There can be no doubt that the biggest question today about Asia's future order revolves around the relationships among three nations - the United States, China and Japan. If a solid and durable foundation can be found for cooperative relations among the three powers, building a sustainable new order in Asia will not be difficult. If rivalry among them escalates, it might become impossible.

The differences between their separate visions are not hard to see. America wants to preserve the status quo in which its leading position remains the keystone of the regional order, and the Chinese acceptance of US leadership is the basis of US-China relationship. While it is willing to consult more closely with China on a wide range of issues as China's power grows, it does not envisage any fundamental change in the nature of their relationship, or of China's role in Asia, over the coming years.

Americans argue that this status quo has worked very well for Asia - including for China - for many years, and they believe that it remains the best basis for regional stability in the future.

China, on the other hand, wants to change the status quo. President Xi Jinping has made this quite clear in his repeated calls for a "new type of major-power relationship". By this, he does not just mean that he hopes the US and China can avoid the rivalry that throughout history has so often escalated between rising and established powers. He also means that to avoid escalating rivalry, America and China should agree on a new basis for their relationship, different from the basis that was agreed between Chairman Mao Zedong and former US president Richard Nixon back in 1972. Clearly, China does not believe that Chinese deference to the US leadership is any longer an acceptable basis for US-China relations.

From America's side, there seems to be increasing concern that China's real aim is to push America out of Asia and establish its own version of regional primacy. They point to China's assertive diplomacy over regional maritime sovereignty questions as evidence of China's malign intentions, and its willingness to use force to shape the regional order in its favor.

From China's side, there is an equal but opposite fear that America's real aim is to contain China's rise in order to preserve US primacy. China points to US President Barack Obama's "pivot to Asia", including its highly-publicized military elements designed to bolster US combat power in Asia, as evidence of America's mala fide intentions and its willingness to use force to achieve them. These suspicions clearly make it much harder for the two sides to contemplate serious accommodation with one another.

Many Americans seem still to underestimate just how much China's wealth and power have grown, and how strong China's ambitions have become. They do not yet take China's challenges to the status quo in Asia seriously. On 30 April, London-based Financial Times had a front-page banner headline that read, "China to take over from US as top economic power this year". The story beneath the headline reported the World Bank's latest comparative survey of the size of national economies in 2011 based on their relative purchasing power.

It showed that on this measure, China's economy in 2011 was 87 percent the size of America's, and was trending to overtake it this year. Perhaps it has already done so.