Event Horizon: Non-Overlapping Radii Explored

[Seppo Turunen]

TL;DR Summary

A thought experiment on cosmological horizons, asking for guidance

I have been reading about general relativity and its applications to cosmology.
The concept of event horizon leads me to the following thought experiment that
I have not been able to align with the theory. I would be grateful of any guidance.

The radius of the event horizon is 16 billion light-years,
which means that we cannot see light sources farther away.
Obviously, an observer standing one mile from us could still see some such sources.
We, however, cannot see any of them when looking past his shoulder.
My question is this: what happens to the light after it passes his shoulder?
It can't just disappear in the air, can it?

 

[PeroK]

Summary:: A thought experiment on cosmological horizons, asking for guidance

I have been reading about general relativity and its applications to cosmology.
The concept of event horizon leads me to the following thought experiment that
I have not been able to align with the theory. I would be grateful of any guidance.

The radius of the event horizon is 16 billion light-years,
which means that we cannot see light sources farther away.
Obviously, an observer standing one mile from us could still see some such sources.
We, however, cannot see any of them when looking past his shoulder.
My question is this: what happens to the light after it passes his shoulder?
It can't just disappear in the air, can it?

Assuming you are standing about $1$ mile behind, you only have to wait another $5 \mu s$ for the light to reach you.

 

[Seppo Turunen]

My question was about light sources that are outside my event horizon but within the event horizon of the other person. According to how the event horizon is defined, light from such sources should never reach me.

 

[PeroK]

My question was about light sources that are outside my event horizon but within the event horizon of the other person. According to how the event horizon is defined, light from such sources should never reach me.

The distance to the event horizon is increasing with time.

 

[jartsa]

The radius of the event horizon is 16 billion light-years,
which means that we cannot see light sources farther away.
Obviously, an observer standing one mile from us could still see some such sources.
We, however, cannot see any of them when looking past his shoulder.
My question is this: what happens to the light after it passes his shoulder?
It can't just disappear in the air, can it?

Hmm well, if people 16 billion light-years away from the observer one mile in the front of us, "front observer", want to send a message to the front observer, that is possible.

If the distance between the front observer and us stays the same, then the message can reach us too.

If on the other hand the distance between the front observer and us increases according to Hubble's law, then the message can not reach us.

That's how it probably works.Of course the distant people sending the message can put into the message some information that they received from some distant place.

 

[Seppo Turunen]

Thank you for your answer, and for bringing up the intriguing idea of using relay stations to overcome the physical limit. What still puzzles me is the following. There is a remote light signal coming towards me past the point where the the front observer is standing. If he would light a torch and point it to me, I am pretty sure that I would see it even if we were drifting apart according to Hubble's law. Why should the remote light signal behave differently from the light beam of the torch?

 

[PeterDonis]

the intriguing idea of using relay stations to overcome the physical limit

This is impossible. Signals that go via relay stations are still limited to the speed of light. The limitation is spacetime geometry, which is the same whether a signal goes via a relay station or not.

 

[PeterDonis]

There is a remote light signal coming towards me past the point where the the front observer is standing. If he would light a torch and point it to me, I am pretty sure that I would see it even if we were drifting apart according to Hubble's law. Why should the remote light signal behave differently from the light beam of the torch?

You are thinking of it wrong. If the object sending the remote light signals is just beyond your event horizon, and the front observer is only a mile in front of you, then that remote object is only just slightly above his event horizon. That means that the light signal coming from that remote object will take a very, very, very long time to even get to him. And by the time it does, he will no longer be just a mile in front of you, but much farther away, because of Hubble expansion.

If, on the other hand you are imagining a light signal just passing him now, then that light signal cannot be coming from just above his event horizon and just below yours, because, as has already been noted, the distance to the event horizon is increasing with time. So back when that light signal was emitted, if it was above his event horizon, it must also have been above yours, and you will be able to see it.

Properly drawn spacetime diagrams can make it a lot easier to deal with these kinds of scenarios. I suggest the classic Davis & Lineweaver paper that discusses the various horizons:

https://arxiv.org/abs/astro-ph/0310808

See in particular the bottom diagram in Figure 1, which is a conformal diagram of our best current model of our universe. Conformal diagrams are the best ones for showing causal relationships, such as which events can or cannot send light signals to which other events.

 

[jartsa]

There is a remote light signal coming towards me past the point where the the front observer is standing. If he would light a torch and point it to me, I am pretty sure that I would see it even if we were drifting apart according to Hubble's law. Why should the remote light signal behave differently from the light beam of the torch?

The sender was near the event horizon of the "front observer". That means it takes a long time for the message to travel, like thousand times 16 billion years. That is the time that the distance between the two observers expands according to Hubble's law, if Hubble's law applies to the distance all the time.

I mean the observers are really far away from each other when the message reaches the front observer.

 

[Seppo Turunen]

Many thanks for your answer! It was of great help for a novice who has just fumbled through the basic math but has trouble interpreting the results. Also, the Davis paper looks way more clear and precise than the material I have been reading so far.

 

[PeroK]

Many thanks for your answer! It was of great help for a novice who has just fumbled through the basic math but has trouble interpreting the results. Also, the Davis paper looks way more clear and precise than the material I have been reading so far.

You could also try this Insight:

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

 

[A.T.]

According to how the event horizon is defined, light from such sources should never reach me.

