The balloon analogy (please critique)

[phinds]

I'm sure there must be umteen dozen sites on the internet that explain the balloon analogy, but many of them must do a really bad job, since we see questions here all the time that show how badly misunderstood it is.

I have tired of responding in detail to these misconceptions, so have created a web page to show not only what the balloon analogy IS, but also what it ISN'T.

I'd appreciate any feedback anyone has, and feel free to link to it yourself for the same reason I intend to.

www.phinds.com/balloonanalogy


...

 

[GeorgeDishman]

I'm sure there must be umteen dozen sites on the internet that explain the balloon analogy, but many of them must do a really bad job, since we see questions here all the time that show how badly misunderstood it is.

I have tired of responding in detail to these misconceptions, so have created a web page to show not only what the balloon analogy IS, but also what it ISN'T.

I'd appreciate any feedback anyone has, and feel free to link to it yourself for the same reason I intend to.

www.phinds.com/balloonanalogy

There is a sticky thread on this where I posted some concerns I have with the balloon analogy (although there has recently been about a page worth of other stuff, see my post #238).

You emphasise how the 3D aspect of the balloon should be ignored but it can serve as an analog of cosmological time with the "big bang" event at the centre.

My biggest concern though is that it implies that the universe is finite which is not implied by real models.

One thing you can refine is to say the pennies are stuck on with grease and are slightly magnetic, thus they clump together if close enough, an analogy for proper motion. That can help people understand why Andromeda is going to merge with us.

HTH

 

[phinds]

Thanks for the feedback

You emphasise how the 3D aspect of the balloon should be ignored but it can serve as an analog of cosmological time with the "big bang" event at the centre.

I completely disagree. I think that is an example of taking the analogy to a place where it doesn't belong.

My biggest concern though is that it implies that the universe is finite which is not implied by real models.

Good point. I'll see about adding something about that, although I disagree w/ you about the implication, I DO see how some folks could see it that way, so a word of caution is in order.

One thing you can refine is to say the pennies are stuck on with grease and are slightly magnetic, thus they clump together if close enough, an analogy for proper motion. That can help people understand why Andromeda is going to merge with us.

No, I have specifically stated that the pennies represent clusters that are gravitationall bound. The balloon analogy is not about what happens inside the clusters.

 

[marcus]

I'm sure there must be umteen dozen sites on the internet that explain the balloon analogy, but many of them must do a really bad job, since we see questions here all the time that show how badly misunderstood it is.

I have tired of responding in detail to these misconceptions, so have created a web page to show not only what the balloon analogy IS, but also what it ISN'T.

I'd appreciate any feedback anyone has, and feel free to link to it yourself for the same reason I intend to.

www.phinds.com/balloonanalogy ...

Seems fine! You might consider adding a paragraph about what you can learn by watching Ned Wright's short animation which, besides galaxies staying the same size and in the same location, has PHOTONS traveling always at the same speed (no matter how large distances get, or how small).

To get the link to the animation, google "wright balloon model".

It's already good the way you have it. But it would be even more instructive, I think, if you got readers to take a thoughtful look at that animation. Maybe there's some way you can paste it in, but if not at least give a link.

If you watch carefully you can actually see pairs of galaxies where the distance between them is increasing faster than the photons move (faster than the speed of light). And you can even see a photon from A eventually succeed in reaching B even though when it started out B was receding from A faster than light (so initially the distance to its goal increased.)

==================
EDIT good point about clusters. Wright's animation is oversimple in just that respect. The little white whirling things look like cartoon galaxies but they symbolize more general gravitationally bound systems. That could be imagined as clusters (remaining approximately the same size). To make it work as a teaching tool he has to eliminate some realistic detail. It has to be schematic, in a sense, or it would be too distracting and the students would not get the essentials.

 

[Mark M]

Thanks for making this Phinds, the balloon analogy is probably the most misinterpreted analogies in any area of physics. Two things I would suggest - emphasize that there is no edge to the universe, even though this is demonstrated by the analogy, many people seem to forget this. Also, mention that even though the surface of the balloon is embedded in 3 dimensions, the universe is not embedded in a fourth dimension. Besides that, it's probably the best explanation I've seen. Once again, thanks for putting the time into make this.

 

[phinds]

Seems fine! You might consider adding a paragraph about what you can learn by watching Ned Wright's short animation which, besides galaxies staying the same size and in the same location, has PHOTONS traveling always at the same speed (no matter how large distances get, or how small).

To get the link to the animation, google "wright balloon model".

It's already good the way you have it. But it would be even more instructive, I think, if you got readers to take a thoughtful look at that animation. Maybe there's some way you can paste it in, but if not at least give a link.

If you watch carefully you can actually see pairs of galaxies where the distance between them is increasing faster than the photons move (faster than the speed of light). And you can even see a photon from A eventually succeed in reaching B even though when it started out B was receding from A faster than light (so initially the distance to its goal increased.)

==================
EDIT good point about clusters. Wright's animation is oversimple in just that respect. The little white whirling things look like cartoon galaxies but they symbolize more general gravitationally bound systems. That could be imagined as clusters (remaining approximately the same size). To make it work as a teaching tool he has to eliminate some realistic detail. It has to be schematic, in a sense, or it would be too distracting and the students would not get the essentials.

Thanks, Marcus. I'll take a look at that other source. It's easy to drop in a link to it.

 

[phinds]

Thanks for making this Phinds, the balloon analogy is probably the most misinterpreted analogies in any area of physics. Two things I would suggest - emphasize that there is no edge to the universe, even though this is demonstrated by the analogy, many people seem to forget this. Also, mention that even though the surface of the balloon is embedded in 3 dimensions, the universe is not embedded in a fourth dimension. Besides that, it's probably the best explanation I've seen. Once again, thanks for putting the time into make this.

Good advice. Thanks.

 

[Calimero]

Hi Phinds. Nice work. I would suggest just one thing. You say:

BUT its (expansion) effects are so totally swamped by the effects of the acceleration (see below) that it is barely relevant.

Which is not quite accurate. Here is the quote from wikipedia article "metric expansion of space" where it is nicely put:

Inertia dominated the expansion in the early universe, and according to the Lambda-CDM model (ΛCDM model) the cosmological constant will dominate in the future. In the present era they contribute in roughly equal proportions.

