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Comment by Gunax | Hacker News Reader

There is a misconception that expanding space prevents us from ever reaching a destination. It's counter-intuitive (https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope) but falls out of the math. If space expands at a constant rate, you could eventually reach any destination at any velocity.

But if the expansion of space is accelerating (which we believe currently), this is not true. There really would be destinations that are unreachable.

You would continue to travel further from your origin, but also witness your destination accelerate away.

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But what if you accelerate faster than it does?

Your top speed is bounded by the speed of light. The thing you’re trying to reach is not, since that acceleration is mostly actually space expanding between you and it. It’s going faster that you can ever go, and as the distance between you and it increases it accelerates even more.

No matter how fast you accelerate, you'll chew up distances at a local(!) rate of less than c, so it's enough to consider the limiting case of light and skip the complications introduced by acceleration. The analogous classical problem is the "ant on a rubber rope". If the endpoint of the rope moves at a constant speed, the ant will be able to reach it, no matter the rope's length. If the endpoint accelerates, the ant might not, and only be able to asymptotically approach some point somewhere on the rope.

Hmm, but if we treat the end of the rope as an object which accelerates at x m/s^2, and I accelerate at 2x m/s^2, wouldn't I eventually reach that object? I don't know what I'm not getting...

> and I accelerate at 2x m/s^2

A constant lab frame acceleration is incompatible with special relativity.

You can never go faster than c, so you can never reach anything that's being moved faster away.

Let's say the universe is turn-based, and consists of a single dimension. At the end of each turn the distance between two points in this universe doubles (because new empty space is created between them). Let the maximum speed in this universe be 300.000.000 distance-units per turn. When two points are, say, 5 units apart, we can easily travel between them (for a couple of turns, at least). But when two points are more than 600.000.000 distance-units apart, we can never again travel between them. Let's try.

We're at turn 0, at point A. Point B is 600.000.000 distance-units apart. We have infinite! acceleration and accelerate to 300.000.000 units/turn, and start our travel to point B. We move 300.000.000 units. Distances double. We're at turn 1. Point A is now 600.000.000 units behind us, and point B is still 600.000.000 units ahead of us. We travel 300.000.000 units! Distances double. We're at turn 2. Point A is now 1.800.000.000 units behind us, and point B is still 600.000.000 ahead of us. We're starting to wonder if we should have stayed at point A... hopefully there is a point C that was between point A and point B that we can still get to, because we don't seem to be making much progress.

The universe is a bit like that, except that it looks more continuous, it has some more dimensions, and it's not doubling quite so quickly.

Hmm, I see, thank you. So it's space itself that expands, not just the objects in it that accelerate apart from one another. But then doesn't that mean that some of that space is expanding inside the objects? Do we know what happens there? How do objects just get more space inside them?

Thinking of spacetime as some sort of expanding fabric permeating every-day objects is not a good analogy in my opinion.

First, like any other gravitational effect, locally, spatial expansion would manifest as pseudo-forces that can be counter-acted by all the other forces that are far more relevant at human scale.

Second, the local effect of spatial expansion should be an indirect one: Friedmann cosmology - which is how we describe an isotropic, expanding universe - is a large-scale approximation. More realistic would be 'swiss-cheese' models, where spacetime in our neighbourhood can look vastly different from the Friedmann one, except that the spacetime patches need to properly fit together to yield the correct large-scale behaviour.

Ah I see, so this all happens at a quantum level that doesn't translate well to our intuition? That makes a certain amount of sense, thank you.

This is still relativity, not quantum mechanics.

Point is, illustrative models and analogies are limited. Ideas like 'space itself expanding' or 'space flowing like a river and falling into a black hole like a waterfall' might help visualize some things, but can also lead to wrong ideas if taken too seriously.

> This is still relativity, not quantum mechanics.

Oh hmm, I see.

> but can also lead to wrong ideas if taken too seriously.

Yeah, and it's hard to know how far to take the analogy unless you're already familiar with the concept it's trying to describe, unfortunately.

(Assuming space expands evenly) we don't notice the expansion of space inside objects because the electromagnetism and gravity are vastly more powerful on the scales we care about and nullifies the effect. That's why atoms and galaxies in the Local Group stay together, but everything farther away is flying further away.

If expansion never stops accelerating, one day in the far future it will overcome all the other fundamental forces and everything will be torn apart in a Big Rip.

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.

So, Zeno finally gets his paradox to work!

You can't go faster than light. Space in universe is expanding faster than light.

Can scientists count the number of far distant stars that are no longer visible due to space accelerating?

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