How big was the Universe 13 billion years ago?

[Endervhar]

How big was the Universe 13 billion years ago??

If we look from the Earth, in opposite directions, at objects that are 13 billion LY away, they are 26 billion LY apart.

We are seeing them as/where they were 13 billion years ago, so they must have been 26 billion LY apart then.

This cannot mean that, 13 billion years ago, the Universe was, at the very least, 26 billion LY in diameter. How do I even start to explain this to someone who seems to expect me to know, simply because I post on a science forum?

 

[tiny-tim]

Hi Endervhar!

Explain them as trains, they started very close to you, and now they're 13 billion LY away in opposite directions.

So what?

 

[Mordred]

Its difficult to figure out what your asking. It sounds like your asking how two objects can be 26 billion LY apart 13 billion years ago. Today the universe is 93 billion LY across. This is not to say this is the edge of the universe. Its the edge of the observable universe today.

How do we see a Universe so much larger than its age. This is due to expansion. In the sticky threads above there is a description of the balloon
analogy. It has a decent explanation

 

[skydivephil]

The short answer is no one knows the size of the universe now so we can't say what it was in the past either. If it's infinite now, then it was so in the past.
A source of confusion is the many different types of distance measure used in cosmology, here is a short guide:
http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Astronomical_distance.html
and here is a more detailed explanation:
http://www.publish.csiro.au/?act=view_file&file_id=AS03040.pdf

 

[marcus]

Endervhar, you are asking about the OBSERVABLE universe, distances now, and in the past, to material that we can now see (or could in principle, with more advanced instruments, see). that's a fine sort of question! When you learn how to read it, this table can help you.

Look at the top row. It says the most ancient light we can see came from hydrogen whose distance THEN from us was 42 million lightyears and that matter is NOW 45.7 billion lightyears (45.7 Gly) from here.

It says that it emitted the light in Year 378,000. That is what 0.000378 Gy means.

Quite possibly you have no trouble at all reading the table and interpreting half the numbers in the top row. The calculator that generated the table is easy to use and has info popups that explain whatever entries you want explanation for. I chose the table to have 30 rows, but you can get it to recalculate with more or fewer rows, and change other stuff ad lib:

{\begin{array}{|c|c|c|c|c|c|c|}\hline Y_{now} (Gy) & Y_{inf} (Gy) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline14&16.5&3280&69.86&0.72&0.28\\ \hline\end{array}} {\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&T_{Hub}(Gy)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline1090.000&0.000917&0.000378&0.000637&45.731&0.042&0.056&0.001\\ \hline856.422&0.001168&0.000566&0.000940&45.550&0.053&0.072&0.001\\ \hline672.897&0.001486&0.000842&0.001381&45.341&0.067&0.091&0.002\\ \hline528.701&0.001891&0.001247&0.002020&45.101&0.085&0.115&0.003\\ \hline415.404&0.002407&0.001839&0.002944&44.825&0.108&0.146&0.004\\ \hline326.387&0.003064&0.002700&0.004279&44.509&0.136&0.185&0.007\\ \hline256.445&0.003899&0.003951&0.006205&44.150&0.172&0.234&0.010\\ \hline201.491&0.004963&0.005761&0.008979&43.740&0.217&0.296&0.015\\ \hline158.313&0.006317&0.008379&0.012973&43.275&0.273&0.373&0.021\\ \hline124.388&0.008039&0.012159&0.018720&42.747&0.344&0.471&0.032\\ \hline97.732&0.010232&0.017610&0.026985&42.149&0.431&0.593&0.046\\ \hline76.789&0.013023&0.025465&0.038867&41.472&0.540&0.746&0.068\\ \hline60.334&0.016574&0.036773&0.055945&40.706&0.675&0.937&0.099\\ \hline47.405&0.021095&0.053047&0.080484&39.840&0.840&1.174&0.144\\ \hline37.246&0.026848&0.076452&0.115738&38.861&1.043&1.468&0.210\\ \hline29.265&0.034171&0.110103&0.166377&37.755&1.290&1.830&0.305\\ \hline22.993&0.043491&0.158470&0.239106&36.507&1.588&2.275&0.442\\ \hline18.066&0.055352&0.227971&0.343537&35.097&1.943&2.818&0.641\\ \hline14.195&0.070449&0.327812&0.493442&33.506&2.360&3.474&0.927\\ \hline11.153&0.089663&0.471192&0.708498&31.711&2.843&4.261&1.341\\ \hline8.763&0.114117&0.677001&1.016667&29.686&3.388&5.192&1.938\\ \hline6.885&0.145241&0.972188&1.457265&27.404&3.980&6.276&2.798\\ \hline5.410&0.184854&1.394848&2.084258&24.837&4.591&7.513&4.036\\ \hline4.250&0.235270&1.998124&2.968150&21.958&5.166&8.885&5.814\\ \hline3.340&0.299437&2.853772&4.190977&18.748&5.614&10.347&8.361\\ \hline2.624&0.381105&4.052600&5.822089&15.215&5.798&11.823&11.988\\ \hline2.062&0.485047&5.694902&7.857010&11.408&5.534&13.201&17.104\\ \hline1.620&0.617337&7.861899&10.128494&7.459&4.605&14.363&24.207\\ \hline1.273&0.785708&10.571513&12.291156&3.574&2.808&15.228&33.862\\ \hline1.000&1.000000&13.753303&13.999929&0.000&0.000&15.793&46.686\\ \hline\end{array}}
Time now (at S=1) or present age in billion years: 13.75330. 'T' in billion years (Gy) and 'D' in billion light years (Gly)
==========
The 0.042 Gly in the top row "Distance then" column is what I was interpreting as 42 million lightyears. The source of the cosmic microwave background (hydrogen then in the form of glowing hot partly ionized gas) was then much closer of course. Over a thousandfold closer than the same material is today. We see it as it was (namely hot gas) but now the same material is not at the same distance, of course.