 

[phinds]

Hi Phinds. Nice work. I would suggest just one thing. You say:

Which is not quite accurate. Here is the quote from wikipedia article "metric expansion of space" where it is nicely put:

Hey, thanks. I was ignorant about that.

 

[Jorrie]

I'd appreciate any feedback anyone has, and feel free to link to it yourself for the same reason I intend to.

www.phinds.com/balloonanalogy

...

I agree with what you wrote. Just another (possible) misunderstanding of what happens at the end of inflation, probably because of the use of certain words, i.e. (from your page):

"EXPANSION --- After inflation, the universe settled down to a more sedate rate of expansion, something like a ballistic affect from the inflation."

This is correct, but it creates the impression that there is a sudden change in the expansion rate (da/dt) after inflation, an impression also enhanced by the usual log-log type graphs used to fit the enormous range onto one graph (see the attached graph example).

Does the 'ballistic effect' and mutual gravity not make the expansion rate smoothly change from that extreme 'end-of-inflation' value to the 'sedate' values that we observe today?

Log-log graphs normally show that as a sharp change in slope, but it represents a sharp change in the extreme acceleration rate during inflation to the steady deceleration after inflation - not a sharp change in expansion rate. My example graph's slope is 1/2 after inflation (radiation dominated), changing to 2/3 (matter dominated) around 100,000 years and will in the far future again increase steadily (dark energy dominated). My timescale (t/t_p) is plotted relative to Planck time and the size scale (r/r_p) is roughly Hubble radius at time t relative to Planck scale.

 

[Drakkith]

Nice job Phinds!

 

[sweet springs]

Hi. I have read only your first comment so if the points below are already mentioned, sorry for it.

As for your FIRST point, I hardly find actual difference between 'there is NO center' and 'there is CENTER but it exists OUTSIDE our world. Our world everywhere has same distance from the CENTER'

SECOND point, balloon has no edge and I think neither does the space.

THIRD point, as you mentioned uniform expansion model would be too rough. Non zero momentum-energy tensor would prevent space there to expand so it makes inflation of the space inhomogeneous in micro scale i.e. smaller than size of galaxy. It is like taped balloon where tape prevent rubber surface to be stretched.

Regards.

 

[neyzenyelda]

nice work! very helpful for me. thanx! :)

 

[Ich]

Like GeorgeDishman said: Don't glue the pennies to the balloon. It amplifies the common misconception that space is dragging things with it unless they resist.
Let them float on the surface like on a soap bubble. This reproduces the actual kinematics of expansion, and the model becomes much more accurate.

 

[GeorgeDishman]

You emphasise how the 3D aspect of the balloon should be ignored but it can serve as an analog of cosmological time with the "big bang" event at the centre.

I completely disagree. I think that is an example of taking the analogy to a place where it doesn't belong.

OK, YMMV, but see the first point by "sweet springs". Identifying the radius as comoving time avoids that problem:

As for your FIRST point, I hardly find actual difference between 'there is NO center' and 'there is CENTER but it exists OUTSIDE our world. Our world everywhere has same distance from the CENTER'

;-)

My biggest concern though is that it implies that the universe is finite which is not implied by real models.

Good point. I'll see about adding something about that, although I disagree w/ you about the implication, I DO see how some folks could see it that way, so a word of caution is in order.

The balloon is often used as a way to explain by analogy how a finite volume can have no boundary so the implication can be taken that "no boundary" implies "finite". I think you have to be careful to avoid accidentally giving that erroneous impression.

One thing you can refine is to say the pennies are stuck on with grease and are slightly magnetic, thus they clump together if close enough, an analogy for proper motion. That can help people understand why Andromeda is going to merge with us.

No, I have specifically stated that the pennies represent clusters that are gravitationall bound. The balloon analogy is not about what happens inside the clusters.

The suggestion was only a way you could extend your explanation, I am not suggesting what you have is wrong.

http://www.atlasoftheuniverse.com/virgo.html

If a coin represents a cluster in the map above, I think the Virgo Cluster will drift away from Fornax and Eridanus, but will those two merge or are they also far enough apart to avoid that fate?

 

[phinds]

I agree with what you wrote. Just another (possible) misunderstanding of what happens at the end of inflation, probably because of the use of certain words, i.e. (from your page):

"EXPANSION --- After inflation, the universe settled down to a more sedate rate of expansion, something like a ballistic affect from the inflation."

This is correct, but it creates the impression that there is a sudden change in the expansion rate (da/dt) after inflation, an impression also enhanced by the usual log-log type graphs used to fit the enormous range onto one graph (see the attached graph example).

Does the 'ballistic effect' and mutual gravity not make the expansion rate smoothly change from that extreme 'end-of-inflation' value to the 'sedate' values that we observe today?

Log-log graphs normally show that as a sharp change in slope, but it represents a sharp change in the extreme acceleration rate during inflation to the steady deceleration after inflation - not a sharp change in expansion rate. My example graph's slope is 1/2 after inflation (radiation dominated), changing to 2/3 (matter dominated) around 100,000 years and will in the far future again increase steadily (dark energy dominated). My timescale (t/t_p) is plotted relative to Planck time and the size scale (r/r_p) is roughly Hubble radius at time t relative to Planck scale.

Thanks for that. I'll look into it and make sure I understand it myself and then update the page.

 

[bapowell]

Phinds,

Thanks for going through the trouble of creating this page. I agree that many of these issues could do with some clarification. I have a couple points/comments (and I apologize if these have been addressed already by others; I haven't read the above posts)

1) Typo: You have "ONLY the fact that all the balloons move away" in the statement of the analogy. I believe you mean "pennies" in place of "balloons."

2) I agree that it's easiest to imagine an infinite rubber sheet, but you might mention that the spherical geometry of the balloon is OK, and can be taken to represent a closed universe. Of course, then you have to explain that the 2D surface of the balloon is analogous to the 3D surface a hypersphere, and that you don't need to postulate a higher dimension within which the balloon is embedded. All that needs to exist is the surface (this would expand upon your discussion of the center of the balloon not being part of the analogy -- it's not part of the analogy because it doesn't exist!)

