# Gonegahgah's rubber sheet example

1. Oct 21, 2008

### gonegahgah

How close is this to what is being meant here?

Let's say you have a big rubber sheet that can continue to stretch and stretch at the same rate and that it remains flat. (Yes a 2D analogy to help envision a 3D thing).

On that sheet are little cars that move over the sheet.

These cars move with their wheels pointed straight with the wheels driving at constant speed while the sheet stretches and stretches around them.

The cars are like galaxies.

So the cars might drive towards each other or away from each other (like Andromeda galaxy will crash with ours eventually).

However the car doesn't measure the speed of other cars by how many times their wheels turn.
Instead it measures their speed by how fast they appear to approach or recede from us.

So the sheet keeps expanding while the cars move about on its expanding surface.

How close is this to expansion theory?

Also I do have another question.
At a particular time in the universes life is the expansion occuring as a percent or as a rate?
ie. is it 100, 110, 121, 133.1, 146.41, etc. or is it 100, 110, 120, 130, 140, etc.?

2. Oct 21, 2008

### marcus

In another thread, where it would have gotten us off track to answer, Gonegahgah asked this. I'm making a separate thread to respond
OK it is good you are visualizing. You should also spend some time watching Wright's balloon model computer animations. Google "wright balloon model". Or remind me to get the URL.

there is a disconnect that comes from the fact that in reality the galaxies are almost not moving so it is more realistic to picture them glued onto the sheet. Then the cars can be photons of light traveling over the sheet while it is stretching.

the reason you should picture the galaxies as almost not moving or approximately stationary is that in real life galaxies only move at speeds like 100 km/s or a few hundred km/s. Like as you mentioned Andromeda is closing in on Milky. But it is only about 50 km/s. These speeds are virtually nothing compared with the rates that distances expand.
So to good approx. consider them to be zero.

Distances expand at rates which (for goodsize distances) are a considerable fraction of c, and often several times c. So as you stretch the sheet you should see some of the glued-on galaxies getting farther apart at rates which compare with the speed the photon-cars are chugging along over the sheet.

You asked about PERCENTAGE RATE. distances (largescale on average) expand about 1/140 percent per million years. But that percentage rate also gradually changes. It hasn't been constant for the whole history of expansion. Nevertheless the change is so gradual that it's OK to use that figure over a scale of tens and even hundreds of million of years. It is very handy.

One of your numbers sequences looks like it is percentage growth. That would be right.

3. Oct 22, 2008

### cristo

Staff Emeritus
I've moved the said post in here.

4. Oct 22, 2008

### gonegahgah

Thanks for that marcus.

Just a couple of quick questions tonight.

Is the expansion supposed to be happening by the same amount everywhere instantaneously; or does it expand differently in different areas?

What changes the speed of expansion? Is it the gravity of matter and dark matter slowing it and the greater anti-gravity of dark energy speeding it? Does this flow through the whole expansion at the same time or is it localised?

Does universe expansion drive itself (ie does it have momentum)?

This is greatly exagerated but does it happen something like 1cm expands to 2cm, then each of those two centimetres than expands to 2cm so that you now have 4cm, then each of those four centimetres than expands to 2cm so that you now have 8cm?

So in this exagerated example the first 1cm becomes 2cm then 4cm then 8cm so that the distance between things accelerates? (Albiet currently by .007% each million years)?

5. Oct 22, 2008

### marcus

Heh heh, just a couple of quick questions! These are good questions, and fairly deep. It would be good if you got perspectives on this from several different people.

different people might say it differently and one put it in the right terms for you.

Remember we are translating a mathematical science into non-math language. Here's my take. Cosmology is about fitting the Friedmann eqns. model to the observational data.
The model assumes uniformity. (you've heard of homogeneous and isotropic?) matter is spread evenly. In the model, spatial curvature at any given moment is uniform as well.

It's a very simple model and it fits data amazingly well. But the model fits overall and on average. It overlooks the dimples and warts of random concentrations of matter and curvature.

So the answer at one level is YES. At any given epoch in time the same scalefactor a(t) governs distances everywhere, the same H(t) which is just another name for a'(t)/a(t).
Did you know that the real definition of the Hubble parameter is the time derivative of the scalefactor divided by the scalefactor? It is one type of expansion rate and it applies to distances everywhere, at any given moment.

But the answer at a more local or microscopic level is NO. If you look down at the level of individual galaxy clusters there is lots of variation. The changes going on in geometry are unimaginably varied. And inside gravitationally bound systems there is no Hubble Law expansion. It's actually hard for me to visualize for myself adequately, even harder to explain in any sensible way.

I'm pretty much limited to generalizations, in replying to you on this score.

That's right. what you say sounds like a fair description. That's all I have time for right now. Maybe I or someone else can get back to the rest of your post later. Thanks for the good questions BTW!

6. Oct 23, 2008

### gonegahgah

Thanks for the guidance Marcus. I realise that there are still some unanswered ones yet so I apologise to add some more already.

We were talking previously about Andromeda which is on collision course with our Milky way (but don't put your heads between your legs just yet of course).

As it is approaching us (slowly on a cosmic scale) instead of moving away does this mean that the space between us and it is actually crunching or is the universe still expanding through us and does the light travelling from Andromeda to us still move through expanding universe?

You mentioned that inside gravitationally bound systems there is no Hubble Law expansion. I would have expected that the universe is still trying to expand between my feet and the Earth but that the greater gravitational attraction the Earth has on me prevents me (or the Earth) from floating away. Doesn't expansion still try to occur but there is too much local attraction to allow separation? Doesn't the universe then just expand through and out of the objects leaving them together? Afterall, a magnet will pull up a piece of metal off the ground but there is still gravity acting on that metal; just not enough to counter the magnetism?