Silly Question Re Distance and Time

[Ian J.]

I've just read this article:

http://www.bbc.co.uk/news/science-environment-24637890

which is about a recently identified galaxy Z8_GND_5296 that is quoted as being 30 billion light years away, and yet the article also talks about the light from the galaxy being 13.1 billion years old (and that we're seeing it as it was only 700 million years after the BB). I'm having a bit of a time of it trying to work out what appears to me to be a discrepancy between the 30 and 13.1. Can someone explain how this can be, in laymen's terms without the use of formulas if possible?

TIA

Ian

 

[Bandersnatch]

Hi Ian,

It's really quite simple. As you know, space expands. Light travels from the source to the destination, which over the time of its journey move away from each other, so it has to cover more space than if it were emitted in a non-expanding universe.

An analogy would be walking on a stretching rubber band. Say you walk 2 metres per second, and at the beginning of your walk the points of origin and destination are 100 metres away. The rubber on which you walk stretches by, say, 1% every second(each and every distance you look at grows by that percentage).
After the first second of walk, you cover 2 metres, but the distance has grown by 1 metre, so you're still 99 metres away from your destination(that's not mathematically very precise treatment, by the way).
After another second, you cover another two metres, and the distance grows by 0.99 metres(1% of 99), so you're 97.99 metres away from your goal. And so on.

You should be able to see that getting from A to B does not simply take time=distance/speed, or in our case 100/2=50 seconds, but quite a lot more. In fact, if in our example you walked with the speed of 1 metre/second, or started walking from the initial distance of 200 metres, you'd never reach the destination, as the expansion of the rubber band would keep "pushing" you away at the same rate as you approach the target.

So, let's say you do get to the target, after roughly 70 seconds(that's the equivalent of ~13 billion years in the article). The point that was 100 metres away back when you started walking(equivalent of 700 million years), has been receeding all this time, increasing the distance by 1% every second(so, growing like money in bank - by more and more every second). By the 70th second, it will have receeded to almost 200 metres total(that's the 30 billion light years).

When thinking about cosmology, one has to wrap one's head around these new intuitions. The 1 light-year per a year of light's journey does no longer hold in expanding space(so, at very large scales), and when hearing of distance to some observed object, it might be necessary to specifiy whether it is the distance now, or the distance at the moment of emission of photons. Which the article did do, as you had noticed.

One of our members has created a handy calculator to help with this kind of stuff:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html
It's a bit daunting for a novice, I'm sure, but if you search for "jorrie's calculator" on the forum, you'll find plenty of good explanation for how to use it properly, should you like to. Marcus' posts are especially informative in this respect.

 

[Ian J.]

I kind of get what you're saying, but I'm still not quite sure if I understand it. I think I'm tripping over the thought in my head that says the universe is approx. 13.7 billion years old and I'm pretty sure that it's not expanding at the speed of light (or anywhere near it), so how can something be 30 billion light years away when there hasn't been 30 billion years for it to 'move'?

I'll leave it for now and sleep on it and see if I can come back to your answer with a fresh pair of neurons.

 

[Bandersnatch]

Oh yes, it most certainly can and does expand at speeds higher than the speed of light. If every distance in the universe increases by a certain percentage(can't remember the number, something like 1/144th of a percent per million years), then if you look far enough, there will be some parts moving away faster than c. I think the fastest observed objects so far move at ~3 times the speed of light.

Jorrie's calculator says the objects moving away at velocities ~c are around 14.5 billion light years NOW, and had been at ~5.8 billion light years when then emitted the light we now see. Everything farther than that(now) is receeding faster than the speed of light.

In our rubber band analogy, if 2 m/s is the speed of light, then a point 201 metres away from the observer is receding at over 2 m/s - over the speed of light.

This does not violate relativity, though. Notice that nothing ever is overtaking light here. It's still the fastest speed anything can move through space.

 

[Ian J.]

I've no problem with the expansion not breaking 'relativity', as the simple example of two objects moving away from each other at, say, two thirds light speed, create an expansion gap 'speed' of one and one third light speed (that's not counting universal expansion underneath them, now that we're mentioning it). I'm still struggling though. It's a new piece of data that I didn't know that the universe expansion is capable of being above even double light speed (which would have been the maximum I would have expected).

