Astrophysics blog - Cosmology - Page 3

On December 01 2016 14:24 Cascade wrote:

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.

On December 03 2016 00:36 Teoita wrote:


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):



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.