“Your greatest trial may not be in the ring,” Howard Cosell once told Muhammad Ali. “It may be with the American public.” The point still stands and is proved again in Bill Siegel’s gut-punching new documentary, The Trials of Muhammad Ali, which revisits what Siegel has described as “the explosive crossroads” of Ali’s life. In a few short but turbulent years, he became the world heavyweight champion, became a Muslim and changed his name from Cassius Clay, refused to join the Vietnam War, saw his title and his livelihood stripped, took his appeal to the Supreme Court, and went on a tour of public appearances, during which the one-time “Louisville Lip,” long known as a loudmouth, spoke up for real. Best known for co-directing the Oscar-nominated 2002 documentary The Weather Underground, Siegel also was a researcher on Hoop Dreams, another perceptive report from the intersection of sports and social critique. With The Trials of Muhammad Ali he has succeeded in delivering a rare and special breed of documentary: the new chronicle we didn’t know we needed. It happens to come on the heels of a new HBO drama directed by Stephen Frears, Muhammad Ali’s Greatest Fight, but in the same way that the world made room a few years ago for more than one movie about Truman Capote writing In Cold Blood, so it surely can allow two retrospective illuminations of Ali’s conscientious objection. Besides, Siegel’s is great.