I'd suggest you bookmark the link to the calculator:
http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html
It's a good learning tool. It makes tables showing the history of the cosmos, where you can specify the range of the table (the start and end) and the number of steps. To get a table with 30 rows you specify 29 steps. that is what I did to make this one. And I specified that the bottom row of the table should be S=1, which is to say the present day. Otherwise I just used the default settings.

 

[Endervhar]

Thanks folks. Quite a lot to wade through, there, might need to sign up for a maths course to stand a chance of getting my head round some of it, :)

I think I may have given the wrong impression originally. The OP was actually the first part of a two part question that I was still trying to formulate in my head.

I have recast that first bit, just to check whether I am asking a question that makes any sense, before (perhaps) progressing to the next bit.

Two objects are measured as being 13 billion ly from Earth, in opposite directions.

The light from these objects has taken 13 billion years to reach Earth; thus they are now observed as being in the positions they occupied 13 billion years ago.

These objects are currently observed as being 26 billion ly apart. Obviously they no longer occupy these positions, because 13 billion years of expansion will have moved them.

However, it appears that they must have been 26 billion ly apart 13 billion years ago.

Is the reasoning sound, so far?

 

[Bandersnatch]

However, it appears that they must have been 26 billion ly apart 13 billion years ago.

Unfortunately, the answer is no.

The light from the farthest objects we see now traveled for 13,7 billion years - that bit is true.

edit:
[strike]But it covered more than 13,7 billion light years, due to the stretching of space as it went.[/strike]
O.k., this was badly put. It's not that it covered more, it's that the point of origin moved away due to the stretching of space as the light travelled, so it's now much farther than 13,7 bln ly.
end_edit

Furthermore, at the moment of emission, the source was 42 million years away.

These numbers all emerge naturally when you consider what it means to have the space expand.

Here's how I'd explain it to somebody using analogies:

Imagine that you're walking through expanding space.

You start at 100 paces away from your target, you make 1 pace per second, and each second all the distances are increased by 1%.

After making the first step you are 99 paces away from your target, and then the distances stretch by 1%(it's easier to think of it this way, but obviously it all happens simultaionously).
So, in effect, after 1 second of travel, you are 99,99 paces away.
You make another step, taking you to 98,99 paces away, and the space stretches by 1%, so you end up 99,9799 paces away.
And so on.

It should be obvious to see that getting to your destination will take much, much more than 100 seconds. That's pretty much why the light that was originally emitted at 42 million ly is only getting to us now.

Another intereting observation to make is that if you were to start at 101 paces away, then you will never reach your destination, as after each step the stretching of space takes you back to 101 paces away. And, obviously, anything initially farther than that will in effect move away despite walking at the same, steady speed of 1 pace per second.
This means that there is a distance beyond which we may never, ever, see. At this particular moment, if you could measure the distances as they are right now, the farthest point from which we will ever receive light lies 16,5 billion ly away. Of course, by the time the light arrives, the original emitter will have moved way farther than that.

Additionally, you might notice than the closer your starting point is to 101 paces away, the longer it takes to reach the destination - by a huge factor, reaching infinity as it approaches the limit at 101 paces.
So there's always some microwave background light you're going to receive, even though it's slowly getting stretched(redshifted) to infinity.

 

[marcus]

...
Two objects are measured as being 13 billion ly from Earth, in opposite directions.

The light from these objects has taken 13 billion years to reach Earth...

But that's not how it works. You're making shaky assumptions.

Look at the table. It shows the distances back THEN when the objects emitted their light that we are now getting. We do not see objects which were 13 billion lightyears (13 Gly) when the light was emitted. We have never gotten their light.

We do receive light from objects which are NOW 13 Gly from us. Look in the table in the D column. You can discover how far they were back THEN when they emitted the light. And the table will show you how long the light took to get here.

Look down the D (the "distance now" column) and you'll find a row for an object which is NOW 12.7 Gly from us. You can see it emitted the light in year 5 billion. The present time is 13.7 billion. So the light took 8.7 billion years to get here.

{\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&T_{Hub}(Gy)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline5.000&0.200000&1.568895&2.340770&23.932&4.786&7.948&4.548\\ \hline4.372&0.228706&1.915830&2.848499&22.312&5.103&8.718&5.571\\ \hline3.824&0.261532&2.337530&3.458116&20.591&5.385&9.519&6.821\\ \hline3.344&0.299070&2.848622&4.183756&18.766&5.612&10.340&8.346\\ \hline2.924&0.341995&3.465480&5.036801&16.839&5.759&11.165&10.202\\ \hline2.557&0.391082&4.205616&6.022104&14.818&5.795&11.977&12.457\\ \hline2.236&0.447214&5.086472&7.132820&12.714&5.686&12.755&15.186\\ \hline1.955&0.511402&6.123474&8.344913&10.548&5.394&13.478&18.474\\ \hline1.710&0.584804&7.327464&9.613886&8.348&4.882&14.126&22.412\\ \hline1.495&0.668740&8.702047&10.877416&6.152&4.114&14.685&27.097\\ \hline1.308&0.764724&10.241950&12.066023&3.999&3.058&15.147&32.633\\ \hline1.144&0.874485&11.932654&13.119328&1.932&1.690&15.513&39.124\\ \hline1.000&1.000000&13.753303&13.999929&0.000&0.000&15.793&46.686\\ \hline\end{array}}

To understand something of the expansion history of the universe doesn't necessarily require high school math (i.e. algebra, calculus...). You can get some notion if you know ARITHMETIC. A table like this can be especially helpful to people who rely on simple logic and arithmetic. Please use it.
You asked about an example of an object that is NOW 13 Gly from here. Take 12.7 Gly as close enough.