3) You might wish to mention that inflation was an accelerated expansion. This way it can be compared to the present accelerated expansion, and is not necessarily a distinct physical process (for example, quintessential inflation (however unlikely to be true) posits that the same field that drove inflation is driving the current expansion.

4) The "ballistic effect" is confusing. It's not clear what you mean by this. It seems to suggest that the end of inflation "propelled" the subsequent expansion of the universe. This is probably not the b est way to think of it; the standard hot big bang phase of expansion following inflation expands for the same reason that it expands without inflation -- it's a matter of boundary conditions.

5) "Attributed to a force that is not understood": I'd say the force is well-understood; it's just gravity. Probably want to say attributed to a "source" or "field" or "matter"

6) Very happy with the comment that there's absolutely no figgin' connection between dark energy and dark matter. Much needed. To be totally honest, though, you might wish to mention that there are proposals linking to the two.

 

[bapowell]

My biggest concern though is that it implies that the universe is finite which is not implied by real models.

Is not a closed universe a "real model"?

 

[phinds]

Phinds,

Thanks for going through the trouble of creating this page. I agree that many of these issues could do with some clarification. I have a couple points/comments (and I apologize if these have been addressed already by others; I haven't read the above posts)

1) Typo: You have "ONLY the fact that all the balloons move away" in the statement of the analogy. I believe you mean "pennies" in place of "balloons."

2) I agree that it's easiest to imagine an infinite rubber sheet, but you might mention that the spherical geometry of the balloon is OK, and can be taken to represent a closed universe. Of course, then you have to explain that the 2D surface of the balloon is analogous to the 3D surface a hypersphere, and that you don't need to postulate a higher dimension within which the balloon is embedded. All that needs to exist is the surface (this would expand upon your discussion of the center of the balloon not being part of the analogy -- it's not part of the analogy because it doesn't exist!)

3) You might wish to mention that inflation was an accelerated expansion. This way it can be compared to the present accelerated expansion, and is not necessarily a distinct physical process (for example, quintessential inflation (however unlikely to be true) posits that the same field that drove inflation is driving the current expansion.

4) The "ballistic effect" is confusing. It's not clear what you mean by this. It seems to suggest that the end of inflation "propelled" the subsequent expansion of the universe. This is probably not the b est way to think of it; the standard hot big bang phase of expansion following inflation expands for the same reason that it expands without inflation -- it's a matter of boundary conditions.

5) "Attributed to a force that is not understood": I'd say the force is well-understood; it's just gravity. Probably want to say attributed to a "source" or "field" or "matter"

6) Very happy with the comment that there's absolutely no figgin' connection between dark energy and dark matter. Much needed. To be totally honest, though, you might wish to mention that there are proposals linking to the two.

Thanks for all the feedback. I've been meaning to get back to that page and update it with some of the comments above, and I'll take yours into consideration as well.

 

[Naty1]

If you haven't already, consider searching these forums under 'balloon analogy'..There are several dozen threads and I'll bet some offer insights that will be of interest, even if only perfecting an explanation you have already considered.

You mention under Doesn't work, #2...forget curved shape you note..but you could mention dimples in the surface as gravitational potential [space]wells...like the rubber sheet analogy which you do reference...

Also, someone posted, and I'd suggest you PM pervect because I think it was him, but may not have been recent, an oustanding list of balloon analogy strengths and weakness...
I will search more to see if I can locate it...

Under DOESN'T WORK: SOURCE OF CMBR might be worth considering ...all observers see a huge spherical source, the surface of last scattering...and also WE ARE AT THE OLDEST POINT IN THE UNIVERSE ...since everybody else is in our past...[and we in theirs!]...Actually, every other observer in the universe sees a slightly warmer CMB than do we - for the simple reason they are observing it in our past.

edit: found this description from Marcus:
Marcus:
One thing the balloon analogy teaches is what it means to be not moving with respect to CMB. The balloon is a spherical surface and as it gradually expands a point that always stays at the same longitude and latitude is stationary with respect to CMB. Distances between such stationary points do increase as the universe expands. They increase at a regular percentage rate (larger distances increase more). In our 3D reality this is called Hubble Law. It is about distances between points which are at rest wrt CMB.

Don't know this source but I liked the description:

What passes for the “LOCATION OF THE CMB ORIGIN” is a large spherical surface called the surface of last scattering where the stuff is that emitted the light we are now getting. In the past we were getting CMB light from other stuff that is nearer, but that light has already gone by us. In the future we will be getting CMB light from other stuff that is out beyond our current surface of last scattering---but that light is still on its way and has not reached us.

"

 

[Naty1]

Also for cosideration:
[Source unknown]

In our 3D reality you know you are at rest wrt CMB if you point your antenna in all directions and get roughly the same temperature or peak wavelength. There is no Doppler hotspot or coldspot in the CMB sky. That means you are not moving with respect to the universe.

Then it was defined as being at rest with respect to the process of expansion---you could tell you were at rest with respect to the universe if the expansion around you was approximately the same in all directions---not faster on one side of the sky and slower on the other, but balanced. It is the same idea but we now use the CMB to define cosmological ‘rest’ it because it is much more accurate. Sun and planets are traveling about 380 km/s with respect to CMB in a direction marked by the constellation Leo in the sky. It is not very fast but astronomical observations sometimes need to be corrected for that motion so as to correspond to what an observer at CMB rest would see.

Expansion: [maybe pervect??]

So if you send a flash of light off in some direction, once the photons have gotten a substantial distance from you there will be a percentage rate of increase of distance (a recession speed) as well as the light's own standard speed.
After a while the flash of light will be farther away from you than you would calculate (for the speed of light alone) if you don't take account of expansion...So that is another thing the balloon analogy can tell you. It can teach you to expect light to manage to get farther away than you expect, even though it is always traveling across the surface at 'c'

and related "Causes of redshift [over the baloon surface] in relativity. The expansion of wavelength correlates pretty much exactly with expansion of distance (that occurred while light was in transit.) It refers to the standard FRW metric and standard cosmological model. cosmo... as the light ray falls into a galaxy's potential well, it gains a blue shift due to the added energy. When it climbs back out, it loses that energy. As long as the galaxy's gravitational potential stays the same during the light ray's passage, then the two effects perfectly cancel and there is no change in the light ray's energy (i.e. no redshift or blueshift).

