- Travel faster than light. This is time travel.
Here is JDlugosz's magnum opus and one of the best explanations I have seen on why FTL means time travel.
Are there any ways to allow some form of FTL travel without allowing time travel?
- Use an Alcubierre drive to effectively travel faster than light.
An Alcubierre drive is a theoretical device which sidesteps the impossibility of moving faster than light by instead manipulating space. It requires exotic forms of matter and a colossal amount of energy.
The Alcubierre metric defines the warp-drive spacetime. It is a
Lorentzian manifold that, if interpreted in the context of general
relativity, allows a warp bubble to appear in previously flat
spacetime and move away at effectively faster-than-light speed. The
interior of the bubble is an inertial reference frame and inhabitants
experience no proper acceleration. This method of transport does not
involve objects in motion at faster-than-light speeds with respect to
the contents of the warp bubble; that is, a light beam within the warp
bubble would still always move more quickly than the ship. Because
objects within the bubble are not moving (locally) more quickly than
light, the mathematical formulation of the Alcubierre metric is
consistent with the conventional claims of the laws of relativity
(namely, that an object with mass cannot attain or exceed the speed of
light) and conventional relativistic effects such as time dilation
would not apply as they would with conventional motion at near-light
The end result is that entities within the warp bubble can reach a destination faster than light, without themselves ever actually having travelled faster than light. Alcubierre was aware that a working device of this sort could be used as a time machine. Various protections to causality have been mooted, none very convincing. Maybe a time traveler would find herself in a closed timelike curve cut off from the timeline where she started and doomed to loop. The most convincing to me is that there is some unrealized fatal flaw in the Alcubierre drive that means it could not really be built. Of these reason it seems to me the most likely is that although theoretically possibly, there is no such thing as negative mass which the original Alcubierre drive requires to work. There are other versions of the drive which use other exotic forms of matter which also might not exist.
There is a fair bit on this stack about Alcubierre drives if you choose this method; read up. There is also some to read on the Physics stack.