Theories

Time Leap or Time Travel theories that has been seen to have been applied in the BU and Save Me storyline.

Different spacetime geometries
The theory of general relativity describes the universe under a system of field equations that determine the metric, or distance function, of spacetime. There exist exact solutions to these equations that include closed time-like curves, which are world lines that intersect themselves; some point in the causal future of the world line is also in its causal past, a situation which is akin to time travel. Such a solution was first proposed by Kurt Gödel, a solution known as the Gödel metric, but his (and others') solution requires the universe to have physical characteristics that it does not appear to have, such as rotation and lack of Hubble expansion. Whether general relativity forbids closed time-like curves for all realistic conditions is still being researched.

Interacting many-worlds interpretation
A variation of Everett's many-worlds interpretation (MWI) of quantum mechanics provides a resolution to the grandfather paradox that involves the time traveler arriving in a different universe than the one they came from; it's been argued that since the traveler arrives in a different universe's history and not their own history, this is not "genuine" time travel.[43] The accepted many-worlds interpretation suggests that all possible quantum events can occur in mutually exclusive histories. However, some variations allow different universes to interact. This concept is most often used in science-fiction, but some physicists such as David Deutsch have suggested that a time traveler should end up in a different history than the one he started from. On the other hand, Stephen Hawking has argued that even if the MWI is correct, we should expect each time traveler to experience a single self-consistent history, so that time travelers remain within their own world rather than traveling to a different one. The physicist Allen Everett argued that Deutsch's approach "involves modifying fundamental principles of quantum mechanics; it certainly goes beyond simply adopting the MWI". Everett also argues that even if Deutsch's approach is correct, it would imply that any macroscopic object composed of multiple particles would be split apart when traveling back in time through a wormhole, with different particles emerging in different worlds.

Presentism vs. eternalism
Many philosophers have argued that relativity implies eternalism, the idea that the past and future exist in a real sense, not only as changes that occurred or will occur to the present. Philosopher of science Dean Rickles disagrees with some qualifications, but notes that "the consensus among philosophers seems to be that special and general relativity are incompatible with presentism." Some philosophers view time as a dimension equal to spatial dimensions, that future events are "already there" in the same sense different places exist, and that there is no objective flow of time; however, this view is disputed. Presentism is a school of philosophy that holds that the future and the past exist only as changes that occurred or will occur to the present, and they have no real existence of their own. In this view, time travel is impossible because there is no future or past to travel to.[66] Keller and Nelson have argued that even if past and future objects do not exist, there can still be definite truths about past and future events, and thus it is possible that a future truth about a time traveler deciding to travel back to the present date could explain the time traveler's actual appearance in the present; these views are contested by some authors.

Presentism in classical spacetime deems that only the present exists; this is not reconcilable with special relativity, shown in the following example: Alice and Bob are simultaneous observers of event O. For Alice, some event E is simultaneous with O, but for Bob, event E is in the past or future. Therefore, Alice and Bob disagree about what exists in the present, which contradicts classical presentism. "Here-now presentism" attempts to reconcile this by only acknowledging the time and space of a single point; this is unsatisfactory because objects coming and going from the "here-now" alternate between real and unreal, in addition to the lack of a privileged "here-now" that would be the "real" present. "Relativized presentism" acknowledges that there are infinite frames of reference, each of them has a different set of simultaneous events, which makes it impossible to distinguish a single "real" present, and hence either all events in time are real—blurring the difference between presentism and eternalism—or each frame of reference exists in its own reality. Options for presentism in special relativity appear to be exhausted, but Gödel and others suspect presentism may be valid for some forms of general relativity.[71] Generally, the idea of absolute time and space is considered incompatible with general relativity; there is no universal truth about the absolute position of events which occur at different times, and thus no way to determine which point in space at one time is at the universal "same position" at another time,[72] and all coordinate systems are on equal footing as given by the principle of diffeomorphism invariance.

Compossibility
According to the philosophical theory of compossibility, what can happen, for example in the context of time travel, must be weighed against the context of everything relating to the situation. If the past is a certain way, it's not possible for it to be any other way. What can happen when a time traveler visits the past is limited to what did happen, in order to prevent logical contradictions.

Resources

 * Compilation from Time Travel