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While getting to the past obviously requires some effort or accident, why (in-universe) are the crews going to such lengths to recreate the time-travel circumstances instead of simply travelling around at almost the speed of light for a while and exploit time dilation to get to the future without much of their own time being spent?

  • Accelerating to almost the speed of light takes a lot of energy. – Mr Lister Oct 1 '15 at 15:49
  • I don't think they can achieve near light speed with impulse. And even when, you have (from your dilated point of view) to accelerate to 1000 times light speed (somewhere at 99,x% Lightspeed for an stationary observer) to have 1000 times dilation. – Hothie Oct 1 '15 at 15:50
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    @Hothie: This is just technically wrong. T = T0 * (1-v^2/c^2) ^ -1/2 – ThePopMachine Oct 1 '15 at 17:26
  • On a side note, in TNG A Matter of Time Rasmussen wanted to go back in time to return home, instead of forwards. – Xantec Oct 1 '15 at 20:48
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    Great Scott! It's because Marty's got to save his kids! – BBlake Oct 2 '15 at 14:07
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Ships did not seem capable of moving fast enough for meaningful time dilation to occur. For example, from https://memory-alpha.fandom.com/wiki/Impulse_drive:

The 'Star Trek Voyager Technical Manual' page 13 has full impulse listed as ¼ of the speed of light which is 167,000,000 mph or 74,770 km/s.

At full impulse, they would still require about 97 hours to travel 100 hours into the future. (sqrt(1 - (0.25)**2) is approximately 0.968). Given that the typical problem is being thrown years or decades (or longer) into the past, time dilation is not a practical solution to the problem of returning to your original point in time.

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    And, of course, "warp speed" puts you in a non-relativistic space, so you wouldn't get time dilation. – FuzzyBoots Oct 1 '15 at 16:56
  • To add to this a bit, if the explanation of relativistic time dilation I was given in Physics class many years ago is correct, traveling at the speed of light is only good for a 50% slowdown, meanwhile your energy requirements approach the mass of your ship... – Perkins Oct 1 '15 at 23:38
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    @Perkins I'm afraid your class was inaccurate, were you to travel exactly at the speed of light (which is impossible since you're not massless) no time would pass for you at all. But as your momentum increases towards infinity then that means for accelerating you'll indeed need more and more energy. Though that last statement of your sounds a bit misleading to me... – Zommuter Oct 2 '15 at 6:06
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    That's a strange limitation, I'd have assumed in space, mostly without fiction, momentum wouldn't be limited, only acceleration... does the technical manual state anything about the why of this? – Zommuter Oct 2 '15 at 6:09
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    Suppose you are 100 years in the past. .8c still means a 60-year trip to get back. Even at .9999c, you're looking at a 1.4 years of travel time, ignoring the issue of engine wear-and-tear and fuel expenditure. Trying to recreate whatever phenomenon threw you back in the first place seems like a no-brainer. – chepner Oct 2 '15 at 19:23
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I have wondered this myself, and I've never seen or read an explanation in (extended) canon to cover this. While chepner's answer does cover that impulse drive alone doesn't achieve the necessary speeds, they could still rig something up to misuse impulse along with thrusters, gravitational slingshots (of the real-world, sub-light variety), and maybe some handwaving with inertial dampeners, static warp bubbles and anti-gravs. These are Starfleet engineers, after all.

Out of universe, I suspect the reasons run toward a combination of dramatic necessity and ignorance of the physics involved.

In universe, one can rationalize. Assuming that they could achieve the speeds needed, they would be traveling a significant distance for an extended period of time, from an outside observers perspective. Even a ship as small as The Defiant or a Bird of Prey would have a hard time not looking like a great big spatial anomaly under those circumstances: they would then run a risk of detection, disrupting the timeline that they are attempting to return to. Their power generation might not be up to maintaining shielding against traveling through the interstellar medium at such high speeds for what might still be an extended period of time from their own perspective. Their ability to course correct at need, and indeed, to brake once they "arrived" at their proper time, is dubious.

None of these things is a greater obstacle than others they have handwaved away in other contexts, but it could give them plausible deniability of the relativistic option if they felt they needed one.

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Getting back to the future isn't so much the problem, the problem is doing it with accuracy. Gravitational slingshot ting works just fine, but a tiny error has compounding consequences in when you land or whether you even survive.

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