Media playback is unsupported on your device Media caption Is the US on the decline - or simply in an economic slump?

The current argument about the United States' standing in the world is an odd thing.

Mitt Romney says the US has abandoned global leadership and is slipping behind, but does not really believe that the country is in long term decline.

President Barack Obama on the other hand, insists that his country, "is back", but appears to harbour private doubts about it.

If it's a neurotic superpower you're looking for, then America's your one Dr Robert Kagan, US Historian

The two men have in part been forced into these positions by the presidential debate. The Romney pitch is essentially that Mr Obama has been a weak ditherer who has conceded ground unnecessarily to the likes of Russia, China, and Iran, and is in danger of pitching the country into an irreversible downward trend.

The Romney people have to believe their champion can reverse this, and Obama's have to insist that the loss of power or influence has not taken place to start with.

Whatever the political contortions required of the two candidates, the debate is fuelled by underlying public attitudes.

Polls suggest that when asked whether the country is "in decline", 60-70% of Americans will say Yes.

In recent years, hundreds of thousands of books have sold in the US with a similar message, leaving one reviewer to comment wearily, "decline has the same fascination for historians that love has for lyrical poets".

Military balance

The terms of this debate need refining. For example, does it refer to an absolute loss of power by the US or a relative increase in the proportion of the world cake consumed by others?

Image copyright AFP Image caption Mitt Romney has accused President Obama of presiding over a decline in US global power

At its heart, the argument is largely about whether China has become the more dynamic and successful country and will outhaul the US within our lifetimes.

By some indices the argument can be settled very quickly - victory goes to China on population or the US by aircraft carrier count.

Almost everyone still agrees that the Americans are still militarily preponderant, although some reputable experts do express concerns about the long term consequences of Chinese defence budgets rising while Pentagon ones fall.

It is clear though that in the wake of hugely costly wars in Iraq and Afghanistan, the White House is determined not to use the military instrument.

Indeed Mr Obama has made a positive virtue out of re-directing attention and resources to the economy, arguing in June "we have spent a trillion dollars on war… now we must invest in America's greatest resource, our people… it is time to focus on nation building here at home".

This has conditioned Mr Obama's attitude to events in Syria and, some even whisper in Washington, evolved into an absolute determination not to go to war with Iran.

National introspection

So if you are resolved not to use the military, what instruments of influence does the United States still wield?

It remains a powerhouse of creativity, that is clear, from Hollywood to the people at Apple. Americans are still confident in their ability to innovate and work their way out of recession, even if they have been rattled by the phenomenon of "jobless recovery".

Those who argue against the "declinist" proposition, such as historian Robert Kagan, believe the current situation mirrors some earlier periods of national introspection.

Image copyright AFP Image caption Barack Obama has sought to make an economic virtue out of military drawdown

In the 1920s or 1970s, for example, a combination of economic hardship and costly foreign wars, produced isolationism or faltering national confidence. "If it's a neurotic superpower you're looking for, then America's your one," Dr Kagan told me.

Dr Kagan's confident assertions that the current mood is cyclical and does not portend a downward slide for America have been quoted by both candidates for the presidency.

He has also pointed out that the relative proportion of the global economy accounted for by China, India, or Brazil has been increasing very slowly.

There are however, some features of today's situation that are new. Nobody is quite sure how the national debt - $16tn and growing - might impact in the long term.

The more sanguine experts point out that only one sixth of this is in the hands of foreign governments, and the more alarmist that US government spending now depends on borrowing money from China.

Chinese stake

Inside the beltway, Washington's foreign policy elite is nervous about the possibility of continued budgetary gridlock, particularly if, as many now think likely, Mr Obama is re-elected, but still has to do business with a Republican-controlled House of Representatives.

When I spoke to Strobe Talbot, chairman of the Brookings Institution think tank, last week, he warned "our dysfunctional politics in Washington cannot help".

Image copyright AFP Image caption Both candidates have been sparring over trade relations with China.

While many argue that Chinese bailouts should not be feared, because they increase that country's stake in US recovery, it is also clear that the public in both countries is often uncomfortable with this inter-dependence.

Mr Romney's campaign has been playing to these fears, insisting that one of his first acts in office would be to label China guilty of unfair trade practices. The countries are already sufficiently locked together that such talk makes many uncomfortable.

Speaking to Richard Armitage, deputy secretary of state under President George W Bush, he said "having a bad relationship right out of the gate with China is not a hopeful way to try to protect our interest".

Mr Armitage also characterised the description by Mr Romney - his own Republican party's candidate - of Russia as the principal threat to US security as, "incomprehensible".

While Mr Romney has come under a good deal of fire recently for gaffes, or shooting from the hip, it is only fair to point out that on China, Mr Obama has been triangulating - or adjusting his policy closer to those advocated by his critics - on trade relations with China.

This week he suggested he might introduce new tariffs on Chinese car imports - and has already quietly been upping the duties on other manufactured goods.

Comparisons with Britain

All of the historians involved in the debate over decline agree that the age of American Imperium cannot go on forever. Rise and fall is what great powers do, after all. Many attempt to calibrate where they think the US is now in terms of Britain's imperial past.

The more pessimistic tend to see analogies with the early 20th Century, after the Boer War and before the cataclysm of 1914, and it is true there are similarities with the British debate about decline during that period and the current American introspection.

Image copyright AP Image caption A Suez moment for the US, in which an imperial rival calls the shots, still seems a long way off

Even if one accepts that view, it took until the early 1940s and World War II for the US to eclipse Britain as the world's greatest military power.

Optimists wind the clock even further back. When I asked Dr Kagan where he put the US now in British terms, he replied with a twinkle in his eye, "Oh about 1840", before conceding that China might overhaul the US during the lifetime of someone who was a toddler now.

Dr Kagan expressed concerns too about the failure to control the budgetary deficit and its possible acceleration of this process. If the trillions keep piling up, he noted, simply servicing the debt will crowd out more productive types of spending, creating a downward national spiral.

Perhaps the moment in Britain's decline that American policy makers should be focussing upon is 1956. During the crisis caused by an Anglo-French invasion of Egypt, the US stopped the fighting by threatening to pull the plug on the British economy.

It marked the end of Britain's ability to act as an independent global power, and it was the country's indebtedness to the US that caused it.

Nobody thinks that China could create a "Suez moment" any time soon. And of course it is that sense that a real reckoning with imperial rivals is some way off in the future that allows candidates for the presidency to avoid too much explicit discussion of American decline.

But the impulse not to engage in too explicit a debate about managing the downward slope of empire may simply be bringing that dread day closer.