Such an object would have been 5.686 Gly from here back then, when it emitted the light.
We see it as it was in year 5.08 billion (when it emitted the light we're getting).
The light has taken 8.7 billion years to get here.

Because of expansion of the distance it has to travel, the light naturally has to take somewhat longer (8.7) than it would with no expansion! It started out when the object was only 5.7 billion lightyears away. So that tells you how long it would have taken without expansion. But the distance increased some while it was traveling. So naturally it takes longer, namely 8.7.

And when the light arrives, today, in year 13.7 billion, the object is already 12.7 billion lightyears from us! That indicates how long some new light would take to get here if you could freeze the expansion process and wait for it. With expansion stopped it would take 12.7 billion years.

Hope this helps.

 

[Endervhar]

Thanks again.

I think things are getting clearer. I shall give it some thought before deciding if I still need to ask the second part of the question.

The passage of light through an expanding Universe seems to have much in common with grasping new concepts as one gets older. It takes longer to get there at 72 than it did at 42. :)

 

[marcus]

Thanks again.

I think things are getting clearer. I shall give it some thought before deciding if I still need to ask the second part of the question.

The passage of light through an expanding Universe seems to have much in common with grasping new concepts as one gets older. It takes longer to get there at 72 than it did at 42. :)

Yes! A very apt comparison! I am 75 and will spare you some of the annoying details you may still have to look forward to The main thing (as we seem both to have discovered) is to be cheerful and keep struggling to understand. Faced with such a beautiful universe, I think it is the only honorable thing to do.

 

[marcus]

Endervhar, I had an idea of how to make that particular table more readable. I just changed the "number of decimal places" down to ONE. (or two)
Jorrie's calculator let's you decide on the desired level of precision in each column. So this is the same as the earlier table except ROUNDED OFF:

{\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&T_{Hub}(Gy)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline5.0&0.20&1.6&2.3&23.9&4.8&7.9&4.5\\ \hline4.4&0.23&1.9&2.8&22.3&5.1&8.7&5.6\\ \hline3.8&0.26&2.3&3.5&20.6&5.4&9.5&6.8\\ \hline3.3&0.30&2.8&4.2&18.8&5.6&10.3&8.3\\ \hline2.9&0.34&3.5&5.0&16.8&5.8&11.2&10.2\\ \hline2.6&0.39&4.2&6.0&14.8&5.8&12.0&12.5\\ \hline2.2&0.45&5.1&7.1&12.7&5.7&12.8&15.2\\ \hline2.0&0.51&6.1&8.3&10.5&5.4&13.5&18.5\\ \hline1.7&0.58&7.3&9.6&8.3&4.9&14.1&22.4\\ \hline1.5&0.67&8.7&10.9&6.2&4.1&14.7&27.1\\ \hline1.3&0.76&10.2&12.1&4.0&3.1&15.1&32.6\\ \hline1.1&0.87&11.9&13.1&1.9&1.7&15.5&39.1\\ \hline1.0&1.00&13.8&14.0&0.0&0.0&15.8&46.7\\ \hline\end{array}}Time now (at S=1) or present age in billion years: 13.8
=========================
So then it is easier to narrate the table. Easier to talk about what it's telling us. Back in year 5.1 billion there was a galaxy at distance 5.7 from us that sent us some light...
And it took 8.7 billion years to get here, during which time the distance 5.7 had expanded to 12.7.

Obviously the light had a tough time making it, but it got here. And some of the other light we are getting had an even tougher time of it, a really uphill battle so to speak. You can read off narratives of other light from other rows of the table.

So far you and I are only using 3 columns of the table: T (the time), D (the galaxy's distance NOW), and D_then (the galaxy's distance back then when it emitted the light we are getting today).

If and when you feel like acquiring some of the other columns, so you can include them in other narratives, just indicate an interest in doing that.

 

[Endervhar]

So far, so good! Some light filters through.

"...it took 8.7 billion years to get here..."

Where did that come from?

 

[Endervhar]

Scrap that last question, the light just arrived!

 

[marcus]

Good! Now I want to lay out an introduction to the fourth column, for when and if you want to proceed to that. There's no rush (especially for us septuagenarians, we absorb new info at a deliberate pace, when we are ready.)

At every age in the history of the universe there is a distance that is growing at exactly the speed of light.

If you are a distance which is LESS than this characteristic one then you are growing at less than the speed of light. If you are a distance which is MORE than this characteristic key distance then you are growing proportionately FASTER. So if you are twice that key distance you must be growing at twice the speed of light: 2c.

It's very handy for keeping track of the rates that distances are expanding, and it changes over time. A Russian mathematician named Friedmann discovered how to describe the expansion history with an equation that simply tells us how this key quantity evolves over time. It's a really really good handle on expansion, and the history of expansion.

The third column of the table gives the AGE of the universe from the moment distances began expanding. The fourth column gives you this key distance---or more exactly it gives the time equivalent. You can read it either in Gy (as shown) or in Gly.

So if and when you get curious about the RATES that distances are expanding at different ages of the universe, you can mull over some narratives involving the fourth column.
==================

Just as an example, looking back at the table:
suppose it is year 4.2 billion and a galaxy which is 5.8 Gly from here sends some light in our direction.

(According to the table that light would be destined to arrive here in year 13.8 billion for us to detect.)

At the time the light was sent, namely year 4.2 billion, how fast was that distance of 5.8 Gly expanding?

The table says that the key distance (a kind of "speed-threshhold" distance) was 6.0 Gly. So that distance of 5.8 was expanding at NOT QUITE THE SPEED OF LIGHT. We can calculate it: 5.8/6.0 c

 

[phyzguy]

Yes! The main thing (as we seem both to have discovered) is to be cheerful and keep struggling to understand. Faced with such a beautiful universe, I think it is the only honorable thing to do.

Well said, Marcus!

