Other is performing pretty well, but what exactly are you expecting other to be?
@DanielGallant @Jono3h @Ansel

How would this market possibly distinguish between the options?

For example: if someone hops in a time machine and goes back in time to kill their own grandfather, and nothing apparently happens, then Fixed timeline, Dynamic timeline, and Multiverse are all still plausible from the perspective of anyone other than the time traveler.

In fact, I can't think of any way to confidently distinguish between these three options using evidence without being the time traveler myself. Once something goes in a time machine and disappears, no matter what happens after that point all three mechanics remain plausible.

Fixed timeline: Any attempt to prove that it isn't Fixed timeline results in some failure of the time machine after it disappears, possibly along with some other time machine from some unknown point in the future resolving any discrepancies while leaving behind false evidence that it isn't Fixed timeline. This is the choice of conspiracy theorists.

Dynamic timeline: Any attempt to prove that it isn't Dynamic timeline is clearly impossible, since any possible evidence could've changed and therefore isn't valid as proof that it didn't change.

Multiverse: Any attempt to prove that it isn't a Multiverse is fraught with difficulty, since there's no way to distinguish between "this time machine came from our universe" and "this time machine came from one of trillions of universes nearly identical to ours in every way." Alternatively, if no time machine ever arrives in our universe but only ever disappears (as is often implied by a Multiverse), then there's no way to distinguish between this scenario and one where the time machine is actually a "stop existing" machine.

Perhaps the theory leading to the discovery of time travel could be determinative, but I highly doubt it. If this market is relying on the theory being opinionated on this, then how will it resolve if the theory is ambiguous, or allows for multiple differing mechanics?

@ForTruth Agreed that it may be difficult. In the unlikely event that this market resolves at all, we'll just have to use whatever is the best evidence available. In particular, if the only time travel that has been demonstrated is a machine that makes things disappear (but never reappear), I wouldn't consider that proof of time travel at all. The reappearing part is definitely critical here, and once you have that part I think a lot of the ambiguities go away because you can just "ask" the time traveler. If they're able to perfectly predict the future and nothing they do causes any deviations from it, then it must be fixed timeline. If they're able to "affect themself" by changing things in the past then it's probably dynamic timeline (this tends to lead to a lot of paradoxes and so seems unlikely, as reflected in the current price, but you never know!). And if they can change things without any weird paradox-like stuff in play it's probably multiverse.

@ForTruth I don't think it would be as hard as it sounds to distinguish between fixed timeline and multiple timeline. You don't have to be a time traveler yourself if you have even minimal trust in the word of time travelers (which is not really any different from resolving any market based on a scientific conclusion by assuming that the scientists are telling the truth).

In fixed timeline, time travelers cannot change the past, and will observe causal loops. You may not even have to be a time traveler to observe the effects of causal loops created by time travelers. Any attempt to change the past will be observably thwarted: You can an experiment that says, "What happens if we try to change the past?", and if it never works, that's pretty good evidence that your time travel method uses a fixed timeline. If you conspicuously can't find anyone willing to do the experiment, that's probably also good evidence for it.

In multiple timeline, changing the past should be trivially easy relative to time travel itself, and you shouldn't observe causal loops.

Here's an experiment by which you can differentiate the two:

Suppose your time-travel method allows you to open wormholes to the past. You decide to create one on a billiard table and knock a billiard ball into the wormhole. But there's a catch: If the ball travels into the wormhole on the trajectory that you originally knocked it in, then it will come out of the past wormhole on a trajectory that intersects this original trajectory in a way that would knock a ball traveling on this trajectory away from the wormhole.

If the fixed timeline is correct, then you have to observe one self-consistent chain of events. The ball can't go into the wormhole on the original trajectory you knocked it on, because then it would knock itself off of this trajectory, a contradiction. It also can't be knocked completely away from the wormhole by its future self, because this would again lead to a contradiction. But it can receive a grazing blow from its future self, enough to slightly alter its trajectory so that it enters the wormhole at a different angle - precisely the angle necessary to cause the grazing blow.

If the multiple timeline theory is correct, then in the original timeline, the ball goes into the wormhole on the original trajectory, and no ball comes out of the wormhole in the past to knock it away. This creates a second timeline where the ball from the original timeline comes out of the wormhole in the past, knocking the ball in the new timeline away to prevent it from entering the wormhole. Therefore, you will always observe one of these two events, depending on which timeline you end up in. Neither of these events matches what would happen in the fixed timeline case, so even a single run of the experiment should be enough to distinguish between the two.

