Last Year - Robert Charles Wilson

Two events made September 1st a memorable day for Jesse Cullum. First, he lost a pair of Oakley sunglasses. Second, he saved the life of President Ulysses S. Grant.
In the near future of Robert Charles Wilson's Last Year, the technology exists to open doorways into the past—but not our past, not exactly. Each "past" is effectively an alternate world, identical to ours but only up to the date on which we access it. And a given "past" can only be reached once. After a passageway is open, it's the only road to that particular past; once closed, it can't be reopened.
A passageway has been opened to a version of late 19th-century Ohio. It's been in operation for most of a decade, but it's no secret, on either side of time. A small city has grown up around it to entertain visitors from our time, and many locals earn a good living catering to them. But like all such operations, it has a shelf life; as the "natives" become more sophisticated, their version of...