This is not correct.

For a constant expansion rate, any signal, no matter how far away it was emitted, will eventually reach you:
https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope

For the accelerated expansion, that we currently observe, the above is no longer guaranteed. But it is still possible for signals sent beyond your current horizon to reach you in the future. Your horizon is not fixed, but expands as well.

 

[Seppo Turunen]

Assuming that the accelerated expansion prevails, it seems to me that my original question is still relevant. To recapitulate: I am standing one mile behind another observer who sees a flash of light coming from a source located, let us say, half a mile beyond my horizon. I am looking past his shoulder but see nothing. What is the solution to this paradox? My guess: there is a difference in red-shifts that makes the wavelength infinite for me.

 

[PeroK]

Assuming that the accelerated expansion prevails, it seems to me that my original question is still relevant. To recapitulate: I am standing one mile behind another observer who sees a flash of light coming from a source located, let us say, half a mile beyond my horizon. I am looking past his shoulder but see nothing. What is the solution to this paradox? My guess: there is a difference in red-shifts that makes the wavelength infinite for me.

This has been explained to you several times already. Light that never reaches you can only reach observers who themselves eventually disappear beyond your event horizon.

If a light signal departs "now" from somewhere beyond your event horizon, then it will never reach someone who remains close to you. (*)

The light might, however, reach a distant galaxy that currently is within your event horizon. But, by the time it gets there (billions of years from now) that galaxy is gone beyond your event horizon.

One thing you must do (see the Insight article) is stop thinking about cosmology in absurdly simplified terms. Your problem is fundamentally not facing up to the challenge of learning the subject properly. Until you do that, you cannot begin to say you understand cosmology and everything will be a "paradox".

(*) In your hypothetical situation: a person who is one mile from you now, will be beyond your event horizon by the time they reach that signal. They won't still be only one mile away. If they are still only one mile away, that's because they are gravitationally bound to you and not moving with the Hubble flow etc.

 

[PeterDonis]

I am standing one mile behind another observer who sees a flash of light coming from a source located, let us say, half a mile beyond my horizon.

As I have already said, you are failing to properly take into account the time it takes for the light to travel from just above the other observer's horizon, to them. I strongly suggest looking at the spacetime diagram in the Davis and Lineweaver paper that I pointed out earlier. If you look carefully at that diagram, you will see that it is simply not possible to set up the scenario described in the quote above "now"--there is no light arriving at the other observer "now" that can possibly satisfy your specification that it is coming from just above the other observer's horizon but just below yours.

 

[Seppo Turunen]

Now I see. The recession speed of the event horizon is always positive, even in the case of accelerated expansion, which makes my scenario impossible. The misconception I had was that the recession speed would be negative in this case. Thanks for your patience!

 

[jartsa]

This is not correct.

For a constant expansion rate, any signal, no matter how far away it was emitted, will eventually reach you:
https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope

For the accelerated expansion, that we currently observe, the above is no longer guaranteed. But it is still possible for signals sent beyond your current horizon to reach you in the future. Your horizon is not fixed, but expands as well.

I see, I got it wrong then. @Seppo Turunen , forget what I said.

 

[hmmm27]

If the event horizon is 16B ly away, then it will take infinity time for the last photon (with a wavelength of infinity, also) to reach an observer from there.

For a person 1ly away (in the obvious direction) from the original observer, it would take infinity + 1 year.

<dons flame retardant suit>

 

[A.T.]

If the event horizon is 16B ly away, then it will take infinity time for the last photon (with a wavelength of infinity, also) to reach an observer from there.

No. See post #12.

ETA: I mistook horizon to mean Hubble sphere, sorry.

 

[Bandersnatch]

For the accelerated expansion, that we currently observe, the above is no longer guaranteed. But it is still possible for signals sent beyond your current horizon to reach you in the future. Your horizon is not fixed, but expands as well.

No. See post #12.

I don't think you have this right. The event horizon expands, yes, but it doesn't mean a signal sent from beyond its extent at the time of emission can ever reach us. If it could, then by definition it wouldn't be the event horizon. The conformal diagram shows this clearly.
Unless you meant 'sent from the current distance to the event horizon, but in the past' (i.e. when the emitter was still inside the then-event horizon). In which case there's no disagreement.

 

[A.T.]

Unless you meant 'sent from the current distance to the event horizon, but in the past' (i.e. when the emitter was still inside the then-event horizon).

What I mean is what is discussed in section 3.3 of the paper linked here:
https://arxiv.org/abs/astro-ph/0310808

The most distant objects that we can see now were outside the Hubble sphere when their comoving coordinates intersected our past light cone. Thus, they were receding superluminally when they emitted the photons we see now.

 

[Bandersnatch]

What I mean is what is discussed in section 3.3 of the paper linked here:

Right, but that's talking about the Hubble sphere not being a horizon, i.e. why superluminal expansion by itself is no obstacle to signal propagation - what the ant on a rubber rope exercise, that you linked to earlier, aims to show. The posts you responded to were referring to the event horizon (in a correct manner), which is a separate concept.
The objections you raised are correct w/r to the Hubble sphere, but not w/r to the event horizon.

 

[A.T.]

The posts you responded to were referring to the event horizon (in a correct manner), which is a separate concept. The objections you raised are correct w/r to the Hubble sphere, but not w/r to the event horizon.

OK, I misread that, sorry.