Of course, that experiment is based on one particular model of time travel (wormholes), but you should be able to do something similar for any method of time travel.

As for distinguishing from dynamic timeline theory, this seems more difficult, but I think the difficulty comes from the fact that dynamic timeline theory is logically inconsistent in the first place. Which means you don't need to distinguish other possibilities from it.

@A

You seem to be thinking of evidence to prove one of the theories correct, but that isn't how theories work. You should be trying to disprove one of them. This makes it obvious that being able to perfectly predict the future doesn't actually imply fixed timeline: A multiverse or dynamic timeline traveler would be able to predict the future just as well in cases where time traveler actions don't change the timeline. Meanwhile in cases where it seems like the time traveler 'should' have caused the timeline to change, but didn't: well, obviously the timeline shouldn't have changed after all, because it didn't. So the time traveler is simply mistaken about what would cause deviations. After all, if he knows what will happen, and does nothing incompatible with what will happen, then there's no reason to believe he is really trying to change the timeline at all. Meanwhile in cases where the time traveler makes a prediction about the future, and the future is not as they predict, then this doesn't disprove fixed timeline either: obviously the younger version of themself will necessarily make the same false prediction after they travel back in time even if they know it's false, because that's what the fixed timeline theory says will happen.

@PlasmaBallin If I'm reading your experiment correctly, you hypothesize 3 potential outcomes:

1. The ball enters the first wormhole and vanishes. All this proves is that the first wormhole transported the ball somewhere, not necessarily time travel at all.

2. A ball appears from the second wormhole and knocks the original ball off its trajectory. All this proves is that some wormhole from either a different universe or from anywhere within this same fixed-timeline universe is connected to the second wormhole. In fact, if this were the outcome and Multiverse were accurate then we should expect far more unpredictable things to come through the second wormhole than the ball. In fact, there's no real reason to predict specifically a ball appearing at all, rather than say a gust of wind. I'd consider this to more likely be evidence in favor of fixed timeline, just with poor control over which wormhole connects to which and different similar experiments interfering with each other.

3. A ball appears from the second wormhole and knocks the first ball through the first wormhole, such that the physics seems to predict the interaction. Maybe this proves fixed timeline, or maybe it simply proves that there are trillions of multiverse timelines all sufficiently similar to ours that a virtually endless chain reaction occurred.

Personally, I'd expect the ball to simply miss itself. That seems like the statistically most likely outcome, unless we can very carefully control the wormholes and all external conditions. But then, if we have that much control then we're also very likely capable of manipulating present experimental results from the future, which easily explains any misleading experimental results against fixed timeline. On the other hand if it's a Multiverse then no amount of control is enough control to predict the outcome, since we can't control all wormholes in all possible universes.

Ironically, dynamic timeline is the only one that could maybe receive strong evidence, by violating other laws of physics. If, say, a time traveler scarred his past self and a corresponding scar suddenly appeared on the future version. Note that this wouldn't actually disprove the other theories, but it would be strong evidence for dynamic timeline simply because no other theory predicts it.

@ForTruth I mean yeah if you set your standard of proof high enough then you can't really prove anything. It's not really clear exactly what kind of experiments we'd be able to do so ultimately it'll just have to be the best scientific consensus based on whatever we do know.

@A Copenhagen Timeline it is for me then.

@ForTruth The experiment that I proposed would only make sense to do in a single run if you're confident that time travel already works in the first place, and you're just trying to figure out which type it is. It's true that the first outcome wouldn't confirm the existence of time travel itself, and the second outcome could in theory be explained as a coincidence. Though I think the second outcome should still lead you to conclude that time travel exists even after a single run - after all, we know that normally billiard balls do not randomly appear out of wormholes, so it would be staggeringly unlikely for this to happen just as you were performing your billiard ball time travel experiment if it wasn't the result of the experiment in some way.

If you repeat the experiment multiple times, it would confirm the existence of time travel either way. If multiple timeline theory is true, then you should expect that about half of the time, the billiard ball disappears, and the other half, it gets knocked out of the way before entering the portal, since every run of the experiment creates one timeline in which each option happens. There's no sensible theory that predicts this other than the theory that the wormholes are indeed allowing the ball to time travel via branching timelines, so this seems like pretty strong confirmation to me. It's at least as strong a confirmation as any other experiment we can do to test other scientific theories (In fact, I think this is a far stronger confirmation than most IRL scientific experiments give for the theories they support).

