# Expanding balloon analogy?

binbots
People often use the expanding balloon with galaxies on the surface to represent the expansion of space. But this view doesn't show how this expansion works in 3d and it doesn't show how gravity comes into play. Instead of putting the galaxies on the surface of the balloon all we have to do is give the balloon depth and place the galaxies inside the surface. Now as the balloon expands it also contracts (Olbers shells). The galaxies closest to us would contract, but overall the whole balloon would be expanding. Like stretching out a piece of gum left to right. The gum contracts in the north south direction, but over all it is being stretched left to right. Now this same analogy seems to explain a lot more. My question is why do I never hear this analogy taken this far? Is it because I am wrong? Is it just not a good analogy? Or am I over stepping my boundaries by saying the expansion of the universe is the same reason for its contraction in local ares?

Gold Member
2021 Award
People often use the expanding balloon with galaxies on the surface to represent the expansion of space. But this view doesn't show how this expansion works in 3d and it doesn't show how gravity comes into play. Instead of putting the galaxies on the surface of the balloon all we have to do is give the balloon depth and place the galaxies inside the surface. Now as the balloon expands it also contracts (Olbers shells). The galaxies closest to us would contract, but overall the whole balloon would be expanding. Like stretching out a piece of gum left to right. The gum contracts in the north south direction, but over all it is being stretched left to right. Now this same analogy seems to explain a lot more. My question is why do I never hear this analogy taken this far? Is it because I am wrong? Is it just not a good analogy? Or am I over stepping my boundaries by saying the expansion of the universe is the same reason for its contraction in local ares?
You don't hear it because it would be grossly misleading, implying as it does the existence to a center. I suggest you read the full explanation of the balloon analogy and its flaws on the link in my signature

binbots
I am not implying a center. Our universe would be contained in the 3d material of the balloon. Not the air inside.

gulfcoastfella
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2021 Award
I am not implying a center. Our universe would be contained in the 3d material of the balloon. Not the air inside.
A 3D balloon expands with a center, so I don't understand you at all. I don't see how you think you are not implying a center.

EDIT: I think you are looking for what is called the "raisin bread analogy"

binbots
The raisin bread analogy doesn't show gravity, only expansion. Let me ask it this way. A balloon does not just have a surface area. The surface has a depth. So now we can think of atoms making up the balloon as being galaxies. As this balloon expands (still no center) for the most part atoms will move apart. But while the balloon expands and stretches the material it is made of gets thinner and contracts. There for all the atoms that are in similar places of depth will contract. Expansion wins when the balloon inflates faster than the material contacts. Gravity wins where the material contracts faster then the overall expansion. There is still no middle as this all takes place only in the balloon material. (I only used atoms as markers, so please don't freak out they they are not obeying QM)

gulfcoastfella
Mentor
while the balloon expands and stretches the material it is made of gets thinner and contracts.

Expansion wins when the balloon inflates faster than the material contacts. Gravity wins where the material contracts faster then the overall expansion.

This is not a good way of interpreting the balloon analogy. The thickness of the balloon does not have any counterpart in the model of the universe that it is supposed to be an analogy for.

It looks to me like the balloon analogy is causing more problems for you than it solves. (You are correct, btw, when you say in your OP that the analogy does not explain how gravity comes into play; but your reworking of it does not solve that problem.) My advice would be to abandon it and look for a better way of understanding how the FRW model of the universe works.

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2021 Award
I have said what I have to say about the balloon analogy in the link I provide in my signature. If you would like to make up your own analogy, feel free, just don't expect other people to know what you are talking about if you call it "the balloon analogy" since that phrase has a specific meaning.

Gold Member
I don't like the Balloon analogy, just because it is a 2 dimensional object and makes me confused when thinking of the 3-spatial dimensions. I prefer instead of using a balloon, looking at the comoving distances where FRW metric is applicable. In that case, as the time-coordinate evolves, your distances (rulers) expand or better - they scale (which can incorporate both expansion and contraction)...
However even this is not flawless because it needs the exact coordinate system , that you see the FRW metric written into, to work...

Mentor

Putting that "rulers" in is not correct. Rulers don't expand. Distances between galaxies, as measured by rulers which remain at a constant length, expand. Don't misinterpret the scale factor in the metric as describing "expansion of rulers". Coordinates are just coordinates. All the scale factor is telling you is how much proper length (as measured by rulers whose length remains the same) corresponds to a given increment of coordinates.

ChrisVer
Gold Member
Putting that "rulers" in is not correct. Rulers don't expand. Distances between galaxies, as measured by rulers which remain at a constant length, expand. Don't misinterpret the scale factor in the metric as describing "expansion of rulers". Coordinates are just coordinates. All the scale factor is telling you is how much proper length (as measured by rulers whose length remains the same) corresponds to a given increment of coordinates.

