"With any tragedy, it's also important to remember the positive things, the beautiful memories that you have about whatever it is that you lost," Gordon-Levitt tells PEOPLE

Joseph Gordon-Levitt on How The Walk Honors the World Trade Center: 'It's a Spectacular Celebration of These Towers'

Joseph Gordon-Levitt is proud that his upcoming film The Walk tells a positive story about the Twin Towers of the World Trade Center.

“I think that whenever we think of the World Trade Center towers, all of us are going to think of the tragedy, and it’s of course worth remembering the tragedy, but I also think with any tragedy, it’s important to remember the positive things, the beautiful memories that you have about whatever it is that you lost,” Gordon-Levitt, 34, tells PEOPLE.

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“That’s a lot of what this movie is. It’s a positive and warm and beautiful, spectacular celebration of these towers,” he adds.

The film, out Sept. 30, tells the story of Philippe Petit, the French tightrope artist who famously walked a wire between the Twin Towers in 1974. Petit’s daring (and highly illegal) act captured the hearts and imaginations of people the world over and brought attention and affection to the World Trade Center, then the world’s second tallest building, which had opened just one year earlier.

Because preparations for the daring feat took six months of secretive missions by Petite and his friends – who posed as everything from construction workers to architectural critics – many scenes of the film take place in the famed building’s lobby.

“They reconstructed the lobby of the World Trade Center quite thoroughly on this big set, they built it,” Gordon-Levitt explains. “It was the same as it was.”

This made for an emotional experience for the entire cast, especially those from New York.

“That day, when we were standing there in the lobby of the towers, and it just looked so much like it, I remember just feeling the impact, like wow, this room doesn’t exist anymore but it does,” Gordon-Levitt says. “Here it is, we’re in it. We’re standing in it.”

“I remember in particular, we had two native New Yorkers in our cast – Ben Schwartz and James Badge Dale – and they both on that day, just standing there on that set, they were getting choked up just standing there,” he continues. “I thought that was a really moving, memorable moment.”