Talking about time travel as a realistic scientific possibility seems... far fetched to me. But I do love conversations about different models of time travel in fiction.

For me, in fiction, there are 3 basic models of time travel:

1. One univerese, you can't change the past, just re-enact it. This is like 12 monkeys. When you go into the past, you can certainly do stuff and feel like you're making choice, BUT those choices are already necessarily part of that past - your actions during your time travels are a necessary part of the past and were already a part of your history, you just didn't know it.

2. One universe, you CAN change the past. This is probably what most people imagine when they talk about time travel. Pretty sure Back to the Future was like this. When you go back to the future, the future you go back to is different from the future you came from, because the past is different now.

3. Parallel timelines. When you go back to the past, you're not going into your OWN past, you're jumping into a parallel universe that's the same as your universe, but in the past. You can make choices in this universe that are different from the past of your own universe, BUT your own universe is still chugging along into the future without being affected by these changes. There are actually some REALLY interesting things you can say with this type of time travel. The Avengers End Game movie kind of had a model of time travel like this.

Those are the basic models, in my view. Some movies are kinda inconsistent with which model they choose. Some movies sort of mix-and-match. The recent film The Flash actually has an interesting model, that's sort of a combination of 3 and 1, with intersecting timelines which turn into spaghetti when you mess with the past.

But if iteration isn't permitted — sime

Not sure what you mean by iteration, or 'permitted'. It's a loop, an instance of reverse causality. It's one loop in our example, and it just is, per non-presentist framing of the situation. There is no 'changing of the past'. I gave an example of a worldline that traverses the loop twice, so that might constitute iteration, but you don't seem to mean that sort of thing.

if iteration isn't permitted then is sending information backwards proof of a loop? — sime

Not sure what kind of evidence you'd consider proof. We have a CTC, which probably involves some huge machine that impossibly makes the right kind of exotic matter needed to hold some sort of pipe open, an effort that must be made at both ends. The empirical appearance of that is something like a white hole, an event horizon out of which stuff comes, but nothing can go in.

On the smaller scale, we have a crystal ball which gives information from 'the future'. It's the same thing, but scaled down to effectively a ticker tape. Yea, a human could pass through that, but only if scan/copy/reproduce technology exists.

So evidence (proof as you call it) would constitute some kind of information of something unexpected that turns out to be verifiable in subsequent time. And yes, sports scores (and to a lesser degree stock prices) are kind of the default thing of this sort, having been used in discussions and fictions.

For if contradictions are ruled out a priori, then what justifies the use of a loop topology?

We wanted an example of time travel that didn't directly contradict Einstein's theories. It is a straw at which we can grasp.

E.g suppose that it is possible to send sports results backwards in time. If this action "changed" history,

If it changed history, then it isn't a CTC (a loop). It would be more of a branching interpretation where multiple histories are meaningful. You can't prove that the branching interpretation is time travel either since it is valid to interpret it as sideways travel, not backwards or forwards.

then many people (including myself) would interpret this as merely referring to the action producing significantly non-local effects in our present, so that we can preserve the meaning of the word "history" as referring to immutability.

All actions produce effects. Non-local meaning retro-causal? But you've no evidence of history having been changed unless a history book (the sports score say) comes back, and is demonstrably different that the changed history that subsequently plays out. But in that case, you just assert that what came out of the portal wasn't from the future, but just random wrongness. Sports outcomes very much would be subject to change by a machine predicting its outcome. In the CTC, there is but the one history, consistent with the information from the loop.

On the other hand, if the action cannot "change" history, then what is the proof that anything has actually been sent backwards?

The sports game being correctly predicted is pretty good evidence, albeit not proof.

To return to the presentist reasoning I sketched earlier, It is logically consistent to believe that the past of our world is generated 'on the fly', as in a roguelike video game that generates the content of the game world as an effect of the adventurers present actions. — sime

I'm unfamiliar with such games, but the stance seem to be a valid one. I've been known to argue that given a premise of the principle of locality, ontology sort of works like that, but caused by interactions, not actions or knowledge.

In such worlds it might appear that information is sent backwards. E.g the adventurer is in an unknown dungeon with a closed door. Only after he opens the door does the game decide what lies beyond the door.

Not at all unlike Schrodinger's cat. But that's not information being sent backwards. Maybe the magic spell is an exception to that, but I don't know the details. At no point in the past does the thing behind the door get information about the future actions of the adventurer, any more than does the cat.

Notably, players don't typically interpret "history change" as time travel

That's good because nobody is finding himself suddenly in a prior time.

when an adventurer uses a magic spell to re-roll the state of the dungeon around him, but merely as magic affecting the global state of the present. Amusingly, a philosophical dispute once arose between players of the single-player roguelike game Nethack. In that dungeon crawler there exists the "Potion of Amnesia", which if drunk by an adventurer causes the game to delete it's record of the adventurer's knowledge of the game world,whilst leaving the actual game world in tact, meaning that the player must rely on their personal memories when their adventurer navigates and relearns the content of old locations.