 

[marcus]

Thanks Phyzguy! If you have any experience or pedagogical ideas, or ways of explaining stuff, that you think might help in this thread---eg to get Ender interested and deeper into subject matter--please share them.

Getting back to the table, there is an ARITHMETIC hurdle to get over. The first row says that at that particular time (year 1.6 billion) distances were growing at the rate of
1/23 of a percent per million years.

Another way to say the same thing is that at that particular time (i.e. that row in the table) the distance that was growing at exactly the speed of light was 2.3 billion ly.

A person ought to be able to work out by simple arithmetic that those two statements are equivalent. In other words

what is 1/23 % of 2.3 billion ly? that is how much the distance grows in a million years. so if the answer turns out to be a million ly, then that son-of-yardstick is growing at the speed of light.

That could be obvious, but it's worth remarking because those are two ways we interpret the fourth column of the table (a percentage expansion rate and as the distance growing exactly at speed of light.)

{\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&T_{Hub}(Gy)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline5.0&0.20&1.6&2.3&23.9&4.8&7.9&4.5\\ \hline4.4&0.23&1.9&2.8&22.3&5.1&8.7&5.6\\ \hline3.8&0.26&2.3&3.5&20.6&5.4&9.5&6.8\\ \hline3.3&0.30&2.8&4.2&18.8&5.6&10.3&8.3\\ \hline2.9&0.34&3.5&5.0&16.8&5.8&11.2&10.2\\ \hline2.6&0.39&4.2&6.0&14.8&5.8&12.0&12.5\\ \hline2.2&0.45&5.1&7.1&12.7&5.7&12.8&15.2\\ \hline2.0&0.51&6.1&8.3&10.5&5.4&13.5&18.5\\ \hline1.7&0.58&7.3&9.6&8.3&4.9&14.1&22.4\\ \hline1.5&0.67&8.7&10.9&6.2&4.1&14.7&27.1\\ \hline1.3&0.76&10.2&12.1&4.0&3.1&15.1&32.6\\ \hline1.1&0.87&11.9&13.1&1.9&1.7&15.5&39.1\\ \hline1.0&1.00&13.8&14.0&0.0&0.0&15.8&46.7\\ \hline\end{array}}Time now (at S=1) or present age in billion years: 13.8
=========================

BTW Phyzguy, have you tried the calculator yet? If not I hope you will. I keep the link in my signature--it is
http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html
You get to set the upper and lower limits of the table, and the number of steps. To get the table I have in this thread you set upper = 5, and lower=1, and steps=12. You should get exactly what we have here. And at the top of each column there is a box with the number of decimal places. You can leave it as it is, or bring the number down to 2 or 1 to make table easer to read.

 

[marcus]

Since we just turned a page, I'll recopy the table discussed in the previous post, to have it available for reference.
This is what you get from
http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html
if you set upper = 5, and lower=1, and steps=12. And at the top of each column there is a box where you can change the desired the number of decimal places. You can leave it as it is, or bring the number down to 2 or 1 to make table easer to read.

{\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&T_{Hub}(Gy)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline5.0&0.20&1.6&2.3&23.9&4.8&7.9&4.5\\ \hline4.4&0.23&1.9&2.8&22.3&5.1&8.7&5.6\\ \hline3.8&0.26&2.3&3.5&20.6&5.4&9.5&6.8\\ \hline3.3&0.30&2.8&4.2&18.8&5.6&10.3&8.3\\ \hline2.9&0.34&3.5&5.0&16.8&5.8&11.2&10.2\\ \hline2.6&0.39&4.2&6.0&14.8&5.8&12.0&12.5\\ \hline2.2&0.45&5.1&7.1&12.7&5.7&12.8&15.2\\ \hline2.0&0.51&6.1&8.3&10.5&5.4&13.5&18.5\\ \hline1.7&0.58&7.3&9.6&8.3&4.9&14.1&22.4\\ \hline1.5&0.67&8.7&10.9&6.2&4.1&14.7&27.1\\ \hline1.3&0.76&10.2&12.1&4.0&3.1&15.1&32.6\\ \hline1.1&0.87&11.9&13.1&1.9&1.7&15.5&39.1\\ \hline1.0&1.00&13.8&14.0&0.0&0.0&15.8&46.7\\ \hline\end{array}}Time now (at S=1) or present age in billion years: 13.8

To this sample of a stripped down history table, could we add some "time-line" contextual information? I don't mean on the table itself, but in our posts commenting on it: as a help to assimilation---some famiiar landmarks to help relate to it?

I was reminded that Deuterium2H posted about when the first rocky planets might have formed. A good guess is around year 4.2 billion: the 6th row of the above table. Here is his post. It's about when the oldest metal-rich stars could have formed.
https://www.physicsforums.com/showthread.php?p=3105934#post3105934
It came up just now in the "earliest rocky planet" thread https://www.physicsforums.com/showthread.php?p=4292203#post4292203

In case anyone is new to the topic, the metal-rich ("Population 1") stars are those enriched in elements heavier than hydrogen and helium---elements such as carbon, silicon, oxygen cooked for them in earlier generations of stars. "Metals" in this context just means anything heavier than helium.

So as a rough guess the first such stars, and rocky planets, could have been appearing around the era labeled stretch 2.6. The light from galaxies in the process of forming such stars will have been wave-stretched by a factor of S=2.6 on its way to reach us. We will be seeing them as they were in year 4.2 billion, when their distance from here was about 5.8 billion lightyears (if one could have stopped the expansion process and measured it.)

And the distance in the universe that was expanding at the speed of light, at that time, was 6.0 billion lightyears---which is to say that distances were expanding at a percentage rate of 1/60 of a percent per million years. (See the previous post for discussion of that.)

