balloonanalogy

The Balloon Analogy … the Good, the Bad, and the Ugly

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This article was written with considerable input from several senior members of the PF community.

The Balloon Analogy is a simple-minded way to help describe (but not completely describe) two facts of cosmology that are difficult for many people to see, namely that the universe is expanding uniformly and that there is no center (and no edge).

The analogy is disliked (often intensely disliked) by serious physicists because it causes at least as much confusion as it is intended to avoid and is often badly misunderstood and/or incorrectly extrapolated to ridiculous points of view and this article is intended to help with that problem.

Presented here is the simple-minded balloon analogy and then a discussion of cosmology and why the balloon analogy is so flawed but also what it does help explain and how. There are many other aspects of cosmology that can get drawn into discussions of the balloon analogy, but I have for the most part resisted discussing any that are not immediately relevant to the analogy, lest I get carpal tunnel syndrome while having this article turn into a textbook on cosmology (which I am not qualified to write anyway).

 

What the Balloon Analogy is intended to describe:

(1) The universe is expanding OUTSIDE of systems that are gravitationally bound, or bound by other local forces (e.g. strong and weak forces). That is, things the size of a local cluster of galaxies and smaller (like the Milky Way, Earth, you, me, atoms, and so forth), do NOT expand.

(2) The expansion has no center and everything is moving away from everything else, with things farther from each other receding faster from each other than things closer together.

 

THE ANALOGY

Think of each gravitationally bound system as a penny, and glue a bunch of these pennies onto a balloon that is only slightly blown up.

Now we blow up the balloon more. ALL of the pennies move away from each other uniformly, and those that are farther away from each other move away from each other faster than those that are closer together. If you choose ANY penny on the surface, it sees ALL of the other pennies moving away from itself and it sees the ones farther away moving away faster than those close by. No penny is the center of the expansion. There IS no center to the universe.

That is the way the universe works and that is what the analogy is intended to show. The fact that all the pennies move away from each other and that ones farther away move away faster and that there is no center.

 

What DOESN’T work in using the balloon analogy and how it can be more usefully thought of

FIRST: NO CENTER there is no center. Only a portion of 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 and you are likely arriving at one of those false conclusions that make physicists grit their teeth at the balloon analogy. So don’t ! There is no center (to the balloon surface in the analogy or to the universe)

SECOND: SIZE/SHAPE The analogy should ONLY consider a portion of the balloon’s surface — it does not make any statements about the size or shape of the universe (other than it is getting bigger). 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. The universe not only has no center, it has no edge, but that does not imply that it is necessarily infinite, it could be finite but unbounded (like the surface of the Earth, for example). Also, the balloon, as we humans look at it and consider only the surface, is a 2D object (the surface is) but we recognize that it is embedded in a 3D world. The analogy is NOT intended to imply that our 3D universe is embedded in some 4D space (I’m not talking about 4D space-time but 4 dimensions of distance) — that just isn’t part of the analogy.

THIRD: LOCAL EFFECTS 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. The most reasonable way to UN-simplify the balloon analogy in this regard would be to consider that the construct is not a balloon with pennies glued to it but rather that it is a balloon in which, somewhat magically, pennies have been embedded such that the circumference of the pennies melds with the rubber and there IS no rubber inside the area of the pennies. When the balloon expands, the pennies get farther apart but THEY do not expand. Even this UN-simplification of the analogy has a problem because actually, dark energy does exist inside of gravitationally bound systems, it just doesn’t have any effect (see the comments at the bottom of the page).

FORTH: NO STRETCHING The surface of the balloon “stretches” and this leads to weird discussions of the “stretching” of space or the “expansion” of space. To further UN-simplify the balloon analogy, what you REALLY need to think of is the construct described in “THIRD” directly above, BUT … take away the actual balloon material and just think of things happening to the pennies as though the balloon WAS there (so as to maintain the pennies’ motion in the analogy). In other words, what cosmology REALLY says is not that space stretches or expands but rather just simply that gravitationally bound systems keep getting farther away from each other. It is DISTANCE that is changing, not space. This is another of those things that are badly served by the balloon analogy. There is of course, in some sense, “more” of something in between galactic clusters as the distance increases, but just what it is that there is “more” of gets to be a theological / philosophical discussion that gets WAY beyond the balloon analogy. I refer you to Metric Expansion of Space

FIFTH: COSMOLOGICAL TIME There are sometimes attempts to bring cosmological time into the analogy by considering that the 3D center of the balloon represents the singularity and the balloon (the universe) expanded from there. This is an excellent example of stretching the analogy WAY beyond where it is intended to go (pun intended).

