# Do different star systems experience time differently?

Somewhat in relation to this question - What could restrain post-singularity societies from spreading across the Galaxy?

I'm assuming not all star systems move at the same velocity in relation to the speed of light...some stars will be moving quicker and therefore the planets around them will also be moving quicker (if this assumption can be challenged, please do). Since time is directly related to the difference between a body's speed in relation to the speed of light, it would stand to reason that one colony could experience 100 years in the same span another colony only experiences 99 years.

Let's say in a distant future, humans colonize a few other star systems. These star systems are moving at different speeds relative to each other.

• What speed difference would there have to be between stars for a 1% time difference? Is it feasible that humans could populate a star that's moving that much faster (or slower for that matter)?

• Is it possible that another race could originate from a star that has only seen a few hundred thousand years while our earth has experienced 4 billion?

Just to give the background...I have the vision of an ancient race whose star saw its end. They relocated to a star moving significantly slower than the majority of those in the galaxy, and as such the galaxy around them aged quickly while they saw a relatively short time span pass.

How feasible is this? Can the speed of stars vary enough to create a pronounced effect on the passage of time between two systems, or does the variation in speed become too great to actually see a noticeable effect?

• – HDE 226868 Dec 4 '14 at 18:33
• The same concept applies to both, no matter what the object. I think you should keep this because you're going to get a lot of creative answers here. Maybe you could note that there's a related question there, but you're looking for imaginative answers. – HDE 226868 Dec 4 '14 at 18:43
• @HDE226868 I couldn't quite follow the answers there, anyway (though I didn't give it much of a try, I admit). Maybe something more definitive for those of us less-well versed in large-scale physics will come from this question. – Crabgor Dec 4 '14 at 18:54
• here's an article about a star spinning on it's axis at 1,000,000 miles/hour space.com/13822-fastest-rotating-star-tarantula-nebula.html Not the same but interesting none the less – bowlturner Dec 4 '14 at 19:43
• Gravity also causes time dilation, so there might also be an effect on systems with particularly massive stars, or systems closer to the galactic center. – KSmarts Dec 4 '14 at 20:59

A 1% change might be feasible, but dramatic variances are unlikely. Time dilation only becomes significant as you start approaching the speed of light. You have to be moving almost 0.2C to see a 1% difference.

While a star system moving at any velocity is possible in a theoretical sense, in reality I don't think you'd encounter systems moving at anywhere near the necessary speeds to see dramatic time differences. To put this in persepective, the speed of light is 299,792 KM/s. Our solar system revolves around the center of our galaxy at about 250 KM/s. Or less than 0.001 C. Another system would have to be moving (relatively) 200 times faster than ours for even a 1% difference.

Here's a graph that shows the time dilation effect at a given speed. The horizontal axis is the speed, in terms of C. The Vertical axis is the factor of the time dilation.

(Wikipedia http://en.wikipedia.org/wiki/Time_dilation)

• @Twelfth: The speed of the local group relative to the cosmic microwave background is about 627 km/s. That's still 0.002c. And $\gamma=1/\sqrt{1-(v/c)^2}$, that's mathematically impossible to be less than 1. – celtschk Dec 4 '14 at 20:12
• @celtschk - now I go over to physics and ask if I can drive my car at speed equal to an imaginary number I guess. :) ty – Twelfth Dec 4 '14 at 22:20
• @Twelfth, v is squared, so driving at an imaginary speed wouldn't help. You need v to exceed c. – Brian S Dec 4 '14 at 23:02
• Also, if your star is near enough to c to see time dilation effects, you also are going to start seeing effects of the starlight being boosted to high energy radiation – Oldcat Dec 5 '14 at 0:00
• @BrianS. i^2 = -1, so the bottom would be 1+v2/c2 – Oldcat Dec 5 '14 at 0:02

You wrote:

Just to give the background...I have the vision of an ancient race who's star saw it's end. They relocated to a star moving significantly slower than the majority of those in the galaxy, and as such the galaxy around them aged quickly while they saw a relatively short time span pass.

