Radiant Historia is more
Quantum Leap than
Back to the Future.
While on a mission with special intelligence, protagonist Stocke has a vision of his subordinates' deaths. The vision comes true, but only after Stocke is granted the power of the White Chronicle. Using the book, Stocke can revisit key moments in history and alter them for the better... or worse.
Early on, time travel looks like a story gimmick rather than a full-blown play mechanic. Once Stocke returns from his mission, however, he's given the choice of either rejoining the military or sticking with his special intelligence group. The choice sets up two parallel timelines, setting up the backbone for Stocke's leaps through time.
Getting back to that Quantum Leap angle, Stocke is an independent agent in both timelines. He can travel through each without causing any major paradoxes, but choices he makes in one can influence the other. Without going into specifics, the solution to a problem in one timeline may require changing something in another. The interplay between events is Radiant Historia's strongest feature. Solutions are never obvious, forcing you to think through decisions and explore different solutions.
Unfortunately, time travel involves a bit of monotony. You'll spend a lot of time retracing your steps in both timelines and replaying certain events. You'll come across a few environmental puzzles also requiring a bit of time travel to solve, though these are more of a distraction and add little to the game beyond a few new trinkets. On the plus side, areas are small and combat goes by quickly.
With so many choices and outcomes, Radiant Historia runs the risk of spiraling into a confusing mess of a plot. All decisions, and their consequences, are stored in the White Chronicle, which helps you keep track of where you've been and how events relate. Though you'll never have to make any massive spacial jumps, you may need to go back to events one or two spaces in the past. The Chronicle also serves as reminder of what happened, allowing you to keep your head in the game's lofty and somewhat complex story.