WhiteDespair
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So you're probably wondering what happened at the end of BioShock Infinite, particularly the Sea of Doors portion after successfully defending the airship and destroying the siphon. This thread is an attempt to explain the meaning of the ending of BioShock Infinite.
NOT THE ENDING YOU THOUGHT IT WAS?
What happened at the end of BioShock Infinite?
SUMMARY
Booker DeWitt is Zachary Hale Comstock. Therefore the only way to stop the creation of Columbia is to kill Booker before he has the chance to become Comstock.
When Elizabeth becomes omnipotent, knowledge of all the universes is common to her and she realizes the implications are much bigger than Comstock and Columbia. She sees that the universes in which the "Booker" character lives lead to the inevitable: a man builds a city, attempts to leave society behind and create a utopia, which ultimately leads to corruption, downfall and destruction -- sometimes the destruction of Columbia, sometimes the destructon of civilization by Columbia. Players of the original BioShock recognize this society as Rapture and the man as Andrew Ryan, whereas BioShock Infinite shows another possible outcome: the creation of Columbia by Zachary Hale Comstock.
As Elizabeth puts it: "There's always a man, always a lighthouse, always a city."
At the end of the game, Elizabeth takes Booker to the lighthouses so he can comprehend things and show him what needs to be done for the greater good. When Elizabeth asks Booker if he fears God, it is a hint that she is a moral person and may feel obligated to do the right thing.
HOW?
After successfully destroying the siphon through use of the Songbird, Elizabeth now has full use of her ability, and is omnipotent. This is because the siphon was preventing her from using her abilities to their full potential. The only thing preventing Elizabeth and Booker from leaving Columbia behind and travelling to Paris at this point is Elizabeth's knowledge of the events leading up to this point. She now wants to stop the events that occurred at their source, Comstock's birth.
Elizabeth leads Booker through several lighthouses, including one which contains Rapture, a city which existed in the first two BioShock games. Through use of these lighthouses, BioShock Infinite simplifies the multiverse theory. The idea that surrounds this theory is that there are an infinite number of universes which exist, based on simple or extreme adjustments made which weren't made in others. To simplify, there is a universe in which Hitler died at a young age, thus several events following his leadership never occurred. This is where the "Infinite" in BioShock Infinite comes from. There are an infinite number of BioShock universes. In BioShock Infinite's case, Comstock came into existence, and created Columbia, whereas in BioShock 1 and 2, Andrew Ryan came into existence, and created Rapture. In Bioshock, if there is a connection between these two, Comstock could be Andrew Ryan as they each created the respective cities, and Booker could be Jack. They are similar worlds and stories, but in different timelines. Please note that Bioshock Infinite takes place in 1912, while Bioshock takes place around 1960.
In BioShock Infinite, we're given two main universes. One in which DeWitt accepts his baptism and eventually becomes Comstock, thus leading to the creation of Columbia. The second is where DeWitt refuses the baptism, thus creating the man you play as throughout the game.
MULTIPLE UNIVERSES
The crucial point in Booker DeWitt's existence is that of the baptism which occurs after the battle of Wounded Knee. Because of this decision at the baptism, there are two main universes which exist in BioShock Infinite. Booker either accepts or denies the baptism.
BOOKER DEWITT UNIVERSE
In the first universe, Booker declines the baptism and remains as himself, has a daughter named Anna, owes a great debt, and gives up Anna to Robert, who is working for Comstock, in order to pay the debt. He changes his mind at the last second, and while trying to pull Anna away from Comstock, who is escaping through a portal created by Rosalind Lutece, her pinky finger is cut off as the portal between their worlds closes.
The Booker in this universe lives in regret and depression for approximately 20 years. At some point during this time, he brands "AD" on his hand, standing for Anna Dewitt. Booker is eventually pulled over into Comstock's world by Robert and Rosalind Lutece. Booker invents an entirely different story within his mind in which he is tasked to retrieve a girl in order to pay off his debt to a man in New York. This is where the opening quote in Infinite by Lutece comes into play: "The mind of the subject will desperately struggle to create memories where none exist." DeWitt needed a reason to be in this alternate place that wasn't entirely his own; his imagined story helped his mind remain stable.