 

EXPANSION(S)

There are really three “expansions” that people get mixed up about.

INFLATION — In a very early and very tiny fraction of second, just after the singularity, the universe “expanded” in an incredibly massive burst. This is known as INFLATION, not expansion, although it IS an expansion as the term is used in the English language. This inflation is NOT a 100% confirmed fact, and there are differences of opinion about it among physicists (and cosmological models), but it is by far and away the best model to explain the universe as we understand it. This “inflation” was in some ways very similar to the current accelerated expansion, and there is some lively discussion in physics circles as to the possibility of a relationship between the two, but that’s getting a bit beyond the balloon analogy.

EXPANSION — After inflation, the universe settled down to a more sedate rate of expansion and THIS is what is normally meant by the EXPANSION of the universe. It is still going on today. This expansion has NOTHING to do with “dark energy” (see the paragraph directly below), although dark energy has been present, as far as is known, since the beginning of the universe AND has been having an effect all along although it did not overwhelm gravity until about 8 billion years after the singularity. There really have been two things going on all along, the expansion I’m talking about here, AND the contribution of “dark energy”, but see directly below for further discussion.

ACCELERATION of the expansion — Up until sometime in the late 1990’s, it was assumed that gravity was slowing down the rate of expansion (as it was understood in the paragraph above, with no reference to “dark energy” and that eventually it would either reach a steady state and just go on at a constant rate forever, or much more likely would reverse direction and contract (the Big Crunch scenario). When the first possible measurements were made, much to everyone’s surprise, it was found that not only is the rate of expansion NOT slowing down, it is ACCELERATING. This acceleration is NOT what is normally meant by “expansion” (see the paragraph directly above), it is the ACCELERATION of the expansion. It is attributed to a force that is not understood, and that has been given the name “dark energy”. The “dark” just means we have no idea what it is (just what it does), and this is TOTALLY unrelated to “dark matter” (which is called “dark” because it is LITERALLY dark … it does not reflect or emit any electromagnetic radiation at any frequency, including visible light). So “dark energy” has been around all along, we now understand, and about 6 billion years ago, it started to overcome gravity and cause the expansion to start accelerating.

 

OTHER NOTES ON COSMOLOGY

Dark energy and dark matter have NOTHING to do with each other and all statements I have ever seen to the contrary have been utter nonsense. It would likely have saved hundreds of thousands of keystrokes here on The Physics Forum if “dark matter” had been more appropriately called “Zwicky matter” and “dark energy” had been called “vacuum energy”

“Dark energy” is so staggeringly weak on local scales (a planet for example) that is has an effect that is described by some as (various forms of the phrase …) “utterly negligible” and by others as “non-existent”. I’m in the “non-existent” camp and my favorite analogy is that it is like an ant pushing on a house. It’s not that the ant has such a tiny effect that it is not measurable, it is that the any has no effect at all. The ant IS pushing on the house, but it cannot to any extent at all overcome the forces that keep the house on its foundations.

Expansion, even with acceleration, is so staggeringly slow on small scales that it might as well not be happening. Over cosmological distances, it has a huge effect, but here’s my favorite analogy to show local effect. Even though the universe is expanding, it’s still going to be hard to find a parking place. This is just a simple-minded way of thinking about the local effects of the expansion. If you could go out into intergalactic space and magically draw a set of parking place lines, it would be about TWENTY BILLION YEARS before they had moved far enough apart to let you park a second car. Now, I’m willing to circle the block a couple of times to get a parking place, but twenty billion years is just too much. I’d be late for the movie.

