My thought is that time travel is impossible. At least to the past. Future maybe a different case.
If i remember my woefully poor physics knowledge, the FTL traveller experiences time differently. For him or her time flows slowly. So, while the outer world moves normally, time slows down for that person. For example the time taken by the travelller's watch to turn from 2 to 3 pm will be the same as the time taken by 'outside' clocks to change from 2 to 4 pm.
Particle physics is a very weird science. Initially, i studied that electrons move in orbits around the nucleus. But then i knew that they don't move in orbits but orbitals which are a kind of 'probability clouds'. Orbital was merely a space in which an electron is supposed to be found with 99% probability. So, its somehow possible that an electron may not even be in an orbital! And these weird structures combine to form bonds and thus elements combine to form compounds, the building blocks of our existence.
Taking these subatomic physics to macroscopic levels would be almost like 'magic'. I would be having both mass as well as wavelength. [Imagine the ripple(wave) created by a pebble is same as the pebble(mass) itself]. Well i am still supposed to have wavelength as per Heisenberg's theory. But its too negligible for larger masses. But as you go to subatomic level the dual nature can't be ignored.
If we go by logic, this too shall not make sense. What we are now is the result of the past. But if the past is changed are we the same? Timeline is a cool theory. But where has the 'new universe' come from? For example this universe has to have carbon dioxide. But where did this carbon dioxide come from? Nothing?