I don't think that anyone really knows the answer to a question like this. Some physicists would say that the edict that no time travel to the PAST is allowed, is written into the very laws of physics that the universe seems to so slavishly obey. At the quantum level, particles seem to have much more freedom to move back and forth in time, if our mathematics are telling us the right story. We can of course travel forward in time as quickly as we want if we learn how to travel close to the speed of light. But this won't be easy the way we are currently designing spacecraft using chemical rockets!