Well, the argument is that quantum indeterminism implies quantum time travel is possible, because the grandfather paradox is solved/migitated by indeterminism in which the grandfather paradox is still a valid outcome. However, quantum indeterminism itself is not yet completely undisputed; some theoretical physicists such as Gerard 't Hooft maintain that quantum mechanics can be both deterministic and consistent with current experiments.
This also raises the following question - if quantum mechanics is undeterministic, then the macroscopic world is at least probabilistic. If probabilistic systems allow the possibility time travel on the quantum scale, would the grandfather paradox also not be solved on classical scales? Since it is possible that me killing my grandfather in the past would fail with some very small probability (due to various quantum effects adding up), would the grandfather paradox then not also be solved in this case? I'm not sure if I'm interpreting the article correctly.
This also raises the following question - if quantum mechanics is undeterministic, then the macroscopic world is at least probabilistic. If probabilistic systems allow the possibility time travel on the quantum scale, would the grandfather paradox also not be solved on classical scales? Since it is possible that me killing my grandfather in the past would fail with some very small probability (due to various quantum effects adding up), would the grandfather paradox then not also be solved in this case? I'm not sure if I'm interpreting the article correctly.