I was reading something about spacetime, and I have a question. Space and time are interwoven with each other and unless my understanding is utterly wrong, as an object's speed increases, time slows down. Thus, time slows with increasing acceleration. As well, the law for all motion under special relativity states that the combined speed of any object's motion through space and its motion through time is always precisely equal to the speed of light. So here is my question: If time stops when the speed of light is approached, would it not be impossible to go back in time even if we (hypothetically) had the technology to do so? There is not enough motion through time left to go faster than the speed of light, which we would need to go back in time? Am I correct? I just wanted to see if I understood this.