Effort to get us all on the same page (balloon analogy)

[oldman]

A health warning for the Balloon Analogy

The balloon analogy is a simple and effective way of visualising how the universe expands. Here it is used to explain how distances between widely separated parts of the universe can increase at rates greater than c. But like all analogies, it's not perfect.

... picture visually how distances between stationary points can increase at a c+ rate. You simply look at a(n expanding) balloon with glued pennies and with photons wriggling across the surface at a fixed rate of one inch per minute.
There will be distances between pennies which are increasing faster than one inch per minute. But no penny ever outraces a photon in its neighborhood. Ned Wright provides the two computer animations of the balloons with wrigglers. To visualize (in an unparadoxical nice consistent way) how distances can increase at c+ rates, that's all you need.

Don't forget that modern cosmology is based on General Relativity, which can describe for us how we perceive a universe filled with gravitating objects. The description has a perspective restricted by the fact that we are not Godlike creatures able to look at happenings all over the universe all at once. But that is just the perspective adopted in the balloon analogy when you 'simply look at an (expanding) balloon'. So don't take this analogy too seriously, unless I've mistaken who You are (in which case, very humble apologies).

 

[TalonD]

is it the purpose of this thread to make it some kind of FAQ? like required reading before first posting? That would be a good idea. After reading some threads I realize there are some new posters even more clueless than myself if that is possible.

A question about the structure of the universe. We don't know for sure the answer yet. Is it Flat, Open, or Closed? if flat or open then it is spacialy infininte yes? What about if it is closed. Then it is finite in size? if that is the case, could you go in a straight line and end up back where you started like going around the globe or the baloon? Also even if it is finite, it doesn't necessarily have to have an edge or boundary or a fourth spatial dimension in which to expand right? That seems to be a concept that a lot of people have difficulty grasping because it is so counterintuitive to our everyday experience.
A question of parallel lines in closed space. Suposedly if the universe is closed then two parallel lines will eventually intersect right? but I can draw parralel lines on a globe in such a way that they don't intersect.
which leads to a really strange question but maybe I should refrain from that one.

 

[marcus]

A question about the structure of the universe. We don't know for sure the answer yet. Is it Flat, Open, or Closed? if flat or open then it is spacialy infininte yes? What about if it is closed. Then it is finite in size? if that is the case, could you go in a straight line and end up back where you started like going around the globe or the baloon? Also even if it is finite, it doesn't necessarily have to have an edge or boundary or a fourth spatial dimension in which to expand right? That seems to be a concept that a lot of people have difficulty grasping because it is so counterintuitive to our everyday experience...

That is a helpful beginning for an FAQ. Thanks Talon, I will paraphrase in the form of a list:

A question about the structure of the universe. Spatially, is it Flat, Open, or Closed? (We don't know yet. The curvature parameter that determines this has not been measured with enough precision yet.)

If flat or open then must it be spatially infinite? (Yes except for the case of some tricky PacMan topology, like a flat square with the edges joined by magic, off to the right comes in at the left etc. which sounds unreal but who knows.)

What about if it is spatially closed. Then it is finite in size? (Yes.)

If that is the case, could you go in a straight line and end up back where you started like going around the globe or the balloon? (Yes if you froze it in time, so that distances wouldn't be increasing at the same time while you tried to make the grand tour.)

Also even if it is finite, it doesn't necessarily have to have an edge or boundary or a fourth spatial dimension in which to expand, right? That seems to be a concept that a lot of people have difficulty grasping. (Right and right. The standard cosmo picture does not have an edge: no space outside of space. And yes many do have trouble imagining that all existence is on the surface of the balloon, so to speak. Takes concentration.)

 

[marcus]

What cosmo stuff can you compute on your own? Hands-on exercise.

what we're coaching here is the a kind of home base for basic cosmo---the standard cosmological model and it's most common variations. The idea is each person can believe anything he wants but we should have a common understanding of the mainstream basics to serve as a cornerstone for deviating off of. Makes communication more efficient if we share a common point of reference.

Cosmology is a numerical science. It deals with mathematical models, and how well they fit observational data. It is not a verbal or philosophical understanding of the world, but a computational-predictive art. So the most straightforward way to test your basic understanding of the mainstream model is to try and see what you can calculate just using what you know already.

Let's see what we can calculate just using two numbers (71 and 0.73) and two simple equations (the Friedmann equations.)

By 71 I mean the estimated current Hubble parameter H(t=now), 71 km/s per Megaparsec.
By 0.73 I mean the current estimated dark energy fraction. Probably everybody knows these versions of the two numbers--they are the default inputs to Ned Wright's cosmology calculator. If and when he revises them, I will too.

Let's all use the Google calculator for doing ordinary arithmetic. You just type stuff in the regular Google search box and press return. It evaluates for you.

Wikipedia has an adequate page on the Two Friedmanns. First Friedmann tells you how the first time derivative of the scalefactor is determined. It tells you a'(t).
The Second Friedmann tells you the second time derivative of the scalefactor: namely a"(t).
Actually the equations give you ratios-----a'(t)/a(t) and a"(t)/a(t).
But the presentday value of the scalefactor is typically normalized to equal one.
a(t=now) = 1.
So the ratios provide a pretty good grip.

