We spoke with four family members who are also members of the museum's board. Paula Grant Berry's husband, David, worked in Tower 2, as did Monica Iken's husband, Michael. Anthoula Katsimatides's brother, John, was in Tower 1; and Tom Rogér's daughter Jean was a flight attendant on American Airlines Flight 11.
Paula Grant Berry: The site radiates something for us all in a very special way.
Monica Iken: That's where the final resting place of our loved ones is.
Lesley Stahl: It has to be there?
Monica Iken: It has to be there.
Voices: Has to be there.
Anthoula Katsimatides: Yes.
Monica Iken: And you can feel it.
Alice Greenwald: This is the remnant of the exterior structure that made up the twin towers.
One of Greenwald's first challenges, in this hallowed space, was deciding where the story of 9/11 should begin.
Alice Greenwald: We begin with the voices of people from around the world remembering where they were when they heard about the attack.
[Someone barged in and said, "Oh my God, a plane has just crashed in to the World Trade Center.]
The idea is to acknowledge that most visitors will bring their own memories of 9/11, which was witnessed within hours by people all across the globe.
[Phone rang, woke me up, my business partner told me to turn on the television]
Greenwald says we are all survivors of 9/11, so it's fitting that visitors will descend to the main exhibits of the museum beside an enormous staircase, now encased in wood, that served as an escape route.
Alice Greenwald: On 9/11, hundreds of people ran to safety down this stair.
The so-called "survivor staircase" is one of several artifacts so big the museum had to be built around them -- like this fire engine lowered in through a hatch in the roof that will honor first responders, 441 of whom lost their lives. And the famous last column, the final massive remnant of the towers to be removed from the site.
But we found that some of the most powerful things on display here...
Lesley Stahl: OK, so that's Flight 11.
Alice Greenwald: Takes off from Boston.
...won't be physical artifacts at all.
Lesley Stahl: Oh look, the second plane...
A large projection on the wall will show the morning of 9/11 as it played out in the air.
Alice Greenwald: Flight 11 is hijacked. Meanwhile, Flight 77 leaves.
...With the simultaneous flight paths of the four planes.
Alice Greenwald: And now, Flight 93 takes off. Impact has already happened in New York.
Lesley Stahl: Oh, look at this.
Alice Greenwald: And then Flight 93 is hijacked, turns around.
Among the agonizing decisions for the museum: Should they include the voicemail messages left by passengers aboard those planes -- and other victims of 9/11 -- for their loved ones? One adviser told Greenwald to think of these recordings as a form of human remains.