The Balloon Analogy .... the Good, the Bad, and the Ugly - Comments

[phinds]

phinds submitted a new PF Insights post

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

Continue reading the Original PF Insights Post.

 

[Greg Bernhardt]

Nice first Insight @phinds!

 

[Geofleur]

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.

 

[phinds]

Nice first Insight @phinds!

The "first" ? AAAACCKK ! You want MORE? I don't know anything else

 

[eaglechief]

well done and thumbs up! I sometimes find myself in sticking too close to the balloon 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"

 

[ShayanJ]

The "first" ? AAAACCKK ! You want MORE? I don't know anything else

I have the same feeling!

 

[timmdeeg]

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'.

 

[JBA]

This is what younget when someone tries to explain something that no one actually understands.

 

[phinds]

This is what younget when someone tries to explain something that no one actually understands.

I don't get you. What is it that "no one actually understands" ?

 

[eltodesukane]

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?)

 

[eltodesukane]

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'.

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

 

[phinds]

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?

 

[PeterDonis]

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".

 

[JBA]

I don't get you. What is it that "no one actually understands" ?

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

 

[timmdeeg]

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.

 

[phinds]

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.

 

[JDoolin]

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?

 

[phinds]

The balloon analogy is primarily used to explain how redshift is NOT caused by relativistic Doppler recession of distant galaxies.

That has not been my experience at all. I have always found the balloon analogy used to simply give a graphic demonstration of how it is that the universe is expanding uniformly from every point and that there is no center. I'm not familiar with its use regarding any discussion of Doppler shift.

 

[JDoolin]

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 * Distance

The 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, yields

Distance = velocity * time

which 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.

 

[Hornbein]

I don't care for the balloon analogy. I like the "baking raisin bread" analogy.

 

[phinds]

I don't care for the balloon analogy. I like the "baking raisin bread" analogy.

I agree, it's a good analogy. Why don't you write an insights article on it? I'm sure Greg would be happy to have that.

 

[JDoolin]

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.

 

[PeterDonis]

In an FLRW model, there is a negligible force pulling things apart

Only if there is dark energy present. An FLRW model with only matter and radiation present is like what you are calling a "kinematic" model; there is no force pulling things apart, only inertia from the initial big bang.

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".

You may not be confused by that description, but many, many people are, as evidenced by the copious threads here on PF caused by such confusion. For one thing, "stretching space" invites the hypothesis that something is doing the stretching; even with dark energy present, the small force it exerts isn't exerted on "space", it's exerted on comoving objects.

 

[phinds]

@JDoolin, you seem to have the impression that my article is targeted towards people who know a lot of physics. Nothing could be further from the truth, and all of the things that I discuss address issues (yes, sometimes in simple terms) that amateurs DO have as witnessed (as Peter pointed out) by a large number of threads here on PF, to say nothing of elsewhere.

Even the very terminology you use is unknown to the target audience, so I do not consider your objections to be relevant to the article.

 

[Haelfix]

I happen to not like the Balloon analogy, as one wastes as much time correcting the mistakes as one would to simply explain the correct mathematics.

A few problems.
1) Topology. The primary problem the balloon analogy leads too is that the student immediatedly visualizes a spherical universe. Then the teacher has to explain that based on our current measurements of certain values (the sign of the cc, the amount of omega matter etc) we actually seem to prefer a universe with a simpler topology that more closely resembles R^4. Then we say something about the lack of a spacetime singularity in the middle of the sphere, that the big bang happened everywhere simultaneously and not at a specific point, that proper distance doesn't necessarily mean that galaxies were all squished together etc. Of course, this statement is also incorrect, or rather uncertain. The correct statement is that we do NOT know at this time what the topology of the universe is. It is perfectly consistent with data to have a universe with a nontrivial topology (although not as it turns out, something identically spherical). If we live in such a universe, then there are loops that can and will contract to a point, and you really do have a pileup of galaxies in principle. Likewise, you also run the risk of having circumlocution (the non detection of mirror galaxies fortunately allows us to put constraints on this effect) and you could in principle have a spacetime singularity at a point (although again we really should talk about geodesic incompleteness and the possible existence of a horizon if cosmic censorship applies).

Which gets to the broader point. GR puts some constraints on the global structure, but it is fundamentally a metric theory. It is absolutely vital to not mix up metric expansion (really the clocks and rulers e.g. the definition of distances between points) from how those events/points are arranged in the more fundamental point set topology. The sooner the student gets this point, the better things will be

2) Questions surrounding the physical properties of the elastic substance of the balloon will come into question. This of course is a disaster as it is exactly the opposite of what we want to show, as the elastic potential will have the wrong sign and completely different properties (it will heat up when you pull it apart, etc).