Maybe you are right. But this also has helped me in understanding the redshift because of expansion, since a ruler that measured at emission time a wavelength $\lambda_{em}$, got "expanded" and gave the observed redshifted $\lambda_{o}$, which are connected by the scaling of the two same "rulers"... I don't know, I feel like we are rephrasing the same thing (you could as well think that the rulers' lengths did not expand, but there was a mismatch between the wavelength at the time of emission and the wavelength at the time of observation as measured by the same length ruler).

"The ball hit the wall or the wall the ball?"

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a ruler that measured at emission time a wavelength ##\lambda_{em}##, got "expanded" and gave the observed redshifted ##\lambda_{o}##,

No, the ruler did not expand, the wavelength of the light expanded. The ruler stayed the same; if it had also expanded, then when it measured the wavelength, it would have gotten the same answer as before, ##\lambda_{em}##, because it would have expanded to the same extent as the light it was measuring. Or, if the ruler expanded but the light stayed the same, then the ruler would measure a shorter length, not a longer one.

I realize that the above is English, not math, and the math is unequivocal regardless of how you try to describe it in English. But if we are going to use English at all to communicate about this stuff, I think it behooves us to try to use English that at least invites the same sort of reasoning that you would do if you were using the math directly, or at least does not invite reasoning that would clearly be incorrect if you were using the math directly. That's why I tried to illustrate above how different ways of describing the math lead to different kinds of reasoning, and some of those kinds of reasoning lead to wrong answers.

binbots
Maybe the expanding balloon analogy does not work because it is always shown as a already inflated balloon expanding. This is a better view of what our universe will look like in the distant future. A better representation of our time in the universe today would be the part before the balloon has it's balloon shape. Not smooth, but full of creases (maybe folds?). These creases are expanding slower than other parts of the balloon. Slower expanding creases are what we perceive as gravity. Better? Worse? Or still just as bad? Expanding Golf Ball Perhaps?

Mentor
A better representation of our time in the universe today would be the part before the balloon has it's balloon shape. Not smooth, but full of creases (maybe folds?). These creases are expanding slower than other parts of the balloon. Slower expanding creases are what we perceive as gravity.

No. What you are calling "gravity" here is really "gravity within isolated bound objects like galaxies, stars, planets, etc.". These objects are not expanding at all, so thinking of them as "creases that are expanding slower" is not correct.

When I said that the balloon analogy doesn't capture the effects of gravity, what I meant was that it doesn't capture the effects of the gravity of all the matter in the universe, when it's averaged out to a continuous "cosmological fluid" with a certain average density and pressure, on the dynamics of the universe as a whole. The balloon analogy doesn't capture that at all. To understand that, you need to look at the Friedmann equations. The internal gravitational behavior of isolated systems like galaxies, stars, and planets is completely negligible on this scale; they all just average out to the cosmological fluid.

I actually like the balloon analogy. It does an excellent job illustrating the Hubble expansion and the cosmological principle. The fact that the surface of the balloon is a 2D analog for our 3D universe forces us to imagine our universe as a 3-sphere with a topology analogous to the 2-sphere. Sure, there's the bit about the center of the sphere and that gets people wondering about that mysterious "4th dimension". But in the process of availing themselves of this misconception, they learn that this ambient space is an illusion, and that gets them to appreciate the important result in GR that the properties of spacetime are independent of imbeddings, etc.

The balloon analogy is only an analogy, and no analogy is perfect (or else it wouldn't be analogy). I'll take the illusory extra dimension if it means being able to use a common household object to explain something as abstract and important as the expanding universe.

gulfcoastfella
Mentor
The fact that the surface of the balloon is a 2D analog for our 3D universe forces us to imagine our universe as a 3-sphere with a topology analogous to the 2-sphere.

But one drawback of this (other than the temptation to ask where the "center" is) is that our current best-fit model has the universe being spatially flat, not closed, and it's really hard to imagine a spatially flat universe as an expanding balloon.

But one drawback of this (other than the temptation to ask where the "center" is) is that our current best-fit model has the universe being spatially flat, not closed, and it's really hard to imagine a spatially flat universe as an expanding balloon.
The models pertain to the *observable universe*, don't forget! So that gives us a great opportunity to teach the distinction between the "whole" universe and just our observable part of it -- that we see just a small patch on this huge inflating balloon. This segues into the analogy with the surface of the earth appearing flat even though it's actually spheroidal.

gulfcoastfella
Gold Member
The models pertain to the *observable universe*, don't forget! So that gives us a great opportunity to teach the distinction between the "whole" universe and just our observable part of it -- that we see just a small patch on this huge inflating balloon. This segues into the analogy with the surface of the earth appearing flat even though it's actually spheroidal.

Do you mean that the Universe as a whole cannot be flat?

