So maybe this is a quantum mechanics question more than a game specific question, but I understand that there are infinite realities all occurring in parallel with each other, but is there an explanation for why time seems to be at different points in these infinite realities? I get that by peeking through tears people could find popular music of other realities, steal them and reconfigure them for Rapture, but how is this not a form of time travel? Is time moving faster in those parallel realities? All theoretical, I understand, but still a bit inconsistent with the "It's not time travel" statements, when the only "twist" that really protects is the fact that Comstock and DeWitt are actually the same age. If it's possible to harness the energy to cause tears across potential realities, is it that much more of a leap of scientific logic to say it could also be tears across time as well?
On a more game narrative level, is the reason Comstock needs/wants Annabelle in the first place because he wants an heir, and who better than his own child from another universe where he wasn't sterile? It just feels weirdly coincidental that Anna/Elizabeth's powers are a total fluke of quantum paradoxes, rather than the designed purpose of drawing her into the Comstock reality in the first place. I understand that the Luteces have to be able to create tears to get Annabelle, so she can't be the source of the tears, but it also feels like there is to some extent that with the budding of Elizabeth's abilities that Columbia is that much more capable in regards to manipulating and pulling from tears.
This is why it's not "Time Travel". It's "Trans-Dimensional Travel".
"So here we go. The trans-dimensional travel is not depending on a specific time or location. We saw throughout the game that the tears that Elizabeth opens are not depending on the location they are currently in. She does not open a tear to 20 minutes ago or 1 hour in the future or even a perpendicular step into a new reality. The time and place that they go to is independent of those factors.
That gate she opens to Paris at the start of the game has no relation to her current position in space. It opened a tear into a particular reality of Paris that has nothing to do with her particular time.
When she's trying to escape from Booker at Fink Manufacturing she opens several tears to simply bring in new objects into their reality to impede his progress. She does the same to help you in the game. They are simply variations from different realities with no relation to the time that they exist within their own reality.
The situation with Chen Lin should clearly shows that they did not travel in time to fix that situation. They completely left their own universe to go into a Columbia where Chen Lin did not die because he was white and not Asian. What form of time travel creates that situation? They could have gone to the moment right before they started the torture, but they didn't because they couldn't.
Toward the end of the game she demonstrates the ability to open a tear into some midwest location with a tornado. Keep in mind they are still in the sky. The time and space that the tears reveal have no connection to her current time or location.
We saw the effect that the dimensional machine had on Comstock by making him sterile and speeding up the breakdown of his body. Lutece points out that not every version of Comstock suffers the same effects. His "time" was not changed. He did not percieve the world around him as being faster or slower. His body simply started to break down as a result of the exposure.
At the end of the game we see that Elizabeth has gained the sort of the control over the multiverse that the Twins seem to have. You see them seemingly move together to the rowing scene and the Lutece's even comment on the futility of their situation. They are not picking a particular moment in time to go back to. They are selecting a specific reality and a specific point in that reality. Booker tells Elizabeth that none of it matters because Comstock is dead. Elizabeth makes no reference to time when she tells him he still exists in millions and millions of worlds.
Your insistence on time travel rests upon the fact that they seemed to create a ripple that prevented the creation of Comstock through the multiverse. Why is that not resolved with the multiverse idea? How is it that every instance in the game tells you "They are jumping between realities" and yet the ending is somehow time travel?"