The monsters behind the door don't get re-randomized? Does it place the player in the prior state as well, doors unopened, health reverted, dead friends un-killt? That would arguably be a time travel spell, but unprovable because information (the wiped memory) didn't go back with it.

But isn't that cheating? Shouldn't a true potion of amnesia change the world itself? Players are divided.

It's just leverage of a dualistic mind. The adventurer's 'mind' (wiped) and the player's mind (not wiped).

For me, in fiction, there are 3 basic models of time travel:

1. One univerese, you can't change the past, just re-enact it. This is like 12 monkeys. When you go into the past, you can certainly do stuff and feel like you're making choice, BUT those choices are already necessarily part of that past - your actions during your time travels are a necessary part of the past and were already a part of your history, you just didn't know it. — flannel jesus

Sounds like the epiphenomenal time travel first mentioned in the OP. There is zero violation of physics with that one, and is equivalent to stepping out of a cinema to cross the hall and watch a different movie, perhaps the same one, but back at the start of the story.

2. One universe, you CAN change the past. This is probably what most people imagine when they talk about time travel. Pretty sure Back to the Future was like this.

Yes, the fictions are kind of full of this, but it is empirically a branching interpretation. OK, BTTF has the photo or something that is evidence of it being one universe, but that trick is entirely inconsistent with any valid view.

When you go back to the future, the future you go back to is different from the future you came from, because the past is different now. — flannel jesus

That part is empirically consistent with the branching model, not any one-universe model, unless the machine has omnipotent powers to actually recreate the entire universe. This whole bit was discussed (ad nauseam) in the other thread, coming to one conclusion that this sort of time travel (one universe, getting altered) has a very low probability of survival.

3. Parallel timelines. When you go back to the past, you're not going into your OWN past, you're jumping into a parallel universe that's the same as your universe, but in the past. — flannel jesus

That's the branching interpretation. The parallel universe has no history prior to your appearance, but they don't know that.
It is arguably not time travel (per my prior arguments), but rather sideways travel.
They can't be travel to pre-existing parallel lines, because if you can travel to those, then one can travel back to the other one from which you came, which is still a loop, with all its problems.

You can make choices in this universe that are different from the past of your own universe, BUT your own universe is still chugging along into the future without being affected by these changes.

That statement presumes that universes 'chug along'. I agree that the old world still exists, and perhaps 'you' don't even leave it when you travel to another world. There's two ways it can happen: You vanish from the one world, or you don't, and there is now two of you, one in each world. The latter is far more consistent with MWI and with physics. I've not really yet done a post on this point since nobody has expressed interest in that scenario until now.

You and others have proffered fanciful alternative realities, curly time, elastic time, ragtime, Miller time or whatever, which I admit to not reading with close attention.
Bottom line: No, you can't travel in any of them. — Vera Mont

How very elegantly argued. I see you even have gained toady support.
I personally came to the same conclusion, but only due to the inability to deliberately create/manipulate the exotic matter necessary, and the OP (had you actually read it) makes the necessary presumption that this restriction isn't there, it having never been proven.

I consider the Butterfly effect as a kind of philosophy of time travel. In the movie The Sound of Thunder, a hapless time traveler in the age of dinosaurs steps off a designated artificial path and crushes a flower or something tiny. He then returns to his time and finds a different President and a city overgrown with vines and lions roaming the streets. In mathematical terms this is called SDIC, sensitive dependence on initial conditions, and is a feature of chaos theory.

But not much is made of situations that are not as sensitive. Stanislaw Lem had an Ergodic theory of time travel in which minor disturbances in the past are evened out over time and are insignificant.

Mathematical models of both these "philosophies" can be constructed, probably using a Banach space with vectors being "incidents". Time might be an operator with features we might not think of out of this context. For example if time contracted events even slightly Ergodic theory could prevail. The contractive element of time might stem from relativity, but probably not. A Banach space has certain conditions to be met.

Here is a path for philosophical conjecture that is more accessible than rambling endlessly in wormholes and loops.

I personally came to the same conclusion, but only due to the inability to deliberately create/manipulate the exotic matter necessary, and the OP (had you actually read it) makes the necessary presumption that this restriction isn't there, it having never been proven. — noAxioms

Oh, okay. I thought you said

First of all, the time travel has to at least be a tiny bit plausible under physics — noAxioms

which it isn't
and

The alternative is magic, and if you posit magic, you can also conclude anything you want. — noAxioms

which is what you et al proceeded to do.

Now that's cleared up, carry on.