Crossing your own timeline, changing the future - how does that work?

There are two logical ways of dealing with time travel paradoxes:

• Stable time loop. When you travel to the past, whatever you do, you won't actually change anything (which pretty much implies there is no free will).

  In fiction, the way this is often done is that the time traveller attempts to change the past, but doesn't succeed, because it was him who caused the final outcome in the first place. Or something like that.

• Alternate timelines. When you travel back in time, you cause the creation of an alternate timeline. So there are now two timelines: the one where you left and the one where you arrived. This means that you can do anything and it won't change the original timeline, so no paradoxes are possible.

Though many films and TV shows (including BTTF and Doctor Who) don't use any of the two approaches and instead use approach that doesn't make sense (people slowly vanishing, monsters killing people because change occured, but only sometimes).

My belief is that the audience is guided towards the nonsensical belief that there are two dimensions of time - ordinary time, and "meta-time" - that is, that before "now" in "meta-time", the universe had such-and-such a history, but one second later in "meta-time", history was "changed", and the past became a different past.

This doesn't actually make sense from a physics point of view, and they are usually careful not to be explicit about it.

I am not talking about "personal time" - how time subjectively appears to a character - although it is easy to get confused between "personal time" and this idea of meta-time, because they are usually coterminous from the point of view of a particular protagonist.

The only way to make it really consistent is if the protagonist who "changes the past" is really God, and everything else is effectively just a figment of his imagination, or a dream in other words. Otherwise, as soon as you start thinking about what would happen if someone else also "changed the past", it all falls apart, because the "personal time" theory doesn't fit.

The highest voted answer makes sense, but it seems to omit a third possibility, which happens to be the theory I subscribe to.

There are many theories. I like this one the most because it makes sense (to me) and is consistent with how the (real world) universe tries to solve similar paradoxes, e.g. when two objects try to occupy the same space at the same time.

First of all, I think we can agree that if there is no paradox, there is no problem. In other words, everything that's not a paradox can be assumed to work, since it doesn't create any problems. We only need to consider how the universe handles near-paradoxical situations.

The universe will do everything it can (including breaking its own rules) in order to avoid a paradox. However, the universe will always favor using the path of least resistance (= the option which requires the least amount of breaking the rules).

Let's use the grandfather paradox. I go back in time, and try to kill my grandfather (before my father was born) by using a sword. The universe cannot allow that, since it could create a paradox. Therefore, I am unable to lethally wound my grandfather.

• When you try to force two objects to occupy the same space at the same time (by pushing really hard), you simply cannot do this. The objects will break long before you'll be able to have them occupy the same space.
• When you try to bring two very strong magnets (with the same polarity) together, they will not allow you to do that. Whenever you bring them close, the magnetic force tends to make you veer off.
• If you use tremendous force, you can bring the magnets together, as long as this tremendous force is (1) bigger than the magnetic repulsion force, (2) smaller than the force needed for the magnets to break and (3) continuously applied.

Therefore, if I try to stab my grandfather, the universe will make my sword veer off course, missing my grandfather. As much as I try to stab him, the universe will provide a counterforce. Just like how a magnet uses force to repel a magnet of the same polarity, the universe will use a force to repel the action that invariably introduces a paradox.

Suppose I don't intend to lethally wound my grandfather, I only stab him on the hand. Then the universe has several options to deal with this:

• If this wound does not change my grandfather's future (he will still end up having my father, my father will still end up having me), then the universe allows it. There is no paradox.
• If this wound precludes my grandfather from having my father (e.g. his injury makes him use his other hand, therefore not spilling the drink that he's supposed to spill on my grandmother when he is supposed to meet her), then the paradox should be equally disallowed (similar to when I try to lethally wound my grandfather).

Note that I mentioned how the universe favors the path of least resistance. Since the universe is "inventing" a force that would make my sword veer off course, that requires X amount of force. But if the universe has a way to avoid the paradox using less force (less than X), then it will favor this alternate route.

If the force needed to veer the sword off course is greater than the force needed to knock over that drink and spill it on my grandmother (thus introducing my grandparents, even if he wasn't the one who spilled the drink), then the paradox can be resolved this way and the universe will favor knocking over the glass as it is the path of least resistance.

This is consistent with Back To The Future.