From here, there are different possible scenarios, one of which is his martyrdom for the Vox. Another stems from when Booker meets the old Elizabeth in Comstock House; she says that Songbird killed him before he could stop her from destroying New York. She then brings him to a universe where he could succeed.
COMSTOCK UNIVERSE
In the second universe, Booker accepts the baptism and becomes Comstock, creates Columbia, and foresees the future through use of Rosalind Lutece's tears in the universe. He looked into the universe in which Booker, the false shepherd, attempted to overthrow him. In this universe he also saw his own daughter lead Columbia after his death, and rain fire over the mountains of man. Before confronting him, near the replica of the siphon, there are panels depicting your exploits in Columbia, the last of which is Comstock standing at the basin. It's possible that he could only see up until the point he died. Because his exposure to these tears made him sterile, he had to open up a tear into the universe in which he had a child and retrieve her.
In the Sea of Doors, we see other instances of Booker and Elizabeth. This means that ours is not the only Booker to make it here. Since there are only a few Elizabeths at the baptism, it could be that there are clusters of universes; most of them do not have an Elizabeth that gets her full powers back, but one universe does. Thus, the other Bookers we see walking are each closing their own cluster of universes. It could also be implying that the other pairs we see are other players who finished Infinite.
DISRUPTED UNIVERSE
At the end of the game, Booker/Comstock once again approaches the baptism scene by the river and is joined by different versions of Elizabeth/Anna who have stepped into this universe and timeline. With their help, Booker finally realizes he is also Comstock. The previous two choices lead to the repeating cycles -- the Elizabeths know that the only way to break out of them is to disrupt the "always a man, always a city" world order and destroy "the man" before he builds the city. The Elizabeths drown Booker; and he doesn't struggle much as he resigns himself to his fate.
The circle is broken and Booker no longer becomes Comstock. As the Comstock universes collapse and Anna is no longer pulled into them, the different grown-up versions of Anna/Elizabeth -- who were pulled into this final, altered universe -- disappear one after the other.
ROBERT AND ROSALIND LUTECE
In the universe where Booker DeWitt exists, Robert Lutece is born rather than Rosalind Lutece. In the universe where Booker becomes the version of Comstock we see in the game, Rosalind Lutece is born rather than Robert Lutece.
Prior to meeting Comstock, Rosalind Lutece's research in the multiverse theory lead her as far as the creation of windows from which she could look into other universes. It wasn't until she received funds from Comstock that she was able to create a machine that could open tears into other universes. This benefited her ultimate goal at the time, which seemed to be acquiring Robert Lutece.
In the first universe, Robert Lutece is assigned with the task of retrieving Anna DeWitt from Booker. At the point which this exchange takes place, a portal is created between the two main universes in order to bring Anna to Comstock. Rosalind is on the receiving end, and attempts to get Robert to come through the portal as well so they can be together. (Note that the tear the machine makes is a perfect circle with no jagged edges). Booker makes a last minute decision that he wants his daughter back, and attempts to pull her away from the tear, but is unsuccessful and her pinky finger is cut off.
Many years later, Robert Lutece, being remorseful for stealing Elizabeth from Booker and setting her on a path to attack the surface, gave Rosalind an ultimatum that he would leave her life if she did not help him send Elizabeth back to her own universe. Comstock, whether aware of this plan or just trying to destroy any chances of word of what he had done getting out, ordered Jeremiah Fink to sabotage the machine to kill Robert and Rosalind. However, their conciousness was instead fused with the possibility universe, giving them apparenty immortality and ability to travel through time and space. This would make it easier to carry out their plan.
It should also be noted that early in the game, when the Luteces had Booker flip a coin, Robert carried a chalkboard with heads marked many times. When Booker is asked to choose, he either says heads or tails, but the coin will always land on heads, as it is a constant. It is revealed later that Robert conducted experiments on different Bookers in different timelines to try to change his choices. The telegram about not picking the #77 baseball, the coin flip, the choice of pendant, etc. were all attempts to do this, but as Elizabeth explains: "There are constants and variables."
