I'm trying to remember a chapter from The Fabric Of Reality by David Deutsch. It deals with time travel, and shows how paradoxes don't actually crop up due to physical laws. It deals with quantum physics in some way, but I can't remember exactly how it works.
But you could do a lot worse than to read that book in its entirety. You'd have to get it ordered in in most cases, but it's well worth the wait.
How far into your book does the paradox occur? Because if you're rewriting and it'll be a long time before the paradox issues arise, then you have time to get The Fabric Of Reality. I've got it on my shelf, but the chapter in question is a long one, and I don't feel like typing it out. But it shouldn't be too hard to find it once you have the book. IIRC it's about 2/3rds through.
It deals with people paradoxes. The one I can't remember deals with meeting yourself (which could be handy for you even though you didn't bring it up) and there's another section on stuff like killing your grandmother.
Actually, I kind of remember it now - it does seem like a cop out, though this is coming from a noted physicist and not just someone wanting an easy way out of a time travel story. It says something to the effect that if you kill your grandmother in the past, it's a different universe to the one you were born in, and due to quantum probabilities, then you would still be born in your OWN universe in order to come back in time, but in this Universe in which you killed your grandmother, you've basically acted to ensure that a you doesn't exist in this future. So, no paradox.
The Fabric Of Reality is all about the quantum multiverse. It's quite interesting, and honestly is the most supported theory in physics that deals with the idea of time travel and quantum properties.
Also, it says that a time machine is a location and not a device - so you can't "travel" a distance in the time machine, only travel in time. Wormholes are the exception. They link 2 places in the universe and allow you to travel faster than light, which is in effect time travel. Like, travelling faster than light is supposed to take you back in time.
So maybe if you're having a time machine that can travel distances, it needs to have wormhole technology inside it, aswell as a way of travelling into the future (which is far more acceptable in physics).
But I'd still recommend getting the book. If you want to write about physics principles, then you'll probably enjoy The Fabric Of Reality.
(And if you want a nice easy explanation of the multiverse, then that happens in chapter one or two, where light travels through slits. You can't have quantum phenomena without the multiverse, even though when I took that subject at Uni they didn't mention the multiverse at all, and a lot of scientists seem willing to accept the quantum nature of the universe for all the good it could do, but don't want to accept the multiverse because it upsets them. Hello, you can't have one without the other! /bitch)