In the first episode of Loki, we got to know that there's only one timeline with the story that we've seen so far. Then why are there multiple Loki's in the same timeline and how?
There isn't only one timeline, and this is something that I think a lot of people aren't understanding. Time is still variable, at any point in time people can do any number of things. However, the TVA exist to set time to what the Time-Keepers deem it should be. That means that if someone veers off the set course as deemed by the Time-Keepers those Variants are removed and time is reset back to what it should be.
Miss Minutes: But then, the all-knowing Time-Keepers emerged, bringing peace by reorganizing the multiverse into a single timeline, the Sacred Timeline. Now, the Time-Keepers protect and preserve the proper flow of time for everyone and everything. But sometimes, people like you veer off the path the Time-Keepers created. We call those Variants. Maybe you started an uprising, or were just late for work. Whatever it was, stepping off your path created a nexus event, which, left unchecked, could branch off into madness, leading to another multiversal war. But, don’t worry, to make sure that doesn’t happen, the Time-Keepers created the TVA and all its incredible workers. The TVA has stepped in to fix your mistake and set time back on its predetermined path.
Loki, Season 1 Episode 1, "Glorious Purpose"
We learn in the first two episodes that there are multiple ways for Variants to stick around and not be reset. The first is what we see with the Loki we are following. He's been removed from the variant timeline he created and taken to the TVA "outside the flow of time". The second is if a variant is not reset before the Nexus event crosses the red line. Presumably this is what happened with the "Loki" the TVA are chasing.
Miss Minutes: Okay, y’all, let’s review what we’ve learned. What happens when a nexus event branches past red line?
Loki: Very bad things.
Miss Minutes: Come on, Loki. What is it?
Loki: (SIGHS) It’s when the TVA can no longer reset a nexus event.
Loki, Season 1 Episode 2, "The Variant"
After reading various interviews with the creators of the show, I've come to the conclusion that they didn't do a very good job of conveying their actual intent within the episodes themselves.
For example, it appears that the 'Sacred Timeline' is actually a misnomer, and that this so-called 'timeline' is actually a bundle of timelines all flowing in the same general direction; a mini multiverse in effect.
This is visually hinted at by a shot near the beginning of Loki S01E06, where the camera flies within the Sacred Timeline, and then moves out of it and pulls way back, to show it from the side. In the zoomed out shot, the Sacred Timeline looks like a thick beam or stream, but from within, it resembles a tube-like structure composed of many strands.
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You can arguably see further visual hints of this when the Sacred Timeline is shown rapidly branching outward near the end of the same episode. Within those branches, you can see bundles of individual strands, and the further along the branches you go, the more those strands separate out into ever-thinner branches.
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In an interview with ScreenCrush, the head writer on Loki, Michael Waldron, appears to confirm that the Sacred Timeline does indeed contain multiple timelines, with its structure resembling "the intertwined strands of a rope." Moreover, he also appears to clarify that the TVA don't have a problem with alternate timelines in principle, as long they don't produce new variants of He Who Remains.
SCREENCRUSH: Okay, understood. So my question is if there is the one “Sacred Timeline” of the Marvel Universe that the TVA has been protecting for some significant stretch of time, then how can there also be so many alternate timelines and variants as well?
MICHAEL WALDRON: Okay, The best I can explain it is our approach with time travel was the philosophy basically that time is always happening. So there are infinite instances of time always occurring at once. So you and I are having this conversation right now. There’s another instance of us having this conversation 10 seconds ago. There’s another instance of time of us having this conversation 10 seconds in the future. Generally, those three instances — you could literally say they’re all different universes in a way different timelines — are all the same. There are minute little fluctuations in each instance of time. So in you and I’s conversation, five times out of ten, I pick up and I say, “Hello.” And four times out of ten, I say, “Hey, nice to meet you.” And then maybe one time out of ten, I’d say, “Hey man, f— you. I don’t want to do this interview.”
SCREENCRUSH: [laughs] Right.
MICHAEL WALDRON: And that’s just how time works. There’s always like different permutations and instances happening. The TVA has their own barometer, their own gauge of what constitutes a deviation from the baseline, the way it’s supposed to go. The way it went that produced He Who Remains. That is their baseline. And so they are constantly calculating, “Okay, we see how time has always...” If you zoomed in on the timeline, it wouldn’t necessarily look like a straight line. It might look like almost the intertwined strands of a rope fluctuating and spiking here and there. When it becomes a problem for the TVA is when, according to their own rules, when could something branch off in a way that it could actually produce a new timeline that could produce a new version of He Who Remains? That is the practical thing that they’re guarding against. Does that answer your question?
It follows then that the TVA don't automatically object to timelines that happen to produce a female Loki, or a black Loki, or a Loki that looks like Richard E. Grant. They only step in and prune a timeline if one of these Lokis does something -- like killing Thor, or stealing the Tesseract -- that He Who Remains predicts would result in a new variant of himself.
(We still don't know what Sylvie's nexus event was, but it must've been something which threatened to do just that. One plausible theory I've seen floated -- based on the way she was playing with her toys as a child in Asgard -- is that she was possibly more interested in becoming a valkyrie and saving Asgard from dragons, than she was in becoming the villain who would later spark the formation of the Avengers... which would mean she wasn't going to fulfil her proper role in history from the TVA's point of view.)
On top of all this, according to an interview the director of Loki Season 1, Kate Herron, did with Murphy's Multiverse, there were always other timelines existing outside the Sacred Timeline. The way she describes it, the Sacred Timeline was only one of multiple 'trees' within the wider multiverse, and the TVA kept pruning its branches to keep it isolated from the others. But when that pruning stopped in Loki S01E06, the branches from the Sacred Timeline were able to grow far enough to connect with those other, wholly separate timelines, like "bridge[s] to another land."
