Time travel is the movement between points in time, analogous to the movement between points in space, in spacetime, typically in four dimensions.
There is time dilation in special relativity and gravitational time dilation in general relativity. The theory of relativity states that the speed of light is the same for all observers in any frame of reference, so time dilation is a direct consequence. A person may use time dilation so that a small amount of proper time passes for them, while a large amount of proper time passes elsewhere, and this can achieve time travel into the future.
General relativity treats the effects of acceleration and the effects of gravity as equivalent, and shows that time dilation also occurs in gravity wells, and it could lead to significant differences in rates of aging for observers at different distances from a large gravity well such as a black hole. An example of this is the black hole Gargantua in the Interstellar Universe.
Traveling to another point and time in spacetime and escaping an instance is associated with technology like a time machine which works with 4d, 5d and 6d.
Travelling to other instances would require megaversal access to 8d via the quantum dimension (7d). It is possible to travel to another instance within a multiverse where if a time paradox event is attempted, you would be thrown into another instance to prevent a causality violation. The effect is that time would decay along this causality line or boundary and all associated matter (including the cause) would follow this decaying timeline.
Michio Kaku has an opinion on the grandfather paradox: The river of time forks into two rivers when you enter a time machine—in other words, the timeline splits. This means that you have killed someone else’s grandfather who looks just like your own grandfather but exists in another timeline in an alternate universe. So the multiverse resolves all time paradoxes.
Traveling to an arbitrary point in the spacetime continuum is connected with wormholes which are natural structures in reality and therefore in 11d. As civilizations get more advanced, they are able to make artificial wormholes and subspace devices that can work with higher dimensions, therefore being able to travel at will to any timeline (instance), for example the TARDIS or tesseract structures.
Beyond 11d it can get weird, as one can travel to before the Big Bang or use subspace conduits or ADs to travel in and out of reality.
Thorne Time Machine[]
A proposal was developed in 1988 by physicist Kip Thorne, and this requires negative energy. According to Stephen Hawking, for all time travel solutions involving wormholes — negative energy is required. A wormhole has to be held open by this exotic negative matter or energy. The two uncharged parallel metal plates of the Casimir effect coming together results in a push, which is a sign of negative energy density in the form of negative energy. The less separation between the plates, the more negative energy there’ll be. What we can currently make could only stabilize a wormhole of a subatomic size. To stabilize a larger wormhole would require an amount of negative energy on the scale of a gas giant like Jupiter.
Instead of two parallel plates, Thorne’s time machine has two spheres, one encased within the other and so close together they’re almost touching. A wormhole connects one set of spheres to another so that each is essentially a mouth that can be traversed. One mouth is carried into space. Traveling at incredibly high speeds, it will experience less time than the mouth which has remained at the source. Upon returning home one sphere will now connect into the past so that entering one end of the wormhole today could mean emerging from the other side at some point in the past.