Flawed logic/premise?

I am already confusing myself just trying to articulate this question. I may be wrong about this so please speak up if I missed something but it seems like the premise of this show is impossible.

It is established in the show that the building exists on every version of Earth. The asian character suggests that every possible version of Earth potentially exists so there would be many worlds (billions and billions and billions and billions) that are different only because of the most minute variation ("One less mosquito"). Just like in Sliders, some worlds would be historical tangents like if Hitler had conquered the world, for example, then everyone would be Nazis. The variation could occur at any point in history so far or have not happened at all yet. If that is true and there are billions of billions of Earths that are identical then logic dictates that doppelgängers of the main three characters on different versions of Earth would all have played out the same scenario entering the building at the same time on their respective worlds.

Assuming that is true, then there must be a unique version of the building on every Earth because otherwise billions of doppelgängers would have appeared in the same building at once and caused a quantum explosion or something. Kind of like if you save something to the cloud from several different devices. So are we to understand that the events unfolding in the show are also unfolding billions and billions times over in parallel? So doppelgängers of the main characters would also be traveling in their own unique version of the building and encountering the same worlds one by one with the same events unfolding?

Disregarding the idea that their would be billions and billions of worlds with absolutely no difference, because the variation hadn't happened yet, this scenario still seems impossible.

Let's break it down. Lets call the three main characters in the show Group A. If we were to observe Group A's doppelgängers, who we will call Group B, from the very next parallel world and we found that there was no variation in their world of any real significance then Group B would also have to have entered the building and be traveling to parallel worlds on a parallel time-line. Theoretically (because either the variation in group B's world was so minute it was inconsequential or the variation had not yet happened) Group B would encounter the exact same world's as Group A at the same exact time. Meaning each time Group A showed up at a new version of earth a billion doppelgängers would have to appear. The only way this could logically work is if each parallel time-line had within it infinite parallel Earths then Group A would never encounter group B.

The asian girl has at least two doppelgängers. Those two doppels would have to have joined her within her (Group A's) time-line. So they must have been on an Earth that she visited and joined her in the building. They could not be from Group B's time-line because Group B is doing the exact same thing as Group A so it would be a paradox for them to exist in the same space (each doppel would have to do exactly the same thing as the original at the same time in the same space). Further more, the asian girl's two doppels must have come from variations of Earth where the events that led the asian girl to the building in the first place never happened. They either came before or after through slightly or completely different circumstances. Otherwise the doppels would have to also be traveling in the building in a parallel time-line.

Its like this: imagine a box with a stone in it (Group A). Next to that box is another box with a stone in it (Group B). Next to that box is another box with a stone in it and on and on to infinity. Lets just say that the temperature in the second box is slightly colder than the first but otherwise they are mirror-images of each other so anything that the stone in the first box (Group A) does, the stone in the second box (Group B) also does. Now imagine taking the stone from the first box (Group A) out and placing it in the second (slightly colder) box. Because the stone in the second box (Group B) is on a parallel time-line that mimics everything that the stone from the first box (Group A) does then the stone in the second box (Group B) would have to be taken out of the box and placed in the third box at the same time the stone from the first box (Group A) is moved. Group A ends up in the second box and Group B ends up in the third box possibly usurping a Group C from their box and so on into infinity.

Group A would potentially never encounter Group B or C or D etc if their time-lines remain as close to parallel as possible. Or just enough to keep all the groups jumping. So when our characters in the show (Group A) enter the building and 'jump' for the first time, you would have to assume that many parallel groups (Groups B, C, D etc) also jumped. You just don't see them or hear about them. But the characters (Group A) 'jump' to an Earth where we are lead to believe their doppels (Lets call them Group X) got blown up in the nuclear blast. So we have to assume Group X is dead because the city was nuked along time ago meaning that Group X never jumped. The next time the characters (Group A) 'jump' they come to an Earth where two of them exist but one does not (Lets call them Group Z). Group Z has obviously not 'jumped' at least yet. The main characters (Group A) encounter Group Z and share the same world but not the same exact space because in Group Z's world something changed in history that made that world slightly more technologically advanced than Group A's home world and they have cool see-through i-Phones etc and they are not following a parallel time-line close enough to make Group Z 'jump'. Group Z could potentially have joined Group A on their time-line 'jumping' to other worlds in the building and I suppose that is how there can be three asian doppels.

