In October last year, five years after the collapse of the Twin Towers, construction workers at Ground Zero found another cache of body parts beneath a manhole cover that had remained undisturbed since 9/11.

Predictably, news of the discovery revived the anguish of the bereaved, especially as many bodies had not been recovered from the wreckage of buildings and planes. Some victims' families demanded that heavy construction should be halted until every inch of the site had been combed again for precious evidence of broken and burned human remains.

The decision to excavate the manhole carefully and thoroughly, but to also continue the construction work, was typical of the disputes and compromises that have shaped the rebuilding of Ground Zero. The episode once again raised the question of whether it is a sacred site or an area of valuable real estate.

Inevitably, the development of the World Trade Center Memorial and Museum is caught in the same vortex of competing political, commercial and personal interests. Even before the formal inception of the museum in 2004, there was fundamental disagreement about the public interpretation of the story of 9/11 on the site where more than 2,500 people were killed.

Architect Daniel Libeskind's masterplan for Ground Zero, named Memory Foundations, originally included a cultural complex for which a new organisation called the International Freedom Center (IFC) was the proposed occupant. According to the IFC, 'freedom is a constantly evolving world movement in which America has played a major part'.

Instead of focusing exclusively on the events of 9/11, the IFC intended to address topics such as slavery and the civil rights movement. This was never going to be acceptable to an outspoken and articulate group of victims' families who rallied in protest at the IFC's presence at Ground Zero under the banner 'Reclaim the Memorial'.

In the words of Debra Burlingame, sister of the pilot of American Airlines Flight 77, which crashed into the Pentagon, the IFC would offer visitors 'a slanted history lesson, a didactic lecture on the meaning of liberty in a post-9/11 world' rather than 'a vantage point that allows them to take in the sheer scope of the destruction, to see the footage and the photographs and hear the personal stories of unbearable heartbreak and unimaginable courage'.

The moral force of Burlingame's campaign was irresistible, and led to the ejection of the IFC from Ground Zero. As a result, attention refocused on the development of a museum component within the most symbolically charged part of the site: the memorial quadrant where the Twin Towers had stood and which, for the families of 9/11, remains a burial ground.

The winning scheme for the memorial, called Reflecting Absence and designed by Michael Arad and Peter Walker, comprises two sunken voids, which mark the exact footprints of the South and North towers respectively. Each void holds a pool of water that is filled from each side by waterfalls.

Around the edge of the pools, visitors will be able to read the names of the 2,973 victims of 9/11, as well as those of the six victims of the 1993 World Trade Center bomb.

But even naming the dead is contentious at Ground Zero. Families of some of the rescue workers argue that their deaths carry a different meaning from those of the office workers or airplane passengers, and that their names should be distinguished accordingly.

The proposed compromise is that a discreet shield or emblem of the fire, police or medical department will be included beside the names of their members, despite objections that even these symbols suggest a hierarchy of heroism among the dead.

The position of the World Trade Center Museum within the memorial quadrant and adjacent to the sunken pools means that it cannot be detached from the same politics of memory and inclusion. Negotiating the museum's autonomy, while being sensitive to the wishes of the victims' families, is the job of its director, Alice Greenwald, a former associate director of the United States Holocaust Memorial Museum, and her chief curator, Jan Seidler Ramirez.

While the detailed content of the museum is still in development, Greenwald and Ramirez have established some basic principles. For example, each of the victims will be individually represented, although quite how is yet to be resolved.

The Oklahoma City National Memorial Museum provides a direct precedent by dedicating a single display case to each of those killed by Timothy McVeigh's bomb in 1995. The problem is that the death toll of 168 in Oklahoma City was relatively low. There is not enough space to commemorate each victim of 9/11 in the same way.

It is part of the official remit of the museum to provide a secure store for those body parts recovered from Ground Zero, which are either so damaged or so insubstantial that they cannot be identified by forensic technology.

Visitors will be aware of this facility, but only family members will have full access to it. Elsewhere, there will be a separate quiet space for the families of the bereaved, for whom the public museum is also a private memorial.

Visitors will enter the museum via a pavilion at ground level, and then descend along a sloping ramp that leads down to the bedrock between the footprints of the Twin Towers. The first exhibition en route will be located at basement level, marking the spot where the truck bomb was detonated in 1993.

As they descend into the void beneath Ground Zero, visitors will pass the box-beam columns that defined the foundation of the towers, before ending up at the so-called 'slurry wall'.

This section of the concrete containing wall, which formed a barrier between the towers and the Hudson River, acquired symbolic significance when Libeskind described its survival during the trauma of 9/11 as a metaphor of the 'durability of democracy and the value of individual life'.

When the museum opens in 2010 - a year after the memorial is scheduled to be completed - this once invisible wall will become the final destination of many visitors.

Meanwhile, the museum's collection is taking shape in a temporary store - an aircraft hangar at New York's JFK airport. Artefacts that somehow survived the attacks range from the banal clutter of an office worker's desk to the last steel column that was left standing beneath the chaos and debris of the collapsed towers.

During the months of excavation and salvage at Ground Zero, the column acquired totemic status among the recovery teams and construction workers, who decorated it with their company names. At the end of the clean-up in May 2002, it was carried out draped in the stars and stripes. When the museum opens, it will be re-sited as a coda to an unfinished chapter in American history.

This is, of course, the greatest challenge for the World Trade Center Museum - how do you interpret an event for which the consequences are still being negotiated in America and around the world?

Plans for the museum suggest that, although the events of Tuesday 9 September 2001 will be powerfully recounted through objects, images and words, Ground Zero still may not be the place to explore the wider meanings of 9/11.

Helen Rees Leahy is director of the Centre for Museology at the University of Manchester. Her visit to Ground Zero was part of a research project funded by the university's School of Arts, Histories and Cultures