However, traveling to the past would be impossible.
My problem with time travel is the movement of the earth. If I go back (or forward) in time won’t me and my time machine be in space? Between the earth’s revolution around the sun, the solar system’s movement through the Milky Way, the galaxy’s there’s a lot of movement to account for.
I guess that would be the ultimate test of whether SpaceTime exists.
A very similar subject is found in the premise of "The Billiard Ball" by Isaac Asimov. A short story everyone should read. One of my favorites.