So here is the problem. Lets put all the stones back in their original boxes. Group A in Box 1, Group B in Box 2 and so on. Now lets label the boxes for the three versions of Earth that the show journeys to. Box 1 would be the 'Real Earth', Box 2 would be the 'Apocalypse Earth' and Box 3 would be the 'Techy Earth'. Lets also create an additional group to represent all the billions and billions of parallel jumpers who have mirrored the actions of Group A completely doing the same things at the same time traveling from world to world. Lets call them Group # (pound sign, I am running out of numbers and letters). Now take the stone for Group A out of the Real Earth Box (Box 1) and place it in the Apocalypse Earth (Box 2). Group B from the Apocalypse Earth were decimated in the nuclear explosion so crush their stone into dust. Now take the stone that represents Group # (the parallel 'jumpers') and place it in the Apocalypse Box also. This is because everything that Group A does, Group # also has to do. Now you have a problem. You have billions of parallel jumpers all showing up at the same world at the same time.

Ok, so what if we say that because the parallel jumpers in Group # are all doing the same thing at the same time in the same space then they just kind of merge into one and you can't really see that their are actually billions of them. They essentially cancel each other out. But now consider that in our original box example (when the boxes did not represent the specific Earths), we said that the temperature in Box 2 (Not the Apocalypse Earth just a box) was slightly colder. So the Group that came from Box 2 would have been slightly different in subtle ways because they were used to a cooler climate. They would not be in complete harmony with the other billions of groups. To make it easier imagine that in Box 2 the white girl from the group had a mustache. When the parallel 'jumpers' from Group # all merged then would the white have a mustache? I will disregard the claim that all the billions of 'jumpers' simply merge into one.

The only possible way any of this could work is if each time-line that follows a group has infinite parallel Earths and time-lines within it and the members from that group can never cross out of their over-all time-line into another over-all time-line.

I understand that its simply impossible in reality in the first place to travel to parallel dimensions but each movie creates its own set of rules of reality and according to this pilot so far it seems so highly unlikely any of this story could happen because of the fundamental impossibility of parallel groups jumping to the same space that it isn't really worth considering the science or basic logic of this show. I haven't even brought up the idea that for there to be variations in all these time-lines in the first place something has to have made that happen. There has to be a reason for it to change. You cannot simply have one less mosquito without a direct cause which would have to be a variation in itself and also need an explanation. Taking the mosquito example further, you could argue that a pregnant mosquito simply laid one less egg. Such things are not as random as we understand them to be. For that to happen there has to be a perfectly good explanation for why biologically. I guess it comes down to Newton's laws. Anything contrary to that is magic.

You could argue that just because the asian chick says some people think every possibility that can exist may exist doesn't mean that is actually what is happening in the film. The evidence is that no other parallel groups show up when Group A jumps. Perhaps there are not so many parallel Earths after all maybe lets say just five billion. Perhaps we are supposed to assume that entering and traveling in the building is itself an anomaly to a person's time-line. This argument could be further supported by the idea that the two siblings in the movie were lured to the building by their father who it turns out is also a traveler and potentially off the standard time-line for all his other doppers. Meaning Group A would have to be an anomaly from their standard time-line and the only group that jumped. The deviation would come down to the moment when their father called them to come to the building. For Group A that changed everything but for all their doppels maybe they just went about their business and never even encountered the building.

I suspect I have answered my own question here. I don't know if that is what the writers really had in mind but it would seem they are saying that only Group A travels from Earth to Earth. Their is no Group # of billions of parallel jumpers. I still have issues with the premise of the building (standing in the middle of ground zero on the Apocalypse Earth without so much as a broken window, maybe on some versions on Earth people don't live in buildings but mud-huts and caves then you look over and there is this huge concrete building, maybe on another Earth that section of the city is underwater or something else is built there, there would be hundreds of homeless travelers because they would wander into the building, the list goes on) but I will give the writers the benefit of the doubt considering they made a point to tell us that the father was not originally from their Earth... Damn! That is a whole other can of worms actually. I give up!