Well, not a logical consequence - you could have travel faster than light without time travel. But it is likely you would have time travel as well.
That's because if you are moving, your sense of simultaneity changes. Difference is subtle for nearby events. But at the distance say of the Andromeda galaxy - if you are just moving at walking pace past someone else in the street, then their idea of what is happening right now in the Andromeda galaxy is different from yours.
This is Roger Penrose's "Andromeda paradox"
Both see the same light from Andromeda, which left Andromeda two million years ago - but they have different ideas of where in the Andromeda time line you put the present moment.
See Special Relativity/Simultaneity, time dilation and length contraction - The Andromdea Paradox
So - if you had some "warp drive" that let you travel almost instantly to the Andromeda galaxy - and then back again to Earth - you could come back here some days into the future or past - depending your notion of simultaneity - so depending on how fast your spaceship was traveling before it went into warp drive. You don't even need to use a black hole for time travel if you can travel as fast as that.
But it depends on how your drive works.
Suppose for instance - don't know of any theoretical reason why this would happen - but just as a thought experiment - that there is a network of space time corridors created in the Big Bang that connect all parts of the universe together - they might connect together times that are all identical "ages" of the universe since the Big Bang.
In the case of us and the Andromeda galaxy - they would connect together times that are exactly the same age since the beginning of the universe.
So in that case - you could travel almost instantly anywhere in the universe - but you would not be able to travel in time.
Same for any other method of travel - if it let you travel to anywhere in the universe but only to places at exactly the same age since the big bang.
One way of measuring that is through the temperature of the three degree background radiation. This temperature is gradually decreasing as the universe expands - and you can tell how fast you are moving relative to the three degree background from the dipole. For instance, our local group of galaxies is moving at roughly 370 km / second relative to the three degree background.
Cosmic microwave background
Here is an image of the three degree background as measured from Earth - the red and purple show the dipole anisotropy due to the speed we are moving relative to the background radiation.
see CMB
So - that gives a local absolute notion of simultaneity which you can measure pretty accurately by looking at the 3 degree background - and an observer at rest relative to the three degree background will see things locally as simultaneous if they are exactly the same age since the big bang.
Piecing those together we get a universal "curved" sense of simultaneity.
So if your faster than light travel never takes you into the past relative to that absolute notion - if it always takes you to places that are at least the same age since the big bang or older - then you can travel faster than light without any time travel.
So it's possible. Whether you can invent some form of space travel, science fiction or speculative future science, that does this is another matter. I don't know of one.
Easiest Sci Fi idea to adapt in this way would be ideas of "magical portals" - doors you step through to get to other parts of the galaxy or universe - the stories where they are not worm holes - but simply - places where you walk through what seems like a doorway and find yourself on another planet or in another galaxy..
If connected by worm holes though or anything else like that where the simultaneity depends on local time of an observer at the two ends - and if the two ends are moveable - or are moving under influence of gravity etc - then you can convert them into time machines by moving one of the ends rapidly in some orbit while keeping the other relatively fixed - until the one of them ages more quickly than the other via the twin paradox.
Then bring those two ends close to each other and you can go backwards in time or forwards in time by going through then.
So it will only work if the portals are - either immovable relative to the background radiation - or - if - as you move them around - they still continue to connect to each other timewise via the "time since the big bang" wherever you put them and not the local time of an observer who follows the path of the portal.
Or - instantaneous magical movement by some other method - if it always moves you to the same time since the big bang. Or fast travel where e.g. every time you travel a light year it moves you forward an hour since the big bang - that sort of travel would be consistent.
In Star Trek - if you want to make sense of their "sub space" communication (see Subspace communication)
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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