One of the most popular iPad apps in Beijing at present is China Air Pollution Index. The app is both addictive and disturbing. When I checked into a Beijing hotel recently, I found that — even from the 40th floor — I couldn’t see further than one block because of the grey smog enveloping the city. So I checked the numbers and discovered that the AQ level, which measures fine particulates that are especially dangerous, was 250 — about five times the level deemed safe.

A few weeks earlier, I had experienced Beijing at 350, a level that made my eyes sting and lungs ache, even inside a car. Back in January, it went as high as 1,000, at which point the US Embassy urged people to remain indoors with the windows shut.

In fairness, when the wind blows the pollution away from Beijing, the sky can be blue and it is suddenly a pleasure to walk around. But a good day in Beijing is often a bad day elsewhere in the country.

Pollution in China is now so bad that it threatens to obscure the vision being laid out by Xi Jinping, the new President. Xi has popularised the idea of a “Chinese dream”, an obvious foil to the American dream. His dream seems to involve increasing wealth at home and increasing power abroad.

However, the choking smog suggests that the leadership needs to rethink its national goals. After all, what is the point of rapid economic growth if it creates cities in which it is dangerous to breathe?

One study, published in the Lancet medical journal last year, suggested that air pollution might have caused about 1.2 million premature deaths in China in 2010 alone — a considerable figure even for a country of 1.3 billion people. Beijing has registered a 60 per cent rise in lung cancer cases in the past decade.

With pollution that bad, otherwise innocent sights take on a sinister aspect. Ma Jun, a prominent environmental activist, says that on days when the smog envelops the city, he winces when he sees children playing football outdoors. Indeed many schools, foreign and Chinese, now forbid children from playing outside on bad days.

The pollution in Beijing is also an international embarrassment. The government went to great lengths to show the city off at its best during the 2008 Olympics. Yet, now, the first thing any foreign visitor wants to talk about is the pollution and many expats talk about leaving.

Even allowing for the installation of air filters in official residences, China’s leaders have to breathe the same air as their citizens. So one may expect them to make pollution their top priority, but the signs are that rapid growth remains goal number one.

That is partly because, in recent decades, the government has derived its legitimacy from growth. Officials speak with justifiable pride about the hundreds of millions of people who have been lifted out of poverty. Influential pro-government academics, such as Shanghai’s Zhang Weiwei, argue that the one-party system does not need a democratic mandate because it has “performance legitimacy”, derived from improving the lot of ordinary people.

Yet, the pollution problem suggests the leadership needs urgently to adopt a “greener” measure of “performance”. It is not just the air. The rivers are often polluted by industrial waste and the country has had a series of food-safety scandals.

Local leaders and businesspeople also need to change direction. For the past 30 years, every provincial governor with an eye on a big job in Beijing knew that they would be judged by the local growth rate. Persuading them that they should now care as much about their city’s air quality will be difficult when their personal and political fortunes are still tied to increasing the rate of economic expansion.

Some of the necessary environmental measures are fairly obvious. Insisting on cleaner fuel for cars and stricter emission standards for factories and power stations is crucial. However, enforcing those rules will involve facing down powerful interests in the state-owned energy and power companies.

If nothing is done, the problem will certainly worsen. Coal-fired power stations continue to open at a great pace and the number of cars on the roads is projected to quadruple by 2030. The latter is, of course, part of the Chinese dream of rising affluence. But personal fulfilment threatens to create a collective nightmare.

China can take some comfort from the fact that notoriously polluted cities elsewhere, such as London and Los Angeles, have been cleaned up. But the task for Beijing will be particularly tough. Ma, the environmentalist, says: “London’s problem was coal and LA’s problem was cars. We have both.”

The fact that environmental activists are allowed to speak out, however, may be a sign that the government wants to act and is willing to encourage a public debate. The air-quality readings for Beijing used to be released only by the US Embassy. Now, the government releases its own figures in real time, which people can check on their phones as they move around the city.

Xi has made it clear that he wants to restore Chinese greatness, but greatness can be defined in many ways. The country can now take rising affluence and international respect for granted. The next dream for China should be cleaner air and water — and an open debate about how to get there.

— Financial Times