[thinkloop]

Your comment perfectly crystalizes everything I'm trying to say. You explain the relationship of time to space very nicely and succinctly and correctly, however you decided to use the word "move", which comes with a lot of 3d baggage, which leads you to start thinking that "any sort of movement within this 4D space is possible". Nothing in relativity shows that freely moving back and forward in the time dimension is possible. The closest semblance is slowing your own time relative to other things you care about, so that, for example, you can have the body of a 30yr-old while earth is at 3000AD, but again that's not "traveling" around time, it's closer to putting food in the fridge so it spoils slower.