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.

Time travel as portrayed in any scfi situation I have ever come across is not possible in our universe.

It is conceivable in the following way in a differently constructed universe.

Imagine (or get MigL to imagine) that you are walking down a road and come across an obstruction, completely blocking the road - say a fallen tree, wall or landslip.

Happily there is a side road just before the obstruction so you can turn down this side road until you come to the next road parallel to the obstructed one and continue your journey along that road.

You could then turn down another connecting side road to return to your original road.

Solid objects can't pass through each other, which is why the road is blocked.
However you can side step because the situation I have described is 2 dimensional in space, even though an individual road is one dimensional.
There is a second dimension in space for you to travel along.

But our universe has only one time dimension so you are stuck with it, like you would be along the road if there was no side turning.

Any form of loop requires 2 (or more) dimensions.

There are two famous problems - riddles in topology that you may have heard of.

The Koenigsberg bridges problem and the connection of 3 services to three houses problem, which can be solved in 3 dimensions but not 2 in order to avoid loops in space.

There are also more complicated situations in 3 dimensional space that can be solved in 4 D to avoid loops.
We call these knots.

https://www.britannica.com/science/Konigsberg-bridge-problem

https://en.wikipedia.org/wiki/Three_utilities_problem

Edit

Oh and don't believe what AL tells you as it is often wrong, although it can be useful if used with caution.

Did you read the disclaimer that comes with all of them ?

It is not gospel.

Edited September 12Sep 12 by studiot

In my opinion parallells between the Potter universe and LLMs like those in ChataGPT are more obvious in the Chamber of Secrets than in Prisoner of Azkaban. After a misadventure, that includes a flying Ford Anglia, Ron Weasley's wand malfunctions and starts to mimic an LLM; when prompted to produce something useful it often spits out crazy sh*t.

IMO time travel is not likely to ever be possible because of the amount of energy required to rearrange the universe to a past (or future) configuration. Furthermore, that configuration will only be similar and not identical, kind of like putting Humpty Dumpty back together again where you would be fortunate to even find every atom of his being, much less reassemble it all in the manner identical to his former self. Also, the future is very much dependent on the past, every event has causation.

If that is true, you couldn't have any "loops in time" because whatever time you are in is THE time and no other exists until you rearrange the universe again to be in a different time. That means the past can't be changed because as soon as you go back, it is no longer the past and you are now on a different path to a different future. As such, it seems trying to change the past to affect the future by going back is a waste of time (😀) when one could just go to whatever future is desired.

2 hours ago, studiot said:

or get MigL to imagine

I actually have a very active imagination @studiot , but, like yourself, I'm aware of the limitations.
Time travel is allowed in 3S+1T dimensions, because of the interconnection between Time and Space.

You and I each have a 'wormhole machine' and we open a wormhole between us.
You and your machine get on a spaceship and fly to another star system, all the while talking to each other through the wormhole, as we enjoy our conversations so much, while 1000 years pass.
Once you get there you realize you miss me a lot, and decide to step through the wormhole to get back, and you find I am the same age as you saw through the wormhole.
In effect, you have travelled through a Closed Timelike Loop, and gone back 1000 years in time.
All valid, according to GR ( and K Thorne ).

Only problem is 'wormholes' are impossible to keep open ...

( no I didn't ask an AI about this )

50 minutes ago, MigL said:

I actually have a very active imagination @studiot , but, like yourself, I'm aware of the limitations.
Time travel is allowed in 3S+1T dimensions, because of the interconnection between Time and Space.

You and I each have a 'wormhole machine' and we open a wormhole between us.
You and your machine get on a spaceship and fly to another star system, all the while talking to each other through the wormhole, as we enjoy our conversations so much, while 1000 years pass.
Once you get there you realize you miss me a lot, and decide to step through the wormhole to get back, and you find I am the same age as you saw through the wormhole.
In effect, you have travelled through a Closed Timelike Loop, and gone back 1000 years in time.
All valid, according to GR ( and K Thorne ).

Only problem is 'wormholes' are impossible to keep open ...

( no I didn't ask an AI about this )

I think you miss my point and what you are describing is not quite the same situation as described in the OP.

My point was that in order for a material object to move along a given singe dimension continuum the path in that single continuum dimension has to be clear (as in unobstructed by other material objects).

Alternatively the object has the leave the defined universe (single continuum dimension) travel in some other universe and return to the original universe somewhere (somewhen) else.

34 minutes ago, studiot said:

Alternatively the object has the leave the defined universe (single continuum dimension) travel in some other universe and return to the original universe somewhere (somewhen) else.

Oh ... like a wormhole ?
In GR, spacelike ( outside light cone ) paths that defy causality allow for travel through time 'around' an event.

No eternal loop. I hope this diagrammatics helps explaining it without much wording on my part (H&H obviously stands for "Hermione and Harry"):

I don't think J. K. Rowling was picturing GR when writing her book, but she did manage to make her idea more or less according to popular sience and decent science fictional accounts.

https://en.wikipedia.org/wiki/Spacetime_diagram

41 minutes ago, joigus said:

I don't think J. K. Rowling was picturing GR when writing her book

However GR does offer quite a few 'solutions' to the EFE where CTCs manifest, including these

• the Misner space (which is Minkowski space orbifolded by a discrete boost)

• the Kerr vacuum (which models a rotating uncharged black hole)

• the interior of a rotating BTZ black hole

• the van Stockum dust (which models a cylindrically symmetric configuration of dust)

• the Gödel lambda dust (which models a dust with a carefully chosen cosmological constant term)

• the Tipler cylinder (a cylindrically symmetric metric with CTCs)

• Bonnor-Steadman solutions describing laboratory situations such as two spinning balls

• J. Richard Gott has proposed a mechanism for creating CTCs using cosmic strings.

