One problematic issue with time travel that no-one seems to think about is that the Earth is in a completely different place in the universe right now compared to where it was even a few seconds ago or where it will be even a few seconds from now. If you jumped back or forward in time without also moving in space to where the Earth was/will be at your destination time you'd end up hanging out in space where the Earth once was or will be in the future. So, you need to move a whole spaceflight and reentry capable vehicle through time, not just a person!
Space-time though. If you're moving through time, you're moving through space