Now how about the Hubble Time? Can you calculate it, with nothing besides those two numbers and two equations?

HUBBLE TIME 1/H(t=now)

Put this into Google box and press return: 1/(71 km/s per Mpc)
You should get 13.77 billion years

HUBBLE DISTANCE c/H(t=now)
Type this in and press return: c/(71 km/s per megaparsec) in lightyears

Type the blue stuff verbatim. It knows what c is. It knows what a kilometer is, and what a parsec is. It knows that Mpc stands for megaparsec. Smart calculator.

CRITICAL (energy) DENSITY 3 c^2 H(t=now)^2/(8 pi G)
You can see from First Friedmann what the critical density has to be. You just set k=0 and solve for rho by 9th grade algebra. Let's get it in energy equivalent terms rather than in kilograms per cubic meter. Put this into Google:

3 c^2 (71 km/s per Mpc)^2/(8 pi G) in joules per km^3

or if you like nanojoules, nJ, put this in
3 c^2 (71 km/s per Mpc)^2/(8 pi G) in nJ per m^3

It should tell you either 0.85 joules per cubic kilometer, or else 0.85 nanojoules per cubic meter.
Since our universe is very nearly spatial flat, that 0.85 is the energy density of our universe (including all kinds)

DARK ENERGY DENSITY 73 percent of 0.85 joules per km^3
Just put this into the box 0.73*0.85
Should get that the density of dark energy is 0.62 joules per cubic kilometer.

 

[Chronos]

A valiant effort, marcus. It will not penetrate the denser skulls.

 

[CaptainQuasar]

Whoa. I had noticed the Google calculator thing but I did not know it could parse and handle all those different units and constants.

I just wanted to ask for clarification on your 2nd answer there, marcus, to TalonD's "If flat or open then must it be spatially infinite?". You replied with a qualified yes but if I'm understanding everything properly I think the answer I've always encountered is "we don't know because the universe simply may not exist beyond the limits of what we can observe." I'm not playing stump the cosmologist or anything, which one should I believe or consider the most mainstream, at least?

⚛​

 

[marcus]

which one should I believe or consider the most mainstream, at least?

In this thread I don't want to say believe in reference to any particular version of cosmology. We are just trying to get the mainstream consensus picture in focus, whether or not one chooses to believe in it. The reason for doing that is that it gets confusing when people want to deviate but don't understand what they are deviating from. So I like your question about what view is mainstream. Let's explore that

.

Whoa. I had noticed the Google calculator thing but I did not know it could parse and handle all those different units and constants.

Yes! It is so great! Try things like "mass of earth" "mass of electron". It treats those things as quantities that it knows. Or maybe you ahve to say "electron mass", I don't remember which works, maybe both work.

I just wanted to ask for clarification on your 2nd answer there, marcus, to TalonD's "If flat or open then must it be spatially infinite?". You replied with a qualified yes but if I'm understanding everything properly I think the answer I've always encountered is "we don't know because the universe simply may not exist beyond the limits of what we can observe." ...

In mainstream cosmology they don't consider the possibility that the universe might not exist outside the limits of what we observe. They assume a kind of conventional uniformity. The distribution of matter and the average geometry is the same all over. Homogeneous.

There are fancy multiuniverse and eternal inflation scenarios where things are quite unhomogeneous, but they aren't used to fit data to. You've heard the terms "homogeneous and isotropic"---that's the conventional assumption.

You need some assumption about what is out beyond what we can see in order to make General Relativity work properly and get useful results---the simplest assumption is that it looks the same. You don't have to believe that, you just use that assumption and see if it works, and it seems to work pretty well.

A more serious lack of knowledge is whether or not space some odd periodic topology, like a PacMan square---off to the right comes in from the left, off at the top comes in at the bottom. As a topology, that is described as toroidal---topologically like a donut surface. But you don't think of it as curved, the way a donut surface is forced to be curved when embedded in 3 dimensional space. You think of the geometry as flat, but simply identified at the edges.

There is a 3D analog to the PacMan square. So a logical question is, could the universe be like that? Could it be spatially flat or nearly flat (as it appears to be) and yet be finite spatial volume because of some curious 3D spatial topology---space looping back on itself so to speak.

So far people haven't been able to rule that possibility out. They can look for repeating patterns, like turning around quickly to see if the person in front of you is also behind you. But they only have so far been able to say things like "if it has a finite circumference then the circumference must be at least so and so big". They have looked carefully for repeating patterns and haven't found any so far. There is a paper by Spergel, Cornish, and Starkman that reports on that search, a couple of papers actually.

And you can argue that we'll never know because we will never be able to see farther an 46 billion lightyears (the presentday distances of the matter that emitted the CMB light that is currently arriving to us.)

The simplest thing (and probably the most mainstream thing) is just not to pay attention to toroidal topology or any other unusual topology. If it looks flat then just assume it's flat. If it looks slightly positive curved, like a big ball, then just assume it is a big ball. That's the most straightforward: not to make up stories about how it could look simple but actually be complicated.

But as I think you were pointing out in your post, we can't logically exclude some of those irritating other possibilities.

