Hogan, James P. Paths to Otherwhere
What if: World War II entailed different alliances or World War I ended in 1916 and a more peaceful, slower-paced world resulted.
Summary: In the earliest 21st century, US researchers exploring the use of multiverse quantum physics in decision-making discover that they can mentally swap places with their analogs in other timelines. As their timeline becomes increasingly dystopian and war seems more likely, they begin to consider permanently switching to the more utopian Otherwhere line.
Published: Baen 1996 (0671877100BUY), 1997 (0671877674BUY).