Another explanation: [analogy to seeing over the balloon horizon??]
"Based on generally accepted cosmological models, it is very UNLIKELY there would be major distinctions in OUR universe just beyond our cosmological horizon. There is no widely accepted model that predicts such distinct variation in cosmological characteristics. In fact, as far as I know all models predict the SAME characteristics throughout our universe.

In other words, the light we observe each succeeding day reveals a bit more of our own cosmos, since more distant light reaches us, and the cosmic background radiation appears to reflect rather uniform, consistent, expected characteristics. Nobody has said "WOW, LOOK AT THAT! ALL OF A SUDDEN WE ARE GETTING AN ENTIRELY DIFFERENT KIND OF CMBR"Chalnoth: "We are at the temporal edge of the universe because nothing in the observable universe is older than us relative to the BB; it also appears we are at the center of the observable universe because we can see equally 'distant' in every direction. It is obviously illogical to be both at the center and edge of any geometrical shape aside from a point. The only logical alternative is the universe has no edge or center.

Marcus: What you see in ordinary mainstream cosmology (something like 99% of the published papers) is a model of the universe as something which is spatially without boundary.

That is, you could say, how the concept of universe is defined: spatially speaking it is the thing that has no boundary. This means that expansion can only be pictured/experienced from the inside. One experiences and measures expansion as the gradual increase of distances between stationary objects.

 

[phinds]

Likely what I'll do is split the page into two parts, BASIC balloon analogy facts and then EXPANDED balloon analogy facts.

That way I can maintain my goal of an initially simple discussion but still bring in some of the more detailed info many of you have presented.

Thanks to all. I'll post a note when I get it updated. Probably this weekend.

Paul

 

[Naty1]

Here is a really tricky one:

https://www.physicsforums.com/showthread.php?t=162727&highlight=current+flow&page=2

[I skimmed the thread, did not see the following...lilely from a link in the above thread]

...Imagine you are in an expanding universe and hold a galaxy at rest with respect to you but at a cosmological distance. According to Hubble’s law a galaxy at that distance should be receding but you prevent this by using a chain or rockets or something to hold it in place. If you let go of the galaxy, what does it do?


I guess the trick is the rate [velocity] of expansion is irrelevant. It is the acceleration of the expansion that tells you what happens. So in a contracting universe the particle could move away, or in an expanding universe the particle could come towards you. You don't intuitively expect this behavior if you think of the universe as a loaf of rising bread filled with raisins!...

The answer you may assume is that since space is expanding the galaxy will start moving away from you, joining the Hubble flow eventually. However in a decelerating (but still expanding) universe the particle actually comes towards you! If you think about it it becomes clear why but Peacock argues in the link I posted that it is the idea of expanding space that leads to these misconceptions and hence should be abandoned.
In the example I gave an increasing but decelerating universe leads to the test particle coming towards you. If you try and think about this situation by picturing a balloon with dots on it you will say the particle moves away even if the rate at which the balloon is expanding is decreasing. This prediction is wrong however. Basically the issue is that the recession of galaxies causes space to expand, not the other way around which people often get confused about if they have taken the balloon or bread baking analogies too far.

 

[phinds]

Here is a really tricky one:

I don't get his statement that the recession of galaxies causes space to expand. Isn't that backwards?

I mean, if the galaxies' expansion CAUSES dark energy, what causes the galaxies to expand in the first place?

Doesn't make sense to me.

 

[Calimero]

I don't get his statement that the recession of galaxies causes space to expand. Isn't that backwards?

Well, he is saying what i was trying to say in number of threads, but people here are persistent in lack of their pedagogical skills. He is saying that behavior of a test particle left at rest w.r. to us at cosmological distance is determined with acceleration of universe. In a universe in which space is still expanding but expansion is decelerating, particle will move towards us, fly past us, and then join Hubble flow at the other end of the sky. Not the kind of behavior you would expect if you take "expanding space" literally.

I mean, if the galaxies' expansion CAUSES dark energy, what causes the galaxies to expand in the first place?

Doesn't make sense to me.

No expansion is not causing dark energy.

 

[GeorgeDishman]

My biggest concern though is that it implies that the universe is finite which is not implied by real models.

Is not a closed universe a "real model"?

What I meant is that in current realistic models, infinite and finite are equally plausible. AFAIK, observations don't currently select one over the other either but the balloon analogy strongly favours visualisation of a finite model hence in that sense it can be misleading IMHO.

I think the WMAP page covers this well:

http://map.gsfc.nasa.gov/universe/uni_shape.html

 

[Naty1]

phinds :
You will find this discussion interesting I think; starts in 2007, and it is long but worth the read thru 2007 at least;

Wallace has some interesting insights...he IS a cosmologist...:

Does space expand

https://www.physicsforums.com/showthread.php?t=162727&highlight=current+flow&page=2
Wallace:
"What do you think? When Cosmologist talk about the expansion of the universe, it is often phrased as space itself expanding. For instance, interpreting cosmological redshifts as due to the photons being 'stretched' as they pass through expanding space, rather than being due to a doppler shift (since for instance at cosmological distances galaxies can be receding at greater than c and hence the doppler formula breaks down).

People use analogies to dots on a balloon or raisins in bread but this seems to imply that the expansion of space (the rubber or the bread) is what carries the galaxies (the dots or raisins) apart.

The idea the space expands has been attacked by various people, including the well respected John Peacock. See here, click on the link 'Expanding Space'

Do people agree with this? Is Expanding Space a 'dangerous idea' or a necessary interpretation of the GR equations for FRW universes? The maths is not in dispute, but the interpretation seems to be..."

A few post examples:

""Expansion of space" is a completely wrong terminology.
It implies that space is some sort of a substance that can expand and contract.

That an observer measures a change in distance is perfectly valid in relativity but it has nothing to do with an expansion or contraction of space.

"Photon's being streched by exanding space" is another one these absurd phrases.

