They did that already in "Back to the Future" — Marty from 1985 goes back in time and meets Doc Brown from 1955.
Dr. Emmett Brown: Then tell me, future boy, who's President of the United States in 1985?
Marty McFly: Ronald Reagan.
Dr. Emmett Brown: Ronald Reagan? The actor? (chuckles in disbelief) Then who's vice president? Jerry Lewis? I suppose Jane Wyman is the First Lady. And Jack Benny is secretary of the treasury!
-"BB"-
Yes, I suppose I could agree with you ... but then we'd both be wrong, wouldn't we?