THERE ARE DIFFERENT TIMELINES?
From the beginning of the game, the Luteces know what's going to happen, because they've been through all of it before with other Bookers. Think of your playthrough of the game as Booker's hundredth or so attempt at preventing Comstock from ever existing.
It could be said that it's Booker's 122 or 123rd attempt, based on the bell-ringing combination at the lighthouse: 1x 2x 2x. Also, after you flip "heads" early on in Columbia and the Luteces mark a 13th notch on the chalkboard, Robert turns around and there are 2 columns of 11 sets of 5 notches, making 123 total notches including your playthrough.
During the beginning of the game while in the boat with the Luteces, Rosalind asks Robert if Booker rows. Throughout each and every attempt they've made to get Booker to Elizabeth, he's never helped row the boat. This was a minor detail Rosalind forgot.
There's a man who Booker finds dead at the lighthouse. This was likely a man sent by Comstock in order to prevent Booker from making it to Columbia. It's also likely that during one of the first attempts to get Booker to Elizabeth, this man killed him. Thus he was killed by the Luteces during any attempts after this one. A note found in the lighthouse that reads, "Be prepared. He's on his way. You must stop him. - C" The C stands for Comstock. This was probably a letter left for whoever the dead man is.
When Rosalind hands Booker the shield during the Comstock Center Rooftops portion of the game, both her and Robert are surprised that it doesn't kill him. This was likely an experimental item that killed Booker in other previous attempts.
There are other various moments in the game which indicate that Booker's been through all of this before, and the Luteces almost treat him like a lab rat in a maze.
In the event that the player gets Booker killed during the game, you often see the black and white flashback to Booker's office again. It is possible that the game treats your "respawn" with that Booker actually having died, while you then continue playing as yet another Booker, one who makes a better choice at that time to prevent his death.
WHERE DID ANNA/ELIZABETH RECEIVE HER POWERS?
She received her powers from the point in time which she lost her pinky finger. The portal closing on her affected her and gave her the powers because it resulted in her partially existing in two universes at once. This is supported by the early voxophone titled "Source of Her Power" where Rosalind states: "I suspect it has less to do with what she is, and rather more with what she is not. A small part of her remains from where she came. It would seem the universe does not like its peas mixed with its porridge."
WHAT HAPPENED AFTER THE CREDITS?
If you managed to stick around after the game's credits rolled by, you would have found yourself back in Booker DeWitt's PI room. Turning toward the right and entering Anna's nursery, he calls out for her, and the game ends before you find out if she was in her crib.
One theory is that through Comstock's death at the baptism, the only universe which remained was that in which Booker declined the baptism, and never attempted to sell his daughter. In this final universe, Booker and Anna are assumed to live happily ever after.
ANOTHER THEORY
Booker's death at the baptism would have brought an end to Elizabeth's existence. Resulting in Booker not having the opportunity to be drowned. Comstock and any Booker that interacted with Comstock would have to die.
Booker's death at the baptism prevented the birth of Comstock, and therefore the creation of Columbia. The interactive cutscene that plays after the credits have rolled is an entirely different story that suggests there is a universe in which Booker and Anna don't confront Comstock or a debt, as explained in the previous section.
However, this is unlikely because Booker's death at the Baptism would prevent every possible scenario of Anna's birth from ever coming into being. Anna's birth requires Booker's denial of the Baptism (although Booker's denial of the baptism may not necessarily lead to Anna's birth). Even if Anna was born before the Baptism, Booker's dying still prevents him with living with her in any universe. Thus, the potential for a Booker/Anna happy life universe is both impossible and implausible.
If you view Elizabeth for what she is however, and how her ability is beyond that of any machine created by the Luteces, you can see where her acts near the end of the game can avoid following most logic. Her goal when drowning Booker was to end Comstock's existence, not Booker's. By drowning Booker, she prevented the creation of Comstock in any universes, and thus eliminated any universes with Comstock in them. This allows for the cutscene at the end in which Booker still has Anna in his possession. Now if only he could get some therapy for his gambling addiction.
