The Many Worlds Hypothesis of quantum physics has inspired a number of SF novels in recent years. The Infinitive of Go (whose title is one of the cleverest puns I've seen) is one of the earliest books to deal with the subject of alternate universes in the way later hard SF stories, with their more updated science, would. (And unlike earlier explorations of the subject, such as that Star Trek episode where Spock has a goatee.) Brunner has thought through the implications of both the science and philosophy surrounding the subject, and managed to pack it all into a nice and compact little speculative brain-muncher that his fans would do well to unearth at the secondhand bookstore.
Justin Williams and Cinnamon Wright are a pair of scientists who have invented the first transporter device, called a Poster. After the first human trials go off without an apparent hitch, the machine is used for the first time in its intended official capacity: to transport an official courier carrying sensitive state secrets. But when the courier turns up in the machine, he somehow isn't himself. He demands identifying codewords no one expected, and, not getting them, kills himself.
In the ensuing chaos, Justin, in order to prove to brusque government types who want to avoid responsibility for a their mistakes that the fault could not have possibly lain with the Poster, volunteers to be transported himself. He is, and turns up in a world that is like his...but changed. He finds that he and Cinnamon are suddenly lovers, and that the financier behind the whole operation is no longer an arrogant petty despot and government toady, but a genuine philanthropist whose support of science is altruistic.
Before long it becomes evident that the Poster isn't merely transporting its subjects from one point in the universe to another through some kind of wormhole. It's actually opening up many different universes, with apparent total unpredictability at work in determining which one will emerge to the hapless subject who steps into the machine. The plot thickens when a scientist who is forced to use the Poster to return to Earth from an orbital station due to a life-threatening on-the-job injury shows up — and isn't even human, but the result of an entirely divergent path of human evolution. (Though he's still essentially the same person, and even speaks perfect English.)
I think fans of The Matrix will get a kick out of this book, as its dialogue is packed to overflowing with wild philosophical speculation and mathematical jargon that will seem like utter mumbo-jumbo to anyone without a Master's. I'm sure some of the science involved here is well and truly dated, and I'm positive the book would have been even more successful had Brunner had a chance to flesh it out — it's barely over 150 pages long, the typical length publishers required paperback SF to be back in the day — and expand upon its obvious potential. But it's still a fun read, a tight example of "what if?" SF that isn't really written in this style any more. Brunner correctly doesn't provide easy answers to the crisis at hand, because, quite simply, there aren't any. (Or is it that there are an infinite number?) And the unresolved ending is something I don't think most editors would let a writer get away with today. Enjoy.