I am looking at the sky, and I see two objects moving away from each other with speed greater than the speed of light.
Light from one object is not fast enough to reach the other. So I decided to help them. I took a mirror, and I reflected the light of one object in the direction of the other.
- Is universe expansion with speed greater than the speed of light is observable?
- Are there objects that we can see, but they will never be able to see us?
Best Answer
The fact that two objects have a relative velocity to one another greater than $c$ in your frame does not imply that their relative velocity in either of their own frames is greater than $c$. Observers with different velocities measure different distances and times such that no relative velocities greater than $c$ are measured. See this wikipedia article for how to composite relativistic velocities.
Universe expansion is not the same as movement and needs to be treated differently.
Much of the below is incorrect. See the linked article from the comments. It does not appropriately consider the changing rate of expansion of the universe. I'm not sure of the precise implications to individual statements.
If two objects with a relative velocity to us of 0 are receding from us because of universe expansion such that the distance between them is increasing faster than $c$, and you see an event on each object that appears simultaneous to you, an observer located with one of those objects at the moment of that object's event will never see the other object's event. Cosmic expansion rate between two points is a factor of distance, and two observers with no relative velocity measure the same distance.
Likewise, they will never see you see the other object's event. By the time the light from each event reached you, the source of the event was already outside of your universe: what you are seeing is the object's distant past, which is still inside of your universe. Likewise, the observer on one of the objects with the events can see Earth's distant past, and the still more distant past of the other object.
Note that you would need an extremely powerful telescope to see objects - even whole galaxies - at such at distance.
We can infer the universe expanding with a speed greater than $c$ based on the redshift of light that has been travelling from a great distance. However, we cannot neither see, nor infer from their effects on other parts of the universe, any events that are emitted by something which was, at the time of the event, receding from us at a cosmic expansion rate greater than $c$. Those events are not part of our universe.
Most of our observable$^1$ universe will never see any event that is part of our present, nor will we ever see events that would correspond to something like "now but on those very distant objects."$^2$
$1$) That is: identifiable through mathematical inference from data collected from extremely powerful space telescopes. Nothing you can see with the naked eye, or even with a moderately powerful telescope, is far enough away that we couldn't send it a signal.
$2$) "Now but over there" is bad physics but I think I can give it a tolerably good definition.
Let $\Delta t$ be however far in the past "a signal from our frame that could have reflected off of a mirror in their frame and come back to us at our present" is in our past.
Let $\Delta s$ be the distance measured in their frame between their frame and the source of that signal at the moment the signal bounced off the mirror.
Let "Now but over there" mean $\Delta t - \Delta s/c$ in the future of the moment in their frame that the signal bounced off that mirror.