Is this statement true?
You can not travel back in time. If I travel fast enough the clock will start to go backwards, but that does not mean I am traveling back in time. It would only mean that the time reference is producing a negative count.
One cannot travel backwards in time.
The physics data we have up to now agree completely with the special theory of relativity. This means you cannot travel faster than the velocity of light, and that you can only approach it as a limit. You will not notice a change in your clock in any measurable way within your travelling system.
Yes, this would be only your impression. E.g. when you are moving away from me then your clock is going slower from my point of view and my is going slower from your point of view. This is because as you are moving away from me the distance between us increases and the light needs longer time to reach you (and this statement is obviously symmetric when we swap me and you). Consequently, the image you'll see of me will be distorted in time and I'll appear to be doing everything slower.
If you would go at the speed of light relative to me (note that this is not physically achievable, but we can discuss this purely theoretically) then all the light from me that could reach you is originating at one moment in my history and consequently it would appear to you that my clock has stopped completely.
Finally, if you were moving superluminally, the light that I emitted as we met and any light I will emit in the future will never reach you (it is simply too slow compared to your speed). On the other hand, as you are moving away, the light that I emitted in the past (and that has already travelled some distance) does have a chance of catching up you. And the further away you move, the older light from me you'll see. Your impression will be that my clock is going backwards. But this is not the end of the story. Because if you were approaching me at the superluminal speeds then it would appear to you that my clock is going forward as usual. Until the point when our wordlines meet. Here's a quick sketch.
The dashed line is you (the superluminal observer), the vertical line is the me (the standing observer) and the 45 degrees lines are light rays I emitted at various events. Note that you'll see me first travelling forward in time upto the event labeled 6 and from the event labeled 7 onwards you'll see me going back in to my past.
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