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Please reality check my place from which one could watch time outside move faster...

A space station constantly moving at near light speed. The space station is created by a race with superior technology. They are running experiments that will take ages to complete so they want time to pass faster for them than the experiments will take. They are long lived but not immortal. If you are on this space station time would move slow, and things outside would go really fast. So…

  • The space station can move at near the speed of light. It reached near light speed through conventional means (ion drive, light sails, mpd engine, etc.) sustained propulsion until it achieved the desired speed.

  • It is heavily shielded so it can withstand the cosmic rays that will constantly slam against it.

  • It is in orbit around a star.

  • For energy it uses the solar energy of the star it orbits (and maybe even the cosmic rays too.

  • It’s close enough to the star to get its energy, but not close enough that it will get pulled into it.

  • It’s large enough to house hundreds of thousands of their race, and is a self-sustaining habitat: Food, water, air. Etc. When they run dangerously close to running out of something they slow down enough to let someone go out to get whatever they need, and when they get back they start up again.

So my main question is: Have I covered all the bases for time to pass faster for the inhabitants of this space station?

My sub-question is: Will the space station moving so fast look like a ring in orbit around the star?

EDIT:

I second guessed myself. I initially thought black hole instead of a star, as many of you are now suggesting, but I was worried about gravitational pull and energy needs for the space station. These are still issues if we switch from orbit around a star to one just outside a black hole's event horizon, yes?

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    $\begingroup$ When they run dangerously close to running out of something they slow down enough to let someone go out to get whatever they need, and when they get back they start up again. I think a steady stream of supplies coming their way could handle this gracefully without the need to stop or slow down whatever they are doing. $\endgroup$
    – The Square-Cube Law
    Mar 9, 2018 at 21:05
  • $\begingroup$ Also I believe that orbiting a star in high speed will have the opposite effect of what you intend... Remember Interstellar. For people in the base time will pass slower, not faster. They might spend a year there just to find out that centuries have passed on most other star systems. Now, if you want this effect so that when they come out they see the results of a long time having passed for the universe at large, but not for them, then I think you've covered the most important details, yes. $\endgroup$
    – The Square-Cube Law
    Mar 9, 2018 at 21:09
  • $\begingroup$ "time moves faster" part is misleading. Until I read the whole question, I was under impression that time should move slower on a relativistic spaceship. $\endgroup$
    – Alexander
    Mar 9, 2018 at 21:09
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    $\begingroup$ "It is in orbit around a star" - it has to be a very heavy and compact star, like neutron star, if you want a stable orbiting at relativistic speed. $\endgroup$
    – Alexander
    Mar 9, 2018 at 21:13
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    $\begingroup$ @Alexander - very heavy and compact. Which would also mean that tidal stresses on the station would be enormous. $\endgroup$
    – jdunlop
    Mar 9, 2018 at 21:46

5 Answers 5

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Just put in orbit near a black hole.

There is no other object that would be massive enough to allow for relativistic orbital speeds. The escape velocity for the surface of a black hole is exactly the speed of light, so you can go up to that fast if you're at the event horizon (but good luck ever leaving). If the black hole is very very large (supermassive) then the spaghettification point will lie within the event horizon, meaning you can get right up next to it without being ripped to shreds.

Additionally, you can have a regular star orbiting right there with you in order to provide light and energy.

I ripped this from another answer, but gravitational time dilation goes like this: $$t_0 = t_f \sqrt{1-{{r_0}\over{r}}}$$ Where,

  • $t_0$ is the proper time between events A and B for a slow-ticking observer within the gravitational field (your station)
  • $t_f$ is the coordinate time between events A and B for a fast-ticking observer at an arbitrarily large distance from the massive object (where the science experiments are)
  • $r$ is the radial coordinate of the observer (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate)
  • $r_0 = {{2GM}\over{c^2}}$ is the Schwarzschild radius of M.

By deciding how far away you want to orbit and how much time per time you want to pass, you can calculate how big of a black hole you need. Or simply use the SMBH at the center of the galaxy and then figure out one of the other two parameters.

I believe that in reality you'll not want to be super close the the black hole and therefore won't need to be traveling super fast for a stable orbit, but for the most accurate results you should calculate using both sources of time dilation. Their combination gets a bit more complex:

$$\frac{dt_\text{E}}{dt_\text{c}} = \sqrt{ 1 - \frac{2U}{c^2} - \frac{v^2}{c^2} - \left( \frac{c^2}{2U} - 1 \right)^{-1} \frac{{v_\shortparallel}^2}{c^2} } = \sqrt{ 1 - \left( \beta^2 + \beta_e^2 + \frac{\beta_\shortparallel^2 \beta_e^2}{1 - \beta_e^2} \right) } \,$$ where

  • $dt_\text{E}$ is a small increment of proper time $t_\text{E}$,

  • $dt_\text{c}$ is a small increment in the coordinate $t_\text{c}$ coordinate time,

  • $v_\shortparallel$ is the radial velocity,

  • $v_e = \sqrt{ \frac{2 G M_i}{r_i} }$ is the escape velocity,

  • $\beta = v/c$, $\beta_e = v_e/c$ and $\beta_\shortparallel = v_\shortparallel/c$ are velocities as a percentage of speed of light c,

  • $U = \frac{G M_i}{r_i}$ is the Newtonian potential, equivalent to half of the escape velocity squared.

