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.
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).
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.