Mysterium_ by Robert Charles Wilson is a very well done, engrossing earlier work of the author's, one that I don't believe has gotten anywhere near the attention of his later works (such as _Darwinia_, _Bios_, and _The Chronoliths_). It is also unfortunately out of print, though there are a great many used copies out there at relatively cheap prices.
_Mysterium_ is a book one could place in the "island in the sea of time" sub-genre of books on alternate history and parallel universes, one made famous recently by of course _Island in the Sea of Time_ by S. M. Stirling (1998), _1632_ by Eric Flint (2000), and _Weapons of Choice_ by John Birmingham (2004) and their sequels, the premise being that some little corner of the modern day world (or a whole fleet instead of an island or a town in the case of _Weapons of Choice_) of our Earth gets sent into the past (which becomes from that point on a parallel universe, when those people from our time interact with the rest of the world). _Mysterium_ differed in two respects; first, this story came first (for whatever that is worth), as it is copyright 1994, and second, the town of Two Rivers, Michigan found itself in is a parallel universe from the beginning, contemporaneous with our Earth but with a history that diverged from our own close to two thousand years ago. But I get ahead of myself.
An archaeological team working in a remote area of Turkey on what was believed to be a rather unremarkable prehistoric site came across what looked like a bit of jade embedded in the soil. Remarkable in its own right, further digging revealed that what was assumed to be a small piece was actually part of a much larger item that was not actually jade but some strange substance with extremely unusual optical properties. Of great interest - and unfortunate to its discoverers - the item was also extremely radioactive, many of those who discovered it dying quickly of radiation sickness. Obviously an item not of this Earth, with Turkey's permission the United States government removed it under heavy protection to a new research facility built just to study it, one set up on an old and largely abandoned Indian reservation near the quiet town of Two Rivers, Michigan. The base, very much aloof and apart from the town, at first piqued the curiosity of the locals, wondering what the meaning of the new base was in an era of declining defense spending and also hopeful of new jobs. When the new jobs don't really materialize to any great degree and the base stayed extremely quiet, they quickly forgot about it.
One night though - a mere twelve pages into the book I would like to add - mysterious bright lights and an explosion at the facility, just visible to those in the town, heralded a bizarre event, one that removed the entire town and the military base to a parallel universe, the exact same spot on the globe on a world with a totally different history, in an alternate Michigan. Fully aware that there was some accident at the base, the townspeople awoke to find the power, water, and phones out, and those few with battery powered radios not able to get any stations except for a very distant one, one that seemed to be putting on some quasi-religious radio play of all things. Most just went on with life for a bit as best they could, hopeful that the utilities would be restored, though several tried to leave town and made an amazing discovery; all roads and trails out of town just stopped, ending in a cut as sharp as if a laser had made it. So sharp was the divide that trees were split right down the middle along the line, bare heartwood exposed for all to see. The other side of the line, inches beyond the road, was virgin forest, deep dark woodlands that had never known an axe.
One of the locals who possessed a floatplane took off, hoping to uncover more of this mystery. He found that the town was now deep in the wilderness, all nearby other roads and towns long vanished, and what should be Detroit had completely different architecture, odd-looking cars, and even horse-drawn wagons. Heading back home, his flight apparently attracted the attention of the authorities of this world, who moved in with aircraft, tanks, and soldiers, putting the town under martial law.
The startled locals learned that they were in an alternate reality; they were not in the United States of America, but in an entity called the Consolidated Republic, a French-English nation that ruled most of North America and was regrettably run by an authoritarian religious theocracy. What's more, it was not a Christianity as the townspeople knew it; it became apparent later in the book that the Christianity in this world was a intolerant descendent of Gnostic Christianity, this world's history having diverged considerably during Roman times, as the Roman Empire never became Christian and indeed even to the present Apollo and other Greco-Roman gods were still worshipped in many countries of Europe (ones at war with the Consolidated Republic). The locals privately derided this world's Christianity as being practically polytheistic, while the Proctors (much feared Gestapo-like religious police of the Bureau de la Convenance Religieuse) despised the Two Rivers Christians as worshipping a "stick figure Christianity," one unbelievably crude and simplistic.
Regrettably, the conflict between Two Rivers and the authorities was much more severe as that, as the Proctors had dire plans for the town, for they believed it to be both incredibly useful as source of advanced technology and weaponry (being about roughly 50 years ahead of them) and as a blasphemous and dangerous threat to their social order. The remainder of the book dealt with the ugly plans of the Proctors and the secret resistance lead by several townspeople and their sympathizers.