As Radiohead and the RSC launch an innovative reinterpretation of Hamlet, a visit to the play's setting in Denmark brings a new dimension to the tragedy.

There's a cold wind blowing from the Øresund Sound as I stand on a platform in front of Kronborg Castle in Helsingør, Denmark, looking out to Sweden. At one end of the platform, a pillar-box red guard post stands beside a row of impressive cannons facing the strait. I'm not here for the view though: I'm looking for ghosts.

This windy spot is the exact location for the opening scene of Hamlet, Shakespeare's best-known tragedy. Here, two guards, Francisco and Bernardo, switch posts in the middle of the night and speak of the ghost of Hamlet's father. The castle behind me, a grand Renaissance pile built in 1574 complete with fairytale turrets, a moat and a grand banqueting hall, is where the rest of the lurid drama unfolds.

This year, the Royal Shakespeare Company is presenting no fewer than three variations on the story: a radical adaptation using Radiohead's album Hail to the Thief as its score (from 27 April); Fat Ham, a comic tragedy that transplants Hamlet's story into the Deep South (from 15 August); and a traditional take in Rupert Goold's production starring Luke Thallon (from 8 February). For context, the last time the RSC staged Hamlet was back in 2006.

"There's something in the air right now saying that the play has resonance," says Tamara Harvey, co-artistic director at the RSC, noting that all three producers had approached the RSC to stage their productions in the same year.

As a play that deals with themes of generational differences and changing world orders, not to mention the sense that "there's something rotten in the state of Denmark" – the idea that society's foundations no longer feel secure – it's hard to miss its appeal.

Today, nothing looks rotten in Helsingør – the modern-day name for Shakespeare's town of Elsinore. The sky is blue and the sun is glinting off a gold flag flying at the top of one of the turrets. I'm on a tour with castle host Louise Older Steffensen to uncover Kronborg's Hamlet connections. Our feet echo as we walk around the stone corridors and into the grand ballroom with its chequerboard floor and soaring wooden ceiling, as she tells me there is no evidence that Shakespeare ever visited Kronborg – but he certainly knew it well.

"We have contracts that tell us that Shakespeare's colleagues visited the castle," she says. "We know that the actors Thomas Pope, George Bryan and William Kempe were here for a season, performing plays for the Danish king. When they returned to England, they set up the Lord Chamberlain's Men, Shakespeare's company."

They may have brought back tales of what happened within its walls. A distinctive celebration is mentioned in the play: a toast followed by the bang of a kettle drum, a trumpet, and a cannon – and it comes from a tradition followed in the castle at that time.

In a dimly lit room next to the ballroom, the tapestries from that era are on display, their gilded threads depicting mythologised kings. Long curtains hang around the queen's bedchamber and around the castle, softening the sandstone walls, dampening sound and making it a fraction warmer – as well as providing opportunities for dramatic intrigue.

Visiting the castle feels like being immersed in the play, walking down the large gallery where the silk dresses of the ladies-in-waiting would have rustled into its beautifully preserved church. It's as if the play itself has........

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