Auto-infanticide, the idea of going back in time and killing your grandfather works in Lewis' 'Paradoxes of Time Travel,' according to one or more theories and/or theorems of quantum physics. The one that comes immediately to mind is the many-worlds interpretation in which each moment in space-time (or, to be clear in Lewis' terminology - each moment in the space-time, personal and external), each moment is a branching point, creating multiple if not infinite paths of events, and therefore infinite path-worlds, aka, infinite universes where a different set of events occurs when a single event is changed. So, the idea is that if one universe were a movie, each frame could potentially have infinite branches into different universes (movies); each time a frame is altered or "alters" - to be consistent with Lewis' idea that each alteration is presently formed with respect to itself.
What is the justification for this? The theory of wave-function collapse, is best exemplified by the famous "double-slit" experiment. In this experiment, light behaves like a wave; but when it is observed, it becomes localized like a particle. The analogous theoretical idea here is that, for us, subjective beings, observe reality as collapsed to one world, when in actuality, it is spread out in multiple potentials. From your point of view, your subjective observation, you can only see or understand one world; ergo, one series of events; either Tim can kill his grandfather or he can't; since Tim's alive, he can't.
In the multiple world interpretation, Tim can, but this would occur in another world/universe, branching off in 1921.
Another famous exposition of this is Schrodinger's cat; basically, inside a box is radioactive material, poison and a cat. The radioactive detector has a 50/50 chance of detecting radioactive material. If detected, poison is released and cat dies. We can only know if the cat lives or dies by observation. Without observing, both potentials are equally likely. Thus, observation would conclude or 'limit' the outcome to one or the other. In the quantum world, deterministic and non-deterministic events occur, so each is likely. Analogously, the grandfather can be alive or dead, but only one is observable to us. The other possibility (alive or dead) must occur in another universe, branched off from our subjective perception of this One world.