How does Time travel work in Harry Potter universe?

Question

In Harry Potter and the Prisoner of Azkaban the logic behind time turner travel seems to obey a Stable Time Loop or Causal Loop, where you fulfill what has already happened.

However in Harry Potter and the Cursed Child,

after the reintroduction of time travel, time turners now seem to work in a Back to the Future/Time Cop kind of way, creating alternative timelines, even though in the end they fix them.

My question is: How does time travel really work in the Harry Potter universe? Are these two canon works really compatible? Should we dismiss incompatibilities as plot holes or is there really a good unifying explanation?

Answer 1

TL;DR: Magic

I think the easiest way to reconcile this is by thinking about what was changed, and how far back they traveled.

said Dumbledore quietly. ‘Hasn’t your experience with the Time-Turner taught you anything, Harry? The conse- quences of our actions are always so complicated, so diverse, that predicting the future is a very difficult business indeed ... Professor Trelawney, bless her, is living proof of that.

In Prisoner of Azkaban, Harry and Hermione only traveled a few hours back in time, and they fixed or altered their own events that we the reader didn't actually know the outcome to. The events did not have time to have ripples that drastically altered the world around then, and Rowling wanted to tie in a time loop style event.

Scorpius and Albus, on the other hand, went back in time 20 years to firmly established events, which massively altered the course of history and, in one instance, resulting in Albus not even being born.

We know that, even in Prisoner of Azkaban, that Hermione states that these "Back to the Future" style time traveling is possible.

‘Exactly! You wouldn’t understand, you might even attack your- self! Don’t you see? Professor McGonagall told me what awful things have happened when wizards have meddled with time ... loads of them ended up killing their past or future selves by mistake!’

Its clear that even originally time travel could act in this way, however, for the sake of her plot in Prisoner of Azkaban Rowling tied it up neatly in Time loop Scenario.

Answer 2

There are two things going on in HP Universe re: time travel.

Croaker's Law (in-universe) and unique time turners:

Cursed Child does establish that the Time Turners used by Albus and Scorpius (and...others) are distinctly different from the kind Hermione used in Book 3 and the collection that was destroyed in Book 5. So...some hand waving makes it moderately consistent.

Draco: No. My father. He liked owning things that no one else had. The Ministry's Time-Turners -- thanks to Croaker -- were always a little vaninlla for him. He wanted the ability to go back farther than an hour, he wanted the ability to travel back years.

It is said in the text, that going back so far back, the changes there ripple forward in time:

Scorpius: Have you heard me, Albus? This is bigger than you and your dad. Professor Croaker's Law - the furthest someone can go back in time without the possibility of serious harm to the traveler or time itself is five hours. And we went back years. The smallest moment, the smallest change, it creates ripples. And we - we created really bad ripples.

Additionally, I don't believe there is evidence that there are 'alternate' realities with co-consistent timelines. It seems like all of time is changed and only the people journeying via Time Turner remember their original reality.

Answer 3

Time travel is complicated

The effects of time travel in Harry Potter depend on a variety of factors. As noted on Pottermore (preserved here) traveling back more than a few hours is likely to have serious repercussions.

As our investigations currently stand, the longest period that may be relived without the possibility of serious harm to the traveller or to time itself is around five hours.

They even mention this in the play itself:

SCORPIUS: Have you heard me, Albus? This is bigger than you and your dad. Professor Croaker’s law — the furthest someone can go back in time without the possibility of serious harm to the traveler or time itself is five hours.

Of course, in The Cursed Child they traveled back far more than a few hours.

Further, Rowling established the possibility of altering the timeline before Cursed Child, both in Prisoner of Azkaban (as discussed in another answer) and on Pottermore:

What is more, her five days in the distant past caused great disturbance to the life paths of all those she met, changing the course of their lives so dramatically that no fewer than twenty-five of their descendants vanished in the present, having been “un-born”.

In addition, there is the general principle that, as with all things magical in Harry Potter, the ramifications of meddling in fundamental issues of magic can be very unpredictable. As Saul Croaker says on Pottermore:

"Just as the human mind cannot comprehend time, so it cannot comprehend the damage that will ensure if we presume to tamper with its laws."

Basically, sometimes you get a stable time loop, sometime you get a change in the timeline. No one knows why, and that's why it's an excellent idea to avoid time travel.