 

[Mordred]

http://www.lanl.gov/science-innovation/science-features/planetary-formation-theory.php

here is one related article. Marcus if you target the 10% metal percentage mentioned in the above. That may help narrow down the age.
This is kind of a fun question to answer

http://www.space.com/17441-universe-heavy-metals-planet-formation.html

according to the above the conditions needed may be earlier than we think as gas giants also may also require heavy metals

 

[Endervhar]

Just a note to say that I'm not ignoring the helpful information that has been posted through lack of interest. Last Tue I was discharged after 10 days in hospital with pneumonia. I thought the enforced inactivity would give me a good opportunity to get to grips with this time/distance stuff, but the recovery isn't going as well as hoped, so I'm not doing a lot of effective thinking.

That's my excuse, and I'm sticking to it!
I have every intention of getting there eventually.

 

[Mordred]

Thanks for letting us know and good luck on your recovery

 

[Endervhar]

Thanks for the good wishes. Recovery is progressing steadily. I think I feel brave enough to return to the table.

I would be wise to check my understanding of the columns we have looked at so far, in case any of my questions arise from misinterpretation on my part.

Col 1 looks as though it might be time from the B B, obtained by prefixing the number in each row with a 1.

Col 3: Time from B B to emission of light.

Col 4: Time/distance at which expansion = c.

Col 5: Distance from Earth now.

Col 6: Distance from Earth at time of light emission.

Recession rate = c if figure from Col 6 over figure from Col 4 = 1.

 

[Endervhar]

Having looked back at the original table, and at the calculator, my interpretation of Col 1 begins to look a bit suspect!

 

[marcus]

Thanks for the good wishes. Recovery is progressing steadily. I think I feel brave enough to return to the table.
...
...
Col 3: Time from B B to emission of light.

Col 4: Time/distance at which expansion = c.

Col 5: Distance from Earth now.

Col 6: Distance from Earth at time of light emission.

Recession rate = c if figure from Col 6 over figure from Col 4 = 1.

Great to hear you are feeling better!

Column 1 is the factor by which wavelengths and distances have been stretched while the light was on its way to us.

S=2 means that distances have doubled since that time in the past.
S=1 means distances are unchanged---so it designates the present.

S is a convenient handle on time, partly because it is directly observable in light received from a distant galaxy. One can compare a pattern of lines recognizable as light from hydrogen with the hydrogen lines measured in the lab. If the wavelengths are all 3 times what they are in the lab spectrum then the light came from S=3. The light itself tells you want S it came from. Then you have to FIGURE OUT (using a mathematical model of the expansion history) what YEAR it came from.

For sending a light signal into the future, you can use the reciprocal of S. If we send a signal flash of light now and it is received at S=0.25,that means its wavelengths will be 4 times what they are now, when the light is received. And distances will be 4 times what they are now.

 

[Endervhar]

Shall have to give that a bit of thought to make sure I've grasped it; but perhaps not tonight.

 

[marcus]

Get plenty of good rest! No rush about understanding or responding, getting well is what matters obviously
Take care.

In case anyone else is reading, and is interested in how the S number labels future times, here is an example of what it looks like when the table is extended to show future times and distances:

{\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&T_{Hub}(Gy)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline5.000&0.200000&1.568895&2.340770&23.932&4.786&7.948&4.548\\ \hline4.257&0.234924&1.993736&2.961797&21.976&5.163&8.876&5.802\\ \hline3.624&0.275946&2.530365&3.733720&19.873&5.484&9.846&7.395\\ \hline3.085&0.324131&3.204929&4.679779&17.622&5.712&10.835&9.416\\ \hline2.627&0.380731&4.046898&5.814584&15.229&5.798&11.817&11.971\\ \hline2.236&0.447214&5.086472&7.132820&12.714&5.686&12.755&15.186\\ \hline1.904&0.525306&6.350729&8.595943&10.110&5.311&13.614&19.206\\ \hline1.621&0.617034&7.856937&10.123842&7.467&4.607&14.361&24.191\\ \hline1.380&0.724780&9.606917&11.603830&4.852&3.517&14.974&30.310\\ \hline1.175&0.851340&11.583300&12.921724&2.337&1.990&15.447&37.744\\ \hline1.000&1.000000&13.753303&13.999929&0.000&0.000&15.793&46.686\\ \hline0.851&1.174619&16.075618&14.817189&-2.158&-2.535&16.033&57.356\\ \hline0.725&1.379730&18.510100&15.398913&-4.071&-5.618&16.192&70.012\\ \hline0.617&1.620657&21.022329&15.794056&-5.753&-9.323&16.295&84.962\\ \hline0.525&1.903654&23.586586&16.053616&-7.214&-13.733&16.359&102.579\\ \hline0.447&2.236068&26.184795&16.220171&-8.474&-18.949&16.397&123.310\\ \hline0.381&2.626528&28.804384&16.325686&-9.556&-25.100&16.418&147.685\\ \hline0.324&3.085169&31.437702&16.391695&-10.482&-32.340&16.428&176.330\\ \hline0.276&3.623898&34.079335&16.432954&-11.273&-40.853&16.433&209.986\\ \hline0.235&4.256700&36.726405&16.458434&-11.948&-50.859&16.458&249.526\\ \hline0.200&5.000000&39.376581&16.474344&-12.523&-62.615&16.474&295.973\\ \hline\end{array}}
Time now ( S=1) year 13.75 billion. S always tells how big the wavelength is HERE and now (when we receive or send some light) compared with what it is at the other end. That is true whether we are talking about some emission in the past, or reception in the future.

 

[Endervhar]

What is the significance of the "z" in S=z+1?

 

[marcus]

It's just the same thing with different notation. If a distance quadruples, becomes 4 times its length, that is S=4 times original. But, you could always say it "increased by 3 times its length added on to what it had to begin with". It would mean the same. So if you like you can take z = S - 1 and talk in terms of that.