If fixed timeline theory is true, we expect the future ball to come out of the wormhole and give itself a glancing blow every time, so observing this in an experiment would confirm fixed timeline theory. It's true that there are other explanations for this, like the infinite timeline theory, though that is a less parsimonious explanation than a single, fixed timeline. Also, in order for the infinite timeline theory to work as an explanation, there would have to be some explanation of why a wormhole from another timeline always appears to give your ball a glancing blow right when you perform the experiment and not at any other time. It could be that it is caused by the experiment itself, e.g., maybe there is a more complicated version of the multiple timelines theory where every run of the experiment actually creates infinitely many timelines, instead of just two, and they are connected in such a way that there is no first or last timeline in the chain. However, there are further tests you could do to rule out such an explanation. You could use a device to probabilistically block the ball from entering the wormhole. Self-consistent time travel predicts that we always observe that either the ball is blocked from entering the wormhole, and no ball comes out of the past wormhole, or the ball is allowed to enter the wormhole but receives a glancing blow from its future self exiting the past wormhole. Infinite timeline theory would not predict this correlation.

Personally, I'd expect the ball to simply miss itself. That seems like the statistically most likely outcome, unless we can very carefully control the wormholes and all external conditions.

Why wouldn't we be able to carefully control the experiment? We can control things to absolutely insane levels of precision in modern physics experiments. Controlling billiard balls to the very low level of precision required for this experiment would be a cake walk. Controlling wormholes obviously depends on how they work, but if the wormholes are so chaotic and unpredictable that they can't be controlled to the degree needed for this experiment, then they probably hardly qualify as a usable time travel method at all.

But then, if we have that much control then we're also very likely capable of manipulating present experimental results from the future, which easily explains any misleading experimental results against fixed timeline.

I don't know what you mean by this. Is the idea that maybe people from the distant future are somehow screwing with our results? I suppose that's possible under fixed timeline theory, but it's also in theory possible for any experiment, and it would be no more likely to happen in this experiment than any other. Plus, there are certain versions of fixed timeline theory where this wouldn't be possible anyway (e.g., any version where you have to actually do something in the past to create the past end of the wormhole - this prevents you from traveling back to an arbitrary time and answers the, "Where are all the time travelers?" dilemma).

On the other hand if it's a Multiverse then no amount of control is enough control to predict the outcome, since we can't control all wormholes in all possible universes.

This is would only be true if the multiverse were so chaotic that any experiment was likely to be ruined by interference from other universes. Since this is not what we observe in real life, we can already rule that possibility out. You don't have to control every possible external factor that could affect an experiment (If you did, it would be impossible in principle to perform any scientific experiment). You just have to know that any external factors affecting the results are doing so to a small degree (which in real-life experiments is quantified as the systematic uncertainty). So maybe the multiverse introduces some systematic uncertainty. That's not fatal to the endeavor.

If, say, a time traveler scarred his past self and a corresponding scar suddenly appeared on the future version.

Yeah, this would probably be strong evidence for any model of time travel that predicts it. Though as it stands, there is no sensible model of time travel that predicts it. It only happens in movies because those movies either don't have an explicit model of time travel or have not correctly worked out the consequences of their model.

@ForTruth in fixed timeline it would not be possible to kill grandfather. Whatever traveller does it had happened. Even if he studies the whole assasination attempt from grandpa's words, and decides to act differently, his decision to act differently was already there in the past, and it lead to this exact survival of the grandpa.

HPMoR has a fixed timeline.

@PlasmaBallin

If multiple timeline theory is true, then you should expect that about half of the time, the billiard ball disappears, and the other half, it gets knocked out of the way before entering the portal, since every run of the experiment creates one timeline in which each option happens.

This seems like a bizarre assumption to me. Why would every run of the experiment create one timeline with each option? Even if you assume that only the experiment can create timelines, and that the timelines are consistently time-synced such that things entering a wormhole always travel exactly the same amount of time backwards regardless of their mass and velocity (even though that's quite the assumption), then runs would be as follows:

1. The ball enters the first wormhole unperturbed.

2. The ball gets hit by the ball emerging from the second wormhole with some extremely high probability p, missing the first wormhole with some extremely high probability p.

