Steins;Gate and Quantum Mechanics[]
In Steins;Gate terms, a world line is a single self-consistent history for the universe, extending from the beginning to the end of time. A very large, or infinite, number of these exist. World line is used as an alternative name for the distinct timelines, or worlds, which together form a continually branching quantum superposition of all possible histories. Contrary to a common misunderstanding, world lines are a feature of quantum mechanics. The physical theory used is based primarily on many-worlds quantum mechanics. The rest of the wavefunction is not physical, but does still exist. It represents the possible worlds that can become real under certain circumstances.[1] Every world line is a part of its respective attractor field, with the Steins Gate World Line as an exception.
Active/Inactive World Lines[]
Crucially, in the Steins;Gate universe it is said that only one of the many world lines exists physically at any one time:[1]
World line — This term refers to an infinite number of possible worlds. However, these worlds do not exist in parallel. Only one exists at a given time. Everything that occurs along a world line, from the past to the future, has been predetermined. Thus, no matter how much you change the past along a single world line, the result will converge to the same outcome. — TIPS, Steins;Gate 0
The one world line that currently has a physical existence is often referred to as the active world line. The remaining world lines, which exist as possibilities in a quantum superposition, could correspondingly be called inactive world lines.[1]
Kurisu: "These superpositioned world lines aren’t parallel worlds, are they?"
Suzuha: "No. At the very end, they’re just possible worlds that exist simultaneously." — Chapter 6, Steins;Gate
World Line Divergence[]
Votuko — Mechanics of Steins;Gate[1]
Each world line can be labelled using a quantity known as divergence.
An equivalent statement is that a world line exists for each constant value of divergence. This perspective highlights that by definition, a world line cannot contain events where divergence changes. We observe this in how ordinary people and objects, bound by the current active world line, remember the divergence as always being its current value.[1]
Suzuha: "Most likely, even if the displayed [divergence meter] number were to change, only Okabe Rintarou would notice." — Chapter 6, Steins;Gate
And the future is also predetermined to follow this path, so that any divergence constitutes a paradox. Should such an event occur, history must reconstruct entirely to match the new active world line, with its new divergence throughout all of time.[1]
In standard formatting, one would write the exact number that identifies a specific world line with a percent sign (%). For example, writing the first Alpha World Line as 0.000000%.
To better convey when world lines are part of a specific attractor field, a Greek alphabet symbol of the attractor field is usually used in place of the percent sign. For example, the first world line in the Alpha Attractor Field is typically written as 0.000000α.
The Present[]
We have established that the universe consists of a superposition of world lines, one of which is physically realised at a time. Divergence is constant along each inactive world line, and in the past of the active world line. The active world line also has a pre-determined future, corresponding to the zero-divergence events it contained when it was inactive. But we know that events happening on the active world line can change divergence.[1]
Changes in the Present[]
Titor: "World lines are like an infinite number of rivers flowing parallel. Along the way, many of them diverge. For example, whether or not you post on this message board has no effect on this world line’s divergence. But, if you were to be killed by a random attacker, then the world line’s divergence would change. However, it probably wouldn’t change any more than about 0.000002%. So that nobody misunderstands, I’d like to add that that means a human is only worth that much. That value skyrockets in the face of war, major acts of terrorism, etc. — Chapter 1, Steins;Gate
It is implied that actions taking place in the Present can change divergence, by an amount related to the significance of those actions. The deletion of Echelon data in the present causing a world line shift, or various shifts in Steins;Gate 0, are examples of this behaviour. (As confirmed by the writers in official Q&As.)[1]
Q25. Why did the timeline shift just because they wiped a log entry from the Echelon database?
A25. John Titor mentions in one of his @Channel posts that if a significant event is changed at any point on a timeline, history will re-construct itself and thus, changing the events that happens following that point in the timeline which, is what happened in this case. — Q&A, Steins;Gate Official Material Book