By historical accident that is how people (like Edwin Hubble) first began talking about it. They made their charts and tables in terms of z (which they called "redshift")

However in the formulas and equations we use it is typically the full multiplication factor that enters. This calculator is executed in terms of S, rather than z=S-1.
It also turns out to be somewhat more convenient for indexing times in the future.

The ancient light of the microwave background has been stretched by a factor S=1090. So each wavelength is now 1090 times its original length.

But you could also say that the ancient light's z = 1089 and that each wavelength is now its original length PLUS 1089 times its original length.
It is just a matter of convenience which notation to use. If you think in terms of z, then you say that
length now = original length + z times original length.

I find it more convenient to just think
length now = S times original length
even though it is still conventional for people to use the z (redshift) number.

 

[Endervhar]

Thanks, I think things are beginning to make sense.

Later this week I should be seeing the friend whose question started all this. I know he will not be looking for a particularly technical/mathematical explanation.

Hopefully, something along the lines of the following will suffice, so I thought I would ask to have a "red pen" run over it to make sure I'm not too far off the mark. (I have used 13.8 Gy as being closest to the age of the Universe).

Light from a distant galaxy has taken 13.8 Gy to reach Earth. The Universe has expanded in that time, so obviously, that galaxy is no longer at 13.8 Gly from Earth. Does this mean it was at 13.8 Gly from Earth 13.8 Gy ago?

This would be the case only if the Universe were static, or if expansion resulted from galaxies moving away from one another through space. As, manifestly, such is not the case, it becomes necessary to calculate where the galaxy would have been, relative to the position now occupied by the Earth, at the time when the light was emitted.

Using the appropriate (simplified) table to calculate time and distance we find that if a galaxy sent some light in our direction in the year 2.3 billion (2.3 Gy post BB), it would then have been 5.4 Gly from Earth. The light would have taken 11.5 Gy to reach Earth, but in that time the intervening distance would have expanded to 13.8 Gly.

 

[marcus]

Ender, in an expanding universe it can be confusing to use LIGHT TRAVEL TIME as a measure of distance. Most often we are using what is called "proper" distance at an indicated moment of time which is how far something was AT THAT INSTANT if you could temporarily freeze the expansion process to measure---say with radar while the distance is not changing.

Light travel time does not have any simple relation either to distance THEN when the light was emitted, or to distance NOW, on the day we receive the light. For example looking at the first row of table.
Suppose a galaxy emits some light in year 1.6 billion, and the galaxy is 4.8 billion lightyears from here. Then the light will be just arriving now (the table indicates) and it will have traveled for 12.2 billion years. (Subtract 13.8 - 1.6)
However the distance to the galaxy NOW is 23.9 billion lightyears.

Distance then = 4.8
Distance now = 23.9
Travel time = 12.2 billion years (the time has no simple practical relation with either distance)

{\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&T_{Hub}(Gy)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline5.0&0.20&1.6&2.3&23.9&4.8&7.9&4.5\\ \hline4.4&0.23&1.9&2.8&22.3&5.1&8.7&5.6\\ \hline3.8&0.26&2.3&3.5&20.6&5.4&9.5&6.8\\ \hline3.3&0.30&2.8&4.2&18.8&5.6&10.3&8.3\\ \hline2.9&0.34&3.5&5.0&16.8&5.8&11.2&10.2\\ \hline2.6&0.39&4.2&6.0&14.8&5.8&12.0&12.5\\ \hline2.2&0.45&5.1&7.1&12.7&5.7&12.8&15.2\\ \hline2.0&0.51&6.1&8.3&10.5&5.4&13.5&18.5\\ \hline1.7&0.58&7.3&9.6&8.3&4.9&14.1&22.4\\ \hline1.5&0.67&8.7&10.9&6.2&4.1&14.7&27.1\\ \hline1.3&0.76&10.2&12.1&4.0&3.1&15.1&32.6\\ \hline1.1&0.87&11.9&13.1&1.9&1.7&15.5&39.1\\ \hline1.0&1.00&13.8&14.0&0.0&0.0&15.8&46.7\\ \hline\end{array}}Time now (at S=1) or present age in billion years: 13.8
http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html This is what you get
if you set upper = 5, and lower=1, and steps=12. And at the top of each column there is a box where you can put the desired the number of decimal places. In this case I brought that number down to 2 or 1 (fewer decimal places) to make table easer to read.

The reason there is no simple relation between the travel time and the distances is that the rate of expansion has changed over the course of history according to a formula. That's basically why a calculator is used to convert between different measures like stretch factor, time, distances etc.

Here's another example: the first rocky planets might have formed around year 4.2 billion: the 6th row of the above table. It's about when the oldest metal-rich stars could have formed, these are ("Population 1") stars enriched in elements heavier than hydrogen and helium---elements such as carbon, silicon, oxygen cooked for them in earlier generations of stars. "Metals" in this context just means anything heavier than helium.

So as a rough guess the first such stars could have been appearing around the era labeled stretch 2.6. The light from galaxies in the process of forming such stars will have been wave-stretched by a factor of S=2.6 on its way to reach us. We will be seeing them as they were in year 4.2 billion, when their distance from here was THEN about 5.8 billion lightyears (if one could have stopped the expansion process and measured it.)

The light will have taken 9.6 billion years to get here, the elapsed time from years 4.2 billion to 13.8 billion.
And those stars' distance from us is NOW 14.8 billion lightyears.

Distance then = 5.8
Distance now = 14.8
Travel time = 9.6 billion years

 

[Endervhar]

Marcus, thanks for your continued, patient input. I had already suspected that something was wrong and had returned to the forum to post the following:

Problem here?

In the example I suggest above, the figure in Col 6 =5.4 and the figure in Col 4 = 3.5.