On the other hand, it has such a huge effect over cosmological distances, that the galaxies at the edge of our observable universe are receding from us at something like 3 times the speed of light. No speeding tickets are issued, because they are not moving faster than light in our frame of reference, they are just getting farther away. It’s like a boat being carried down a fast river. To someone on the boat, it’s traveling 10 mph but to someone on the bank, it’s moving 25 mph. It’s the 10 mph that has to be compared to the speed limit; the 25mph is irrelevant to the speed limit.


NOTE: measures of distance and time in cosmology, as well as the shape/extent of the universe and the fact that “space” is really “space-time”, are all very complex topics and my simplistic ways of talking about them in this article are just that … simplistic. My point here was to produce a fairly modest, but correct (with some simplifications) analysis of the balloon analogy without, as I noted at the beginning, writing a text on cosmology.

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Studied EE and Comp Sci a LONG time ago, now interested in cosmology and QM to keep the old gray matter in motion. woodworking
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  1. Geofleur
    Geofleur says:

    Nice article! I just used the balloon analogy today with my students, and I didn't say any of those wrong things. But I worry now that my students would draw those spurious parallels themselves. I may have them read this.

  2. eaglechief
    eaglechief says:

    well done and thumbs up! I sometimes find myself in sticking too close to the ballon model, but it helps in the beginning.perhaps in future one comes back to the balloon-model by taking it more by word like "what behaves on the surface like a balloon might behave in the inside like a balloon, as well"

  3. eltodesukane
    eltodesukane says:

    Many of those interpretation problems do not appear if we consider matter contracting instead of space expanding.Those are equivalent point of views as far as we know.All we can measure are ratios of distances.(If fraction a/b is increasing, is a increasing or b decreasing?)

  4. JDoolin
    JDoolin says:

    I think there really are more than one model out there that you have to address.  It's really not fair to just say "A lot of people think that the center of the balloon represents the big bang singularity, but that's just not true."The balloon analogy is primarily used to explain how redshift is NOT caused by relativistic Doppler recession of distant galaxies.  However, I think if you take the balloon analogy, but only the TWO features you said were true, and "caveat" the FIVE features you said were false, there is no material way that your model actually conflicts with the idea of Doppler recession velocities.So is there a valid feature of the Balloon analogy that actually contradicts with Doppler recession?

  5. JDoolin
    JDoolin says:

    Here, look at this page on wikipedia regarding the cosomological scale factor:  https://en.wikipedia.org/wiki/Scale_factor_(cosmology)The article begins with the assumption that the scale factor exists… and comes down to v = H d;  e.g. velocity = Hubble's Constant * DistanceThe implications here is that Hubble's constant is… well, a constant.  And the velocity and distance relationship is… well; weird.However, a simple modification to the equation; stating that Hubble's constant is the reciprocal of the age of the universe, yieldsDistance = velocity * timewhich you teach to students in Junior High.In my experience, very smart people are very uncomfortable with the idea of DIstance = Velocity * Time being applied at cosmological scales.  They will definitively say "No, that is NOT it."  And usually, they will use some version of the balloon analogy to make their point. However, here, you seem to have debunked all aspects of the balloon analogy which would have actually conflicted with the kinematic description.My point, I guess, is that as soon as you invoke that scale factor, a(t), then you are strongly implying that space is (or at least could be) stretching over time–perhaps in an unknown and unpredictable way.

