So Chat GPT has been trying to explain the workings of this to me and honestly, I think my brain is melting out of my ears trying to get my head around it. My thought was that the time travel in the story would cause a permanent loop but Chat GPT tried to explain to me that it doesn't work like that. We have been going around and around and I am not sure if I am getting it so I will explain how I see it working and then I will post an explanation written by Chat GPT and then I will leave the forum open to other people to comment.

For those who have not seen the film, a brief explanation of what happens is this:

Harry, Hermione and Ron go to visit Hagrid to see if they can convince him to free Buckbeak, a Hippogriff that is about to be executed for reasons that are unimportant to this discussion. While at his house, a stone flies in through the window and hits Harry, causing him to look out of the window in time to see that the Minister for Magic, Dumbledore and the executioner are approaching the house. They leave through the back so as not to be seen.

A bunch of other things then happen in the story that will simply confuse this discussion if I go into too much detail, so I will just say that the end result is that a character called Sirius Black is caught and will be executed, which Harry, Ron and Hermione wish to prevent. Ron is injured and stays behind, but Hermione and Harry go back in time to just before their visit to Hagrid's house.

They witness their past selves and Ron going into the house, and shortly afterwards they see the Minister, Dumbledore and the executioner approaching. However, Hermione realizes that none of them—Ron, Hermione or Harry—is looking out of the window. Future Hermione therefore throws the stone that hits Harry and causes him to look out of the window.

The Hermione and Harry from the future then leave the area so as not to be seen by their past selves and they take Buckbeak with them and then they go on to do a bunch more things that end with them saving Sirius Black.

How I see it: When Hermione and Harry go back in time, there is then two Hermiones and two Harrys in that timeline even though they are the same people, The Hermione from the future has already been through everything that the Hermiony from the present is going through. This is where it gets confusing because the Hermione and Harry from the future will go on to save Sirius Black but the Hermione and Harry from the present will have to go back in time to rescue Buckbeak and Sirius Black. does that not mean though that once they go back in time then the whole thing starts over again. Basically from the perspective of each person, they only go back once but from the perspective of time itself doesn't it become an endless loop?

How Chat GPT sees it: I see it as one self-consistent timeline rather than an endlessly repeating series of loops. There is only one Hermione, but for a short period there are two versions of her present at the same external time because different points in her personal timeline overlap.

From Hermione's perspective, the sequence is linear. First, she goes to Hagrid's house with Harry and Ron and is hit by the consequences of actions performed by her future self. She then continues through the events of the evening until she uses the Time-Turner. She travels back several hours and becomes the “future Hermione” whom her younger self had unknowingly encountered earlier. She throws the stone, helps save Buckbeak and Sirius, and then continues normally into her future.

The important point is that the younger Hermione does indeed eventually travel back in time—but when she does, she doesn't create another future Hermione or begin another iteration of the loop. She becomes the future Hermione who was already there. The two Hermiones we see are therefore not two independent people whose timelines will each continue through another cycle. They are two different ages of the same person at different points along one continuous personal timeline.

So, viewed from outside, the timeline contains a section in which Hermione's path through time doubles back and overlaps itself. That structure exists permanently in the history of that evening, but it doesn't have to “run” repeatedly. There was never a first version of events in which Hermione didn't throw the stone, followed by a corrected version. The stone was always thrown by the Hermione who would later travel back in time.

In other words, the loop exists as a feature of the timeline, but it isn't an event that has to keep happening again and again.

Does the time-travel loop in Harry Potter and the Prisoner of Azkaban actually make logical sense?

As I remember it, Harry and Hermione's personal clocks never run backwards, so within their personal timelines, they are never duplicated. However their worldlines have been 'magically' bent back on themselves temporarily effectively akin to taking a hypothetical superluminal round trip in our universe that has returned them to a spacetime location adjacent to where they were some hours previously (in Hagrid's hut). Focussing purely on their personal clocks, there is no period when there are duplicate Harrys and Hermiones in existence at the same time. Therefore there is only ever one now and one chain of events in all timelines. The past is never altered. Merely an number of adustments to future outcomes based on hindsight. However, Buckbeak will almost certainly be aware of an apparent duplication of Harrys and Hermiones for some period in his own timeline. But as a magical animal, this may not be entirely unexpected.

Let me see if I got this straight ...

You have an imaginary 'process' happening in an imaginary movie, and you want to know if a LLM, designed to keep you entertained, has given you a reasonable explanation.

NO !
It's not reasonable at all.