You're driving along a remote farm road in the middle of nowhere. Your car passes thru an odd-looking fogbank. Suddenly you come upon a small town where everybody is dressed in pioneer clothes, buildings are 19th century era, and horse drawn wagons are seen on the dirt streets. You have entered.......a time slip! Check out these others: http://paranormal.about.com/od/timeanddimensiontravel/a/time-travelers.htm
Time is a measure of change. It is now accepted by most physicists time doesn't actually exist as a medium. TL;DR version: the universe isn't a tape recorder. These people could make good writers! Interesting stories! Fictional, but interesting!
Today if not the early 1960s also: After the principle character made a decision toward the end that could have grave consequences for him/her, the Serling twist would be that they actually blundered into an historical reanactment event.
I have a theory that I often time slip into the future into a historical reenactment of Portland Oregon circa 2014.Everyone stays in character, even the kids walking home from those old fashioned buildings called schools.
