A place from which one could watch time outside move faster

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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!

Answer 4

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.

Answer 5

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.