The World Line (世界線) is a concept that was described by John Titor, to describe timelines that Okabe Rintarou passed through.
Titor’s explanation of World Lines is that there are multiple world lines, and within them many divergences. These world lines have something called an attractor field, which will force events that have been pre-determined. However, Titor says that it isn’t really fate that things happen, and that the theory behind world lines is more closely related to the Copenhagen interpretation of quantum mechanics.
An attractor field (アトラクタフィールド) is a concept describing why certain events in a world line cannot be changed. For example, if someone’s death has been pre-determined, then it will happen regardless of what others try to do, even with time travel. These fields essentially warp the world line such that despite all the divergences, the final outcome will still result in the event happening. It can also prevent events from occurring as well; so if someone was pre-determined to die at a future date, they would not be allowed to die before then no matter what. These fields have an effective range of hundreds of years, and are usually triggered or affected by large events.
However, the fields are only known to warp the world line such that the event happens; not what results from the event. From this, it is theoretically possible to change the result of an event without actually changing the event. This could include things like someone taking a bullet and appear to be seemingly dead; one result from this event is that the person is actually dead. Another possible result is that the person took the bullet to a bulletproof vest, and was knocked out cold from the shock.
Changes at this level, however, will change the divergence in the world line, along with a high possibility of passing into another world line. This is particularly true if the changes involved resulted in people being alive as opposed to being dead.
The fields also appear to be somehow linked to what people observe; depending on the level of observation, it may not be possible to change specific properties of a pre-determined event. However, this is more likely to apply only to a person attempting to change the world line based on what he or she observed.
(Source: VN Science Wiki)
