What happens if I just keep going?
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.
A constant lab frame acceleration is incompatible with special relativity.
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.
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.
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.
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.
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.
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.
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?
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).
edit: also, thanks for the explanations - i think i need to learn more and/or head to physicsoverflow ;)
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.
But “not getting to anything past the furthest thing we can see from earth today” seems fundamentally incompatible with the idea of reaching those farthest points in a reasonably bounded timeframe. There is stuff beyond the limits we can see, it’s just further than light has had a chance to travel so far (and may ever travel).
My intuition is that as you approached those far objects, you’d observe them rapidly evolving forward in time until they reached their “present day” situation, able to see billions in light years in all directions with Earth right at the edge.
But then what happens when you look at Earth? Surely you don’t see it’s billions of years old past. You’d have to see it at least as old as it was when you left. But something doesn’t seem quite right about that to me. Surely I’m missing something.
If you go far enough, stuff moves fast enough away from us than the speed of light. Thus, some places can't be reached from someone starting at our present location, ever, even though we might still see their light. That light is closer to us than the object that sent it out.
Things without mass, instead, can only travel at the speed of light (photons for instance).
Finally, there is a quirk in the math that would allow for the appearance of faster than light travel. If you compress the spacetime in front of you and expand it behind you you could can move faster than light without turning into a black hole or needing infinite energy (Google Alcubierre drive for more information). It is only an appearance than faster than light travel because you would still move at sub-luminal speed in your bubble of "normal" space time, but the compression/expansion effect would drag you through space-time at faster than light speed. This, however, require so called "exotic matter", ie matter with negative energy density (this is not anti-matter, but matter that has a repulsive gravitational field) and it is probably only a quirk of the math and nothing more.
You are quite right that no matter nor energy nor information is traveling faster than light here.
That way, there really isnt a point that is traveling or moving, its just our perception mistaking it for a point because it looks and move like one.
The thing is that lots of our 'concrete' real world objects have more in common with the later pointer point than with physical reality. Concreteness is a bit of an illusion, it's all wave functions at the bottom.
(Of course, real world objects still can't go faster than light.)
We are able to see gravitational waves at this point. Where is a gravitational turbulence, created by the massive expansion?
(Non-native speaker, but you got the idea).
If you can get there in 45y, that doesn’t mean 45y has passed at that location. In fact if it’s 18bnly away, that means you’d arrive in 18bn years from their perspective. And not 18bn years from what you saw when you left, but 18bn years from when they saw you leave. By that time, space will have expanded enough that it’s no longer possible to see past.
I don't know whether you observe this or not.
So you're still as far away from your destination as in the beginning (or even further), but now you're the same distance from your starting position as well and are effectively stranded.
Though perhaps the amount of energy it would take to accelerate that much exceeds the available energy in the universe? So maybe that's what balances it.