Travel Back In Time?

Ever since H G Wells' 'Time Machine', time travel has been the topic of science fiction and has fascinated human minds - young and old alike. However, modern say research in physics shows that this actually is not possible. Particularly after the revolution of the theory of relativity, it is known that space and time are intertwined in a complicated manner such that any body that has mass causes the space-time around it to curve so that it accommodates that body with mass. In addition, although, you can move forward and back in any of the three spatial directions, you can only move forward in time.