The only part of time that is "real" is "now."
The past is gone and the future is not "now." The concept of time travel is to go back and interact with what was. The only part of the past that exist "now" is photonic reflections, and propagating vibrations. Wherever we seem them, they will be gone when we get there. It would be to chase illusions relative to space.
Time travel does exist in the Mind of Man. We look upon "now" with a past reference point. We skip over "now" as a brief pause between the past and future. In doing this we live in illusion. We see reality as we want it to be. This is how the few can control the many.
All they need do as make you "believe" it, and it is true to you. Welcome to the matrix...