 

[CaptainQuasar]

Thanks!

⚛​

 

[TalonD]

we don't know because the universe simply may not exist beyond the limits of what we can observe

This quote sounds like another way of saying that the universe has an edge.

From my limited knowledge so far, I think the standard model doesn't explicity state whether there is an edge or not? but everyone in the know, seems to prefer the idea that there is not one but do we know for certain one way or the other? obviously in the baloon analogy there is an infinity of horizons depending on where you are standing on the baloon, but never an edge.

Also from my layman's viewpoint,
HST can show us an image of some distant early galaxy. That galaxy at this current point in time would be close to 45gly away and would be a mature 13.7gy old galaxy. Then suppose there is some critter living in that galaxy, If the universe doesn't exist beyond what we can observe then what would that critter observe if he looks in the direction opposite of us?
somehow I don't think he would see an edge, but would instead just have his own 45gly radius horizon.

am I right or wrong or we don't know?

 

[CaptainQuasar]

That was my question and marcus answered it above.

⚛​

 

[TalonD]

sorry, I'm a little slow

 

[marcus]

This is a good way to think about it IMO.

...Also from my layman's viewpoint,
HST can show us an image of some distant early galaxy. That galaxy at this current point in time would be close to 45gly away and would be a mature 13.7gy old galaxy. Then suppose there is some critter living in that galaxy, If the universe doesn't exist beyond what we can observe then what would that critter observe if he looks in the direction opposite of us?
somehow I don't think he would see an edge, but would instead just have his own 45gly radius horizon.
...

I agree. Thinking about it in concrete terms definitely helps. Also it's intriguing to reflect that what we see when we look at the CMB sky is a hot (3000 K) fog of partially ionized hydrogen in the process of clearing (by settling into the unionized more transparent state)
and that that very fog has itself in the meantime condensed into galaxies and most likely evolved critters!

And a core idea in standard cosmo is that (if there be such critters) they too see the 2.7 kelvin CMB in all directions, and when they look in our direction they see the hot (3000 K) fog made of OUR matter, which later condensed into the Milkyway and evolved us, and the light from our matter, which they are seeing, has been stretched out by the same 1100-fold factor by the time it reaches them, so it is 2.7 K.

For some reason this makes me chuckle---the idea that my matter was the source of somebody else's cosmic microwave background radiation. The root of this idea I think really goes back to William Okham's idea of simplicity (Okham Razor, don't make it more complicated than needed). And Nicolas Copernicus. Or whoever was responsible for the Copernican idea that other critter's POV are the same as ours---our planet and POV isn't special. The Copernican principle can be seen as a way of obtaining greater simplicity. The picture is simpler because you don't have to add extra junk like a centerpoint or a boundary to it---you can posit fewer entities. So that other critter is taking a look at my matter when it was a clearing fog of 3000 kelvin gas because it's simpler that way. something about that is just plain amusing.

sorry, I'm a little slow

Are you? I hadn't noticed. In any case if things work out right we have over a billion years to enjoy this show, and get to understand it.

 

[CaptainQuasar]

Oops, Talon, I missed your 2nd question there about critters, sorry. I only asked the one about the universe having an edge.

⚛​

 

[TalonD]

not sure if this question belongs in this thread but... the expansion is just a pattern of increasing distance between us and distant galaxies, so there is no space/time substance that is stretching right? so in GR gravitation, what is it that is curved?

 

[marcus]

... so there is no space/time substance that is stretching right? so in GR gravitation, what is it that is curved?

heh, heh. Very good question. I also appreciate that you put it in context of a particular theory. General Relativity is a time honored classical theory and from a modern perspective it may seem a bit skimpy, unsatisfactory. Looking back from almost 100 years later, we might feel it leaves a lot out, a lot unanswered that we would like answered.

In GR it is the metric, the distance function itself, which possesses curvature. One might say that the metric describes an abstract set of relationships called geometry. Geometry is not a substance but rather a bunch of relations like the sum of angles of triangles and the relation of radiuses to areas.

It is geometry which can be flat, or non flat. Depending on how the angles add up, and suchlike.

GR only tells you about the gravitational field (which is the metric, which is the geometry) it does not tell you what is the underlying space. It does not even consider that points of spacetime have physical existence, they lose their identity unless anchored to some physical event, like a collision or emission of a particle.

This reticence of GR is always hard for us to accommodate intuitively.

There is always this question "Yes geometry, I understand, geometry is dynamic, the flow of matter affects it, it interacts with matter...but what is it the geometry OF?"
Heh heh.

Well. Maybe it is the geometry of something. If quantum gravity research succeeds then matter and geometry will be aspects of the same thing---the same microscopic degrees of freedom. Then we will understand how matter connects to geometry and deforms it, because we will see both matter and geometry as arising as manifestations from the same ground. They will be joined at the root.

Or maybe quantum gravity research will not succeed, and geometry will remain a kind of abstract disembodied thing with only an ad hoc connection to matter, an unexplained linkage.

In any case we can't say confidently now. GR is wonderfully precise, but it is reticent. It does not say what happens at its singularities, or tell us about the fractally foamy uncertain churning that may be happening (that Schroedinger would insist is happening) in the geometry at very small scale.