3. The ball enters the first wormhole unperturbed with some extremely high probability p.

4. The ball gets hit by the ball emerging from the second wormhole with some slightly less high probability p^2, missing the first wormhole with some slightly less high probability p^2.

...

I hope it's obvious that eventually the vast majority of universes become those where the balls miss each other completely. Alternatively, perhaps they settle into an equilibrium with a glancing blow indistinguishable from your fixed-timeline prediction, although I suspect this is less likely. This is true no matter how perfectly you control the experiment, because you cannot control it that perfectly.

I'll grant that it's possible to build up a preponderance of evidence that fixed timeline is false, as you need to hypothesize more and more elaborate causal chains to explain any observed discrepancies. The problem is that if fixed timeline is true, then such elaborate causal chains are predicted by the theory. That's why I called it the theory chosen by conspiracy theorists. Literally any evidence disproving the theory is actually predicted by the theory by virtue of the evidence having already occurred.

Presume this experiment: Take something out of the time machine. If it's a blank piece of paper, then scribble on it and put it in the time machine. If it isn't a blank piece of paper, then put a fresh blank piece of paper in the time machine. Now, regardless of what you take out of the time machine, it necessarily disproves fixed timeline, unless you break experimental procedure. If a theory predicts that experimental procedure would be broken, then any results can be dismissed as experimental procedure being broken. Assuming fixed timeline is true: What would you expect would happen in this experiment? Experimental procedure being obviously broken or some unknown externality causing the experiment to give misleading results?

Either way, the experimental results are obviously invalid. All such experiments which could disprove fixed timeline are invalid for the same reason: Any disproof of the theory becomes predicted by the theory as soon as that 'disproof' is observed!

HPMoR's fixed timeline is super fun, it almost makes me want our timeline to be a fixed timeline.

But I'd definitely prefer multiple timelines because it makes the possibility of cross-time travel. I want to see alternative histories!

Isn't it possible to prove multiple timelines by making duplicates of something by moving it from one timeline to another? Like if you moved a unique atomic clock from our timeline to another you could show it's the same clock from the exact same point in time as the one in the other timeline

You take atomic clock in timeline A and jump to timeline B in hope to have 2 clocks at a time.

But what if then you find out B version of you took the atomic clock B and jumped away at the same time?

So for the observer you just teleported, but did not break the matter conservation law.

Fixed parallel timelineS model.

Hmm, what about just bringng a cable connection to a Stratum 0 reference clock back in your own timeline & using it to predict the precise time on the clock in this timeline

I do not understand the cable idea.

Do you image timeline-gate as a doctor-strange portal? Otherwise i do not see how cable could be used.

I’m thinking wormholes or something like it will be the most likely way that time travel works yeah

I imagine timeline-gates to be not space-continious.

How substantial does the time travel have to be? Do humans have to be able to go back in time, or would discovering Planck-scale closed timelike curves count? If the former, this is pretty much guaranteed to resolve N/A, but if it's the latter, there's a small chance that they will be discovered.

@JosephNoonan Short duration can count, even very short, but if it boils down to "we did a thing in a lab and read some numbers off a screen" rather than "I went back in time and talked to my great-grandfather" then there needs to be very strong proof that it's really time travel and not just a lab error or some fluke of quantum physics that we don't fully understand yet.

@A Also something like "technically positrons are electrons travelling backwards in time" or similar would not count as time travel if it doesn't actually change any observable properties of the universe for us.

@A Absorber theory being confirmed (perhaps in some more advanced iteration) wouldn’t count either I guess? What if there is strong evidence in favor of a theory that predicts time travel but also predicts that it cannot be possibly observed? By comparison GR solutions like the Schwartschild metric work perfectly behind the horizon at r=rS but also predict that while it’s possible to go there you won’t be able to come back or signal back. In that sense the region behind the horizon exists (within the theory) but is predicted to be inaccessible empirically.

@mariopasquato From what I can understand of absorber theory it wouldn't cause this question to resolve, though if there's a big breakthrough there maybe we'll have to ask some real physicists their opinions. If we don't observe any new time-travel-like phenomena and it's just new math for explaining existing physics that wouldn't count.

I'd be skeptical about any theory that predicts time travel that can't be observed, since how do you know the theory doesn't break down under the extreme conditions that supposedly cause time travel? I think we would need to at least have some kind of direct observation related to the time travel itself in order to resolve this question.

@A Ok perfect! Thanks