Do you mean that the Universe as a whole cannot be flat?
No, it can be, just that the observations are mum on this. I don't mean to imply that the universe is necessarily spherical just because the balloon analogy suggests this. If it is, then what I wrote above stands. If it is instead some other topology, then the balloon analogy is still useful for illustrating Hubble expansion and the cosmological principle, as well as the distinction between local and global geometry.

gulfcoastfella
Mentor
it can be, just that the observations are mum on this

More precisely, observations are mum given the assumption that inflation happened, and expanded the universe to such an extent that the observable part we see is too small a patch of the whole for our observations of flatness within the observable part to tell us anything useful about the spatial geometry of the whole. That's not to say that the assumption is wrong, just that the "observations are mum" conclusion does depend on that assumption, so there is a sense in which it is model-dependent.

binbots
So this analogy will never be able to show expansion and gravity? No matter how much we change it?

Gold Member
More precisely, observations are mum given the assumption that inflation happened, and expanded the universe to such an extent that the observable part we see is too small a patch of the whole for our observations of flatness within the observable part to tell us anything useful about the spatial geometry of the whole. That's not to say that the assumption is wrong, just that the "observations are mum" conclusion does depend on that assumption, so there is a sense in which it is model-dependent.

But inflation made the whole universe flat... even if we are just in a patch of the whole, if the "whole" began from inflation, then it should have been fine-tuned to flat as well..

Mentor
So this analogy will never be able to show expansion and gravity? No matter how much we change it?

I don't think it will be able to show the effect of gravity on the expansion as a whole, no.

Mentor
inflation made the whole universe flat

Inflation makes the universe expand by a very large factor, but that doesn't mean it changes the spatial topology. If the universe had the spatial topology of a 3-sphere before inflation, it has the spatial topology of a 3-sphere after inflation--it's just a much, much bigger 3-sphere, so big that our observable universe is just a small patch and we can't tell it's a 3-sphere. When people talk about inflation solving the "flatness problem", they are referring to our observable universe, as bapowell said, not to the whole universe.

gulfcoastfella
binbots
I am aware of how bad the balloon analogy is. That is why I started this post. If it is so bad then why do we keep hearing about it? Space is expanding and matter is forming a web like structure. There has to be a better way of describing this to people than with a expanding balloon.

More precisely, observations are mum given the assumption that inflation happened, and expanded the universe to such an extent that the observable part we see is too small a patch of the whole for our observations of flatness within the observable part to tell us anything useful about the spatial geometry of the whole. That's not to say that the assumption is wrong, just that the "observations are mum" conclusion does depend on that assumption, so there is a sense in which it is model-dependent.
I think they are mum given the easier assumption that the particle horizon doesn't mark the edge of the whole universe. Inflation is just one reason this might be the case.

gulfcoastfella
So this analogy will never be able to show expansion and gravity? No matter how much we change it?
It does show expansion. It is the thing that it shows rather successfully. What do you mean by "gravity"? In a homogeneous universe (a smooth balloon surface) the gravitational potential is zero.

gulfcoastfella
I am aware of how bad the balloon analogy is. That is why I started this post. If it is so bad then why do we keep hearing about it?
The answer that I've suggested is that it isn't so bad. It does a good job of illustrating certain aspects of the expansion and geometry of the universe.
Space is expanding and matter is forming a web like structure. There has to be a better way of describing this to people than with a expanding balloon.
It successfully models the former, the latter not so much. The balloon analogy illustrates a homogeneous and isotropic universe, which is true on cosmological scales. So if you're going to imagine galaxies in your balloon analogy, they'd be microscopic specks uniformly distributed across the surface. If you wish to understand structure formation, which is about the evolution of inhomogeneities, that is beyond the intent and use of the balloon analogy. It's not a panacea.

gulfcoastfella
Mentor
What do you mean by "gravity"?

He's referring to what I said in earlier posts, that the effect of the gravity of the matter in the universe on its dynamics (i.e., the Friedmann equations) is not captured in the balloon analogy.

gulfcoastfella
binbots
So matter would be microscopic specks, not pennies. Well there you go. This analogy is already getting better. Any other improvements we can make?

Gold Member
If it is so bad then why do we keep hearing about it?

Because it can be dealt with classical mechanics [without GR] quite easily I guess... At least I still remember having such a problem in my Classical Mechanics course...
And explains just 1 thing out of the X there might be... that's why it's an analogy... the rest X-1 don't have to apply for it...

binbots
These microscopic specs would not have any mass because they would only be on a 2 dimensional (no volume) surface right? . Is that where the whole analogy breaks down?

Mentor
These microscopic specs would not have any mass because they would only be on a 2 dimensional (no volume) surface right?

It's not that they "can't" have any mass. It's that the concept of "mass" doesn't even have any meaning in the analogy. All the analogy describes is geometry; it doesn't describe anything else. Mass is something else.