  From Closed timelike curve - Wikipedia

4 minutes ago, MigL said:

However GR does offer quite a few 'solutions' to the EFE where CTCs manifest, including these

• the Misner space (which is Minkowski space orbifolded by a discrete boost)

• the Kerr vacuum (which models a rotating uncharged black hole)

• the interior of a rotating BTZ black hole

• the van Stockum dust (which models a cylindrically symmetric configuration of dust)

• the Gödel lambda dust (which models a dust with a carefully chosen cosmological constant term)

• the Tipler cylinder (a cylindrically symmetric metric with CTCs)

• Bonnor-Steadman solutions describing laboratory situations such as two spinning balls

• J. Richard Gott has proposed a mechanism for creating CTCs using cosmic strings.

  From Closed timelike curve - Wikipedia

I absolutely agree. However, and for the sake of good-old fantastic narrative, it'd better be one in which Sirius Black keeps on living his merry life instead of perpetually falling back to a life-threating situation. At least that's what I hope JKR had in mind. 😅

Never actually read JKR, or watched those dreadful movies.
Fantasy is not my 'thing'.

And the fact that GR doesn't disallow it, doesn't require a logical, or reasonable, explanation to the OP.

Sorry I mentioned fantasy. My point was one of logical consistency. I think the story as far as it goes, is logically consistent and does not require an infinite loop in time, which would also be logically consistent, but at variance with the narrative.

I'm not that terribly interested in what ChatGPT has to say about it at this point. That doesn't mean I'd be terribly surprised if it got it right either.

Even light itself is subject to the constraint I mentioned.

Light travels along worldlines orthogonal to the time axis and is obstructed where ever its world line intersects that of a material object.

2 hours ago, studiot said:

Light travels along worldlines orthogonal to the time axis

Are you sure ?
On a time-distance graph it travels along a 'slope' of 186000 if using miles, 300000 if using kilometers, and 45^o if using normalized units.
Orthogonal is 90^o, implying 'instantaneous' travel.

1 minute ago, MigL said:

Are you sure ?
On a time-distance graph it travels along a 'slope' of 186000 if using miles, 300000 if using kilometers, and 45^o if using normalized units.
Orthogonal is 90^o, implying 'instantaneous' travel.

Relativity dear sir.

Photons do not experience time, all their journeys are executed in zero photon time.

2 minutes ago, studiot said:

Photons do not experience time, all their journeys are executed in zero photon time.

There is no valid frame where that is true.
So who can observe this ?

Any discussion of physics is moot; this is a work of fiction, which doesn’t have to obey the laws of physics. Further, it involves a particular type/school of magic, which most definitely does not.

All you can ask is that it be logically self-consistent under some cursory level of scrutiny, to the point you can suspend disbelief, and I think it is. They go back in time and experience the three hours again in a different physical trajectory, and the individuals in the first timeline can observe themselves in the second.

The unresolved issue is whether they have freewill in the second pass through the timeline, because there is interaction between them . e.g. since, in the first timeline, they never observe their second-pass selves, they are not free to remain in plain sight in the second pass, but we don’t know what, exactly, compels them to make the right choices and execute the correct actions. When they e.g. throw something, it must hit the target that was struck the first time around. The issue is determinism, not physics.

In any case, if you want to discuss relativity, though, the concept should be pseudo orthogonality. But I agree that the problem is just logical consistency as far as suspension of disbelief goes.

Leaving free will aside, there's the question of what would have happened had their past selves spotted them. I can think of thousands of alternative futures going on. One of them could be Hermione and Harry telling their past selves something like 'don't worry about this; it is a kind of magic you're still not familiar with, you'll understand later'.

2 hours ago, MigL said:

  4 hours ago, studiot said:

Light travels along worldlines orthogonal to the time axis

Are you sure ?

@studiot is incorrect. Lightlike vectors are not orthogonal to timelike vectors. As null vectors, lightlike vectors are orthogonal to themselves. A vector that is orthogonal to a timelike vector is spacelike.

4 hours ago, swansont said:

Any discussion of physics is moot; this is a work of fiction, which doesn’t have to obey the laws of physics.

Aw, what do I know.
I have never seen the movies or read the books.
My 'suspension of disbelief' in time travel is deeply rooted in Star Trek.
( and don't get me started on parallel universes where Spock sports a full goatee )

3 hours ago, MigL said:

Aw, what do I know.
I have never seen the movies or read the books.
My 'suspension of disbelief' in time travel is deeply rooted in Star Trek.
( and don't get me started on parallel universes where Spock sports a full goatee )

It's a Van Dyke! I thought Mirror Spock looked great with one.

The best time travel plot, despite the usual logic holes you can drive a bus through, is ST IV.

Don’t tell me, you’re from outer space.

No, I’m from Iowa. I only work in outer space.