Leading article: A visit that will test how far two countries have come

This is a state visit like no other. No walkabouts, no crowds of schoolchildren waving Union Jacks and an awful lot of police and security barriers. Try as politicians might to present the Queen's arrival in Ireland as evidence of just how normal Anglo-Irish relations have become, they're still not quite.

The first visit of a British head of state since independence was always bound to stir memories, at least in some quarters, of the tragic and troubled relationship these islands have had for much of their long, shared past. From whether Irish leaders will curtsy to the Queen to whether she will acknowledge bitter memories about the Famine of the 1840s and the Partition of 1921, a cloud of potential difficulties surrounds the whole event. It will require surefootedness on the part of the Queen and her advisers to ensure that a long-overdue state trip helps, not hinders, the still incomplete healing process between the two countries.

What the Queen has to try to do in Ireland is to acknowledge the complex and fraught nature of British-Irish history – unique, in fact, because Ireland is the only independent European state that Britain once ruled – without allowing ghosts of a sombre past to overshadow the sunnier present. What most people in Ireland will make of it all is hard to say. But it would be unfortunate if the predictable protests of an embittered minority were allowed to overshadow the mix of indifference, curiosity and genuine enthusiasm with which most Irish people probably regard the Queen's presence on Irish soil.

If there aren't too many security alarums from outraged keepers of the Fenian flame, the royal tour will be an occasion to celebrate the almost miraculous transformation in relations between Britain and Ireland, especially since the signing of the Good Friday agreement in 1995, which helped desensitise the neuralgic subject of Northern Ireland. We tend to forget just how rotten those relations were within living memory, from the fraught 1940s, when Irish neutrality in the Second World War prompted Winston Churchill to contemplate invading the country – again – to the 1970s, when a mob in Dublin burnt down the British Embassy in retaliation for the Bloody Sunday shootings in Derry.

Today, thank goodness, we live in a different world. From the British cult of Jedward to Irish interest in "Kate and Wills" – considerable, if Irish viewing figures of the royal wedding are anything to go by – the two cultures reveal a growing tendency towards convergence, even if only at the level of a joint fascination with celebrities.

What has taken much of the sting out of Anglo-Irish friction, meanwhile, has been Ireland's economic revival since the 1980s. Right now, any mention of the Celtic Tiger, unless it is ironic, evokes derision. But it would be absurd to suggest that Ireland's serious economic difficulties threaten to recreate the grimly poor society that existed only a few decades ago, and when almost the only option facing anyone of ambition was to emigrate. The fact that the Queen is visiting Ireland at a time of economic flux should be put to good use. As a new government wrestles with the crisis, this is an opportunity for Ireland to show off its continuing potential as well as its most inexhaustible asset, its natural beauty.

The Anglo-Irish relationship will never be as normal, cloudless – and distant – as this country's ties to, say, Holland or Denmark, and no royal visit will change that. Our relations could still be better, and would be, if in this country we paid more heed to the horrors visited on Ireland in Britain's name, and if everyone in Ireland was willing to let go of the past. Reconciliation remains a work a progress. The reaction in Ireland to a British monarch's presence will be a sign of how far we have come, and have yet to go.