  6. JDoolin
    JDoolin says:

    I'm not sure if any further discussion is coming, so I'll try to make my observations a little clearer.You've listed five misconceptions of the balloon analogy.  I think only the first two you listed are actual misconceptions.  The last three are actual features of an FLRW model universe, but not a kinematic model.(First: No Center)  I agree, this is a misconception. The two (spatial) dimensional balloon surface with a center in (spatial) 3D space might imply that the universe is a three-dimensional structure with a center in a 4D space.  (Second: Size/Shape) I agree; another misconception.  The shape of the balloon might imply that you can get back where you started by going far enough in a straight line.(3) (Third: Local Effects).  I disagree that this is a misconception.  There is a big difference between an effect that is negligible, and an effect that doesn't exist.  An ant, pushing on a house, still exerts a force.  If the house were sitting on a frictionless plane, it would accelerate.  In an FLRW model, there is a negligible force pulling things apart; but it is so tiny that gravity and electrical forces hold it together.  In a kinematically expanding universe, there is no force pulling things apart.  You just have inertia, from the initial big bang event.(4) (Forth: No Stretching)  I disagree that this is a misconception.  As I described in my last post, the cosmological scale factor is generally presented as a changing scale of the FLRW universe as a whole.  I would be hard-pressed to find a better description for that than "stretching space".  Again, in a kinematically expanding universe, you could say "no stretching".(5) (Fifth: Cosmological Time) The balloon analogy highlights a very important difference between a kinematic model of the universe and the standard model.  In a kinematic model, every particle is literally touching at the moment of the big bang, and they separate because of their velocity.  In the balloon analogy, every particle was already separated by a distance on the balloon surface, but the scale factor of the universe was equal to zero, so the balloon, itself, was contracted to a point.  That behavior at the singularity is an essential difference between a kinematic model universe and a FLRW metric universe.

  7. Edriven
    Edriven says:

    Beautifully written.  It is a bad model.  I wanted to touch briefly on dark energy. How does a rocket move in space. It burns fuel and creates thrust. If rocket wants to go faster, it must burn longer. Or use bursts to add speed. Basically longer burn equals acceleration. What have the stars been doing? Are they not pushing away from one another?  SOLAR THRUST. the opposite force of gravity.

  8. 1oldman2
    1oldman2 says:

    As a "layman"(barely) I find the balloon analogy and related conversations very useful and interesting in regards to my understanding of the principles discussed.I must add at this point that I'm no scholar, we won't be collaborating on any papers and the Nobel prize is safe from me. in fact if intelligence is relative then compared to yours mine would be measured on the Planck scale.My point is when someone takes the time to develop good analogies such as the balloon one here then a much broader segment of society is able to learn these concepts and hopefully get interested and excited about the sciences in general. Good job !! looking forward to more writing in this manner.

  9. timmdeeg
    timmdeeg says:

    Hi phinds, I think you article is extremely helpful to the ‘interested layman’.
    The only thing I would recommend to reconsider is the wording ‘the rate of expansion’ is slowing down or is accelerating, resp. This could confuse the layman who knows about the Hubble constant, which isn’t accelerating. The expansion of the universe is either accelerating or decelerating. Or perhaps, but I’m not sure, it’s more precise to say the universe expands at an increasing rate, in order to avoid the term ‘the rate of expansion’.

  10. phinds
    phinds says:

    Many of those interpretation problems do not appear if we consider matter contracting instead of space expanding.
    Those are equivalent point of views as far as we know.
    All we can measure are ratios of distances.
    (If fraction a/b is increasing, is a increasing or b decreasing?)

    And how would “contracting matter” explain the red shift of light from distant galaxies?

  11. PeterDonis
    PeterDonis says:

    Many of those interpretation problems do not appear if we consider matter contracting instead of space expanding.

    Perhaps not, but you now have a whole new set of problems. Such as, if matter is supposedly contracting, why is the size of the Earth not changing?

    All we can measure are ratios of distances.

    On cosmological scales, perhaps this is true, since converting between the various cosmological distance scales is basically taking ratios of different indirect distance measurements. But ultimately all of those cosmological distance ratios are calibrated to distances that are not measured as ratios. I used the size of the Earth as an obvious example above, but perhaps a more relevant example for this discussion would be distances to stars measured by parallax. That gives an absolute reference for distance that cannot be interpreted as “contracting”.

  12. timmdeeg
    timmdeeg says:

    The point is that the so called “Hubble constant” is not a constant over time.

    That’s right and therefore it might be better to use the term Hubble parameter, which means the ‘rate of expansion’.

    In short, during the epoch of inflation the universe expanded exponentially (driven by the cosmological constant only) and thus the ‘rate of expansion’ was constant (roughly). Since then it is decreasing and will be approaching asymptotically a constant value in the very far future again, due to the dominating dark energy then, at least according to the current model.

  13. phinds
    phinds says:

    What is actually driving the observed acceleration and expansion/inflation of our universe.

    OK. I agree w/ that. I wasn’t sure if you meant what it doing as opposed to what causing it.

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