There are various ways in which classical and quantum physics deals with the possibility of paradox in time travel, encapsulated in the question, "What would happen if I went back into my past and killed my grandfather?" The ways in which authors deal with the possibility of paradox are just as varied.
Connie Willis tells the tales of a series of academic chrononauts from a university in England, traveling to the Black Death (Doomsday Book), the WWII bombing of London (Fire Watch and To Say Nothing of the Dog) and the defense of Britain (Blackout and All Clear).
Initially, Willis' time-transiting historians are firmly convinced of the Penrose cosmic censorship principle: travelers can only arrive at times in which no change to the past is possible.
Contrast this with the premise presented in the Ray Bradbury short story A Sound of Thunder: Tiny changes in initial conditions (the death of a butterfly in the Jurassic) can wreak immense shifts in present-day society. This Chaos Theory, also called "the butterfly effect", means that time travelers can completely remake their worlds.
Then consider the Novikov self-consistency principle, from quantum theory and the thought experiment popularly known as Schrödinger's Cat. If every possible event has a certain statistical probability to occur, opening the box does not change the cat's status. It is what it is, alive or dead. Likewise, killing your grandfather has no effect on your life, because what happened, happened whether you traveled in time or not. If it would change the future, you would not be permitted to perform the act. This is sometimes restated as "time's self-correction capability". No paradox can be created.
One way to get around the creation of a paradox is to create a new universe: in one, Schrödinger's Cat is alive, in another, it is dead. In such a "multi-verse", every act that can change the future spawns a new universe.
I must admit when I first began reading Zero Time by Kenneth D. Reimer, I thought it was going to be a multi-verse story. As I read onward, I began to wonder if he meant to travel Bradbury's path. Chaos abounds in the story, a direct consequence of his main characters traveling through time and arriving "back in the present" out of sequence with each other.
Then Reimer explicitly brought up Schrödinger's Cat, and I began to see implications of quantum corrections occurring. More and more, the story began to challenge causality and our perspective of linear time.
In the end, the author has done something really clever and disturbing: He has woven a web of time transit with a malevolent entity sitting in its center, waiting for the souls of time travelers to be caught in its strands—with causality paradoxes and butterfly effects, a clockwork monkey of evil appearance, time-crossed lovers, and a soupçon of physics and philosophy to flavor it nicely.
What emerges when you reach the end (but not until then) is a thoroughly twisted and enjoyable novel that succeeds in challenging the usual either-or choices of time travel.
I'm glad it's fiction. And I'm glad I read it.