Cosmological time dilation of high-redshift quasars

[Cerenkov]

TL;DR Summary

https://www.nature.com/articles/s41550-023-02029-2

A fundamental prediction of relativistic cosmologies is that, owing to the expansion of space, observations of the distant cosmos should be time dilated and appear to run slower than events in the local universe.

Hello.I read this article today... https://www.eurekalert.org/news-releases/994149 ...and followed the link to this Nature Astronomy page.

https://www.nature.com/articles/s41550-023-02029-2I was wondering if this finding could be explained in a way that could help me grasp it better?

To be honest I'm struggling to understand what it means for the universe to be 'running five times more slowly' a billion years after the big bang.

Would this mean that processes like galaxy formation in the early universe appear to us to somehow run at a different rate?

And could this apparent difference in any way account for the appearance of more evolved galaxies than we might otherwise expect?

As (tentatively) suggested by some popular-level articles of the recent JWST observations of the very early universe? Thank you for any help given.Cerenkov.

 

[Bandersnatch]

Imagine you're looking at a clock that's stationary. Every time a second ticks on the clock, some light is reflected from its dial and arrives at the observer a while later. The time between the arrival of consecutive signals is one second, regardless of how far the stationary clock is. You see it ticking at one second per second, as it should.
Now, imagine the clock is moving away. It ticks one second, and some light is reflected from its dial towards you. But when it ticks again, it will have moved away a bit. So the light reflected from its dial then, showing the second tick, has a tiny bit longer to go before it reaches the observer. Longer distance to cover results in the light arriving a tiny bit later between ticks, and you see the clock running slower than it should. The faster you make the clock recede, the longer the delay.

Or, if you were receiving letters from a friend who's travelling. The friend posts a letter every day, but the farther goes the longer it takes for the postman to get to you. So even though the letters are written and sent every day, you get news every other day or so. You observe the news of your friend's exploits unfolding at a slower rate.

In terms of light signals again, if you think about what redshift does to a light wave - it increases the distance between the peaks of the wave - it must necessarily mean that it takes longer for the peaks to arrive. It takes longer by exactly the same factor as the redshift z, +1.
The +1 is there because of how redshift is defined: since we want zero redshift to mean it's the same amount of time, and not zero amount of time, we need to add 1 so that $t_0*(z+1)=t_1$.
z+1 is the reciprocal of the scale factor, and is sometimes, more intuitively, called stretch. It's all over the place in cosmology. For example, when you see something at a redshift, say, z=2, it means the universe was z+1=3 times smaller back then (both the light and the universe were 'stretched' this much between the emission and the reception of the light you observe).
All the processes observed at that redshift would be seen as z+1=3 times slower.

Now, all you need to test if this is really happening is some very distant clocks to observe. The SN Ia supernovae is one such clock, as their light decays in a very specific way over a number of weeks, with a sharp peak in brightness and gradual dimming - i.e. their light curve has a certain shape.
Observations of extragalactic supernovae show this light curve stretched in proportion to their redshift. I.e. it takes longer for receding supernovae to dim, consistent with expansion of the universe. This is well established.

The study you refer to uses quasars to do the same, in some more involved way (unlike the SN Ia supernovae, quasars are not standard candles, so it's not as easy to come up with a way to measure this with those).
The quasars they use go up to ~z=4, so the cosmological time dilation at that distance would be z+1 = five times slower.

 

[Ibix]

I can also only see the abstract.

I think one key point here is that redshift of light from distant objects is well known, but GR says that in an FLRW universe this ought to apply to the appearance of all processes as well. Contrast something like "tired light" where the redshift is supposed to be due to photon energy loss (from scattering or something) in a static universe - distant clocks would still appear to tick at the same rate as local clocks in that model, although they would appear redshifted.

So it's a testable prediction of GR that distant clocks will apparently tick slow by the same $(1+z)$ factor that they are redshifted. This work has tested that out to $z=4$ using quasars as clocks.

 

[vanhees71]

https://arxiv.org/abs/2306.04053

 

[Cerenkov]

My thanks to Bandersnatch for his excellent explanation, pitched exactly right for me.

I also thank Ibix and vanhees 71 for their helpful input.

To be honest, I'm going to have to go away and think carefully about your replies.

Quite when I'll return to this thread with a measured response and possibly some questions, I don't know.

I think I've just had the back of my head blown off and I need time to pick up the scattered pieces of my cranium, gather up the brain matter and put it all back before coming back here.Thank you,Cerenkov.

 

[PeterDonis]

Would this mean that processes like galaxy formation in the early universe appear to us to somehow run at a different rate?

Appear. Yes. But...

And could this apparent difference in any way account for the appearance of more evolved galaxies than we might otherwise expect?

No, because it's only an appearance, due to the expansion of the universe between the time the light was emitted and now. It has nothing to do with the actual rate of processes; that was the same back then as now.

 

[Hornbein]

"the cosmological time dilation at that distance would be five times slower."

! I had no idea.

 

[Ibix]

I must say I'm not sure I'd really call this "time dilation". It's just that the way GR creates the redshift means that all timescales are predicted to be redshifted, not just the light. I suppose they do need a term other than redshift since they are considering the possibility that redshift of light is a distinct process from the frequency change in other processes that we can see in the same source. But "time dilation" sounds like a loaded term to me. In both gravitational and kinematic time dilation you establish some method of saying that two pairs of events on two worldlines were simultaneous and you compare the elapsed time between the events on one worldline to the elapsed time between events on the other. But to apply that definition here our simultaneity surface would have to be our past lightcone which is a null surface not a spacelike one. Adding to that, the result they have is that the same $z$ applies to all phenomena they've looked at, so there's no effect detected except redshift.

Put in less technical language, I think "time dilation" is a fine term for the various "clocks tick slower over there/at that speed" effects. I'm less comfortable with broadening the term to include "clocks ticked slower back then", especially since the result of this work can be read as "they didn't".

 

[PeterDonis]

I'm not sure I'd really call this "time dilation"

I would agree. Another consideration that points in this direction is that you can't compare clock rates now and far in the past by exchanging light signals, the way that, for example, two observers at rest at different altitudes in the gravitational field of a planet can.