5.4/3.5 = (roughly) 1.543. Would this mean that at the time of emission the recession rate was above c? In which case the light would not reach Earth?

I think the main trouble is that I have still not got my head round the use of the calculator.
I followed your suggestion and " set upper = 5, and lower=1, and steps=12.", but I have to confess that I didn't really know what I was doing.

Feel free to give up as a bad job. :(

 

[marcus]

...
In the example I suggest above, the figure in Col 6 =5.4 and the figure in Col 4 = 3.5.

5.4/3.5 = (roughly) 1.543. Would this mean that at the time of emission the recession rate was above c? In which case the light would not reach Earth?...

You are asking just the right question! In fact it would eventually reach earth! this is a surprising thing that most people do not realize.

As you point out it would at first LOSE GROUND. It would be swept back at the rate of about 0.5c as you calculate. But if it hangs in there and keeps trying it will eventually make it.

It starts in year 2.3 billion and in fact in the next 0.5 billion years it will only be swept back a total of 0.2 billion ly, and it will be at a distance of 5.6 billion ly from us. Look at the next row of the table.
in year 2.3 billion the ratio you calculated before is now 1.3333 (5.6/4.2) and if you average those recession speeds (1.5 and 1.3) you get 1.4. So for the first 0.5 billion years he is losing ground at an average rate of 0.4c, therefore he has lost 0.2. therefore he is at 5.6!

But that is also on track. If a galaxy is at distance 5.6 in year 2.8 and emits some light, that light will also get here today. Even though the distance to the galaxy is increasing at 1.333 c and the light initially gets swept back at 0.333c.

In the next 0.7 billion years he will only get swept back, again, by 0.2 . So in year 3.5 he will be only a little worse off---at distance 5.8 from us. You see these numbers in the next row?

Now he's essentially safe! because that distance is only increasing at about the speed of light, so he is not making headway but at least he is not getting swept back. He is "breaking even" so to speak.

For the next 0.7 billion years (from 3.5 to 4.2) the average recession speed is about the average of 5.8/5 and 5.8/6 which is 1.06 so he is only losing 0.7 times 0.6 or 0.04 billion lightyears. At year 4.2 billion he is still essentially at distance 5.8!
And then he starts gaining ground!

Any photon of light that, in year 4.2 billion is only at distance 5.8 from us, you can see from the table is making HEADWAY!
The distance is only increasing at 5.8/6 c, that is less than the speed of light. And he is proceeding towards us at the speed of light. So he is gaining. And it gets better and better as he gets nearer.

In a universe with expansion like ours, the real light cone is PEAR SHAPE. Photons at the bottom get swept outwards away from us at first but they hang in there and keep trying and eventually come up the rounded side of the pear and start to come in towards us. The D_then column of the table outlines the teardrop or pear shape of the light cone. (it would only be a cone in a static non-expanding universe). the basic reason is the fact that the Hubble radius is increasing.

I hope you are feeling better and making a full recovery from the pneumonia! Don't worry about doing this stuff. I am learning how to use the table to help explain basic cosmology stuff so I'm satisfied to have the practice. Just do the amount that is right for you.

 

[Endervhar]

Suppose a galaxy emits some light in year 1.6 billion, and the galaxy is 4.8 billion lightyears from here. Then the light will be just arriving now (the table indicates) and it will have traveled for 12.2 billion years. (Subtract 13.8 - 1.6)
However the distance to the galaxy NOW is 23.9 billion lightyears.

OK with that, except; how do you discover from the table that the light will be just arriving now?

 

[marcus]

==quote==
Suppose a galaxy emits some light in year 1.6 billion, and the galaxy is 4.8 billion lightyears from here. Then the light will be just arriving now (the table indicates) and it will have traveled for 12.2 billion years. (Subtract 13.8 - 1.6)
However the distance to the galaxy NOW is 23.9 billion lightyears.

Distance then = 4.8
Distance now = 23.9
Travel time = 12.2 billion years (the time has no simple practical relation with either distance)

{\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&T_{Hub}(Gy)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline5.0&0.20&1.6&2.3&23.9&4.8&7.9&4.5\\ \hline4.4&0.23&1.9&2.8&22.3&5.1&8.7&5.6\\ \hline3.8&0.26&2.3&3.5&20.6&5.4&9.5&6.8\\ \hline3.3&0.30&2.8&4.2&18.8&5.6&10.3&8.3\\ \hline2.9&0.34&3.5&5.0&16.8&5.8&11.2&10.2\\ \hline2.6&0.39&4.2&6.0&14.8&5.8&12.0&12.5\\ \hline2.2&0.45&5.1&7.1&12.7&5.7&12.8&15.2\\ \hline2.0&0.51&6.1&8.3&10.5&5.4&13.5&18.5\\ \hline1.7&0.58&7.3&9.6&8.3&4.9&14.1&22.4\\ \hline1.5&0.67&8.7&10.9&6.2&4.1&14.7&27.1\\ \hline1.3&0.76&10.2&12.1&4.0&3.1&15.1&32.6\\ \hline1.1&0.87&11.9&13.1&1.9&1.7&15.5&39.1\\ \hline1.0&1.00&13.8&14.0&0.0&0.0&15.8&46.7\\ \hline\end{array}}Time now (at S=1) or present age in billion years: 13.8
http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html
==endquote==

OK with that, except; how do you discover from the table that the light will be just arriving now?

I may have to try several answers. Bear with me. One answer is that THIS IS WHAT THE TABLE IS ABOUT. It is about light that is arriving just now. If we examine the light and discover it has been stretched by a factor of 5, then we figure out, from the model, that it was emitted in year 1.6 by something that was distance 4.8 from here at that time.

the equations have been worked out, the equations constitute the model universe, in which everything adds up right and it fits the data. what the table does is make the model more visible in a way. It is like a window into the equation model.

 

[Endervhar]

Makes sense, thanks.