As for the sub question:

Will the space station moving so fast look like a ring in orbit around the star?

No, it won't. I know that when you picture a station whipping around a black hole it's easy to imagine it whipping around in a blur. But consider the star S2. It orbits the supermassive black hole at the center of our galaxy called Sagittarius A. This isn't too different from what you want to do (perhaps it even has a slow station around it!). This star is 15 times more massive than our Sun and at its closest approach is moving at nearly 1.7% the speed of light (which we're going to observe in mid 2018). Still, S2 takes 15 years to orbit the black hole.

Even if you were orbiting the very edge of this supermassive black hole at the speed of light it would take over four minutes to complete an orbit. And you would be moving so quickly that very little light would be reflecting off of you back to any observer. However, you'll be going significantly slower at a significantly larger radius, so you'll be visible as a moving point, but not a ring.

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  • $\begingroup$ So assuming our space station inhabitants are K2 then you suggest an orbit just outside a black holes event horizon? If so could the space station somehow get its energy from the black hole and/or a nearby sun? $\endgroup$
    – Len
    Mar 12, 2018 at 17:33
  • $\begingroup$ @Len You should be as far away from the event horizon of the supermassive black hole as your story can tolerate. You get less time dilation, but you also have a more feasible escape. You can get energy from the nearby sun more easily than from the black hole (as far as I know, a K2 civ would know better). $\endgroup$
    – Samuel
    Mar 12, 2018 at 17:38
  • $\begingroup$ If you want a very high degree of time dialation, a rapidly spinning black hole is better, the faster you spin, the closer the Inner most stable circular orbit will be to the black hole. $\endgroup$
    – blademan9999
    Dec 17, 2022 at 10:46
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Although moving near the speed of light would cause massive time dilation and essentially 'speed up' time on the ship, having it orbit a star is going to be a problem.

By definition, a star emits light. Thus, the escape velocity of that star must be below the speed of light. Thus, a ship traveling very near the speed of light will not be able to orbit it as it is likely traveling above escape velocity. If the object was massive enough for the escape velocity to be above the speed of light, you'd have a black hole. To travel near the speed of light around the black hole, you'd have to be orbiting outside the event horizon, or more specifically just outside the photon sphere. The photon sphere is the radius where light can (somewhat) stably orbit the black hole, so your ship's orbit would have to be a bit outside of it since it is traveling just below the speed of light.

Thankfully, if your ship was that close to a black hole and could somehow survive, gravitational time dilation would be giving your time dilation another significant boost.

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  • $\begingroup$ +1 for mentioning the photon sphere - I think most people don't know that there are no stable orbits between the photon sphere and the event horizon. On that note, I wouldn't say "just outside the event horizon" - the radius of the photon sphere is 50% larger than that of the event horizon. $\endgroup$
    – Rob Watts
    Mar 9, 2018 at 23:06
  • $\begingroup$ @RobWatts: Thanks for catching that! Fixed, plus I added the bit you mentioned about why that's where the orbit would be. $\endgroup$
    – Giter
    Mar 9, 2018 at 23:42
  • $\begingroup$ @RobWatts No stable unpowered orbits, but a powered spaceship can feasibly orbit inside the photon sphere (while still outside the event horizon, of course). $\endgroup$
    – Samuel
    Mar 9, 2018 at 23:46
  • $\begingroup$ @Samuel technically true, but it would probably take a ridiculous amount of energy to try to orbit within the photon sphere - not what you want for a "self-sustaining habitat". Also, you don't get anything from being inside the photon sphere - at the photon sphere, a stable orbit requires traveling at the speed of light, so you can dilate time as much as you want just by getting close while still being outside. $\endgroup$
    – Rob Watts
    Mar 10, 2018 at 0:05
  • $\begingroup$ Would time go backwards for a ship traveling at the speed of light at the center of a black hole? I.E., the summation of gravitational time dilation AND velocity time dilation? $\endgroup$
    – Justin Thyme
    Mar 10, 2018 at 0:06
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A Matryoshka Brain.

https://en.wikipedia.org/wiki/Matrioshka_brain

In other words they live in a simulation, or their minds do.

Because it's a simulation, time is subjective and they can slow it down all they want. Occasionally they need something from the outside world, maybe they want to investigate alien life.

So they can do 1 of a few things,

  • They can clone a biological body and load mind in it.
  • They can create a robotic body and load a mind in it.
  • They can grow a child and just teach them the old fashioned way.

They would then send this agent out to gather information, and return with it.

Not sure if it fits your story, but I wanted to pick something not mentioned before. Looking at some of the other answers, I think they addressed your original, relativistic, ideas in better detail the I could have hoped to. So I just wanted to present another idea that met the core requirements of slowing down time.

Cheers!