PARADOX THEORY
Many theories are not able to reconcile how it was possible that a non-Comstock, post-baptism Booker was alive in the scene following the credits, or forget that Elizabeth specifically says that she needed to kill Booker *before* he made the choice whether to be baptised. Being that he was drowned before the decision, neither version of Booker/Comstock would live. However, this can be explained with a paradox and the theory that nature will always correct a paradox.
If Booker always refused the baptism, he would continue to live and have Anna and would never have to give her up to Comstock. But being that this choice is a variable, Booker choosing to refuse it means there are always universes in which he accepts the baptism and becomes Comstock, resulting in some version of the events of the game. This includes Elizabeth becoming omnipotent and drowning Booker before the baptism.
However, the act of drowning Booker before the baptism means that Elizabeth would no longer have ever existed, and would therefore not have been able to drown him after all. When Booker accepts the baptism, it leads to the series of events that results in Elizabeth becoming all-powerful and drowning him before he even makes the decision. Because of this fact, the choice to accept the baptism creates a paradox, meaning it is not a possibility. This means that the only possibility allowed by nature is to refuse the baptism, making the refusal no longer a variable, but a constant. Thanks to Elizabeth, no branching universes are created at this point and Booker goes on to raise Anna without her being taken away by an alternate version of himself.
AMENDMENT TO THE PARADOX THEORY:
The problem with the Paradox Theory listed here is that if there are infinite universes, i.e. infinite post-baptism-refusal Bookers for the Luteces to choose from (which the game seems to imply that there are), there is not only one Booker who goes to the river to consider the baptism but infinite. In other words, alternate universes are branching off constantly and at all variable points, instead of the single arbitrary point of whether or not Booker chooses to be baptized. Only this constant branching could provide infinite post-baptism-refusal Bookers to the Luteces, since universes would need to be branching off constantly based even on Booker's minor decisions. But if Booker's minor decisions after the baptism decision result in the creation of new universes, so do his minor decisions before the baptism.
This means that there are an infinite number of Bookers in different universes all go to the river and have a chance to make the baptism decision.
Drowning Booker before he is baptized (in one of these, as happens in the ending) then eliminates the infinite number of worlds in which that Booker becomes Comstock and in which fire rains from the sky, etc., but there still remain another infinite number of worlds where slightly different Bookers accept the baptism, and an infinite number of Comstock worlds branch out from each of these.
This is incompatible with the idea that all the universes collapsing except for one in which Booker keeps Anna, but supports the idea that the other Bookers and Elizabeths seen on the docks in the end come from other parallel worlds in which Booker succeeded in rescuing Elizabeth and defeating Comstock, and that those Elizabeth/Booker combinations are all on their way to other versions of the baptism scene to shut down other infinite-branches in which Booker becomes Comstock.
IN THE END
Because of the "constants and variables" idea almost any ending you conceive has happened, is happening, will happen. If you look at it this way, we are all right.
ANOTHER THEORY
In two Voxophone recordings (#003: Everyman, All at Once and #079: The Mirror of Sin), ZH Comstock asks what happens to the man "left behind" or "lies submerged" in the baptismal water. Similarly, Elizabeth asks Booker how he deals with all the things he's done shortly after he rescues her and he replies that he just learned to live with them. One of the central themes, then, is whether or not a man can truly leave his sins behind him by participating in a ceremony. Despite being baptised, washed of his sins and born again, Comstock goes on to commit further atrocities despite Wounded Knee ("burnt the teepees with the squaws inside"), possibly because he believes himself to be truly another person following the baptism. However, he remains the same ruthless, cruel man internally.
In this sense, then, the drowning death of Booker at the end of the game could be viewed, not as a physical death, but as a metaphysical one where Booker relinquishes the concept that his sins can be washed away solely by the act of baptism without an internal change. By accepting this, all of the alternate realities where Comstock existed are closed off and Booker is reunited with an infant Anna/Elizabeth.