 

[mysearch]

At some point, people get around to asking questions like:

o Is Hubble’s constant calculated or measured?
o Does a spatial flat universe require a critical density?
o How were the relative energy densities determined?

If so, I would recommend Marcus response in this post:
https://www.physicsforums.com/showpost.php?p=1973468&postcount=18

Is there a cosmology library section?
Maybe posts like this should be formalised into it?

 

[marcus]

Here's an outstanding set of 77 slides. They are for Ned Wright's 28 October 2008 UCLA Faculty Research Lecture, an annual event. It's a great introduction to cosmology.http://www.astro.ucla.edu/~wright/CMB-MN-03/FRL-28Oct08clean.pdf

Also not to be missed, Smoot's 20-minute TED talk given May 2008

http://video.ted.com/talks/podcast/GeorgeSmoot_2008P_480.mp4
Smoot's talk was illustrated by some remarkable animations of early universe structure formation, by Kravtsov
http://cosmicweb.uchicago.edu/filaments.html
http://cosmicweb.uchicago.edu/group.html
thx to Orion for pointing out Smoot's talk.

 

[marcus]

A famous Einstein quote about an important feature of General Relativity known as general covariance.
“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität."

“Thereby time and space lose the last vestige of physical reality”.

source links here:
https://www.physicsforums.com/archive/index.php/t-166997.html

also see page 43 of
www.tc.umn.edu/~janss011/pdf%20files/Besso-memo.pdf[/URL]
==quote==
In a letter to Schlick, he again wrote about general covariance that
“thereby time and space lose the last vestige of physical reality” (“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität.” Einstein to Moritz Schlick, 14 December 1915 [CPAE 8, Doc. 165]).
==endquote==

 

[atyy]

not sure if this question belongs in this thread but... the expansion is just a pattern of increasing distance between us and distant galaxies, so there is no space/time substance that is stretching right? so in GR gravitation, what is it that is curved?

Spacetime (4D) is curved. However, there are usually "special" ways to split spacetime into "space" (3D) and "time" (1D). These are "special" splits because they don't simply pick an arbitrary coordinate as "time", but among other things they also ensure that the "time" direction at every "spatial location" points to the future and is the potential worldline of an observer. If you do this split in empty flat spacetime, two observers at "rest" in "space" don't find that the distance between them increases with "time". But when you do it in the matter-containing curved spacetime used to model our universe, two observers at "rest" in "space" do find that the "spatial distance" between them increases with "time". (Actually, you can do split flat spacetime so that "space" expands with "time", but then observers have to be massless and energyless, so that's not realistic. But it shows that one should remember that the description of curved 4D spacetime as expanding or being a pattern of distances that increases with time depends on a choice of 3+1D split that is permissible and convenient, but not unique.)

Also, curvature is the distance between objects at different locations. If we use a piece of string and a protractor to measure distances between objects on a football, we will find the pythagorean theorem doesn't hold, so the football is curved. If we replace the football with spacetime, the piece of string with a ray of light, spatial distance with spacetime interval, and objects with events, we can find out if spacetime is curved.

 

[TalonD]

A famous Einstein quote about an important feature of General Relativity known as general covariance.
“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität."

“Thereby time and space lose the last vestige of physical reality”.

source links here:
https://www.physicsforums.com/archive/index.php/t-166997.html

also see page 43 of
www.tc.umn.edu/~janss011/pdf%20files/Besso-memo.pdf[/URL]
==quote==
In a letter to Schlick, he again wrote about general covariance that
“thereby time and space lose the last vestige of physical reality” (“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität.” Einstein to Moritz Schlick, 14 December 1915 [CPAE 8, Doc. 165]).
==endquote==[/QUOTE]

[quote="atyy, post: 1994176"]Spacetime (4D) is curved. However, there are usually "special" ways to split spacetime into "space" (3D) and "time" (1D). These are "special" splits because they don't simply pick an arbitrary coordinate as "time", but among other things they also ensure that the "time" direction at every "spatial location" points to the future and is the potential worldline of an observer. If you do this split in empty flat spacetime, two observers at "rest" in "space" don't find that the distance between them increases with "time". But when you do it in the matter-containing curved spacetime used to model our universe, two observers at "rest" in "space" do find that the "spatial distance" between them increases with "time". (Actually, you can do split flat spacetime so that "space" expands with "time", but then observers have to be massless and energyless, so that's not realistic. But it shows that one should remember that the description of curved 4D spacetime as expanding or being a pattern of distances that increases with time depends on a choice of 3+1D split that is permissible and convenient, but not unique.)

Also, curvature is the distance between objects at different locations. If we use a piece of string and a protractor to measure distances between objects on a football, we will find the pythagorean theorem doesn't hold, so the football is curved. If we replace the football with spacetime, the piece of string with a ray of light, spatial distance with spacetime interval, and objects with events, we can find out if spacetime is curved.[/QUOTE]

Marcus, on the other hand... cogito ergo sum --Descartes

Atyy, as a non physisist layman, I find that kind of hard to follow, can you restate that in a simpler easier to understand way? I understand the football analogy but the previous paragraph was a little confusing.

