If you went back in time and met your teenage parents, you could not split them up and prevent your birth - even if you wanted to, a new quantum model has stated. Researchers speculate that time travel can occur within a kind of feedback loop where backwards movement is possible, but only in a way that is "complementary" to the present. In other words, you can pop back in time and have a look around, but you cannot do anything that will alter the present you left behind. The new model, which uses the laws of quantum mechanics, gets rid of the famous paradox surrounding time travel.
You can read the original paper online. This is the abstract:
We introduce a quantum mechanical model of time travel which includes two figurative beam splitters in order to induce feedback to earlier times. This leads to a unique solution to the paradox where one could kill one's grandfather in that once the future has unfolded, it cannot change the past, and so the past becomes deterministic. On the other hand, looking forwards towards the future is completely probabilistic. This resolves the classical paradox in a philosophically satisfying manner.
Hack through the math and go read the conclusion.