• Marty mistakenly intervenes in how his parents fell in love, thus endangering his future. However, the universe has allowed this to happen, as no (unavoidable) paradox has yet been created.
• Marty does start fading away at the end of the movie, because the paradox is getting closer and closer to becoming unavoidable. For example, if Marty took several years to get his parents to fall in love, then they probably would have had Marty at a later stage in life (thus creating a paradox).
• However, so long as Marty's parents are still able to fall in love, on time to give birth to Marty at the right time, the universe has not yet deleted Marty, as he is still possible.
• Marty ends up fixing the problem by getting them to fall in love in a different way. Marty has changed the past, but in a way that the future is unaffected. Changes have been introduced, but no paradox, and therefore the universe does not intervene.

This is the same as the drink that gets spilt on my grandmother. Both the spilt drink and Marty's parents falling in love invariably leads to my grandparents giving birth to my father, and Marty's parents giving birth to Marty.

Minor note: In my example, the glass gets knocked over by the universe. In BTTF, Marty is the driving force behind the correction. However, it's possible to argue that the universe helped Marty along in order to achieve his goal (e.g. making him run faster just so he gets to his destination on time, if being late causes the paradox to become unavoidable). This possibility only applies if helping Marty costs less effort than the universe fixing it by itself.

This is also consistent with Doctor Who.

• In the episode where they are trapped inside a dying TARDIS, the Doctor, Clara and three guests are being chased by monsters (who look like burnt zombies).
• It is revealed that these burnt zombies are actually future Clara and the future guests, who have been burnt by the TARDIS' main reactor.
• Two zombies are attached to eachother. The Doctor realizes that these are the two remaining guests (the third one was already dead).
• The Doctor tells the alive guests to never touch eachother again, because not touching eachother makes it impossible for them to fuse together, thus creating a paradox (the Doctor wants to create a paradox here).
• As long as they never touch, their future selves (the merged zombie) is impossible. And if it is impossible, then the universe should delete that future (similar to how Marty fades once he becomes an impossible future).
• This works for a while, and the future seems to be rewritten. However, the guests forget about not touching eachother, and touch eachother. As if by force, they are immediately joined together and burnt, becoming the burnt zombies.

This force was supplied by the universe. Rather than deleting the future zombies (which takes a lot of effort to rewrite the future), the universe favors bumping the two guests together, as this requires less force and it ensures that the future is actually correct and therefore does not need to be deleted.
Note that Clara has managed to avoid her burnt future. Because the guests have managed to stall the inevitable (touching eachother) long enough, they have changed the future enough to delete burnt Clara (as she is no longer possible), but they did not stall long enough for their own futures to be rewritten.

I can't speak to Looper, as I haven't seen it.

Conclusion

That's proof of how it should work, according to me. We've seen both cases: trying to prevent changes to the future (BTTF) and trying to create changes to the future (Doctor Who).

In both cases, the universe applies the same rules: it maintained logical consistency at all costs, even if that means it has to invent a "phantom force" (which breaks the rules of the universe, specifically the first law of thermodynamics). In order to minimize how much it breaks its own rules, the universe tries to apply the least amount of "phantom force" (= the path of least resistance).

This is a variation of Flater's answer about the universe "preventing" the paradox. At first I was going to comment that it requires a sort of "God" or "Deus Ex Machina" to intervene on behalf of the plot. But think of it slightly differently:

Quantum physics tells us that there is an inherent randomness in the universe. Maybe someone with more knowledge of it can explain it better, but essentially each action and object is actually the average of zillions of probabilities. So while two things might appear identical, at a subatomic level they are completely different.

Now at first glance, the Grandfather paradox is an infinite loop. But what if because of the quantum randomness, each iteration is actually different at a quantum level if not at a macro level. This means that there is an infinitesimal, but non-zero chance that you will fail to kill your grandfather. (Or fail to travel back in time)

But with infinity, even the ridiculously improbable will eventually happen. So even if it takes a gazillion journeys through the time loop, one will eventually occur where you fail to kill your grandfather. And since this one does not prompt a recurrence of the loop, this is the one that will "stick".

You'll forget all the iterations of the loop that have been replaced by this one. This will only happen with paradoxes of course, because if there isn't a paradox there isn't an infinite time loop.

Because it's a time loop, all occurrences of the loop happen at the same time so you don't notice the bazillions of epochs that the loop has been through. So it will appear that the universe or some power does intervene to prevent paradoxes.

If the time travel is branching, then it needs no explanation, but if it's linear, then I'd imagine it's because time travelling protected them? For example, and I hope this is not just in the CW show, the Reverse Flash, mortal enemy of the Flash (I hope you could've figured that one out on your own), is able to basically exist in every time period because the Speed Force protects him and there's versions of him... everywhen?

But Marty began to disappear in BTTF, whereas Reverse Flash isn't affected at all in his time travelling.

Different worlds have different rules so it depends on the specific universe.