What Are the Limitations of the Balloon Analogy in Cosmology?

[thehangedman]

The analogy always used is to draw two points on the surface of a balloon and then blow air in the balloon. The points move away as the balloon expands. The issue I have with this is: now draw a "meter stick" on the surface of the balloon. It expands too, at the same rate, so that the number of meters between the two points doesn't actualy change as the balloon expands.

So, what gives? Are the points really moving apart? What is broken with the analogy as compared the the actual theory? If there is no change in the distance, as measured in the system itself (as opposed to the person standing outside the system, looking down at the balloon), then how can there be a red shift?

Also, with the balloon, the universe would actually be compact. If you walk in any direction you eventually end up where you started. How does a compact universe differ from one with constant curvature? I've seen and read explanations of Kaluza-Klein but none of them talk about curvature in that fifth dimension...

 

[bartek2009]

One thing to notice is that the expansion only occurs on a cosmological scale
(distances of order ~100Mpc) so the stick would not change its initial length.

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[thehangedman]

But why? The balloon example essentially implies that space-time is expanding "locally" as well as globaly. Is this not true? If its not true, and expansion is only on a global scale (in other words, only in regions of space that span the large distances between matter like galaxies) then the question I have shifts to why that would the case? What is special about space-time close to matter as opposed to in the gap and what would happen then if your meter stick was floating in space between galaxies (for example). Would it expand too?

 

[bartek2009]

If bodies are bound by strong forces the expansion does not affect them.
Take an atom for example, the expansion of the universe does not change
the mean distance between the nucleus and the electrons. Same principle
applies to solar system or even distances between galaxies in local group.

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[George Jones]

The analogy always used is to draw two points on the surface of a balloon and then blow air in the balloon. The points move away as the balloon expands. The issue I have with this is: now draw a "meter stick" on the surface of the balloon. It expands too, at the same rate, so that the number of meters between the two points doesn't actually change as the balloon expands.

So, what gives? Are the points really moving apart? What is broken with the analogy as compared the the actual theory? If there is no change in the distance, as measured in the system itself (as opposed to the person standing outside the system, looking down at the balloon), then how can there be a red shift?

It's only an analogy, and, as with all analogies, it has its weak points and its strong points. There has been lots of debate, both in the peer-reviewed litreature and here at Physics Forums, about the usefulness of this analogy.

Also, with the balloon, the universe would actually be compact.

The balloon models space, not spacetime. All the Friedmann-Robertson-Walker models of the universe are non-compact spacetimes. In fact, it's easy to show,

https://www.physicsforums.com/showthread.php?p=1254758#post1254758,

that any compact spacetime must have closed timelike curves (time travel). In FRW models, spacetime is foliated by spacelike hypersurfaces. In a closed universe, space (i.e., each hypersurface) is compact; in an open universe, space is non-compact.

The balloon example essentially implies that space-time is expanding "locally" as well as globaly. Is this not true? If its not true, and expansion is only on a global scale (in other words, only in regions of space that span the large distances between matter like galaxies) then the question I have shifts to why that would the case? What is special about space-time close to matter as opposed to in the gap and what would happen then if your meter stick was floating in space between galaxies (for example).

Spacetime is not homogeneous on small scales (i.e., matter is lumpy) on small scales. See

https://www.physicsforums.com/showthread.php?p=2132218#post2132218.