How feasible is this?

Not very. It does depend on a few things, though.

# Velocity time dilation

According to special relativity, an object moving relative to another measures time differently; this phenomenon is known as time dilation. An observer in motion measures a time interval $$\Delta t'=\frac{\Delta t}{\sqrt{1-v^2/c^2}}=\Delta t\gamma$$ where $$\gamma$$ is known as the Lorentz factor and $$\Delta t$$ is the interval measured by a stationary observer. We should be able to compute $$\gamma$$ for any star in a galaxy.

Stars don't orbit like a rigid body rotates (e.g. where their tangential velocity is proportional to their orbital radius). Similarly, they don't have Keplerian orbits. In reality, they follow rotation curves - plots of velocity as a function of radius - that are complicated, thanks to both dark matter and the fact that the galaxy isn't a point mass.

I decided to look at some real data, so I turned to galkin (more information here), which has data from a large number of observations of the Milky Way. In particular, it generates rotation curves from data from gas clouds, masers, and stars.

I took the speeds of the stars tangent to the galactic center as computed by galkin. I first plotted a rotation curve, which is fairly flat beyond $$r=5\text{ kpc}$$.:

I then calculated $$\gamma$$, the Lorentz factor, relative to a stationary observer at infinity: $$\gamma=\frac{1}{\sqrt{1-v^2/c^2}}$$ where $$v$$ is the star's tangential velocity. As expected, $$\gamma$$ is close to $$1$$ for all $$r$$; there is little time dilation due to the motion of stars.

# Gravitational time dilation

Time also flows at different speeds for an observer in a gravitational field. The galaxy's gravitational field isn't large, and so we can apply something called the weak field limit: $$\Delta t'\approx\Delta t\sqrt{1+\frac{2\Delta\phi}{c^2}}$$ where $$\Delta\phi$$ is the difference in potential between two observers. To compute the potential, I used a model by Flynn et al. 1996. It reproduces the observed rotation curve very well, using a three-component model:

By setting an observer at infinity, I let $$\Delta\phi=\phi$$, and thereby calculated the proportionality constant at all $$r$$. It turns out to be quite close to $$1$$, meaning that there is very little gravitational time dilation.

I am not a physicist, so take this with several grains of salt, but...

Your basic assumption is wrong, all "frames of reference" have the same velocity in relation to the speed of light. This is what causes relative velocity time dilation, actually, so you can't even hand wave it away. (Otherwise, FTL travel might help.) The consequence of this would be that both systems would have the exact same velocity difference in relation to each other, and consequently, the exact same time dilation in relation to each other. The effect would be symmetrical.

Basically your question is malformed in the sense that it is the changes in velocity made by travelers, not the difference in the constant velocity of planets, that matters. This is the classical "twin paradox". Just as you'd like this would result in the time having passed more in the galaxy, than for the travelers.

But there is a rather big issue. The effect relies on the traveler having made two relativistic trips. Or in short, you can't use FTL. You'd have to use some slower than light method of travel, and I don't think that getting the time dilation you want is really practical with STL. It would simply take too long. And really only be useful for single trip (for story purposes). And require unrealistically efficient engines.

On the other hand, if you assume FTL, you can fiat rule that time passes slower in FTL, and say that the ancient civilization actually escaped there...

GrandmasterB provided a good answer concerning time slowing down due to high velocities. Let me fill the gap with the gravity. Time dilatation in gravitational field is given by the Schwarzschild metric. From it follows that the factor that gives you how much slower the time flows is

$$\delta t=\sqrt{1+\frac{2G M}{R c^2}}\;,$$

where $c$ is the speed of light, $R$ is radius of the planet, $G=6.672\cdot 10^{-11}\;\mathrm{s/kg}$ is the gravitational constant and $M$ is mass of the planet in kilograms. So for example for Earth, time flow rate differs by 0.9999999993 compared to space. (I.e. there is almost no difference).

