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The balloon analogy (please critique)

  1. May 2, 2012 #1


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    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.


    Last edited: May 2, 2012
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  3. May 2, 2012 #2
    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.

  4. May 2, 2012 #3


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    Thanks for the feedback

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

    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.

    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.
  5. May 2, 2012 #4


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    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.
    Last edited: May 2, 2012
  6. May 2, 2012 #5
    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 in to make this.
  7. May 2, 2012 #6


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    Thanks, Marcus. I'll take a look at that other source. It's easy to drop in a link to it.
  8. May 2, 2012 #7


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    Good advice. Thanks.
  9. May 2, 2012 #8
    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:
  10. May 2, 2012 #9


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    Hey, thanks. I was ignorant about that.
  11. May 3, 2012 #10


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    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.

    Attached Files:

    Last edited: May 3, 2012
  12. May 3, 2012 #11


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    Nice job Phinds!
  13. May 3, 2012 #12
    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.

    Last edited: May 3, 2012
  14. May 3, 2012 #13
    nice work! very helpful for me. thanx! :)
  15. May 3, 2012 #14


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    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.
  16. May 3, 2012 #15
    OK, YMMV, but see the first point by "sweet springs". Identifying the radius as comoving time avoids that problem:


    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.

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


    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?
  17. May 3, 2012 #16


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    Thanks for that. I'll look into it and make sure I understand it myself and then update the page.
  18. May 8, 2012 #17


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    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.
  19. May 8, 2012 #18


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    Is not a closed universe a "real model"?
  20. May 8, 2012 #19


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    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.
  21. May 8, 2012 #20
    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:
    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.

    Last edited: May 8, 2012
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