That an emitter and an absorber of a photon measures a different frequency is perfectly valid in relativity but it has nothing to do with a change in the state of the photon."Marcus:
"Mainstream professional cosmologists (Wallace is one, SpaceTiger also) use a particular model (associated with names Friedman Lemaitre Roberson Walker and abbreviated FRW sometimes) into which you can plug various parameters ---and it gives you nice simple solutions to the main (Einstein) equation that you can try to fit to observational data.

And this FRW model has an idea of universal time..."Pervect:
"While it may not make sense to use a pure FRW metric to describe a bound system, there are some papers that take the approach of using for instance a Schwarzschild De-sitter metric..."

Marcus
"...there is NO problem of "where extra space comes from" because space is not a material substance-----it is just the distances between things a web of geometric relations----you DONT HAVE TO MAKE MORE..."

Depending on whether you want to make your balloon analogy discussion a career or not, perhaps a 'basic' and advanced section would help clarify things for different readers...

 

[Naty1]

phinds...
maybe you can start a 'movement' here to ban the term 'expansion of space'...??

maybe use something like 'increases in distance' or 'increase in observed distance'...[which makes the connection to different frames more apparent] and relate such a terminology to changes in the acceleration of expansion rather than changes in the 'velocity' of expansion...just a thought. In such a sense, your balloon analogy is a reasonable fascimile since there is no 'new' balloon surface being created...but distances ARE increasing...!

 

[phinds]

phinds...
maybe you can start a 'movement' here to ban the term 'expansion of space'...??

maybe use something like 'increases in distance' or 'increase in observed distance'...[which makes the connection to different frames more apparent] and relate such a terminology to changes in the acceleration of expansion rather than changes in the 'velocity' of expansion...just a thought. In such a sense, your balloon analogy is a reasonable fascimile since there is no 'new' balloon surface being created...but distances ARE increasing...!

Yes, I have been thinking along exactly those lines for the update, and I appreciate your input in the previous post as well. Thanks.

 

[George Jones]

From the Conclusion of

http://arxiv.org/abs/0707.0380:

In this paper, we have shown how a consistent description of cosmological dynamics emerges from the idea that the expansion of space is neither more nor less than the increase over time of the distance between observers at rest with respect to the cosmic fluid.

 

[GeorgeDishman]

This is a bit older and covers some different points but may also be of interest:

http://arxiv.org/abs/astro-ph/0310808

 

[Ich]

Ok, as there is evidence that the page doesn't get across an important point, let me stress once more:
Expansion doesn't drag things along.
But a balloon drags things along that are glued on it. So this is misleading. Better let the pennies float freely.
FWIW, here are some calculations I've done a while ago. There's also a paper out there examining the slippery balloon analogy.

 

[sbrothy]

...ONLY the fact that all the balloons move away from each other and that ones farther away move away faster.

Surely, you mustt mean that the pennies move away from each other or the analogy is getting really silly. Heh.

 

[Naty1]

phinds

I've been plowing through the old thread #162727.

There is a wonderful post by pervect, #90, that further explains an earlier insight by Wallace about different models providing superluminal or sub luminal speeds, and clarifies for 'non experts' a difficulty of interpreting 'distance' in cosmology:

The issues with measuring cosmological distance is the problem of "what curve" to measure length. In the usual notion of distance, one separates space-time into space and time. One then measures the distance over some hypersurface of constant time. Unfortunately, the split of space-time into space and time is in general arbitrary and depends on the choice of coordinates.

The usual notion of distance ("proper distance") defined in this manner (measuring the distance along a curve of constant cosmological time) does not actually measure the distance along a straight line (or the equivalent of a straight line in a curved space-time, a space-like geodesic).

A curve of constant cosmological time [along which we would like to measure a proper distance’ ] connecting two points in a FRW universe is not a "straight line", i.e. it is not a geodesic

and the following post cements the idea:

The so called 'physical' distance in cosmology doesn't have the status of invariance (independence of coordinate system) like the line element ds^2 because the 'physical' distance is a coordinate quantity.

So for me, three key concepts from this thread which are not captured by the balloon analogy are that 'expanding space', balloon stretching, is misleading, distance increases are dependent on acceleration, not speed, characteristics, and distances are both model and coordinate dependent meaning, observer dependent. These issues are well illustrated by Wallace's example about deceleration.

edit: Depending on how far you wish to take all this, a short explanation of FLRW measures,conventions, assumptions, and how they compare with the balloon perspective could be helpful.

Here is a first draft list [in no particular order] : FLRW is the standard [cosmological] model; FLRW metric [distance measure] is an exact solution to the EFE but only approximates our universe because it assumes the universe is homogeneous and isotropic; how you measure things, your choice of coordinates, the model chosen, affects you answers. ..., being at rest with respect to Hubble flow and that is what defines the universal cosmological time parameter utilized; superluminal expansion distances are are result of the FLRW model metric; those FLRW distances are NOT great circles nor geodesics on the balloon, the FLRW metric starts after the initial inflationary epoch, the LCDM is a 'fine-tuned version' of the general FLRW where the parameters are chosen to get the best possible fit to our universe, the most common distance measure ,comoving distance, defines the chosen connecting curve to be a curve of constant cosmological time and operationally, comoving distances cannot be directly measured by a single Earth-bound observer, etc... took me a long time to gather those insights, most from expert posts here...!

edit; Does the balloon analogy model the Hubble parameter accurately??: wiki mentions:

"..the Hubble parameter seems to be decreasing with time, meaning that if we were to look at some fixed distance d and watch a series of different galaxies pass that distance, later galaxies would pass that distance at a smaller velocity than earlier ones..."

I still have not found the excellent description of balloon analogy pros and cons previously posted!

 

[Ich]

'expanding space', balloon stretching, is misleading, distance increases are dependent on acceleration, not speed,

You can fix those if you let the pennies (in fact all matter) swim on the surface.

characteristics, and distances are both model and coordinate dependent

True, but the balloon is a model of the FRW metric and nothing else. You can't easily discuss different coordinates in that analogy, so this should not be added. Maybe a short remark in that direction would do.

those FLRW distances are NOT great circles nor geodesics on the balloon

They are. They are measured along geodesicss of FRW-space. These are not geodesics of spacetime, though, which brings a lot of trouble if one doesn't appreciate this fact.

