rival since the British more than half a century ago. America today is as unaccustomed to global economic competition as the British were at their apex. The U.S. often seems lumbering and ill-suited to the demands of economic rivalry.

The only way to avoid Britain's fate and meet the challenge of China is to reinvigorate economic life. This is a multiyear endeavor that must be done primarily through innovation, not legislation. America needs to retool its domestic economy to build on the global success of many U.S. companies. It must focus on inventing new products and generating new ideas, rather than defending the rusty industries of yesterday. Fights over health care and climate change are the cultural equivalent of fiddling while Rome burns.

China thrives because it is hungry, dynamic, scared of failure and convinced that it should be a leading force in the world. That is why America thrived a century ago. Today, such hunger and dynamism seem less evident in American life than petulance that the world is not cooperating.

The U.S. is in danger of assuming that because it has been a dominant nation on the world stage, it must continue to be so. That is a recipe for becoming Britain.