Lots more thinking to do!

 

[Endervhar]

Just an update. My friend visited and was quite happy with what I could tell him. I have to say there is still quite a lot more I want to sort out. However, I'm awaiting a date for admission to Hosp. in London, so things will be a bit disrupted for a while.

I wanted to say thanks for the patient support, and "I'll be back".

 

[Endervhar]

This may seem a little off topic, but its a question that arose from my thinking about the subject matter of this thread.At the time of the BB the Universe was smaller than an atomic nucleus. It is sometimes described as being "infinitely small".

Unless, at t = 10^-43s, the Universe had a diameter greater than 10^-35m, every part should have been in contact.

If this is the case, why is inflation necessary in order to explain the uniformity of the CMB, which, presumably, reflects the uniformity of the temperature of the Universe at the period of last scattering?

 

[marcus]

This may seem a little off topic, but its a question that arose from my thinking about the subject matter of this thread.


At the time of the BB the Universe was smaller than an atomic nucleus. It is sometimes described as being "infinitely small".

Unless, at t = 10^-43s, the Universe had a diameter greater than 10^-35m, every part should have been in contact.

If this is the case, why is inflation necessary in order to explain the uniformity of the CMB, which, presumably, reflects the uniformity of the temperature of the Universe at the period of last scattering?

Ender, I'm sure you realize this: you have to be very cautious about believing whatever you get from the popular media.
When they talk about the "universe" being at one time amazingly small, they are talking about the currently OBSERVABLE portion, not the whole universe. We don't know if the entire universe is infinite in size (in which case it would have been infinite at the start of expansion) or finite in size. If it is finite then its size could still be many times larger than the observable portion---we don't know!
So it is useless to talk about the size or the "diameter" of the universe at the start of expansion.

To make it mean something definite you have to specify that you are talking about the currently observable portion of it. We have a pretty good idea how big that is at present.

That's just a minor point, but it needs to be made to avoid unnecessary confusion.

 

[Endervhar]

I generally regard anything in the popular media with extreme suspicion, unless you include popular science books in this, in which case I might drop the "extreme".

John Gribbin suggests using Universe (higher case U) for the detectable universe, universe (lower case) for any other proposed universe and cosmos for everything there is or could be.

Obviously I should have been more specific, but it was the Universe sensu Gribbin I meant.

 

[marcus]

... why is inflation necessary in order to explain the uniformity of the CMB, which, presumably, reflects the uniformity of the temperature of the Universe at the period of last scattering?

That's a good question. People have different views on that. Some experts challenge the necessity of inflation to explain uniformity of CMB. They argue that the uniformity could have other explanations.What makes the whole discussion so interesting is that the answers depend on how you model the start of expansion. The usual consensus cosmology DOES NOT COVER the exact beginning of expansion---the old conventional math model breaks down there. So there are various rival ways to fix that which different people are working on. And some of these can explain uniformity without inflation. But they may still involve some episode of inflation for other reasons.

Inflation is really great, it helps explain several different things. Even if you don't need it to explain uniform CMB temperature (because your model has uniformity already without it) you might still want to include some form of inflation in your model for other reasons.

I'd like to recommend a video lecture to you, because I admire the guy as a critic of inflation even though I don't accept what he is offering in its place.

Google "steinhardt pirsa" and see what you get. Princeton's Paul Steinhardt recently gave a talk at Perimeter Institute saying what he sees wrong with the usual inflation ideas. PIRSA stands for perimeter institute recorded seminar archive. An intelligent contrarian can be someone good to listen to, a bit, even if you don't buy the whole message. I think the first 25 or 30 minutes is probably all you need to watch.

 

[marcus]

...
John Gribbin suggests using Universe (higher case U) for the detectable universe, universe (lower case) for any other proposed universe and cosmos for everything there is or could be.
...

I'd never seen that suggested! Most people here seem to say "observable universe". That's what my prof at UC berkeley taught us to say. And then universe for the whole thing, and what you mean by that depends somewhat on your model.

Gribbin's books are supposed to be very well written and quite popular, but I'm sorry to say I haven't read one.

He's on the right track there in the sense that we really must make the distinction in our nomenclature. But his particular notational device (upper/lower case) has yet to be widely adopted.

 

[marcus]

As you probably know, one bunch of people doing Quantum Cosmology are working on the "bounce" idea that at very high density quantum effects make gravity repellent, so collapsing geometry rebounds.
With that, one can go back in time past the start of expansion. No mathematical breakdown ("singularity") occurs.

So then, in that line of research, the question is not "how big?" but "what density?" at the start of expansion.

You don't have to address the question of overall size.

A calculation about 5 years back, in LQC (socalled Loop quantum cosmology) came up with a figure of 41% of Planck density. that was the point where the rebound occurred. It started at around 1% of Planck density, when repellent quantum corrections to gravity began to appear. So that picture prevailed in Lqc for a while.
But just this past year a young researcher named Edward Wilson-Ewing has challenged that. According to him if you include the temperature or kinetic energy of matter in the calculation the quantum bounce occurs earlier, at a lower density. I forget the exact figure, my impression is that he was talking about something on the order of a billionth of Planck density instead of 41%
It's confusing to get inconsistent signals like this, I know. But I just wanted to mention it. It's a complicated subject, involving work in progress, and frequent surprises.

I doubt you'd want to read Wilson-Ewing paper but just in case you want to glance at the abstract or introduction to it I will get the link.
http://arxiv.org/abs/1211.6269
Smart young guy, well respected. we should probably pay more attention to what he says about the critical bounce density being much lower than previously calculated.

 

[Chronos]

My objection to Wilson-Ewing is they suggest black holes could achieve a critical bounce density. I realize that possibility has been previously suggested, but, strikes me as implausible. We have no evidence to suggest our universe is an inverted black hole.