kw: time travel
In 1950, hearing his colleagues discussing if "Martians" or other aliens were "out there", Enrico Fermi abruptly spoke up, "Where is everybody?" (a paraphrase, no doubt). Concerning the possibility of travel through time, you could ask the same thing. If in the future actual time travel becomes possible, one would think that time travelers interested in their own history would be overrunning significant events such as 9/11 or the Kennedy assassination.
Time travel into the future is, effectively, what we do by doing nothing. Time passes at the rate of one second per second. However, a "second" is a bit variable, depending on certain effects of general relativity (acceleration and gravity). Speeding up futureward progress can be done by traveling somewhere very fast, then turning around and returning equally fast. But "very fast" means something over a billion km per hour, or some 10,000 times as fast as the fastest spacecraft that has been sent out, to date, or about 40,000 times as fast as the orbital speed of the International Space Station. The energy required is unfeasible until we learn how to harness a few percent of the Sun's output into propulsion (or that of any convenient nearby star).
Going backward in time is another proposition entirely! Even though quantum tunneling provides a way for photons or perhaps even subatomic particles to briefly exceed c, which sends them back in time a few nanoseconds, no means is known for complex items such as molecules or humans to do so.
But let us suppose a device is invented that can move freely along the time axis, taking someone along with it. Just as relativity tells us that motion in space affects time, deliberate motion in time is likely to affect space. For example, suppose you go ten minutes in either the future or the past "direction", more or less instantly. Will you remain stationary in space? Does that question even have meaning? Stationary with respect to what?
Let's consider that we all are moving, even when sitting still. With respect to the center of the Earth, I am moving about 1,280 kph, or 0.356 km/s. Anyone right at the equator is moving even faster: 1,670 kph, or 0.464 km/s. But Earth is moving, at 29.8 km/s relative to the Sun, the Sun is moving at about 200 km/s as it orbits the center of the Galaxy, and the Galaxy is moving at just over 625 km/s with respect to the Cosmic Microwave Background (CMB) radiation that is thought to represent a stationary reference frame for the Universe, at least that part of it we can see. But even that idea is questionable according to special relativity.
Is it possible that time travel allows your personal coordinate system to be pinned to the surface of the Earth? If not, during that instant jaunt through ten minutes of time, you might find you have moved 200-300 km and probably several km upward, or perhaps almost 18,000 km relative to Sol, or 120,000 km relative to the Galaxy, or as much as 375,000 km in the Universal reference frame. That'll get you into the vicinity of the Moon.
I suspect the last figure is most correct. Whoever invents a time machine has to start out with time jumps in the range of a microsecond. Then if the CMB is the actual reference frame, the distance jumped will be only 62.5 cm. You'll need to put your time machine into a vacuum with at least that much elbow room in all directions, so the jump will not be into solid matter!
If this is the consequence of mastering time, it will simply not be practical unless we also learn to make corresponding jumps in space, either to compensate, or perhaps to go to a where/when of our choosing. I wonder if we could ever find out how to locate Dallas, TX, Nov 3, 1963, a certain grassy knoll…
And that is why I think we won't ever have time travelers showing up. Even if one's location in time and space could be chosen at will, knowing where/when a target event is "located" in the spacetime continuum may be impossible to determine, except for very short jumps.