No.

The last light that can arrive would be stretched out over the rest of time. So the light from the last (say) year of quasar that can reach us would spread out from now until infinity. The light would be increasingly red-shifted and faded as we travel away, but it'd never completely stop.

The ants-on-balloon may or may not be useful here, but I'm sure you can stretch the analogue to cover this situation with some imagination.

Uh this is not entirely correct. The reason for that is that there's a difference between the speed of expansion of the Universe, and the speed of motion; therefore, it's actually very, very tricky to associate a given redshift with a given velocity for far away objects (say high redshift quasars).

For nearby sources (say local galaxies), you can safely measure a redshift, and tie it to an expansion velocity through v = c*z. This falls off once relativity comes in play, which is why we see plenty of sources with redshifts greater than 1. The farthest galaxy ever observed has a redshift of 11, the farthest quasar of 7, and the farthest Gamma Ray Burst 9 i believe.

Special relativity would tell you (if you looked at it very, very roughly) that any speed can not exceed c; however, that has to be the actual, physical speed of something traveling in space, not the apparent speed of something that is traveling along with spacetime, which is what happens during the expansion of the Universe. For that, you need general relativity; spacetime in general relativity is not free to change over time.

In General Relativity, the velocity-redshift relation for nearby distances (and therefore low relative speeds) reduces to v = c*z, but for higher velocities it depends on the model, specifically on what kind of Universe you live in. Values above c are just fine because, again, you aren't talking about physical motion in spacetime, but about the apparent velocities of something traveling along with spacetime. This means that velocity and redshift lead are not very well tied together.

This is from wikipedia; the shaded area around the GR curve is to show that the exact expansion speed depends on the model (ie, what is in the Universe, which regulates how it is expanding):

[image loading]

A better way of thinking about cosmological redshift (which is what you do in real world cosmology) is to not think about relative velocity, but about relative distance. If the Universe is expanding, you can imagine any distance should be written as R = a(t) * x. x is the distance between two objects if you neglect the expansion, and a(t) is a function, called the scale factor, which tells us how distances have changed over time. It's defined so that at the current time it equals 1; in the past it was lower than 1, and in the future it's greater than 1. For any given Universe with a certain amount of matter, radiation, curvature and dark energy, you can solve the Einstein equations to find the appropriate scale factor from the Big Bang to any arbitrary point in time.

The reason i'm bringing up the scale factor is that it can be shown to be tied to redshfit; the formula you find is 1 + z = a(now)/a(t). a(now) is the value of the scale factor now (so, 1), a(t) is the value of the scale factor at the time the photon was emitted, z is the amount of redshift of your photon. Redshift tells you how distant something is, because it tells you the value of the scale factor at the time when the photon was emitted. You can associate an expansion velocity to that, but it it does not mean that something is physically travelling in space away from you at that velocity.

You are correct that photons are infinitely redshifted when they are emitted by something that is physically moving at close to the speed of light though. We expect this to happen for particles radiating as they fall on a black hole for example, because in this case there is actual motion through spacetime.

I hope that made sense.

Cascade

Australia5405 Posts

December 06 2016 03:22 GMT

#42

On December 03 2016 00:36 Teoita wrote:

Show nested quote +

I think I understand mostly what you are saying, but I don't see how that contradicts what I wrote. The question was what happens when objects leave the visible universe, as in, the light from the object after a certain time will never reach earth. I said that the last light will stretch out over the rest of earth's time, and it'll be increasingly red shifted. Is that not correct? I didn't talk about velocities of anything at any point, or even distances.

(Edited phoned swipe typo, sorry)

Teoita

Italy12248 Posts

December 06 2016 09:40 GMT

#43

Oh shit i misunderstood the question. It's actually not that simple now that i think about it.

The reason photons get infinitely red-shifted near a black hole is due to the fact that as they move faster and faster towards the event horizon, the GR equations (as written for an observer away from the black hole) give you a bunch of infinites specifically because there's a black hole there. I doubt the same holds true for the cosmological event horizon because there is no singularity anywhere in its description, but i'm not sure. Really really funky things happen when you try to treat the cosmological event horizon in GR.

Either way, this is not tied to how fast the Universe is expanding; as i said we can still see objects "moving" away from us at faster than the speed of light.

Finally, the visibile Universe is defined in a completely different way, which is unrelated to the cosmological event horizon (thankfully it's also simpler). It is the region of space between us and the CMB. The CMB acts as an opaque screen that keeps us from seeing any light behind it; it's like trying to look at a room next to you through a wall.