Hi Bethann,
did you happen to watch the computer animation? The small white whirling things are galaxies. They stay at the same latitude-longitude position on the balloon. The colored wigglers are photons of light. They travel across the face of the balloon even while it is expanding, always moving at the same speed. If you watch closely you will see that they change color, a graphic way of reminding us about redshift, and their wavelengths get stretched out, again symbolizing redshift.
The balloon model is not meant to be an exact representation, just an analogy. But it can help, and one way it can help is by focusing your questions.
Another way is by helping realize that (since there are different ways to describe locations on a sphere) there can be different kinds of motion. In the toy model, the galaxies do not change their latitude-longitude, so in that sense they are at rest. The photons of light, if you watch carefully, DO change their latitude longitude position, they DO travel. If you could wait long enough at least with this toy model one of them might even make it all the way around!
I've broken up your post into separate questions, that I can gradually munch on, during the day. Haven't had time to respond yet, but the system here let's us edit for a few hours so as time permits I will get back to these questions and reply.
Bethann said:
I feel like the distance between us and an object 10 billion LY away was shorter 10B [years] ago...
I agree with one minor correction. Since time is measured in years, I changed the sentence to read "years ago". But otherwise that makes perfect sense. Distances between objects do increase.
You are talking about an object whose distance from us NOW is 10B light years. To give that a definite meaning, assume we could freeze expansion while we measure. Then we send a flash of light and it would take 10B years to get there. Or 20B years for a round trip. That is what I'll mean by the distance of an object, at some given time.
If you go back in time, the distance (measured the same way) is certainly less.
BTW one of the most effective teachers of cosmology on the web is, I think, an astronomy professor in Iowa named Siobhan Morgan. She has this calculator that calculates distances like those we are discussing. You could have a look to see what I mean:
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html
She intentionally puts in wrong numbers for the matter density (she puts in 1, so you have to change it to .27 ) and cosmological constant (she puts in 0 so you have to change it to .73). It is a way of making students aware that these numbers are important and what answer you get depends very much on them. The calculator only gives the right answers if you put in our current best estimates of these basic numbers.
When I use her calculator, I always put in 0.27 and 0.73 , in those top two boxes, and I normally change the 70 to 71, although that doesn't make much difference. Just gets it closer to the current best estimate.
If you do that, and then click on the "calculate" button, it will give you distances. Like a galaxy that TODAY is 10.8 billion light years from us, BACK THEN when the light started off on its journey to us the galaxy WAS 5.4 billion light years from us.
Have to go, back soon.
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Back now. Using that calculator is a good way to get familiar with the redshift number, always written "z".
z is the fractional increase in the wavelength. In Morgan's calculator you can put in different numbers for z and you will get different distances.
If you put in .25 for z that means that the wavelengths of all the light from that galaxy have been expanded by 1/4 or 25%, while the light has been on its way to us. The waves arrive 25% longer than when started out.
So the now wavelength is 1.25 times the length of the waves back then (when the stars of the galaxy you are looking at shined out their light which is today arriving here.)
The wavelength now is always 1+z times the original length when the waves began their journey.
So z is a good handle on how far the light has traveled and how long. The calculator, and others like it, are mainly for the purpose of converting z numbers into distance and travel time numbers.
You might be someone who never touches a calculator, but in that case I would still invite you to make an exception and try Professor Morgan's calculator. She's a smart teacher---made it for her students to use, and made it fairly simple and user-friendly.
... With the 2D balloon model I can see that the distance to all the farthest objects are at the same. But I find it hard to think that we are not moving through the universe. I guess the universe by its expansion, is the thing that is moving. ...
Well as I see the 2D balloon model, all the distances between galaxies are increasing, including if you pick one galaxy and ask about the distance to the farthest one. The farthest one is the one way around on the other side of the balloon. And the distance to it is half the circumference. And the circumference keeps growing.
About whether a galaxy is moving in that 2D universe. Well if you like it depends on some arbitrary choices, like numbers you pick to describe locations. With an arbitrary choice of coordinates different people could attribute different motion to a thing. But I would simply point out that if you look at the balloon movie you will see that
no galaxy is going anywhere in that 2D universe.
No galaxy is getting closer to anything, no galaxy has any special preferred direction or destination.
What is happening is merely that all the distances are increasing. That is different from the ordinary type of motion we are used to.
I guess the universe by its expansion, is the thing that is moving.
I think that's a good way to look at it! At least it is the thing which is changing. The geometry of space is allowed to change. Distances are allowed to change, unless they are tied to something material, kept stable by the forces that hold material things together.
At very large scale these material forces are too weak to make a difference, and geometry can evolve of its own accord (basically it evolves according to an equation first discovered by A.E. in 1915, but that is not the important thing) the main thing for us, in this discussion, is to realize essentially what you just said.
That geometry itself is "alive". It can change. And among other possible ways it can change, it can have an overall tendency for distances to increase between otherwise peacefully resting objects.
I won't go on and make this post longer, except to say what the percentage rate of increase is at present. This is for really large scale distances.
They increase only very gradually and slowly actually. Distances across largescale intergalactic space increase only by about 1/140 of one percent every million years.
Wait a million years and you find that the distance you are looking at has increased by
less than a hundredth of one percent! It seems like almost nothing, but that is the kind of thing we are talking about here. Admittedly the percentage rate has been greater in the past, but that is what it is now, and it is only changing very very slowly indeed.