 

[TalonD]

I was just thinking that it is interesting that the baloon or flat rubber sheet analogy when used to explain gravity to the lay public would lead one to an obvious common sense conclusion that pressure has an effect on gravity. Yet without the analogy, for a physisist using mathematics it might seem unexpected. I realize the analogy is not reality and that it's the math that counts (excuse the pun) but still, I thought that was interesting.
:P

 

[atyy]

Atyy, as a non physisist layman, I find that kind of hard to follow, can you restate that in a simpler easier to understand way? I understand the football analogy but the previous paragraph was a little confusing.

On the football (the spherical sort), if two observers start out at the north pole and follow straight lines of longitude, they find that the latitudinal distance between them increases, so their universe is "expanding". After they pass the equator, their universe starts to "contract".

 

[TalonD]

On the football (the spherical sort), if two observers start out at the north pole and follow straight lines of longitude, they find that the latitudinal distance between them increases, so their universe is "expanding". After they pass the equator, their universe starts to "contract".

ok, I'm going to expose some of my ignorance in this question but here goes...

Thanks for the clarification. I still have some confusion though, maybe because I am trying to take the analogy too far. on a globe if you move along the lines of longitude it depends on whether you are moving toward or away from the equator as to whether you converge or diverge. So if our universe has a positve curvature rather than being flat. then would two objects traveling in parallel eventually converge no matter what direction they are traveling, but in an open universe they would eventually diverge right? The only problem I have with that concept is that it is easy enough to draw two parallel lines on a globe and make them stay parallel all the way around. but presumably in a univere with positive curvature you couldn't keep them parallel right? So since we know that on a large scale everything in our universe is diverging does that mean we are headed towards some kind of cosmic equator and when we pass it, everything will start to converge towards a big crunch? Could the question of continued expansion vs. a big cruch have to do with the ovearall geometry of the universe in adition to the critical density? well of course the geometry of the universe is dependent on the density so I guess that answers my own question.

Then there is gravity. I can understand that two objects traveling near each other in space would follow the curvature and converge. but why do to objects that are initially at rest relative to each other spontaneously start moving together?

 

[atyy]

Thanks for the clarification. I still have some confusion though, maybe because I am trying to take the analogy too far. on a globe if you move along the lines of longitude it depends on whether you are moving toward or away from the equator as to whether you converge or diverge. So if our universe has a positve curvature rather than being flat. then would two objects traveling in parallel eventually converge no matter what direction they are traveling, but in an open universe they would eventually diverge right? The only problem I have with that concept is that it is easy enough to draw two parallel lines on a globe and make them stay parallel all the way around. but presumably in a univere with positive curvature you couldn't keep them parallel right? So since we know that on a large scale everything in our universe is diverging does that mean we are headed towards some kind of cosmic equator and when we pass it, everything will start to converge towards a big crunch? Could the question of continued expansion vs. a big cruch have to do with the ovearall geometry of the universe in adition to the critical density? well of course the geometry of the universe is dependent on the density so I guess that answers my own question.

Yes, you've answered your question. But let me comment on not taking the analogy too far. On the spherical football, it is 2D spacetime which is curved. However, it does not make sense to say that each spatial slice has intrinsic curvature, because the spatial slices are 1D lines of latitude. In contrast, for the universe, each spatial slice is 3D, for which it does make sense to ask if it has intrinsic curvature. So one should distinguish between the curvature of 4D spacetime, and the curvature of 3D spatial slices.

Then there is gravity. I can understand that two objects traveling near each other in space would follow the curvature and converge. but why do to objects that are initially at rest relative to each other spontaneously start moving together?

The objects themselves produce spacetime curvature. It is not possible to be at rest in time, so it is not possible to be at rest in spacetime, so the objects move together.

 

[navneet023]

First of all, sincere apologies to everyone who feels offended by my post. But couldn't help posting, I had to!

I have come across the information that what we see(visible matter ) is just 4% of the mass of the universe. Rest is some DARK matter and energy.
I have a doubt. We have studied that light comes in the packets(quanta) and so does other forms of energy. Could it be possible that its like a sprinkler, which constantly changes its direction and comes to same direction after some time, hence causing temporary lack of water(or light, for that reason). So, matter is always there, only we can't see it due to lack of continuous radiation. Could it be logical by any means?

Just a point i want to make. Hope I haven't offended anyone. :)

 

[marcus]

Navneet, you might enjoy this 20-minute talk by Nobelist George Smoot. Links here:
https://www.physicsforums.com/showthread.php?t=274265

This mp4 version is slow to download but higher resolution, I think.
http://video.ted.com/talks/podcast/GeorgeSmoot_2008P_480.mp4
You click on it and go away and do something else for 5 or 10 minutes and then come back and start it.

Thanks also for these! The Kravtsov computer simulations are excellent. I like this especially:
http://cosmicweb.uchicago.edu/filaments.html
I see that Smoot used Kravtsov's movies in his TED talk.
This was a good one too:
http://cosmicweb.uchicago.edu/group.html
I watched the halfsize MP4 version of the movie because it is very easy to download, only about 2.4 MB.

