Time travellers may be somehow prevented from even thinking about shooting their grandfathers or perhaps they can make the decision to shoot only to be foiled in some other way. “Nature wouldn’t care much whether it interferes with my synapses or with the workings of my Colt 45,” says Steinberg.
While you shouldn’t expect Marty McFly to show up in a DeLorean any time soon, the value of one particle in the present has proven capable of determining the value of another particle in the past — unless the goal is to create a paradox, in which case the time travel fails.
In more practical terms: if you (or, more precisely, a quantum replicant of you) tries to travel back in time to visit a former you, the only successful trips will be the ones in which nothing significant changes.
Or, in other words: even when time travel becomes possible, despite your best efforts, you always will have been doing whatever you did before.
The entire 5th season of Lost was devoted to this theory.