The 9/11 Museum: Curating memories of terror and tragedy

Lesley Stahl gets the first in-depth look at the National September 11 Memorial Museum currently under construction seven stories below ground at ground zero

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The following script is from "The 9/11 Museum" which aired on April 21, 2013. Lesley Stahl is the correspondent. Shari Finkelstein, producer.

At times like these with the bombs in Boston, many of us can't help but be drawn back to the horrific events of Sept. 11, 2001. About a year from now, at ground zero in New York City, one of the largest and most ambitious memorial museums in the world is scheduled to open its doors to tell the story of that day -- the National September 11 Memorial Museum.

It'll actually be located below ground - seven stories down. It's a project that's been plagued by delays, funding battles, even a flood thanks to Hurricane Sandy. But if you can believe it: those things were the easy part. The bigger challenge: How do you convey the horror of 9/11 without making it unbearable? Memorialize a day most of us wish we could forget?

Tonight we'll take you down below for a first in-depth look at what our nation's 9/11 Museum will be.

Ground zero above ground is today a place of rebuilding, and remembrance. At its center is a serene memorial plaza with two giant cascading pools -- twin voids set into the footprints where the towers of the World Trade Center once stood. Each pool is surrounded by names - 2,983 of them -- plus some who didn't even have a name.

It's quiet and powerful as people come -- over seven million so far -- to touch and feel and in some cases mourn fathers, sisters, children. But you won't find anything here about what actually happened on 9/11; nothing about the buildings, the planes, nothing about the terrorists. All that will be the job of the museum, and its director Alice Greenwald.

Alice Greenwald: We occupy literally the space below the Memorial Plaza.

Lesley Stahl: So we're walking--

Alice Greenwald: --you're walking on the roof of the museum.

This is not Greenwald's first job on a project about a painful subject. She came here from the Holocaust Museum in Washington, D.C.

Alice Greenwald: Just watch your step, Lesley. It is a construction site.

But at this construction site, the issues go far beyond where to put the walls. Virtually every decision here is fraught with meaning, as you descend past two 50-ton beams recovered from the wreckage into a space...

Alice Greenwald: Welcome to Foundation Hall.

...that takes your breath away.

It's haunting and a little chilling knowing you're in the belly of ground zero. In the place where so many innocent people lost their lives.

Lesley Stahl: So here we are, we're right where the buildings collapsed. We're in it.

Alice Greenwald: Most museums are buildings that house artifacts. We're a museum in an artifact.

Lesley Stahl: Where we are is almost sacred.

Alice Greenwald: I think you are become super conscious of where you're standing. And that's a powerful thing. It's a very powerful thing.

Anthoula Katsimatides: It's the authentic site of loss.

Monica Iken: It is sacred and hallowed space.