KATE HERRON: So what we have is like... so, there's the branches, right, which is like the alternate reality. But then something, you'll see it, it's very subtle, but in the very last shot where you see the multiverse, there's like basically other bigger physical timeline branches. So, it's almost like these different separate trees are now connecting, is probably the best, I guess, shorthand way I could have of explaining it. It's almost like the branches of different trees are connecting.
CHARLES MURPHY: Well, that becomes the concern is those branches that will intersect with each other.
KATE HERRON: Yeah, it's almost like a bridge, like, if you imagine the branch... it is like another reality, but like if the branch extends beyond a certain point, it will then connect to other physical timelines. That's the best way I can describe it. Maybe like a bridge to another land, I guess. But if people... that last shot we did, there are other like thicker [branches] that are meant to be like our timeline. And there are other timelines like that, and the branches are the connectors, basically.
I think the image below is probably the "last shot" she was referring to, and I guess I can kind of see what could be three or more 'mini multiverses' (my words, not hers) like the Sacred Timeline now joining up into one, bigger multiverse, but I never would've guessed that's that what I was looking at without having read/seen these interviews.
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The 'Sacred Timeline' doesn't exclude the possibility of multiple versions of the same person overlapping due to time travel. It is essentially a single set of events and outcomes approved by the TVA which can include time-travelling events.
This is explained in episode 1 when Loki questions why The Avengers were allowed to travel through time. When they did, multiple versions of themselves existed in the same times, but the overall outcome of the time-travelling events were approved by the TVA.
Spoiler for episode 2:
And of course, having met the 'variant' Loki being pursued by the TVA, it is clear that it is not the same Loki anyway.
With the sacred timeline if someone steps off and creates a nexus event, they stepped off as that individual. They would then exist in both timelines and the TVA would have to get the variant from the multiversal timeline and reset time as per the sacred timeline.
The variant couldn't change appearance just from stepping off the sacred timeline though. There would have to be parallel (complete) timelines for Sylvie (and the other thousand or so Loki variants) to even exist.
If the sacred timeline is less like a single thread and more like a rope made out of many different threads, does that mean the sacred timeline is made up of all these parallel universes that hardly ever interact, but still follow the same direction of time?
In short, the multiverse is a concept in theoretical science which posits that our known universe exists alongside a potentially infinite number of alternates. In the show, the quantum multiverse theory is adopted, in which a new universe is created when a diversion in events occurs, referred to as a nexus event.
As stated by miss minutes, the original multiverse was plagued by war across the realities in a way similiar to the avengers - pop in, steal an infinity stone, and be back to your own reality with none the wiser, but having completely changed the course of another reality.
Although vague, the presented information states that the sacred timeline was created, probably a single strand of the universe, to stop the multiverse war, most likely time travelers wreaking havoc or exploiting the past peoples with the advantage of knowledge and in the process creating new multiverses which is mentioned to be destablising (destablising as to what though is yet to be revealed).
The entire point of the TVA it seems is to prevent the creation of new multiverses by sticking to a single "sacred" timeline that is apparently for the greater good. If a diversion in events would occur a new parallel universe would be created. This is reflected in the show as any time the TVA enter the timeline area they take great care to cover their tracks and return it to its original state so as to not trigger a multiverse splitting event.
As mentioned in one episode, destructive events take no bearing on the previous state of things and create something anew from its constituents - for example the destruction of a planet bears no memory on the state of its configuration (people, cities, plants) for its contents are essentially atoms. For example it would make no difference if you were at the bus stop or the library if the earth was destroyed - either way we would become atoms in the cosmos, and unless by some miracle of gravity and geometrics, creating of a new universe would be significanltly unlikely, since our atoms will only be absorbed by a neighbouring gravitional body such as the sun or jupiter in which case randomness or entropy would obscure all memory of the previous configuration.
Hence why the second variant is able to obscure herself in the midst of chaos as her presence does not really increase the chances of a multiverse by any significant amount.
So, to answer your question: How is it possible that if only a single universe is allowed there can be multiple variations of the same man?
So the TVA cannot stop the splitting of a universe into two but they can guide the events so that the result of a split recombines into the same outcome and resolves into a single universe once again, as long as the split was not large enough to be irreversible.
For example, if there was by some way of accessing true chance, you could effectively split the universe IF and only IF the outcomes of the dice throw were magnanimous in effect.
For example, thanos when he equips the five-stoned gauntlet, if he decided five fates for the nine realms - obliteration, relocation, preservation, and some others - each with a completely different outcome based on true chance that could not be recombined into the same result after taking effect - then you could effectively create five universes and five Thanos variants.
But the TVA being the TVA would not allow this to continue and would probably guide the entire galaxy in each universe which contained thanos and everyone else in the avengers show into a black hole in which case only the mass of galaxy - unchanged by the split of the universe into five - would be important and that all memory of the orientation of the galaxy would be lost forever, thereby forming the multiverses into a single universe again as the timelines again become identical, as the same mass had been added to the black hole in each case and the resulting effect was the same.
In a nutshell, yes there are multiverses created spontaneously to account for variants, however these multiverses are guided back to the original design or "scared timeline" for the universe by the TVA. As a result these multiverses recombine into the original scared timeline, which is easiest done at the time of the split, before the two parallels universes grow apart and become difficult to recombine to a shared and homogenous destiny (as the show demonstrates by not wasting any time after Loki originally escapes).
At least that's my take.