It really depends upon how Time Works, which we really do not know yet. One theory is that time is a constant 4th dimensional motion inherent in all matter. where all motion is relative due to slight variations in the time motion vector---sorta like two cars matching speed on the highway--having no relative motion and one then veering off--then there IS relative motion--the greater the veer angle the greater the relative speed. The other car also would drop back a bit too as its highway speed does not change--a geometrical illustration of "time dilation"--moving objects drop back in time..
It also explains the light speed limit as the relative speed cannot exceed twice the highway speed of the cars (at a veer of 180 degrees)--any more angle and the relative speed decreases again.
So the inherent 4D motion speed of matter (Time) is c over the square root of 2, making c the highest possible relative speed in the 3D universe at a 90 degree vector difference. Its NOT 180 degrees because this is not a 2D highway in the car example, and at any vector angle beyond 90 degrees, RELATIVE TIME effectively runs backwards---so the two objects our out of each others frame of reference.
Now there may not be actual 4D movement as such, but a rapid transfer from one static 3 D parallel universe to another, each representing an "instant" of time, (similar to "frames" of a movie film) perhaps due to a constant change in some matter wave attribute, like" frequency" as an example. The parallel universes being separate and non interactive based on a unique "frequency". we may "hop" from being a part of one universe to another, as the particles in our body/mind change.----Of course this is just another way of looking at the first situation--things will behave the same, but a stack of parallel universes at different frequencies would comprise the total universe, and TIME TRAVEL would be theoretically possible if we could change the matter wave frequency attributes to match ANOTHER of these "parallel' "FRAME UNIVESES"---then we would become a part of a universe in the PAST. (the FUTURE may be more problematical as futures can change)
And don't worry about Paradoxes--they cant happen in the Past any more than they can happen in the present--you cant be in New York and Chicago at the same time can you? In the past you simply will not be able to carry out any action that could have affected your going back to the past to begin with. Like a kind of "force" (or really lack of available force/energy) to pull the trigger on a gun pointed at your grandfather.---you cant cut your own timeline---It would be like an electric relay switch having the coil wired through the normally closed contact.--the bar keeps cutting off the energy before it can move down.