I’m trying to wrap my head around an apparent paradox. I could not find this by searching and I apologize if this breaks the rules for hypotheticals.
The Hubble volume is a region in space containing everything we can physically interact with. Objects outside of our Hubble volume are receding away from us faster than the speed of light and are therefore impossible to interact with for us.
Now consider an object A at the very edge of our Hubble Volume. It is receding away from us near the speed of light. Near object A is object B. Object B is at a greater distance from us than A, such that B lies outside of our Hubble volume. According to my understanding of the Hubble volume, we can never interact with Object B under any circumstances.
However, imagine the following complication of this setup: Object B is a spaceship, and it maintains an equal distance to Object A at all times by firing its thrusters very rarely to make up for the distance increased between it and Object A due to the expansion of space.
Now, Object A is inside our Hubble volume. Object B is outside of it, but at a constant distance from Object A.
We now travel to Object A. By the time we reach Object A, where is Object B? Can we reach it? Similarly, could the captain of Object B launch a dropship in advance to Object A to meet us when we arrive?
In: Physics
To answer that.
Yes.
If B maintains its position relative to A.
Passing the Hubble volume “Barrier” is irrelevant. Well.. it is, but B is only outside and A is inside because of where you consider the Hubble Barrier to be between them. (From a viewing position)
If A can see B and B can see A and the Hubble Volume Barrier is from our position (Earth) We’d see A but not B since this Barrier is between them. If we are at position A, we’d see B as the Barrier will have extended out past B as much as it would have view from Earths location.
If Object B is able to use enough (theoretical thrust) to maintain a constant distance from Object A, then it will remain at that constant distance from A and be reachable since its negating the whole problem of the universe expanding at an accelerating rate. Also, the Hubble volume is relative to your position within the universe. If someone is at Object B, then Object A would be within their Hubble Volume and remain reachable, so they could meet us.
The concept of the Hubble Volume is that from our current position, things at the edge of that “bubble” are accelerating faster than the speed of light that even if we could travel at 99.9999~ and so on the % of the speed of light from this very moment, we wouldn’t be able to reach it. However, if we were a light year over when we started at this very moment, we could reach it.
No. You’re ignoring the fact that the expansion of the universe is accelerating and that causes the Hubble Sphere to shrink. If Object A is at the Edge of the Hubble Sphere sitting still, the light shining from Object A will reach us, but by the time anyone from Earth could get out that far, Object A itself would have disappeared beyond the Hubble Volume, even if we ourselves moved at the speed of light, because the space that was expanding only at just below the speed of light now accelerates faster. We cannot actually reach stationary objects sitting at the Hubble Volume, even at the speed of light, just see them.
Object A would have to move at light speed or very near it straight at us to not disappear behind the Hubble Volume due to the space around it pulling it away from us at that speed. This would mean Object B also has to move at that speed and direction to keep up with Object A. Except it can’t, because the space between Object A and B is expanding too, and Object A is moving away from Object B at lightspeed, so even if Object B is also moving at lightspeed, it can only recede away from Object A due to the expansion of the universe.
Object B is outside the Hubble Volume, meaning it is moving away from us faster than light, which means if we move at light speed, we still would never reach it. Once Object A and us meet, our Hubble Sphere would match, which means that Object B would have had to have expanded outside Object A’s Hubble Sphere at some point in the journey.
There is a lot to this question but im going to adopt the more theoretical approach.
This is a huge complication for species at the top of the Kardashev scale that worry about galaxy hopping. Essentially yes if object B could slow itself relative to the expansion of space between A and B then we could hop to A and proceed to hop anywhere in A’s hubble volume. Interestingly, spacetime is not uniform everywhere, depending on B’s own mass as well as A’s, its possible that a large enough body could distort space to create a kind of pimple on our otherwise uniform hubble diameter.
Technically speaking, the Hubble volume does NOT mean you will never be able to interact with it, it just implies that nothing moving slower than light speed could catch up as the expansion of spacetime has reached “terminal velocity”. We do however know its theoretically possible to create bubbles of isolated space that kind of move around the expansion of spacetime but there’s a many more problems beyond being conceptually possible. (You gotta figure out how to accelerate it to beyond light speed while its completely isolated from anything it could use to gain momentum)
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