Does this Booker have any knowledge of the events in the game, like a bad dream? I think so. Elizabeth asks Booker near the end if he is afraid of God and he answers in the negative. I'd like to think that Booker has been shown Divine Grace.
NOT THE ENDING YOU THOUGHT IT WAS?
What happened at the end of BioShock Infinite?
SUMMARY
Booker DeWitt is Zachary Hale Comstock. Therefore the only way to stop the creation of Columbia is to kill Booker before he has the chance to become Comstock.
When Elizabeth becomes omnipotent, knowledge of all the universes is common to her and she realizes the implications are much bigger than Comstock and Columbia. She sees that the universes in which the "Booker" character lives lead to the inevitable: a man builds a city, attempts to leave society behind and create a utopia, which ultimately leads to corruption, downfall and destruction -- sometimes the destruction of Columbia, sometimes the destructon of civilization by Columbia. Players of the original BioShock recognize this society as Rapture and the man as Andrew Ryan, whereas BioShock Infinite shows another possible outcome: the creation of Columbia by Zachary Hale Comstock.
As Elizabeth puts it: "There's always a man, always a lighthouse, always a city."
At the end of the game, Elizabeth takes Booker to the lighthouses so he can comprehend things and show him what needs to be done for the greater good. When Elizabeth asks Booker if he fears God, it is a hint that she is a moral person and may feel obligated to do the right thing.
HOW?
After successfully destroying the siphon through use of the Songbird, Elizabeth now has full use of her ability, and is omnipotent. This is because the siphon was preventing her from using her abilities to their full potential. The only thing preventing Elizabeth and Booker from leaving Columbia behind and travelling to Paris at this point is Elizabeth's knowledge of the events leading up to this point. She now wants to stop the events that occurred at their source, Comstock's birth.
Elizabeth leads Booker through several lighthouses, including one which contains Rapture, a city which existed in the first two BioShock games. Through use of these lighthouses, BioShock Infinite simplifies the multiverse theory. The idea that surrounds this theory is that there are an infinite number of universes which exist, based on simple or extreme adjustments made which weren't made in others. To simplify, there is a universe in which Hitler died at a young age, thus several events following his leadership never occurred. This is where the "Infinite" in BioShock Infinite comes from. There are an infinite number of BioShock universes. In BioShock Infinite's case, Comstock came into existence, and created Columbia, whereas in BioShock 1 and 2, Andrew Ryan came into existence, and created Rapture. In Bioshock, if there is a connection between these two, Comstock could be Andrew Ryan as they each created the respective cities, and Booker could be Jack. They are similar worlds and stories, but in different timelines. Please note that Bioshock Infinite takes place in 1912, while Bioshock takes place around 1960.
In BioShock Infinite, we're given two main universes. One in which DeWitt accepts his baptism and eventually becomes Comstock, thus leading to the creation of Columbia. The second is where DeWitt refuses the baptism, thus creating the man you play as throughout the game.
MULTIPLE UNIVERSES
The crucial point in Booker DeWitt's existence is that of the baptism which occurs after the battle of Wounded Knee. Because of this decision at the baptism, there are two main universes which exist in BioShock Infinite. Booker either accepts or denies the baptism.
BOOKER DEWITT UNIVERSE
In the first universe, Booker declines the baptism and remains as himself, has a daughter named Anna, owes a great debt, and gives up Anna to Robert, who is working for Comstock, in order to pay the debt. He changes his mind at the last second, and while trying to pull Anna away from Comstock, who is escaping through a portal created by Rosalind Lutece, her pinky finger is cut off as the portal between their worlds closes.
The Booker in this universe lives in regret and depression for approximately 20 years. At some point during this time, he brands "AD" on his hand, standing for Anna Dewitt. Booker is eventually pulled over into Comstock's world by Robert and Rosalind Lutece. Booker invents an entirely different story within his mind in which he is tasked to retrieve a girl in order to pay off his debt to a man in New York. This is where the opening quote in Infinite by Lutece comes into play: "The mind of the subject will desperately struggle to create memories where none exist." DeWitt needed a reason to be in this alternate place that wasn't entirely his own; his imagined story helped his mind remain stable.