 

[petm1]

FIRST: there is NO center. ONLY the surface of the balloon is to be considered in the analogy. This is difficult for some people to get their head around because it is so obvious that the balloon is really a 3D object with a center. Well, yes it is, BUT NOT IN THE ANALOGY. Only the surface counts in the analogy, so if you insist that there IS a center, you are completely misunderstanding, and misusing, the analogy.

SECOND: Forget that the surface of the balloon is curved. That's NOT intended to be representative of the actual universe. It is actually more reasonable to think of a flat sheet of rubber that is being stretched equally in all directions. That would be a better analogy, but you'd have to confine the analogy to only a section of the sheet. Edges would NOT be part of the analogy. The analogy is not intended to comment in any way on the shape of the universe, whether it is open or closed, flat or curved, or ANY of those things. Those are NOT part of the analogy.

THIRD: The pennies don't change size (gravitationally bound systems don't expand and nothing inside of them expands), they just get farther apart and none of them are at the center. There IS no center.

No edge, no center, and pennies don't expand, What proof does this analogy for an expanding universe give.

first; Every point on the surface of the balloon is just as much the center as any other point, no proof here of no center just that all points are equivalent centers.

second; Edges of the universe that we can see are the bound systems themselves, we may not be able to see an inner edge to the universe but we always see the outside edge.

third; If gavitationally bound systems don't expand and nothing inside of them expands then how can we see them?

 

[Calimero]

No edge, no center, and pennies don't expand, What proof does this analogy for an expanding universe give.

first; Every point on the surface of the balloon is just as much the center as any other point, no proof here of no center just that all points are equivalent centers.

First it doesn't offer any proofs. It is just analogy to help you better visualize metric expansion, which is obviously doing well even for skeptics like you, 'cause you justifiably conclude that all points are equivalent centers.

second; Edges of the universe that we can see are the bound systems themselves, we may not be able to see an inner edge to the universe but we always see the outside edge.

third; If gavitationally bound systems don't expand and nothing inside of them expands then how can we see them?

I have no idea what you mean with inner and outter edges. But we can see gravitationaly bound systems. What makes you think that we shouldn't be able too see them?

 

[Mark M]

No edge, no center, and pennies don't expand, What proof does this analogy for an expanding universe give.

Part of the goal of the balloon analogy is to show how thew universe can expand without boundaries. It would be nonsense to say the universe had some sort of edger or boundary. Spacetimes don't just abruptly 'end'. Perhaps you are confusing the comoving patch (the observable universe) with universe as a whole?

first; Every point on the surface of the balloon is just as much the center as any other point, no proof here of no center just that all points are equivalent centers.

That is the same exact statement as saying the universe has no center. When someone with no experience in cosmology hears about a center of the universe they instantly imagine some point from which all other expand from. To say there is no center is to say that there is no preferred direction to expansion.

second; Edges of the universe that we can see are the bound systems themselves, we may not be able to see an inner edge to the universe but we always see the outside edge.

The universe, once again, does not have an edge. Are you confusing the observable universe with the actual universe? The balloon analogy represents the universe as a whole.

third; If gavitationally bound systems don't expand and nothing inside of them expands then how can we see them?

What? Why would this preclude us from seeing them?

 

[petm1]

There IS no center to the universe.

First it doesn't offer any proofs. It is just analogy to help you better visualize metric expansion, which is obviously doing well even for skeptics like you, 'cause you justifiably conclude that all points are equivalent centers.

I am not a skeptic of the analogy, I just think that all points are equivalent centers, there may not be a preferred center but that is not the same a there is no center.

The universe, once again, does not have an edge. Are you confusing the observable universe with the actual universe? The balloon analogy represents the universe as a whole

Saying the universe once again does not have an edge is misleading, there are particles in my universe and they make up the edge of the world I walk on, we only see because this outside edge is where the interaction between photons and matter occurs. We always "see" the outside of the particles edge.

THIRD: The pennies don't change size (gravitationally bound systems don't expand and nothing inside of them expands), they just get farther apart and none of them are at the center. There IS no center.

If the pennies, don't change size and nothing inside of them expands how do you explain the photons we see, after all they are expanding from the inside of the gravitationally bound systems.

This is a good analogy for what we observe but making statements like there is no edge nor a center to me is misleading.

 

[phinds]

This is a good analogy for what we observe but making statements like there is no edge nor a center to me is misleading.

The balloon analogy is not supposed to prove those ideas but I present them WITH the balloon analogy for two reasons

1) because they are true
2) because the anaolgy sometimes leads to confusion on those two points (among others)

 

[Mark M]

Saying the universe once again does not have an edge is misleading, there are particles in my universe and they make up the edge of the world I walk on, we only see because this outside edge is where the interaction between photons and matter occurs. We always "see" the outside of the particles edge.

What? Are you referring to the particle horizon? If so, this is the boundary to the OBSERVABLE universe, NOT the universe as a whole.

I think you are misunderstanding my use of the words 'edge' and 'center'. Many people who aren't familiar with cosmology, when hearing about the big bang model, get this image of a bomb going off at some point in space, and identify this as the 'center of the universe'. When they hear that the universe is expanding, they get the idea there is some mysterious 'edge' that is growing. Neither of these are true, the point of the balloon analogy is to show what the big bang actually is, and that the universe can expand without having a boundary. Nothing is misleading there.

 

[GeorgeDishman]

The usual notion of distance ("proper distance") defined in this manner (measuring the distance along a curve of constant cosmological time) does not actually measure the distance along a straight line (or the equivalent of a straight line in a curved space-time, a space-like geodesic).

A curve of constant cosmological time [along which we would like to measure a proper distance’ ] connecting two points in a FRW universe is not a "straight line", i.e. it is not a geodesic.

It is however the distance that goes into the Hubble Law as explained here By Ned Wright:

http://www.astro.ucla.edu/~wright/cosmo_02.htm#MD

So for me, three key concepts from this thread which are not captured by the balloon analogy are that 'expanding space', balloon stretching, is misleading, distance increases are dependent on acceleration, not speed, characteristics, and distances are both model and coordinate dependent meaning, observer dependent.

