He could have said nothing.

Asked about the Scottish independence referendum, President Barack Obama could have chosen the safe option of saying it was a matter for the Scottish people, but in the event he did not stay silent. Instead, he chose to comment on the UK in what amounted to the most unexpected and spectacular international intervention in the debate so far.

On the face of it, the president was not endorsing one side or the other and he did underline the fact the decision was for Scots alone. But Mr Obama is a highly effective communicator and knows every nuance can be significant, so when he said that the UK appears to have worked pretty well and the US has an interest in ensuring one of its strongest allies remains a strong, united and effective partner, the implied support for unity rather than independence was clear.

The question now is: how much does it matter and what effect could it have? Naturally, the president was looking at the question from a US perspective and considering the consequences for the security of the US and its allies, and that is a legitimate area of concern. It may also tap into worries many undecided voters have about the issues of defence and security.

As the president said, it is important the UK is strong, robust and effective but the answer of the nationalists is that Scotland alone can be just as strong, robust and effective an ally as the UK; in the words of the First Minister Alex Salmond yesterday, America would have two great friends and allies rather than one.

But questions remain about the security implications of independence. The SNP's White Paper proposed a Scottish security and intelligence service that would work with the US in the way the UK does now, but respected think tank the Royal United Services Institute said that was improbable. There is also the question of the SNP's stance on Trident: would the US and Nato be relaxed about one of the nuclear powers being cut in two? President Obama's comments would suggest he is worried.

His intervention yesterday will also remind voters of these areas of uncertainty, but whether it could influence the debate is less certain. During the referendum in Quebec in 1995, President Bill Clinton said the US would prefer a united Canada. The No campaign then went on to a narrow win but it is impossible to know whether Mr Clinton could have changed voters' minds.

What Mr Obama's comments certainly do is add to the impression that the momentum in recent weeks has been with the No campaign, which left the nationalists with the delicate task of how to respond. They could not dismiss Mr Obama as an unpopular foreigner, as they do with David Cameron, but in the end Mr Salmond played it well when he said his message to the president was "yes we can".

Clever as that was, it does not change a central fact, one implied in the president's comments: the idea of independence raises deep questions about Scotland's place in the world, its influence and its security, and most of those questions are still unanswered.