The country has historically reacted with doubt or indifference when African-Americans speak of police officers who brutalize — or even kill — people with impunity. Affluent and middle-class white Americans who were treated with respect by the police had difficulty imagining the often life-threatening mistreatment that black Americans of all walks of life dealt with on a daily basis. Perhaps those days are passing away.

You can see that from the multiracial cast of the demonstrations that have swept the nation since Wednesday, when a grand jury decided not to indict a white New York City police officer whose chokehold killed Eric Garner, an unarmed black man.

In city after city, white and nonwhite citizens have surged through the streets chanting or bearing signs with Mr. Garner’s final words: “I can’t breathe.” Others chanted: “Hands up; don’t shoot” or “Black lives matter” — slogans from the racially troubled town of Ferguson, Mo., where another grand jury declined to indict the officer who shot to death 18-year-old Michael Brown.

The viral spread of the demonstrations — and the wide cross section of Americans who are organizing and participating in them — shows that what was once seen as a black issue is on the way to being seen as a central, American problem.