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It seems the best shot for humans to visit other stars is a relativistic rocket, such as the hypothetical 1g rocket, which would dilate time in order for the mission to be completed in the crew's lifespan. Unfortunately, even travelling to the nearest star (Proxima Centauri, 4.26 LY), according to 1g rocket calculator tools online, would take 3.5 years ship time. I have also heard that 1g rockets can reach 0.99999999996 C, but only after 12 years ship time, and would take another 12 years ship time to decelerate.

My question is, can a relativistic rocket ever dilate time enough to be practical? Like say, travelling 500 lightyears in only 12 days ship time?

I have heard that rockets can't accelerate much faster than 1g without killing the crew, and that an equal amount of time is needed to decelerate at 1 g. But couldn't the rocket accelerate at 1g as close as possible to C, and then decelerate at freefall speed, keeping the crew closer to C as long as possible, and increasing the time dilation experienced? I'm sure someone who knows better can tell me why I'm wrong.

I'm also assuming this is a laser sail, and have read of hypothetical laser sail methods to accelerate small payloads to 0.26 C in ten minutes. I highly suspect that would kill the crew. Intuitively, I feel using beams to accelerate the ship would be more subtle, and not cause the ship to experience high G forces, but once again, I'm sure somebody who knows more about it can tell me why I'm wrong.

So, that's the question, is there anyway to accelerate a human crew, without killing them, close enough to C and fast enough that the time dilation shortens interstellar trips to weeks or months ship time, thus making it a more practical mode of travel.

What's the absolute most we could shorten, say, a 500 lightyear trip for them?

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    $\begingroup$ Hi! Did you mean to post this to Physics perhaps? $\endgroup$
    – msh210
    Aug 30 '21 at 6:12
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    $\begingroup$ I agree with msh210 above - this should probably be migrated to Physics.SE. $\endgroup$
    – Stiv
    Aug 30 '21 at 6:29
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    $\begingroup$ What do you mean by "decelerate at freefall speed"? Unless I'm missing something, if the rocket decelerates, so would everything inside it, unless they exit the rocket (they will hit the inside of the rocket when they move faster than the rocket). Same for this: "Intuitively, I feel using beams to accelerate the ship would be more subtle, and not cause the ship to experience high G forces" -- if the rocket accelerates (regardless of how), everything inside it has to as well (the inside of the rocket will bump into them when it moves faster than them). This is why we should wear seatbelts. $\endgroup$
    – SpiritFryer
    Aug 30 '21 at 15:04
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    $\begingroup$ "acceleration" is the rate at which your speed is changing. By coincidence, 1g of acceleration is very close to 1 light-year per year per year. That is, in a non-relativistic universe, it takes a year of accelerating at 1g just to reach the speed of light. There is no shortcut. To get near the speed of light faster means your speed changes faster, which means you are accelerating at more than 1g. Because of relativity, your speed will increase slower, but that is far too much to explain in a comment. $\endgroup$
    – Paul Sinclair
    Aug 31 '21 at 19:49
  • $\begingroup$ Please don't answer or discuss answers to completely off-topic questions in the comment section. $\endgroup$
    – bobble
    Sep 2 '21 at 19:49
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can a relativistic rocket ever dilate time enough to be practical? Like say, travelling 500 lightyears in only 12 days ship time?

Difficult at reasonable accelerations. 1G can be exceeded, but not by much. I doubt you'd want to sit in a 3G chair for days at a time.

couldn't the rocket accelerate at 1g as close as possible to C, and then decelerate at freefall speed, keeping the crew closer to C as long as possible

There is no "as close as possible to C". In the magic world where you can accelerate forever, you can always go faster. The equation is assuming that you'll accelerate as long as you possibly can, which is halfway.

You are of course free to stop accelerating and coast for part of the journey, but that will take longer than one where acceleration is done constantly.

If you want to limit the outbound acceleration to 1G, you have to limit the arriving deceleration to 1G as well.

is there anyway to accelerate a human crew, without killing them, close enough to C

In terms of technology that we can imagine, no. Even the laser accelerators are completely theoretical and can't decelerate at their destination.

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