From here, there are different possible scenarios, one of which is his martyrdom for the Vox. Another stems from when Booker meets the old Elizabeth in Comstock House; she says that Songbird killed him before he could stop her from destroying New York. She then brings him to a universe where he could succeed.
COMSTOCK UNIVERSE
In the second universe, Booker accepts the baptism and becomes Comstock, creates Columbia, and foresees the future through use of Rosalind Lutece's tears in the universe. He looked into the universe in which Booker, the false shepherd, attempted to overthrow him. In this universe he also saw his own daughter lead Columbia after his death, and rain fire over the mountains of man. Before confronting him, near the replica of the siphon, there are panels depicting your exploits in Columbia, the last of which is Comstock standing at the basin. It's possible that he could only see up until the point he died. Because his exposure to these tears made him sterile, he had to open up a tear into the universe in which he had a child and retrieve her.
In the Sea of Doors, we see other instances of Booker and Elizabeth. This means that ours is not the only Booker to make it here. Since there are only a few Elizabeths at the baptism, it could be that there are clusters of universes; most of them do not have an Elizabeth that gets her full powers back, but one universe does. Thus, the other Bookers we see walking are each closing their own cluster of universes. It could also be implying that the other pairs we see are other players who finished Infinite.
DISRUPTED UNIVERSE
At the end of the game, Booker/Comstock once again approaches the baptism scene by the river and is joined by different versions of Elizabeth/Anna who have stepped into this universe and timeline. With their help, Booker finally realizes he is also Comstock. The previous two choices lead to the repeating cycles -- the Elizabeths know that the only way to break out of them is to disrupt the "always a man, always a city" world order and destroy "the man" before he builds the city. The Elizabeths drown Booker; and he doesn't struggle much as he resigns himself to his fate.
The circle is broken and Booker no longer becomes Comstock. As the Comstock universes collapse and Anna is no longer pulled into them, the different grown-up versions of Anna/Elizabeth -- who were pulled into this final, altered universe -- disappear one after the other.
ROBERT AND ROSALIND LUTECE
In the universe where Booker DeWitt exists, Robert Lutece is born rather than Rosalind Lutece. In the universe where Booker becomes the version of Comstock we see in the game, Rosalind Lutece is born rather than Robert Lutece.
Prior to meeting Comstock, Rosalind Lutece's research in the multiverse theory lead her as far as the creation of windows from which she could look into other universes. It wasn't until she received funds from Comstock that she was able to create a machine that could open tears into other universes. This benefited her ultimate goal at the time, which seemed to be acquiring Robert Lutece.
In the first universe, Robert Lutece is assigned with the task of retrieving Anna DeWitt from Booker. At the point which this exchange takes place, a portal is created between the two main universes in order to bring Anna to Comstock. Rosalind is on the receiving end, and attempts to get Robert to come through the portal as well so they can be together. (Note that the tear the machine makes is a perfect circle with no jagged edges). Booker makes a last minute decision that he wants his daughter back, and attempts to pull her away from the tear, but is unsuccessful and her pinky finger is cut off.
Many years later, Robert Lutece, being remorseful for stealing Elizabeth from Booker and setting her on a path to attack the surface, gave Rosalind an ultimatum that he would leave her life if she did not help him send Elizabeth back to her own universe. Comstock, whether aware of this plan or just trying to destroy any chances of word of what he had done getting out, ordered Jeremiah Fink to sabotage the machine to kill Robert and Rosalind. However, their conciousness was instead fused with the possibility universe, giving them apparenty immortality and ability to travel through time and space. This would make it easier to carry out their plan.
It should also be noted that early in the game, when the Luteces had Booker flip a coin, Robert carried a chalkboard with heads marked many times. When Booker is asked to choose, he either says heads or tails, but the coin will always land on heads, as it is a constant. It is revealed later that Robert conducted experiments on different Bookers in different timelines to try to change his choices. The telegram about not picking the #77 baseball, the coin flip, the choice of pendant, etc. were all attempts to do this, but as Elizabeth explains: "There are constants and variables."