To get more general estimate that is very nicely imaginable and can be approximately used for any place in the galaxy, we can use interesting fact, that for Scwarzchild solution, the escape velocity is given by the same formula as for the Newton's gravity,

$$v_e=\sqrt{\frac{2GM}{R}}\;.$$

Putting these equations together, we can calculate that the time slowdown at given place is given by the escape velocity to infinity like

$$\delta t=\sqrt{1-\frac{v_e^2}{c^2}}\;.$$

Interestingly, this is the same formula as in the special relativity for time dilatation GrandmasterB plotted in his answer! Escape velocity from our galaxy is approximately 500 km/s, so time here flows 0.9999986 x time in the intergalactic space. So, unfortunately, you do not get any significant time shifts unless you are really close to neutron stars or black holes.

• Looks like I need to ask another question here with this answer as an inspiration. Thanks for this Irigi. – Twelfth Dec 5 '14 at 18:14
• The galactic escape velocity is not a constant: The closer you get to the core of the galaxy, the higher it becomes. S2 (en.wikipedia.org/wiki/S2_(star) ), for instance, can move at 5000km/s around the central black hole of our galaxy without even coming close to escape velocity... – cmaster Dec 15 '18 at 7:58
• In addition to what @cmaster said, the Schwarzschild solution is essentially only valid around a spherically symmetric body, and the galaxy is decidedly not so - certainly not within the disk. While the end result - that time dilation is negligible - is still the same, you need a different expression for the gravitational contribution (which might not have an analytical solution). – HDE 226868 Dec 17 '18 at 5:32

some problems (or, perhaps, opportunities) that would have to be possible:

1. if the ancients wanted to hop from one world to another that happens already to be moving at near light-speed, they would have to have a way of attaining that kind of speed themselves, so that they could then land on the planet.

2. until they reach that kind of speed, I suspect it would be very difficult for them to even detect the existence and location of such planets, because they're moving so fast.

3. they would also have to happen to be moving in a direction that brings them closer to the planet.

4. would they have to be on a course that intersects the planet's trajectory, so that they don't have to be moving at faster than light speed in order to catch up to it?

Reports of the fastest objects in the universe [1,2] posit that there could exist planets that travel as fast as 30 million miles per hour, or 0.04473 times the speed of light. This works out to a small but noticeable time dilation. When 1000 days have passed in the rest of the universe, only 999 days have passed on the high-velocity planet. [3] In a hundred years, only 99 years, 10 months and 24 days pass on the hypothetical planet.

You have to consider two points when comparing two stars systems. First is the relative Velocity of the solar system in respect to another. (as relative velocity increases it slows down time), then you have to consider a gravitational field (provided by the mass of a solar system).

Time dilation in a gravitational field does not depend on the local strength of the field, but rather "how deep you are inside" one. If the gravitational field is nearly uniform, so that it is almost as strong way up high as it is near the ground, then there will still be gravitational redshift of light climbing up against gravity. (the influence of time dilation in a gravitational field is negligeble unless you are orbiting close to a neutron star, blackhole).

So two differen systems lets imagine a massive star and a white dwarf both at speed differences and different gravitational fields would create a difference in the passage of time relative to each other. Processes in the slower less masive star system will happen slower relative to the small solar system.

**the time will always be calculated by rotations, a full planet rotation would be a day that can be > or < than an Earth day. A year would be also >/< than an Earth year. The average speed of a stellar system would be +/- X % of the Solar System.

The average onward-propelling speed will also be +/- Y %. one cannot talk about clocks any more, as, in human terms, we will be living within biological time, limited by stellar-dependant time/s that could be measured by time indicators:

1. indicator of the Earth time (etalon);

2. indicator of the Stellar System;

3. indicator of the Constellation/s;

4. inner-spaceship indicator;

5. average time indicator;

6. etalon human life indicator;

7. individual human biological indicators.

Ivan Petryshyn

• Welcome to Worldbuilding, Ivan, I have edited your answer to make it easier to read by rearranging paragraphs. You need to click the ENTER key twice to separate paragraphs. – a4android Aug 12 '17 at 4:50