The distances are dependent only on the scale factor.

edit: Depending on how far you wish to take all this, a short explanation of FLRW measures,conventions, assumptions, and how they compare with the balloon perspective could be helpful.

.. FLRW metric [distance measure] is an exact solution to the EFE but only approximates our universe because it assumes the universe is homogeneous and isotropic

One way to convey this is that the universe is more like the skin of an orange than a balloon.

superluminal expansion distances are are result of the FLRW model metric; those FLRW distances are NOT great circles nor geodesics on the balloon .. the most common distance measure ,comoving distance, defines the chosen connecting curve to be a curve of constant cosmological time and operationally, comoving distances cannot be directly measured by a single Earth-bound observer

If you are referring to Ned Wright's Java balloon, assuming the wiggles representing photons move at constant speed and in that case the great circle distances are the proper distance between the galaxies. Comoving distance is the proper distance divided by the scale factor.

http://www.astro.ucla.edu/~wright/Balloon2.html

If you imagine slicing the balloon through the centre, you get a graphic similar to this:

http://www.astro.ucla.edu/~wright/omega_2.gif

(It's from this page: http://www.astro.ucla.edu/~wright/cosmo_03.htm )

The radial lines are the worldlines of the comoving galaxies and the angle between two such lines is the comoving distance. In order to make surface distances the proper distance, the radial coordinate in Ned's balloon is the scale factor.

The light cones and red lines representing our past light cone of course assume the radial parameter is cosmological time so it isn't quite accurate.

Does the balloon analogy model the Hubble parameter accurately??: wiki mentions:

It's not easy to discern the Hubble Constant from the image.

"..the Hubble parameter seems to be decreasing with time, meaning that if we were to look at some fixed distance d and watch a series of different galaxies pass that distance, later galaxies would pass that distance at a smaller velocity than earlier ones..."

For the radiation and matter-dominated eras, the Hubble Constant is inversely proportional to cosmological time but in the energy-dominated era it reaches a minimum value as the expansion becomes exponential.

 

[GeorgeDishman]

Saying the universe once again does not have an edge is misleading, there are particles in my universe and they make up the edge of the world I walk on, we only see because this outside edge is where the interaction between photons and matter occurs. We always "see" the outside of the particles edge.

What? Are you referring to the particle horizon? If so, this is the boundary to the OBSERVABLE universe, NOT the universe as a whole.

Not if he is walking on it. He seems to be talking about looking down at the surface of the Earth.

 

[hitchiker]

metric expansion of space -When space expands, it does not claim previously unoccupied space from its surroundings. I've been gnawing on these concept for long,though i understand it... i can't take it to heart that this weird phenomenon is happening right now on universe

finally i give up balloon analogy and made one my own

☼ metric expansion happens ONLY in flat space between galaxies that are not gravitationally bound ☼

why can't we take for example movement of continents on our planet as expansion of space ? africa was once closer to asia but now distance between asia & africa has increased ppl in asia can say africa is receding from us though 2 continents are not expanding distance between 2 asian cities is same distance between 2 african cities is same but distance between asia and africa is increasing..and also we can compare dark energy to ocean

it works for me ...

 

[Whovian]

☼ metric expansion happens ONLY in flat space between galaxies that are not gravitationally bound ☼

But "flat space" doesn't exist.

Also, this suggests that there are regions of the Universe that are moving away from each other instead of just gravitationally bound systems, like the plates, which is rubbish. I might be taking the analogy too far here, though.

Another problem, which I am almost certainly not taking too far, is that at the same time, a North American city is getting closer to anyone Asian city. (Well, the Earth is round, so technically, in this case, it's moving further away, but that's taking it too far again.) So ... remember that in this analogy, things are also going to be getting closer together ...

 

[Ich]

distances are both model and coordinate dependent meaning, observer dependent.

The distances are dependent only on the scale factor.

I think you completely missed Naty1's point: the "cosmological proper distance" - which is only dependent on the scale factor for comoving objects - is just one of the infinitely many distances you may define in GR.
And, importantly, it is not consistent with the common definitions of distance we encounter outside cosmology.

 

[GeorgeDishman]

I think you completely missed Naty1's point: the "cosmological proper distance" - which is only dependent on the scale factor for comoving objects - is just one of the infinitely many distances you may define in GR.

Agreed, there are many distances used but that was not what Naty1 said, I'll comment on his post below to clarify.

More importantly the balloon analogy uses one specific definition. In particlular Ned Wright's balloon animations show "photons" crawling over the surface at constant speed relative to the local rubber which is great for explaining why superluminal rates of expansion don't violate SR. They're not the only balloon illustrations on the web of course but can be taken as representative, for a layman introduction we shouldn't need to be concerned about subtleties of distance definitions.

And, importantly, it is not consistent with the common definitions of distance we encounter outside cosmology.

If I am given two dots drawn on a sheet of paper and asked to find out the distance between them, I would place a ruler passing through the dots and read off the distance. The ruler is on the sheet for the duration of the measurement and I understand that to be a measurement made "now". Cosmological distance is defined as the sum of a set of rulers which happen to be laid exactly end to end at a particular cosmological time which directly corresponds to the ruler on a sheet of paper. I would suggest that is the most common understanding of distance you will find if you ask random members of the public.

On the other hand, if I send a radar pulse to a distant target and measure half the return time, I get "radar distance", the locations of the end points of the path are measured at different times. If you consider when the distance has the measured value, it was at the instant the signal was reflected, not "now" when it is received and the measurement is obtained.

In fact I inluded this graphic previously to illustrate the loci (past history worldlines) of comoving galaxies and photons on our past light cone:

http://www.astro.ucla.edu/~wright/omega_2.gif

The return path of a radar distance would be measured along the red line so obviously isn't the distance along the circumference of the balloon. One point Naty1 and others have made is that the distances are not measured along geodesics. The average person who is learning about cosmology from the balloon analogy probably has no idea what a geodesic is anyway. Just as for all light-like worldlines, the red line in the graph is a null geodesic.

