The Probability Broach
The Probability Broach is the first novel (1980) by American science fiction writer L. Neil Smith. It is set in an alternate history, the so-called Gallatin Universe, where a libertarian society has formed on the North American continent, styled the North American Confederacy (NAC).
Plot summary 
Edward William "Win" Bear is a Ute Indian who works for the Denver Police Department in a version of the United States projected (by 1986) to be controlled by an anti-business, ecofascist faction complete with a new Federal Security Police (FSP, or "SecPol" as it is more commonly known) reminiscent of the Gestapo. Called to investigate the unusual murder of physicist Vaughn Meiss, Bear eventually finds himself projected into the NAC by means of the "Probability Broach," an interdimensional conduit originally developed as a means for interstellar travel in the NAC by the dolphin physicist Ooloorie Eckickeck P'Wheet and her human compatriot, the gorgeous Dr. Dora Jayne Thorens.
Win encounters his NAC counterpart, Edward William "Ed" Bear, and Ed's neighbors, most notably the beautiful "healer" Clarissa Olson and the incorrigible Lucy Kropotkin, who is later revealed to be 135 years old. Lucy's life becomes the vantage point by which Win is acclimated to life in the NAC and Laporte (the NAC equivalent to Denver). Win and Ed unravel the mystery of the Meiss murder, learning that he was killed to hide an effort by SecPol to conquer the NAC with the help of Hamiltonian forces on the NAC side, led by John Jay Madison, a.k.a. the infamous Prussian expatriate and 1918 war hero Manfred von Richthofen, known here as the Red Knight of Prussia. Win, Ed, Lucy and Clarissa lead the effort to notify the nascent NAC government of the threat. En route to the meeting of the Continental Congress, Ed & Clarissa are kidnapped, leaving Win & Lucy to reveal the plot. After fighting (and winning) a duel with a SecPol agent, Win and Lucy rescue their friends, and track the Madison and the Hamiltonians to a small town outside Laporte. Win sets off an explosion that eliminates all of the Hamiltonians.
Win elects to remain in the NAC and marries Clarissa. Ed marries Lucy (who at the time of the story was awaiting a delayed "regeneration" due to an accident involving massive radiation exposure), they then set out for the asteroid belt to build a new life for themselves on the NAC frontier. The Continental Congress agrees to begin a massive propaganda campaign to force Win's United States (and the rest of the globe) toward a similar Gallatinist revolution.