I Does it make sense to speak about the Grandfather paradox in QM?

[jordi]

Since QM is not deterministic, the future state B is not determined by the previous state A (at time A, B was only a possibility, not a certainty).

Then, when we are at time B, and assuming we could move back in time (of course, we cannot do that, but let us make a Gedankenexperiment), it just makes sense that moving back in time should also be probabilistic, not deterministic.

So, with a high probability, if we could move back in time, we would not end up in state A, but in state C (whatever it is).

Only a big coincidence could result in C having the grandfather alive (most possible states would be with no grandfather whatsoever).

So, if we use QM as a framework, the Grandfather paradox does not exist (or it could exist, but with an exceedingly small probability).

In fact, here one could ask: what does going back in time means in QM, if we do not end up in the "original" A state? Wouldn't this evolution towards the past analogous to (another) dynamics into the future? Which experiments could be done to really be sure we had gone back in time?

 

[PeroK]

There has been some research done on closed-timelike-curves and QM. E.g.

https://arxiv.org/pdf/1005.2219.pdf

 

[PeterDonis]

Moderator's note: Thread moved to QM forum.

 

[PeterDonis]

when we are at time B, and assuming we could move back in time (of course, we cannot do that, but let us make a Gedankenexperiment)

You can't make a valid thought experiment that violates the laws of physics. So you can't just wave your hands and assume "we could move back in time". You have to figure out if the laws of physics allow such a thing. @PeroK referred to one way that the laws of physics might allow it, namely closed timelike curves; but most physicists do not believe closed timelike curves can actually exist, since the mathematical solutions in relativity that include them have properties that most physicists think are physically impossible.

it just makes sense that moving back in time should also be probabilistic, not deterministic.

No, it doesn't, because measurement in QM, at least as it is handled in the basic math, is not time symmetric. (What various QM interpretations say about this is another question, discussion of which belongs in the QM interpretations forum.) You have multiple possibilities before a measurement, but only one of them is observed to happen. There is no "backward in time" analogue in QM where you have multiple possibilities after a measurement but only one before.