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It's pretty simple, in fact: the universe is organised in such a way that “it costs space to move time”, and because there is no such thing as negative space, then there is no such thing as negative time! So voilà, here we go.
It also “costs time to move space”, but this one is more obvious so there is no need of discussing it.
There is no paradox with time travel, time travel is just entirely impossible as it breaks the total constance of the energy (which is a symmetry in the structure of the universe so it really can't be avoided).
