How can Booker and Comstock meet?

From what I understood, Comstock is Booker, Booker is Comstock, Comstock being Booker if he had been baptized in a different parallel universe. Comstock entered the universe you play in through a machine (shown in the cinematic where = Elizabeth/Anna's finger is cut off) that created a portal to that universe.

EDIT: Booker + baptism = Comstock = No Elizabeth/Anna

Booker - baptism = Booker = Elizabeth/Anna

Booker + Comstock + Portal Machine = Bioshock: Infinite

Basically Booker let himself get killed by Elizabeth/Anna to kill every Comstock.

Booker becomes comstock because he gave his daughter away and gets baptised to rid himself of his "sins" aka all the stuff in the war, the gambling, drinking then giving her away ect..

Rebaptised as Zachery Comstock he became obsessed with getting his daughter back and other fanatical ideas through redemption of religion.

As Comstock the prophet he gains wealth and funds the Scientist/physicist Lutece's time tear portal machine. Comstock travels back to a troubled booker who has been gambling and drinking(and i assume lost his wife everything)Then gets the Luteces to offer to wipe his debts/sins for the Girl(his daugher Anna who will become Elizabeth) and Comstock takes her back to his timeline.

i assume Elizabeth has time tearing skills due to being a child from a past/different timeline being brought into one she isnt supposed to be in through a time portal.

The Lutece's question their actions as wrong after being killed by Comstock but realising they still exist in different timelines.

The Lutece's send The Booker(our booker we know) that gave his child away to the future, but his memories are muddled and he thinks hes going "to get the girl to wipe his debt"..

In the end he realises this time line will keep happening as he will become comstock no matter what because this booker GAVE AWAY ELIZABETH. So he lets them drown him to end this timeline.

after the credits it is implied he wakes up to have anna/Elizabeth in the next room.. meaning a NEW COMSTOCK FREE timeline has begun because now he wont give her away and wont become comstock.

its all basically to do with Quantum Physics, mind blowing when you think about it all!

What a lot of people don't seem to realize is that Comstock is a completely different person that the Booker we play as. Yes, they are the same person physically, but mentally they went on to live completely different lives after a turning point in their lives. We don't even know his original purpose in kidnapping Elizabeth from our Booker. I'm sure it has something to do with the Lutece twins though and his need for an heir.

My theory is that Comstock has his reasons for wanting to purge the world in fire(most likely because of what happened at the Battle of Wounded Knee). So at some point he probably meets the Letece twins and they help him create the machine to go into other worlds. Now we also know that he needed an heir for his throne according to the Arc Angel Gabriel, well the problem is, he's sterile. So he most likely gets the idea to kidnap Anna/Elizabeth from our Booker. He uses Booker's debt as a means to acquire her from him.

So now that Comstock has Elizabeth he has to get rid of anyone who knows the truth i.e. the Letece twins and Lady Comstock. But the Twins are aware that they exist in more than one universe and because of that they use Booker to undo all the wrong they did. Thus the events of the game unfold. The same thing applies to Elizabeth, at the end of the game she realizes that she is a constant force in every universe, that is also why she says she can see through all the doors and see each outcome.

Comstock's reasons for keeping Elizabeth locked up are: A) He does not want Booker getting to her B) He is preparing her to take over as his heir

So back to the ending we learn that Booker is just a pawn in a never ending cycle that is slightly different each time, hence why they say "Constants and variables". The Constants are Elizabeth, Booker and Comstock and the variables are all the small changes that happen to him. So now that Booker learns he will always become Comstock and always stay as Booker Dewitt he let's Elizabeth kill him to stop everything from happening. By doing this he cancels out the cycle stopping any of these events from happening.

But by doing this he creates a new cycle where he keeps Anna/Elizabeth as a baby. This also means he most likely has no memory of anything that happened in the game.

The reason I think Elizabeth has all these powers is possibly because she came from a different universe and grew up reading books on Quantum Physics enabling her with the ability to manipulate the fabric of time.

Now one of my theory on the visit to Rapture in the end is that it's just another outcome of "Constants and Variables". Andrew Ryan is Comstock, Booker DeWitt is Atlas and Elizabeth is Jack and Rapture in Columbia. Now you also have to take into account all the different variables that could have happened to lead to this outcome.

It is also possible that Bioshock 1 and 2 could just be another part of the cycle and have nothing to do with Infinite besides the fact that they exist in the same universe.

The whole thing makes your head hurt when you try to figure it out, which is what makes me love the story so much. Nothings better than a game that gets you thinking. I will say though the story in this game really takes away from the first 2, It's like why do those stories even matter, but I guess the best way to look at it is a new story in a never ending book. Also this is all just my take on what happened and how I think everything went down.

The title also makes sense now, It's called Bioshock Infinite because there is an infinite number of possibilities.

what i got from it was that comstock was sterile after the baptism, and needed an heir, and as comstock is booker anna/elizabeth is a suitable heir. the reason that anna/elizabeth drowned booker was to prevent the future of comstock and booker therfor destroying all that has happened and preventing the wars, however there would still be a realm where he has decided that he wont be drowned and live on making booker and comstock again.

As I writed in other answer, looking at this ending without post-credit scene is not complete experiance.

This last moments make me think that DeWitt earns his redemption by killing all wrong/bad possibilities or maybe like a Siren he lives between death and living in his dream with Anna.

Here's what I've worked out so far:

There is a single moment in Booker's history that forks into two sets of multiple universes.

In one set, he does not go through with the baptism, so all his sins from the war still weigh on him, making him spiral out of control into drinking and gambling. Some time after the (failed) baptism he gets married and has Anna (I don't know if there is an official source that says he has Anna before the baptism, but everything works if he had her after)
In the other set, he goes through with it, he becomes Comstock, builds Columbia, becomes sterile, needs an heir, and decides to buy Anna from a Booker in the previous set.

This happens a lot of times, in a lot of universes, with always the same (similar) results.

The first Booker regrets the decision, tries to get her back, and everything that happens in the game unfolds as he tries to find her with the help of Luteces, who have their own agenda (to undo what they did, specifically, building the machine which is tearing the space-time continuum).

So, the only reason to stop the multiverse from collapsing, is to avoid building the machine, ie, stopping Columbia from being built.

What we see at the end, is Elizabeth drowning all the Bookers from the second set, all versions that would become Comstock are killed (smothered while being born, as Booker says near the end).

I believed they only killed the ones from that set, so the original Bookers are still alive, but they never sold their Annas, and that's what we see in the scene at the end (post credits)