It's just that my lack of a scientific education means I'm missing some understanding that others here will be used to, and I'm on something of a very steep and very slow hill climb whenever I try to get my head round these things, so I still need to sleep on it a while.

 

[Chronos]

We don't see anything in the universe as it appears NOW, we only see it as it appeared when it emitted the photons we now observe. That galaxy at z=7.5 is as it appeared 700 million years after the Big Bang. Its distance NOW is utterly irrelevant.

 

[Ian J.]

Oh yes, it most certainly can and does expand at speeds higher than the speed of light. If every distance in the universe increases by a certain percentage(can't remember the number, something like 1/144th of a percent per million years), then if you look far enough, there will be some parts moving away faster than c. I think the fastest observed objects so far move at ~3 times the speed of light.
...

I think I've got it now that I've had a bit of sleep. The universe, being as big as it is, and the expansion being percentage-based and applicable everywhere, means that over the distances we're talking about the effective expansion gap 'speed' can be big, in your example ~3c. I suppose, given an infinite universe, that the expansion gap 'speed' could be infinite also.

OT: By the way, what is the precise meaning of the tilde ~ in your reply? I'm taking it to mean 'greater than' (which I would normally use '>' for), but on looking it up on Google I get the idea it's used as 'not equivalent to'.

 

[Bandersnatch]

I think I've got it now that I've had a bit of sleep. The universe, being as big as it is, and the expansion being percentage-based and applicable everywhere, means that over the distances we're talking about the effective expansion gap 'speed' can be big, in your example ~3c. I suppose, given an infinite universe, that the expansion gap 'speed' could be infinite also.

Right. Just remember that what we can observe is certainly not infinite.

OT: By the way, what is the precise meaning of the tilde ~ in your reply? I'm taking it to mean 'greater than' (which I would normally use '>' for), but on looking it up on Google I get the idea it's used as 'not equivalent to'.

That's actually meant to be "somewhere in the ballpark of", "close to this value", or something like that, since I couldn't remember the actual value. Now that you mention it, I'm no longer so sure whether this usage is standard.
(o.k., the wiki article list this use as well, so I'm absolved of my doubts: http://en.wikipedia.org/wiki/~#Mathematics)

Of course, I could've just plugged the redshift value from the article into Jorrie's calculator to get the precise result of 3.3 c(that's the speed at the moment of emission; the NOW speed is lower, but as Chronos said, talking about the NOW in the cosmological sense is not entirely productive, since we can only ever "see" the moment of emission).

 

[cepheid]

*sigh*, we get this question all the time and as a result we have *an FAQ* thread for it:

https://www.physicsforums.com/showthread.php?t=506987

(Scroll down to "Nonmathematical description" and just read that paragraph).

EDIT: Actually, you know what? I take it back. That FAQ doesn't seem very good to me for explaining this in lay terms. Looks like Bandersnatch has that covered.

EDIT 2: Attempt at a concise explanation:

If the universe were static, then the distance to a galaxy would have to be equal to the light travel time between it and us (multiplied by c). However, since the universe is expanding, that galaxy was initially closer to us when its light left, and has been steadily receding away from us since, so there is no longer a straightforward relationship between its *present* distance from us, and the amount of time its light has spent traveling here.

 

[vatzis]

So, sorry to go off topic, but when traveling faster than the speed of time, would then time be infinite if traveling at that speed? I.e. if there was matter (such as a planet) on the outskirts of the universe, would living things be living for a very long time. Or is time relevant and just hard to describe in those terms?

 

[cepheid]

The question as asked is sort of nonsensical.

So, sorry to go off topic, but when traveling faster than the speed of time, would then time be infinite if traveling at that speed?

What is the "speed of time?" I don't believe this is a meaningful concept. If you meant the speed of light, it is not possible to travel faster than the speed of light.

I.e. if there was matter (such as a planet) on the outskirts of the universe, would living things be living for a very long time. Or is time relevant and just hard to describe in those terms?

There is no such thing as the "outskirts" of the universe, because the universe has no boundaries. It also has no centre, so there is no one preferred place that can be considered the centre, and the rest "outskirts." Every point can equally-well consider itself to be the centre.

From any particular observer's point of view, time always passes at the same rate. It's only when comparing the time interval between two events as experienced by two different observers that there can be disagreement.