THERE ARE DIFFERENT TIMELINES?
From the beginning of the game, the Luteces know what's going to happen, because they've been through all of it before with other Bookers. Think of your playthrough of the game as Booker's hundredth or so attempt at preventing Comstock from ever existing.
It could be said that it's Booker's 122 or 123rd attempt, based on the bell-ringing combination at the lighthouse: 1x 2x 2x. Also, after you flip "heads" early on in Columbia and the Luteces mark a 13th notch on the chalkboard, Robert turns around and there are 2 columns of 11 sets of 5 notches, making 123 total notches including your playthrough.
During the beginning of the game while in the boat with the Luteces, Rosalind asks Robert if Booker rows. Throughout each and every attempt they've made to get Booker to Elizabeth, he's never helped row the boat. This was a minor detail Rosalind forgot.
There's a man who Booker finds dead at the lighthouse. This was likely a man sent by Comstock in order to prevent Booker from making it to Columbia. It's also likely that during one of the first attempts to get Booker to Elizabeth, this man killed him. Thus he was killed by the Luteces during any attempts after this one. A note found in the lighthouse that reads, "Be prepared. He's on his way. You must stop him. - C" The C stands for Comstock. This was probably a letter left for whoever the dead man is.
When Rosalind hands Booker the shield during the Comstock Center Rooftops portion of the game, both her and Robert are surprised that it doesn't kill him. This was likely an experimental item that killed Booker in other previous attempts.
There are other various moments in the game which indicate that Booker's been through all of this before, and the Luteces almost treat him like a lab rat in a maze.
In the event that the player gets Booker killed during the game, you often see the black and white flashback to Booker's office again. It is possible that the game treats your "respawn" with that Booker actually having died, while you then continue playing as yet another Booker, one who makes a better choice at that time to prevent his death.
WHERE DID ANNA/ELIZABETH RECEIVE HER POWERS?
She received her powers from the point in time which she lost her pinky finger. The portal closing on her affected her and gave her the powers because it resulted in her partially existing in two universes at once. This is supported by the early voxophone titled "Source of Her Power" where Rosalind states: "I suspect it has less to do with what she is, and rather more with what she is not. A small part of her remains from where she came. It would seem the universe does not like its peas mixed with its porridge."
WHAT HAPPENED AFTER THE CREDITS?
If you managed to stick around after the game's credits rolled by, you would have found yourself back in Booker DeWitt's PI room. Turning toward the right and entering Anna's nursery, he calls out for her, and the game ends before you find out if she was in her crib.
One theory is that through Comstock's death at the baptism, the only universe which remained was that in which Booker declined the baptism, and never attempted to sell his daughter. In this final universe, Booker and Anna are assumed to live happily ever after.
ANOTHER THEORY
Booker's death at the baptism would have brought an end to Elizabeth's existence. Resulting in Booker not having the opportunity to be drowned. Comstock and any Booker that interacted with Comstock would have to die.
Booker's death at the baptism prevented the birth of Comstock, and therefore the creation of Columbia. The interactive cutscene that plays after the credits have rolled is an entirely different story that suggests there is a universe in which Booker and Anna don't confront Comstock or a debt, as explained in the previous section.
However, this is unlikely because Booker's death at the Baptism would prevent every possible scenario of Anna's birth from ever coming into being. Anna's birth requires Booker's denial of the Baptism (although Booker's denial of the baptism may not necessarily lead to Anna's birth). Even if Anna was born before the Baptism, Booker's dying still prevents him with living with her in any universe. Thus, the potential for a Booker/Anna happy life universe is both impossible and implausible.
If you view Elizabeth for what she is however, and how her ability is beyond that of any machine created by the Luteces, you can see where her acts near the end of the game can avoid following most logic. Her goal when drowning Booker was to end Comstock's existence, not Booker's. By drowning Booker, she prevented the creation of Comstock in any universes, and thus eliminated any universes with Comstock in them. This allows for the cutscene at the end in which Booker still has Anna in his possession. Now if only he could get some therapy for his gambling addiction.
