wait - does this mean that some super capable civilisation could link the various galaxies in their inter-galactic empire with a space-railway (i.e. using actual physical tracks between them in space) assuming they have the staggeringly vast amount of matter and/or energy needed, then this would gravitationally bind them together and space between them could not expand?
No, "gravitationally binding" is not a thing that you can do by connecting things via railways. Over the long distances, the railways would be torn apart by expansion.
If you could drastically increase the mass of the local group, then you could increase the range at which gravitational attraction to it was dominating, but it would require seriously increasing the mass of the local group.
> over the long distances, the railways would be torn apart by expansion
i'm not sure i get it. as i understood it, it was the fact that forces over a small scale dominate the effects of space expanding that prevents e.g. atoms getting bigger. so why would my space-railway tracks (made of continuous welded steel space-rails) not stay the same size (2m wide by thousands of light years long) as well?
Imagine a rope, and an infinite crowd of people wanting to play tug of war. If the rope is only 4 meters long, only a few people can tug, and the rope stays together. Now imagine the rope is 1 light year long. Say each person needs about 1 meter of rope, and 1 light year is about 9,5e+15 meters. So we can make two teams of almost 5 quadrillion people each, and they can start tugging. The rope is probably going to snap.
The space expansion effect is very weak at small scales, so it's easily overcome by small objects, such as a short rope (or a railway). But this small force acts on the entire object, so when the object is twice as long, it pulls twice as hard. When distances become extreme, it always wins. Imagine a railway where the the far ends are moving apart from one another faster than the speed of light. It's either an infinitely stretchy railway, or it's breaking (probably long before we got to this point).
so, how does this square with the statement claiming "[...] galaxies in the Local Group stay together" despite space-time expansion, since a galaxy seems rather larger than my proposed space-railway...
edit: also, thanks for the explanations - i think i need to learn more and/or head to physicsoverflow ;)
Galaxies in the Local Group stay together because they are already gravitationally large enough and close enough to outweigh spacetime expansion. So, adding railways between them wouldn’t help or hurt. If you tried to add railways between galaxies that were not already gravitationally bound, they would keep moving apart and just tear the railway.
At the risk of adding yet another analogy. Imagine we have built an enormous balloon the size of a small moon. You and I are put on the balloon with our two vehicle and a steel winch. If they continue to blow up the balloon, things will get farther apart, but it isn’t going to tear the front times from the ear tires, and if we put the cars 1 meter apart, and connected the steel winch cable, it wouldn’t be an issue. At 1 meter, the balloon is expanding by a centimeter an hour. But if you drove 150 kilometers away from me, with the cable connected, and we tried to hold them together at the same distance, the balloon is moving at 25 meters per minute. To each of us, things would look and feel normal, but the pressure on the cable would snap it immediately. If you then decided to keep driving, there would be a point where you could never drive back to me because the distance between us as the balloon was expanding, would be more than the top speed of your car.