Naty1 specifically said:

So for me, three key concepts from this thread which are not captured by the balloon analogy are that 'expanding space', balloon stretching, is misleading, distance increases are dependent on acceleration, not speed,

That is not true, the "acceleration" is only the rate of change of "speed" and "speed" is only sensibly defined as rate of change of distance anyway.

characteristics, and distances are both model and coordinate dependent meaning, observer dependent.

While it is true that they are model dependent, the balloon analogy is only illustrating one specific model, the Friedmann Equations or "FLRW model", just note how often Naty1 used "FLRW" in his reply, there were more in the sections I've omitted:

Here is a first draft list [in no particular order] : FLRW is the standard [cosmological] model; FLRW metric [distance measure] is an exact solution to the EFE but only approximates our universe because it assumes the universe is homogeneous and isotropic;

Obviously it is no use for say a steady-state model.

superluminal expansion distances are are result of the FLRW model metric; those FLRW distances are NOT great circles nor geodesics on the balloon,

Specifically they are great circle distances on the balloon. One of the positive features of the balloon analogy is that (in Ned's version at least) you can see how photons move over the surface, always at c while widely separated points can move apart faster thus illustrating how superluminal rates of increasing distance in the FLRW model do NOT contradict SR, a point that puzzles many laymen. You can also see how some photons moving towards a distant galaxy are failing to catch up to it, hence how there can be a horizon to our observable universe.

I kept my reply concise because I didn't want to focus on these few points, the majority of Naty1's reply was on the ball and IMO a very useful contribution but since you have raised the point, I've had to clarify what I was hinting at. Since this is being considered for a web page which may be viewed by many people for many years, and the author has had the courage to open his work to peer review, I think it is important that we should do our best to provide accurate and constructive criticism for him to consider.

 

[Naty1]

On the balloon analogy, Lineweaver and Davis:

A good analogy is to imagine that you are an ant living on
the surface of an inflating balloon. Your world is two-dimensional;
the only directions you know are left, right, forward
and backward. You have no idea what “up” and “down”
mean. One day you realize that your walk to milk your aphids
is taking longer than it used to: five minutes one day, six minutes
the next day, seven minutes the next. The time it takes to
walk to other familiar places is also increasing. You are sure
that you are not walking more slowly and that the aphids are
milling around randomly in groups, not systematically crawling
away from you.
This is the important point: the distances to the aphids are
increasing even though the aphids are not walking away. They
are just standing there, at rest with respect to the rubber of
the balloon, yet the distances to them and between them are
increasing. Noticing these facts, you conclude that the ground
beneath your feet is expanding. That is very strange because
you have walked around your world and found no edge or
“outside” for it to expand into.

edit: This approach avoids glued down versus floating pennies concerns and illustrates that galaxies [ants] move locally with respect to expansion while experiencing its effects. It also relates increasing distance measures to a conclusion of expansion.

 

[Ich]

for a layman introduction we shouldn't need to be concerned about subtleties of distance definitions.

No offense, but IMHO you're saying that because you're not aware of said subtleties. But I agree in this case, as I already said, the balloon analogy is not the right place to discuss them. In a general layman's introduction, it is necessary, though.

Cosmological distance is defined as the sum of a set of rulers which happen to be laid exactly end to end at a particular cosmological time which directly corresponds to the ruler on a sheet of paper. I would suggest that is the most common understanding of distance you will find if you ask random members of the public.

You forget the this ruler is made out of infinitely many segments which all have relative velocity wrt each other. Which is not exactly what you have in your household. And which leads to interesting, not widely known facts. For example, the so-called recession "velocity" is rather a rapidity, which goes quite naturally beyond c. This is important if one wishes to discuss "superluminal" recession "velocities", even in pop sci.
It's just that in the balloon analogy, the ruler looks much more natural than it really is, and therefore it makes no sense to discuss these subtleties here.

 

[Naty1]

George and Ich: interesting comments and I'll go back and think about them more.

...the author has had the courage to open his work to peer review, I think it is important that we should do our best to provide accurate and constructive criticism for him to consider.

yes,yes...well said!

I want to share an 'advanced version' of the balloon model...but one that has it's own issues. I think this illustration would be a good follow on for phinds to consder adding as a link to his balloon site.

[If you click on the illustration it will blow it up...necessry if you are old like me! ]


http://en.wikipedia.org/wiki/Metric_expansion#Understanding_the_expansion_of_Universe

The purple grid lines mark off cosmological time at intervals of one billion years from the big bang. The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day. The orange line shows the present-day distance between the quasar and the Earth, about 28 billion light years.

Note the orange line [present day distance] follows the purple grid curve of constant time.
Thats the arbitrary but convenient used to measure cosmological distance. You can see from this illustration there are many other curves we could pick...and each gives a different measurement. The orange [FLRW metric distance] line is not directly observable from Earth and that is why it doesn't compare closely in my opinion with the curved surface distance of the balloon analogy.

You experts on all this stuff can correct me on this but I did NOT think the orange distance a curve could possibly be the 'geodesic' light would follow...since light takes a finite time to travel.

I always pay close attention comments from ICH, but I don't think I get this one yet.

[me] those FLRW distances are NOT great circles nor geodesics on the balloon.

[Ich] They are. They are measured along geodesics of FRW-space. These are not geodesics of spacetime, though, which brings a lot of trouble if one doesn't appreciate this fact.

I don't see the first part right off since I thought we can pick space and time coordinates arbitrarily. And we are not moving with the expansion as we measure, but we can measure I guess at a fixed time...maybe that's the implication..

I agree on the last sentence and that is clearly a constraint of the balloon analogy. The Wikipedia illustration does better on the score since we can visulaize a fixed, universal, time coordinate.

To my way of thinking, so far, one could pick any number of curves on the balloon surface to measure penny separation distances. We would need to agree on a convention, and a great circle arc would be a natural. That does seem analogous to choosing a convention for a distance metric


Here is an issue I had not thought about before:
What about dips around pennies to illustrate local galaxy gravitational irregularities?? Maybe the idea of 'dip' is a non starter because the FLRW metric assumes homogeaneity so we skip those in our calculation. I dunno, but CMBR sure has to follow such dips when we measure redshift, right...but there is supposedly no expansion within galaxies, no distance increases, so no redshift, so no observational effect?
got to go. be back.