IMO the simplest resolution of things like the grandfather paradox are obtained by including quantum mechanics in the equation. Usually in quantum mechanics we

IMO the simplest resolution of things like the grandfather paradox are obtained by including quantum mechanics in the equation. Usually in quantum mechanics we find that waves are quantized because they must be periodic over very tiny reaches of space, and the quantization comes about because only certain frequencies of wave can meet themselves over these distances. But if we have time loops, it's pretty much the same thing, except the consistency conditions can be experienced on arbitrarily large scales - the quantum state where I kill my own grandfather is not a self-consistent loop, and won't exist as a solution to the wave equations. In essence, the "wave" that describes me killing my grandfather will interfere with itself over the time loop, and will eventually (hopefully? I don't have a proof...) converge on a wave that does reinforce itself, and ends up consistent. This may require a pretty serious divergence from what we'd usually assume about classical physics, even at the macroscopic scale. So quantization is the real reason we shouldn't worry about the grandfather paradox; any solution to the equations of QM will have to be self consistent over a closed timelike loop, even if the results are ridiculous as far as classical mechanics is concerned.