 

[Polter]

I was just wondering, if the galaxies are like coins on a balloon -- accelerating away from each other -- then how is the Milky Way-Andromeda Galaxy Collision possible?

 

[marcus]

I was just wondering, if the galaxies are like coins on a balloon -- accelerating away from each other -- then how is the Milky Way-Andromeda Galaxy Collision possible?

That's another bad thing about the analogy.

Galaxies come in clusters. Galaxies within the same cluster interact, orbit each other, are bound together by their common gravity.

The balloon can't show this. It is a schematic oversimplified cartoon.

It is only widely separated galaxies---those not bound---that obey Hubble law, and act like the pennies of the model

 

[thaddeus]

If it is to be asserted that the Big-Bang was not of "point" origin then how is it justified in terms of -everything- expanding away from other items .. as though it were simply an outward expansion .

IF as positioned earlier the bigbang is not to be seen as a point radiation but as a whole universe instantaneous? radiation then stuff should be flying in all directions equally .. yes or no ?

And just because the claim is that there is no point origin of the big bang .. how can it be asserted logically that this means there is no center point to the universe ?

Maybe it would make more sense as a hypothesis that matter is shrinking lol .. sometimes feels that way mumble mumble .. .. :)

 

[geronimo]

Having ditched the balloon analogy as being too simplistic, I am visualising the mechanism as more like expanding gap-filling foam. This allows me a more realistic three dimensional picture and allows variations in local expansion caused by chaotic quantum anomalies, causing "lumpiness" on whatever scale you like. This model also allows the "bubble" to assume a non-regular shape eventually.

As for the singularity point of origin, this also becomes unecesary and indeed as a result of uneven expansion would not be definable.

I am becoming increasingly drawn to cyclic universe notions in which any debris from one cycle would affect the expansion and "lumpiness" of the next, or each expansion drives through the ghost of its predecessor. This in turn could mean that unexplained cosmological anomalies may not be caused by our present cycle on its own.

I could ramble on at length and dig myself into a hole because this model suggests to me many interesting scenarios. ( including a way to reconcile string and quantum theories) So I wont.

Perhaps Marcus would care to comment?

Merry Christmas to all.

 

[Chilli]

On the balloon analogy and the Cosmic Microwave Background radiation ...

If a particle radiates from location A in the direction of location B, once it leaves location A it is no longer there, although A may remain the particle's apparent location from any number of viewing perspectives over time. What I don't understand in the balloon analogy is where are the "A" locations that are null of radiation? Does the CMB radiation just continuously criss-cross itself? If yes, why is the radiation still uniform? If no, where are CMB radiation source locations in the model?

Kind regards

 

[marcus]

Having ditched the balloon analogy as being too simplistic, I am visualising the mechanism as more like expanding gap-filling foam...

No special comment needed, I think. Neither balloon nor foam represent a mechanism.
The balloon image is intended to aid visualizing how distances between stationary points increase. And how they increase at a percentage rate, so that longer distances increase more. Meanwhile (if you recall Ned Wright's animations) wriggles of light slowly travel from one stationary point to another. So this says nothing about how the universe works, it is an key exercise in picturing changing distance relations---in visualizing Hubble law. If foam helps you assimilate Hubble law better than balloon, go with it! Of course neither provide a physical analog to the Friedmann equations, so neither teaches you any understanding of how geometry and matter actually work. Once you can visualize the pattern, if you want to explore the mechanism one way is to experiment with the online calculators which embody the Friedmann equations. I don't know any physical analog (like a balloon or whatnot) but the calculators are fun to play around with.

On the balloon analogy and the Cosmic Microwave Background radiation ...

If a particle radiates from location A in the direction of location B, once it leaves location A it is no longer there, although A may remain the particle's apparent location from any number of viewing perspectives over time. What I don't understand in the balloon analogy is where are the "A" locations that are null of radiation? Does the CMB radiation just continuously criss-cross itself? If yes, why is the radiation still uniform? If no, where are CMB radiation source locations in the model?

Kind regards

Chilli, think of it this way: Everybody in the universe is currently receiving CMB radiation which was emitted by matter which is currently at a distance of 46 billion lightyears from them. And that matter has gone thru a lot of changes since it emitted the light that's now arriving.

In line with your example pick spots A and B on the balloon surface.
At a certain time (380,000 y) space is more or less uniformly filled with hot glowing stuff and it is turning transparent for the first time, as it cools below 3000 kelvin.
The balloon is small and A and B are close together (only 42 million ly)

All points including A and B send out light uniformly in all directions. Some of A's light heads towards B, some of B's light heads towards A.

The light doesn't get there right away, or any time soon, because of expansion of distances. The original distance of 42 million ly increases a thousand-fold while the light is traveling. More exactly by a factor of 1090. So today the distance between A and B is 46 billion ly, and this light has traveled 13.7 billion y and is just now arriving.

The balloon is 1090 times bigger now than it was. Some of A's light is arriving at B and some of B's (that didn't go in other directions) is arriving at A.

