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Time travel wouldn't be by jumps but by contionous change in perpendicular* time dimension.
So earth wouldn't escape from your feet as you would move with it, just like you are doing right now with just one dimension.
*time travel would be imposible if you can move only in positive direction. ~~Then the 2nd time dimension would need to be under some funky angle (3/4π>α>1/2π and α≠π and α≠0)~~ i am wrong
Edit: After some thought, to truly time travel the second dimension would need to be parallel to the original one but backwards. So some people would be living in reverse time. (I have seen that concept in Sci-Fi)
Still the perpendicular time dimension is too funky of a concept to truly give it up.