One of the more interesting articles I've seen on Physorg: Time travel experiment demonstrates how to avoid the grandfather paradox (also the abstract is available here)
Ok, so they didn't actually experiment with "time-travel" (that would be kinda hard given current technology), that's just sensational journalism. From what I can tell what they actually did was model a theory of time travel off of quantum teleportation and then performed an experiment on that, the outcome of which supports the idea that, in my own laymans terms, you can only travel in time if your journey is consistent with itself (i.e. time travel is possible but only in cases that prevent this particular paradox).
In slightly more technical terms, it seems that they theorized closed timelike curves operate like quantum channels used in teleportation, and also that closed timelike curves are post-selected for consistency. The experiment then involved entangling two qubits in a single photon, then attempting to change the state of one of the qubits. The other qubit can then only teleport if the previous qubit's state was unchanged in the experiment. In terms of the grandfather paradox it seems the teleporting qubit would model the grandfather while the one being flipped would model the grandchild. The states of the qubits are measured before and after the experiment to see if they are consistent (being inconsistent would be the equivalent of the grandchild having "killed" the grandfather).
Honestly I'm not sure what the great value of this really is, except that they've developed an "alternative quantum formulation of CTCs based on teleportation and postselection" and performed an experiment which gives similar results to what they predict. Regarding that they're quoted as saying:
Ok, so they didn't actually experiment with "time-travel" (that would be kinda hard given current technology), that's just sensational journalism. From what I can tell what they actually did was model a theory of time travel off of quantum teleportation and then performed an experiment on that, the outcome of which supports the idea that, in my own laymans terms, you can only travel in time if your journey is consistent with itself (i.e. time travel is possible but only in cases that prevent this particular paradox).
In slightly more technical terms, it seems that they theorized closed timelike curves operate like quantum channels used in teleportation, and also that closed timelike curves are post-selected for consistency. The experiment then involved entangling two qubits in a single photon, then attempting to change the state of one of the qubits. The other qubit can then only teleport if the previous qubit's state was unchanged in the experiment. In terms of the grandfather paradox it seems the teleporting qubit would model the grandfather while the one being flipped would model the grandchild. The states of the qubits are measured before and after the experiment to see if they are consistent (being inconsistent would be the equivalent of the grandchild having "killed" the grandfather).
Honestly I'm not sure what the great value of this really is, except that they've developed an "alternative quantum formulation of CTCs based on teleportation and postselection" and performed an experiment which gives similar results to what they predict. Regarding that they're quoted as saying:
Although one would need a real general relativistic CTC actually to impose final conditions, we can still simulate how such a CTC would work by setting up the initial condition, letting the system evolve, and then making a measurement. One of the possible outcomes of the measurement corresponds to the final condition that we would like to impose. Whenever that outcome occurs, then everything that has happened in the experiment up to that point is exactly the same as if the photon had gone backward in time and tried to kill its former self. So when we ‘post-select’ that outcome, the experiment is equivalent to a real CTC.