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No, Assuming Science-Based as a Prerequisite

There are a few iffy assumptions here if you're going with the science-based tag. They kind of leave the "bases" uncovered.

  • Conventional means of propulsion. From approximately a cold start, assuming, we'll say, a 10 000 tonne spacecraft (not too big, but a pleasantly round number), your difference in energy between 0 and 0.9c would be

    10000000kg / (~0.44) * (270000000m/s)**2 = ~1.65E24 joules.

    In comparison, global energy consumption in 2013 was circa 1E20 joules. So being powered by solar energy and cosmic rays is a non-starter, and conventional means of propulsion are going to fall short in terms of having that amount of energy available in terms of propulsion mass (for ion drives and similar, at least).

  • As pointed out in the comments, the faster you're going, the more massive the object you're orbiting is going to have to be. If it's going to be an active star (to provide solar energy), you're going to have to be a fair distance away. While I haven't run the numbers in entirety, to maintain an orbit at 0.9 around our sun, you'd have to be 1km from its centre of mass. This would leave you orbiting in the sun's iron core, which is obviously untenable. I don't believe you could possibly maintain a relativistic orbit that would result in substantial time dilation around anything less massive and compact than a black hole.

  • This leads to its own problem - gravitational stresses on the station are going to make armoring against cosmic rays/relativistic micrometeorites seem like a minor problem. Unless your hypothetical advanced aliens can control gravity, they are likely to be spaghettified, and if they can control gravity, you don't need your relativistic space station.
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  • $\begingroup$ #1 would not be an issue for Kardashev type II civilization, #3 is valid and suggests that supermassive black hole is the only viable candidate. $\endgroup$
    – Alexander
    Mar 9, 2018 at 22:33
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    $\begingroup$ I'd suggest putting the energy requirement in terms of mass - in this case, 18000 tonnes. In other words, you'd need to have double the mass of the ship as a fuel that could be converted into kinetic energy with near perfect efficiency. And you also have the tyranny of the rocket equation - you'll be using some of that fuel just before you get to your max speed, so your spaceship will be even heavier at the start and need even more fuel. $\endgroup$
    – Rob Watts
    Mar 9, 2018 at 23:14
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    $\begingroup$ Actually, you'd probably be able to get most (if not all) of that energy just from entering orbit around the black hole, but you would need to spend that much energy to escape from the black hole. $\endgroup$
    – Rob Watts
    Mar 10, 2018 at 0:06
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    $\begingroup$ The Kardashev level of the civilization is irrelevant; you would need more energy than you could possibly carry or collect with the surface area of the station. You could collect energy by dropping material into the black hole, but you'd need a constant supply of material, or beamed power from an enormous collector/external power source. $\endgroup$
    – jdunlop
    Mar 12, 2018 at 17:58
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    $\begingroup$ @Len - if you're still sticking with "science-based" and "reality-check", then TANSTAAFL comes into play. Most studies suggest that you can't get any more energy out of the Casimir Effect or Vacuum Energy than you put in. Which is probably a good thing, because reducing the energy of the vacuum might well have negative consequences. (They're also very, very small energy values, but it's safe to say that highly advanced aliens could scale them up.) $\endgroup$
    – jdunlop
    Mar 13, 2018 at 1:18
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When they run dangerously close to running out of something they slow down enough to let someone go out to get whatever they need, and when they get back they start up again.

Every time that happens, everyone will get a lot older, and they won't get younger by returning to regular speed. That could have vast implications.

Since everyone and everything in that world would all experience the same relative time, it might be entirely irrelevant in terms of their own frame of reference, but I think the shift in their relative time would put them out of sync with their experimental world.

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  • $\begingroup$ I see the logic here, but maybe for sake of the OPs question, elaborate more on this? Perhaps if it's a self-sustaining habitat, wouldn't that mean they could avoid slowing down all together? Just a thought. $\endgroup$
    – Carlo
    Mar 10, 2018 at 5:18
  • $\begingroup$ @Omniwombat - OK, but I don't see what that has to do with the question, or my answer. Sounds like you're actually giving another answer to the question: Have I covered all the bases - your answer is 'How exactly are they going to just 'slow down and start up again'? $\endgroup$
    – Vector
    Mar 10, 2018 at 6:37
  • $\begingroup$ @bumpy - I quoted the OP when they run dangerously close to running out of something they slow down... - OP asked if they're missing something, so I pointed out this problem. $\endgroup$
    – Vector
    Mar 10, 2018 at 6:39
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    $\begingroup$ @Vector your answer reminded me of the movie Interstellar, btw. But I think the logic used in the question is that if you slow down to the appropriate speed, the lifespan shouldn't alter, right? That's why I asked maybe elaborate on it more. $\endgroup$
    – Carlo
    Mar 10, 2018 at 6:45
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    $\begingroup$ @bumpy the lifespan shouldn't alter - lifespan is never altered, the question is relative time. But I suppose it wouldn't really matter because everyone/everything would go through it, so nobody would notice anything - they'd all have the same relative time. I added to the answer... $\endgroup$
    – Vector
    Mar 10, 2018 at 8:35

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