The Long Earth, by Terry Pratchett and Stephen Baxter
I've been meaning to read this series for so long, and somehow just never picked up a copy. But then The Long Earth came to me -- somehow or other -- and I put it on my TBR shelf and finally got to it. I love it! It's great stuff! I can't wait to start the next one, which I just checked out of the library.
Twenty minutes into the future, instructions appear online for a gadget that appears to have no purpose or meaning -- and its power source is a potato. Kids promptly start building their own gadgets, and the startling result is that they are transported sideways, to another Earth in another dimension. Pretty soon everyone has a 'stepper' and is experimenting with dimension-hopping; there appears to be an infinite number of pristine Earths, each ever so slightly different than the last, and all uninhabited by humans. Suddenly resources are infinite, as long as you can get to them.
As groups of people start leaving the original Earth to settle elsewhere, we get to know certain people well. Joshua is a natural stepper, used to having Earths to himself, until he's hired to explore as far as anyone can go. Monica is a police officer and one of the first people to have to deal with the fallout, starting with inexplicably disappearing children and ending with a terrorist, a kid whose family left him behind when they stepped away to start new lives.
I'm really looking forward to the next book! This is a great SF novel.