How is traveling back in time different from traveling at a negative velocity? [closed]

A simplified explanation of why you can't travel through space faster than the speed of light is that you are already traveling at the speed of light, through spacetime.

If you are stationary in space, you are traveling at c in time. If you speed up to c in space, time appears to be stopped and you are not traveling in time.

To travel backward in time, you'd want to go faster than c in space, so that time will be forced to be negative.

By my logic, that means that you have to also be able to do the opposite, travel back in space. Except, if you slow down to 0 and the keep accelerating, you'll just be traveling forward in the opposite direction.

Is this line of reasoning correct? How would time travel be possible considering this? I'm not talking about alternate universes and similar things that are time travel in name only.

closed as off-topic by sammy gerbil, Chris♦, Mozibur Ullah, Kyle Kanos, ZeroTheHeroAug 30 '18 at 12:37

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• @NSteinle See en.wikipedia.org/wiki/Four-velocity – PM 2Ring Aug 30 '18 at 0:00
• Péter, keep in mind that there is no absolute space, and no absolute frame of reference, so velocities must always be given with reference to some (inertial) frame. If you aren't accelerating, then in your frame you're always at rest. To say that X is travelling at .5c is meaningless unless you also say what that motion is in reference to. – PM 2Ring Aug 30 '18 at 0:06
• Your first two paragraphs are correct. See the link above by PM 2Ring and don't listen to the old timers who don't get it. The rest is incorrect. Special Relativity is a geometry of a flat hyperbolic spacetime. If you visualize this spacetime, you would see that neither a superluminal speed not travel in time exists without bending the spacetime. If you want to entertain the idea of time travel, forget Special Relativity and graduate to General Relativity where hypothetically time loops may exist. In SR, faster than light is not impossible to achieve, but does not exist in the geometry. – safesphere Aug 30 '18 at 3:55
• I'm voting to close this question as off-topic because of lack of prior research. – ZeroTheHero Aug 30 '18 at 12:37

Is this line of reasoning correct?

First, according to SR, it is just the case that one cannot "speed up to $c$ in space".

Second, as has been stated here many times, there is no inertial frame of reference with relative speed $c$ so statements like "time appears to be stopped" are problematic (there are no clocks with relative speed $c$).

Third, despite some popular accounts, it seems that the notion of "traveling at the speed of light, through spacetime" is conceptually incorrect. See, for example, this answer by Ben Crowell.

This idea seems to be something that the popularizer Brian Greene has perpetrated on the world. Objects don't move through spacetime. Objects move through space. If you depict an object in spacetime, you have a world-line. The world-line doesn't move through spacetime, it simply extends across spacetime.

Greene's portrayal of this seems to come from his feeling that because the magnitude of a massive particle's velocity four-vector is traditionally normalized to have magnitude c , it makes sense to describe the particle, to a nonmathematical audience, as "moving through spacetime" at c. This is simply inaccurate.

Fourth, and regardless of the above, speeds are positive. That is, two velocity vectors $\mathbf{v} = v\hat{\mathbf{x}}$ and $\mathbf{v}' = -v\hat{\mathbf{x}}$ have the same speed $v$ so it isn't clear to me how your logic leads you to your conclusion.