By now both A and B have matured in the sense that they are no longer hot glowing gas---the gas has condensed into stars and galaxies and some stars have planets and some planets may have life and so on. So each of A and B could have creatures that construct antennas and receive the light----whose wavelengths are now longer by a factor of 1090.

Does the CMB radiation just continuously criss-cross itself? If yes, why is the radiation still uniform?

I'm not sure what you have in mind by continuously criss-crossing, but I think yes it does because there is uniform radiation going in all directions at every spot at all times. It is almost perfectly uniform because the whole shebang that emitted it was approximately uniform---all space filled about evenly with hot partly ionized hydrogen etc. all at about the same temperature and all turning transparent at the same time. There is no way that a lot of non-uniformity could arise. Some perhaps, but not a lot.

Remember that in the balloon analogy, all existence is concentrated in the 2D surface of the balloon and there are no directions off the surface. So if radiation starts out uniform it will always remain so.

==========
BTW Chilli is an excellent choice of name---reminds me of a favorite comic gangster movie. Looks like the above was your first post: welcome to the forums!

 

[Chilli]

Marcus, thank you for your explanation and for your kind welcome!

Let’s see if I’m getting any closer … Setting aside post-inflationary expansion (because I really don’t have the math), say I am at location B, and it’s 13.7 billion years o’clock. I am receiving CMB radiation that was emitted in the year 380,000 from a location A that is presently 46 billion lightyears away. Location A was only 42 million lightyears away in the early universe, but a particular wriggle of light didn’t take the whole 46 billion years to reach me at location B because the expansion itself carried (stretched?) A’s particle wave to within 13.4 billion lightyears of B (yes/no?).

With my question about whether the CMB radiation criss-crosses itself, I meant to ask: when individual light waves hit each other, might they cancel or strengthen each other?

=========

Given this thread is to identify things that help or hinder intuition with regard to the balloon analogy, for what it’s worth, here’s some feedback from a clueless newbie.

When you say the balloon is now 1090 times bigger than it was, I reflexively picture the expansion as a slow and steady inflation, analogous to me blowing up a party balloon. And this let's me picture how the ‘coins on the surface of the balloon’ get further away from each other, and also let's me picture the timeline of the balloon, equating small to young, large to old (with us being old). But, assuming the Inflationary Model is correct, the balloon became pretty large when it was still very young, which goes to the uniformity of the CMB in the first place. And this is where the powerful balloon analogy becomes intuitively confusing to me.

For me, picturing all the coins on the surface of the balloon as radiating wriggling cosmic microwaves turns the surface of the balloon into a seething mass of tiny worms. Which might actually work in imagining a uniform distribution, but a spherical balloon also conjures some less helpful tangents.

* Firstly, if a wriggle of light keeps traveling around a sphere, it’s going to end up back where it started. Given the Earth is a sphere, it feels perfectly logical to imagine that the universe is also spherical, and thus a layman like myself automatically connects the balloon analogy with the shape of the universe. Of course, what we really need is a good homespun image to grab onto for the shape of space-time. (Pringles just don’t cut it.) If there was a big bang from a high-pressured source with no particular obstacles to free motion, then intuition says the universe is a big round thing with a definite (if empty) centre. Without an alternative, the balloon analogy is the best ‘big round thing’ image on offer from Cosmology, so, it is destined to be used in—creative—ways.

* Secondly, since the coins themselves stopped emitting their original CMB radiation long ago, then I expect the timeline of a given location A to include periods in which there is no CMB. Ie, the time period after emission and before reception of the first waves of radiation from other sources, and the time period after all radiation waves have passed by. But this idea isn’t compatible with the balloon analogy because the radiation simply circles around the balloon forever.

I greatly appreciate your efforts to try to help beginners such as myself receive the analogy more correctly, Marcus!

 

[marcus]

Let’s see if I’m getting any closer … Setting aside post-inflationary expansion (because I really don’t have the math), say I am at location B, and it’s 13.7 billion years o’clock. I am receiving CMB radiation that was emitted in the year 380,000 from a location A that is presently 46 billion lightyears away. Location A was only 42 million lightyears away in the early universe, but a particular wriggle of light didn’t take the whole 46 billion years to reach me at location B because the expansion itself carried (stretched?) A’s particle wave to within 13.4 billion lightyears of B (yes/no?).

Sounds like you are closer. But have you watched the short movie yet?
Google "wright balloon model". Ned Wright is a good teacher. his whole website is a useful resource. He usually has two balloon movies and its worth watching both.

All this stuff we are talking about is post-inflation expansion. If inflation happened it was by some exotic not-understood mechanism way early, like in the first second.

We are talking about stuff beginning at year 380,000 which is LONG past the end of inflation.

BTW there is an issue with arithmetic. If you have 13.7 billion years and you take away one million years, what do you have? You have 13.7 billion years.
That is, actually 13.699 but it rounds off to 13.7.

Likewise 13.7 billion minus 380,000 is still 13.7 billion. Even more true this time because 380,000 is less than a million.

So we are talking about an episode in history lasting from year 380,000 to year 13.7 billion, during which distances gradually increased only about 1000-fold, more precisely 1090-fold.

That period lasted about 13.7 billion years and I predict that if you watch the Ned Wright movies several times you will easily understand how at the end of 13.7 billion years a photon can find itself 46 billion lightyears from its point of origin.