PARADOX THEORY
Many theories are not able to reconcile how it was possible that a non-Comstock, post-baptism Booker was alive in the scene following the credits, or forget that Elizabeth specifically says that she needed to kill Booker *before* he made the choice whether to be baptised. Being that he was drowned before the decision, neither version of Booker/Comstock would live. However, this can be explained with a paradox and the theory that nature will always correct a paradox.
If Booker always refused the baptism, he would continue to live and have Anna and would never have to give her up to Comstock. But being that this choice is a variable, Booker choosing to refuse it means there are always universes in which he accepts the baptism and becomes Comstock, resulting in some version of the events of the game. This includes Elizabeth becoming omnipotent and drowning Booker before the baptism.
However, the act of drowning Booker before the baptism means that Elizabeth would no longer have ever existed, and would therefore not have been able to drown him after all. When Booker accepts the baptism, it leads to the series of events that results in Elizabeth becoming all-powerful and drowning him before he even makes the decision. Because of this fact, the choice to accept the baptism creates a paradox, meaning it is not a possibility. This means that the only possibility allowed by nature is to refuse the baptism, making the refusal no longer a variable, but a constant. Thanks to Elizabeth, no branching universes are created at this point and Booker goes on to raise Anna without her being taken away by an alternate version of himself.
AMENDMENT TO THE PARADOX THEORY:
The problem with the Paradox Theory listed here is that if there are infinite universes, i.e. infinite post-baptism-refusal Bookers for the Luteces to choose from (which the game seems to imply that there are), there is not only one Booker who goes to the river to consider the baptism but infinite. In other words, alternate universes are branching off constantly and at all variable points, instead of the single arbitrary point of whether or not Booker chooses to be baptized. Only this constant branching could provide infinite post-baptism-refusal Bookers to the Luteces, since universes would need to be branching off constantly based even on Booker's minor decisions. But if Booker's minor decisions after the baptism decision result in the creation of new universes, so do his minor decisions before the baptism.
This means that there are an infinite number of Bookers in different universes all go to the river and have a chance to make the baptism decision.
Drowning Booker before he is baptized (in one of these, as happens in the ending) then eliminates the infinite number of worlds in which that Booker becomes Comstock and in which fire rains from the sky, etc., but there still remain another infinite number of worlds where slightly different Bookers accept the baptism, and an infinite number of Comstock worlds branch out from each of these.
This is incompatible with the idea that all the universes collapsing except for one in which Booker keeps Anna, but supports the idea that the other Bookers and Elizabeths seen on the docks in the end come from other parallel worlds in which Booker succeeded in rescuing Elizabeth and defeating Comstock, and that those Elizabeth/Booker combinations are all on their way to other versions of the baptism scene to shut down other infinite-branches in which Booker becomes Comstock.
IN THE END
Because of the "constants and variables" idea almost any ending you conceive has happened, is happening, will happen. If you look at it this way, we are all right.
ANOTHER THEORY
In two Voxophone recordings (#003: Everyman, All at Once and #079: The Mirror of Sin), ZH Comstock asks what happens to the man "left behind" or "lies submerged" in the baptismal water. Similarly, Elizabeth asks Booker how he deals with all the things he's done shortly after he rescues her and he replies that he just learned to live with them. One of the central themes, then, is whether or not a man can truly leave his sins behind him by participating in a ceremony. Despite being baptised, washed of his sins and born again, Comstock goes on to commit further atrocities despite Wounded Knee ("burnt the teepees with the squaws inside"), possibly because he believes himself to be truly another person following the baptism. However, he remains the same ruthless, cruel man internally.
In this sense, then, the drowning death of Booker at the end of the game could be viewed, not as a physical death, but as a metaphysical one where Booker relinquishes the concept that his sins can be washed away solely by the act of baptism without an internal change. By accepting this, all of the alternate realities where Comstock existed are closed off and Booker is reunited with an infant Anna/Elizabeth.
Does this Booker have any knowledge of the events in the game, like a bad dream? I think so. Elizabeth asks Booker near the end if he is afraid of God and he answers in the negative. I'd like to think that Booker has been shown Divine Grace.
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