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Intergalactic voyages are long, they go over quite large distances, but you, a human in the Milky Way, want to see a galaxy beyond our own with your own eyes and live there. At 99% the speed of light, the journey to Centaurus A, your destination, will take you 14 million years in real time, but due to special relativity it will appear to be 2 million years. That sure is an improvement, but despite the advances in life-extension technology, no human or alien has survived more than 10,000 years of relative time.

Also, like most people, you are afraid that if you freeze your body, when you wake up again, you will be dead, so joining a sleeper crew is not an option for you. How much do you need to abuse general and special relativity in order to get the travel time down to around 9,000 years, short enough you can spend your latter days in the galaxy of your choice. How much faster will you need to go, or how much bigger of a black hole will you need to have, in order to survive a trip to more and more distant galaxies?

For the sake of the question, just assume that we have powerful enough protection that being hit by particles in the intergalactic void or CMB radiation isn't an issue and that we can move a black hole of arbitrary size at any relativistic speed without breaking anything. Feel free to talk about how unrealistic the contraption is you come up with, but right now I am trying to understand how much general relativity and special relativity impact the subjective experience of time.

Also, the ship can't be in the black hole event horizon obviously so there's probably no need to have a black hole of any size as there is probably a maximum amount of time dialation you can get from general relativity while remaining outside of the event horizon.

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    $\begingroup$ Umm, just wondering if you’ve heard of this thing called a line break. Paragraphs are a lot friendlier than a wall of text :) $\endgroup$ Commented Jun 9, 2023 at 22:35
  • $\begingroup$ A person does not survive an intergalactic voyage, the idea is preposterous. The nearest large galaxy to our own (Andromeda) is so far away that the human species didn't even exist when the light we are now seeing from there left its source. $\endgroup$
    – Slarty
    Commented Jun 10, 2023 at 7:59
  • $\begingroup$ @Slarty - if one has a power source capable of infinite energy, and can avoid (as the OP suggests) the consequences of travelling at near-luminal speeds (in terms of collisions with things), then a person can readily survive an intergalactic voyage. Accelerating at 1G for a human lifetime would take a person across the observable universe. $\endgroup$
    – jdunlop
    Commented Jun 10, 2023 at 8:09
  • $\begingroup$ But a power source capable of infinite energy, avoiding the consequences of travelling at near-luminal speeds in terms of collisions with things and accelerating at 1G for a human lifetime are all preposterous. You might as well claim that they can instantly teleport or use magic. Its nonsense on stilts. $\endgroup$
    – Slarty
    Commented Jun 10, 2023 at 17:47

2 Answers 2

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Just Go Faster

The equation for time dilation is $\Delta t' = \frac{\Delta t}{1 - \frac{v^2}{c^2}}$. If you want $\Delta t$ to be small, you need the denominator to be very small to make the observer ($\Delta t'$) see you travel for fourteen million lightyears.

But you have no trouble hitting space dust at near-luminal speeds, so this is not a problem. If your destination is fourteen million lightyears away (we won't bother adjusting the time travelled for velocity because it'll be close enough to $c$ not to matter), and you want to experience the trip in 9000 years, then $1 - \frac{v^2}{c^2}$ has to be 9000 / 14000000 ~= 0.00065.

Solving, we get $0.999674947c$.

(It's worth remembering when thinking about special relativity that something travelling at the speed of light would experience the entirety of the life of the universe in a single instant - infinite dilation. So you just need to get close enough but not quite divide-by-zero.)

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  • $\begingroup$ I should note that since I casually rounded off other numbers, I probably should've rounded off the final solution for v as well, but it's more fun when it's Lt. Commander Data unrealistic precision. $\endgroup$
    – jdunlop
    Commented Jun 10, 2023 at 0:18
  • $\begingroup$ So you would only need to reach a speed of N4? (I am thinking up a system that would be used to refer to speeds where the amount of time experienced is more important than than the actual travel time, so the "NX" engines refer to the number of nines after the decimal point. $\endgroup$
    – skout
    Commented Jun 10, 2023 at 2:25
  • $\begingroup$ I mean "only" is doing a lot of heavy lifting there. At that velocity, any further acceleration is accelerating effectively 32 times the mass of the vehicle, and that value is asymptotically approaching infinite mass as well. You'd need effectively a magic energy generator to accomplish this at all. $\endgroup$
    – jdunlop
    Commented Jun 10, 2023 at 7:08
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My normal answer would be that people are just too fragile and brief for this sort of thing. That's boring: let's assume we are doing it.

Suppose you could live many lifetimes. Every time you went into suspended animation, this would be a chance to repair your body. You could rewind your telomeres. If you heart or other vital organs are getting old, you could grow replacements and have them put in while your system is down. You could change the colour of your hair or eyes if you felt like it. While this is happening, your brain may degrade and lose some of its memories. This would be harder to fix, unless we can develop a human/digital hybrid cable of being backed up.

Maybe the solution to memory loss would be as simple as keeping a diary and a photo album. When you awoke from Long Sleep, you might feel younger and like a different person. The earlier memories belonged to 'past you', and the the records of you as you were might feel as remote as the pictures of my childhood seem to me now.

How would you be after many 'lifetimes' like this? I would imagine you might reach some sort of 'steady state'. You might dimly remember writing a novel, or playing the piano, or researching mathematics, but you might not have all the talents at once.

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