Expansion makes the distance that the photon has already traveled grow like money you put in the bank, in your savings account, at a percentage rate. The rate actually changes over time but that is of secondary importance to what I'm saying.

You can see this happening in the movies. The photon travels a certain ways on its own, at the usual speed of light (say one millimeter per second on the balloon model). But because of expansion after a while it is a long long ways from where it started.

I think you are getting this, or have already gotten. It has nothing to do with inflation.

With my question about whether the CMB radiation criss-crosses itself, I meant to ask: when individual light waves hit each other, might they cancel or strengthen each other?

At ordinary energies, beams of light that cross do not interact. Try it with two flashlights.
Positive and negative interference effects are something else, two beams of monochromatic light (both the same frequency) meeting on a projection screen. CMB is not monochromatic. It is a big mix of frequencies. Not to worry about interference.

When you say the balloon is now 1090 times bigger than it was, I reflexively picture the expansion as a slow and steady inflation, analogous to me blowing up a party balloon. And this let's me picture how the ‘coins on the surface of the balloon’ get further away from each other, and also let's me picture the timeline of the balloon, equating small to young, large to old (with us being old).

That's right.

But, assuming the Inflationary Model is correct, the balloon became pretty large when it was still very young, which goes to the uniformity of the CMB in the first place. And this is where the powerful balloon analogy becomes intuitively confusing to me.

Like I already said. Inflation is relevant to the first second. Not part of the picture of what happened only after 380,000 years had gone by!

Maybe inflation expanded some portion of the universe from the size of an atomic nucleus (say 10^-15 meter) to 100 million kilometers. That is the expansion factor the inflation scenario-makers typically attribute to an inflation episode. That still is not even the radius of the Earth's orbit!

After inflation, what is now the observable universe (radius about 46 billion ly) is still not very large. Inflation, if it happened, would have increased size by a large factor, typically they use a figure of e^60. But if you start with something very small to begin with, a large factor doesn't mean the result is necessarily large in absolute terms.

I wouldn't bother trying to include inflation in your visual picture. Just start some time after the universe has attained some reasonable size----like for example on the order of 42 million ly.

* Firstly, if a wriggle of light keeps traveling around a sphere, it’s going to end up back where it started.

Nah. Watch the movies. In the case he shows where it keeps expanding, they never make it around. Say you are a caterpillar traveling 1 mm per second on the balloon surface and the circumference of the balloon is increasing 10 mm per second, and this rate is accelerating. How are you ever going to make it around? We can do this with numbers, but it is almost as good to do it visually-intuitively with Ned Wright's animations.

* Secondly, since the coins themselves stopped emitting their original CMB radiation long ago, then I expect the timeline of a given location A to include periods in which there is no CMB.

At the time the CMB was emitted, space was entirely filled with a uniform glowing hot cloud. It only later began to condense into stars and galaxies. So the pennies are not a perfect representation of matter. They are sort of the right picture once matter condensed into clusters of galaxies. But it is still just an analogy, not accurate in detail.

So we have been receiving CMB radiation steadily for the whole 13.7 billion years. As time goes on, the glow emitted by more and more distant hot cloud comes in. Because the cloud was uniformly distributed. So the radiation would not have been sporadic.

 

[Chilli]

Sounds like you are closer. But have you watched the short movie yet?

Yes, but I don't have trouble picturing the expansion of distance between gravitationally sticky blobs.

BTW there is an issue with arithmetic. If you have 13.7 billion years and you take away one million years, what do you have? You have 13.7 billion years.

You do, indeed! (I did say my math was lacking.)

I predict that if you watch the Ned Wright movies several times you will easily understand how at the end of 13.7 billion years a photon can find itself 46 billion lightyears from its point of origin.

An optimistic prediction, but I say hold that dream!

I think you are getting this, or have already gotten. It has nothing to do with inflation.

Agreed.

I get that photons traveling at the speed of light can find themselves at a distance from their point of origin which, due to expansion, is further away than lightspeed alone could have achieved, and that they're destined to never exceed the speed of expansion, leading to an ultimately black and cold universe. What I was trying to do was point out challenges with the use of the balloon analogy.

Firstly, in offering a 2D construct in the form of the surface of a balloon, that surface can be misinterpreted as an expanding boundary to the universe, undermining all sorts of unbounded models. And then, of course, balloons don't expand forever; they burst, so, in looking at Wright's animation, or even just a static drawing, the balloon will (perhaps subliminally) be perceived as somehow finite in its expansion. And if expansion is finite, and light keeps travelling, light will eventually circle the balloon. I'm not saying such thoughts are of any use; quite the contrary, they merely muddy things.

Balloons tap into the layman's wealth of experience with birthday parties, sore lungs, and aching fingertips. It's why people look at the balloon as being the shape of the universe and then, quite logically and incorrectly, see the centre of the balloon as the centre of the universe. And I circle back to my earlier point that what is needed (what I need) is a proper analogy for the shape of space-time. Something that will let the balloon analogy be used purely to convey the concept of swelling distances between big things that are more or less at rest.

Kind regards