World Line Shift due to a D-Mail
Divergence on inactive world lines is fixed and everything follows its predetermined path. Now we come to the Present moment of the active world line, where divergence can be changed.
In concrete terms, it is possible to contradict the predetermined events of the currently active world line. The universe resolves this potential paradox by choosing a different world line to become active, out of the infinite superposition of inactive world lines. Physical reality is reconstructed accordingly.[1]
Titor: "When the world line changes, every cause and effect is reconstructed from past to future in order to prevent paradoxes." — Chapter 2, Steins;Gate
How Does This Work?[]
Suppose that it is written in the history of the current world line that Okabe absolutely will drink Dr. Pepper on a certain day. (Perhaps a time traveller has already confirmed this for you, or you have a God’s-eye view of the world line structure.) For some reason, he instead chooses to drink Coke. This is a contradiction, so the current world line must change to one inwhich it was predetermined that Okabe would drink Coke. On a sufficiently sensitive meter, a divergence change is detected.[1]
World Line Is not Shifting to Just any World Line[]
Votuko — Mechanics of Steins;Gate[1]
In particular, the world line after a change should be the one that is most similar (in events, or divergence) to the previously active world line, out of those that are consistent with the newly created Present. In many cases, this means that the past (and future) can remain largely unchanged. However, that assumes the existence of appropriate world lines. If Okabe was actually born with a genetic predisposition to choose a favourite drink and only ever drink that one drink, then there is no such world line where he drinks Dr. Pepper one day and Coke the next. By changing his choice on one day, history would be forced to reconstruct such that Okabe had always drank Coke, and always will.[1]
Small Shifts[]
The final mechanic to mention is the effect of divergence shifts that are too small to detect on the divergence meter. In an ideal world, one might hope that these followed the exact same rules as large divergence changes, but small shifts do actually behave in a qualitatively different way.
Examples of small shifts are the various "test" D-mails, such as Daru’s D-mail attempt. The general behaviour is that a D-mail is sent successfully, indicated by it disappearing from the sender’s mail outbox and arriving in the receiver’s inbox with an arrival date in the past. We infer therefore that there has been a world line shift. However, people on the new world line still remember the D-mail being sent, which does not happen for large divergence changes. Okabe remembers the events of the previous world line but does not experience the sensation of Reading Steiner.[1]
A guidebook summarises the situation as:
Regarding modifications of the past which hold near-zero influence, the reading will not shift even by a degree of 0.000001%, bringing about a phenomenon in which memories are not reconstructed regardless of slight alteration(s). — Chaos;Head & Steins;Gate: Science Adventure Series Maniacs
Events Unchanged by World Line Shifts[]
When the active world line shifts, reconstruction selects the world line most similar to the previous one (but which also accommodates whatever change caused the shift) to become active. This fact is crucial to answering a number of related questions.
For example, it is often asked why Okabe is usually stood in the same position after a world line shift. Some claim that the butterfly effect of changing the past should lead to him being in an essentially random position. But this is a complete misunderstanding of what a world line shift is. Sending a D-mail does not cause a new world line to branch off the current one; every world line already exists. Rather, the D-mail causes which world line is active to change. There will be inactive world lines where Okabe stands in many different places, but because reconstruction favours the world line most similar to the current one, it will select one to become active where his position does not have to change.
The corollary to this is the few times where a world line shift does change Okabe’s position. This happens when there is no available world line where Okabe standing in the same place is consistent with whatever caused the shift. For example, in Faris’ ending Okabe finds his position changed after sending the second threatening D-mail to Faris’ father. Rather than remaining in the lab, he finds himself stood on the street. This happens because the world has entered the Omega Attractor Field, where the lab did not form. Since the Okabe of this attractor field has never entered the building, there was no inactive world line available that maintained his position there.
Another question that can be answered similarly is why the characters are so similar after a world line change, if history is different. In particular, people are surprised by how similar male Luka and female Luka are. Again, this is because world line shifts work this way, with reconstruction choosing the world line which changes the minimum number of things.
Lastly, certain events remain on the active world line even after their cause has been changed, because reconstruction chooses the most similar world lines possible. For example, in the history of the Beta world line that followed the escape from Alpha (1.130205%), the lab also found an IBN 5100, without Suzuha’s help or motivation. Or as another example, we see the Mayuri of Beta (1.130426%) lose her metal Upa in the prologue of Steins;Gate, then are told by mail that she also lost one in Alpha (0.571024%). This is all to be expected; the world changes an event only if something forces it to.[1]