3) The analogy is fundamentally Newtonian. It is likely one of those strange and quirky mathematical accidents, but the FRW solution happens to be originally derived for Newtonian cosmology without the need for GR. There we really do have an expanding spherically symmetric ball of radiation that behaves exactly as one pictures in the analogy (without CC). But we know this is wrong. It is wrong the second one wants to put in inhomogeneities into the equations, at which point you have a solution that behaves nothing like what you might guess based on your Newtonian intuition. There you really need the full power of GR.

Which gets to the last point. Normally we correct the balloon analogy with the raisin bread analogy to avoid the messy question about why we don't feel atoms in our body or say planetary orbits blowing up under the influence of expansion, and the teacher says that that local gravitational interactions are much more important and that the model only represents long range phenomena, but then the student instantly wonders how a theory of spacetime (gravity) is suddenly chopped up into regimes of validity. Which gets back to doing things correctly by introducing legitimate GR corrections in the form of inhomogenieties.

Anyway, it gets complicated correcting all the mistakes, so I prefer limiting the analogy as much as possible around bonafide physics students..

 

[JDoolin]

Only if there is dark energy present. An FLRW model with only matter and radiation present is like what you are calling a "kinematic" model; there is no force pulling things apart, only inertia from the initial big bang.

Is the Kinematic model just an example of the FLRW model universes, or is it something entirely different? Have a look at the following descriptions--they seem to imply that the FLRW models, there is NO INERTIA from the initial big bang event.

http://www.indiana.edu/~geol105/images/gaia_chapter_1/big_bang_was_not_a_fireworks_dis.htm

"the completely wrong impression that the event was like an explosion and that the universe is expanding today because the objects in it are being flung apart like fragments of a detonated bomb."

https://4gravitons.wordpress.com/2014/12/05/the-three-things-everyone-gets-wrong-about-the-big-bang/
"The problem here is that, despite the name, the big bang was not actually an explosion."

https://answers.yahoo.com/question/index?qid=20130811144132AAgWtf0
"How do we know that the big bang wasn't really an explosion?"

http://physics.stackexchange.com/qu...ig-bang-the-biggest-explosion-in-the-universe
'The big bang is not an explosion in the conventional sense of the word. The big bang corresponds to an exponential expansion of spacetime and it is this incredible rate of expansion that can be dubbed "explosive".'

However, I can also see that taking the description of the scale factor of the universe.

$$H(t) = \frac{da/dt}{a}$$

$$H(t) = \frac{da/dt}{a}=1/t$$

$$a = \frac{da}{dt} t$$

Mathematically, then, you could argue that the kinematic universe is an example of the FLRW metric with Hubble Parameter equal to the reciprocal of the age of the universe.

However, even if the math is the same, the FLRW metric explains that changing scale factor between objects as a stretching of space (or a change in distance, if that seems more comfortable) between comoving objects, so there would be no inertia. The kinematic model would explain that changing scale factor as a velocity between non-comoving objects, so there would be inertia.

So no, I don't think the kinematic model is an example of the FLRW metric. It is an entirely different theory, based on entirely different assumptions.

You may not be confused by that description, but many, many people are, as evidenced by the copious threads here on PF caused by such confusion. For one thing, "stretching space" invites the hypothesis that something is doing the stretching; even with dark energy present, the small force it exerts isn't exerted on "space", it's exerted on comoving objects.

Confusion usually comes from a failure to define your terms. If I define "stretching space" to mean an increase in distance between comoving objects, then the FLRW metric definitely describes stretching space.

Perhaps in other minds, the word "stretching" has a different connotation. For instance, in order to stretch something, you need two hands, pulling away from each other, and a substance in between. But there's no substance in space, and there are no hands on either side, so it can't stretch.

I think that the idea of stretching space should invite the hypothesis that something is doing the stretching. The alternate hypotheses are that there is no stretching, or that the stretching represents a phenomenon without any cause. And then the hypothesis that there IS stretching should lead you to a prediction that there should be a negligible but finite repellant force between comoving objects, which would be a function of their mass, their distance, and the age of the universe.

 

[JDoolin]

@JDoolin, you seem to have the impression that my article is targeted towards people who know a lot of physics. Nothing could be further from the truth, and all of the things that I discuss address issues (yes, sometimes in simple terms) that amateurs DO have as witnessed (as Peter pointed out) by a large number of threads here on PF, to say nothing of elsewhere.

Even the very terminology you use is unknown to the target audience, so I do not consider your objections to be relevant to the article.

I wish that my comments could be seen as something other than objections. I don't "object" to your statement that there is no such thing as cosmological time. I don't "object" to your statement that space does not stretch. To the contrary, I agree with you.

But in our agreement, I don't think we agree with the standard model of cosmology.

But I'm not trying to establish, right now, whether we are right, or we are wrong. What I'm trying to get at is whether these are actually two distinct models, or if they are the same model.

I think they are two completely different models, and a lot of people don't realize that they are different. The point is that the differences show up strikingly in your analysis of the balloon model, and I thank you for that!

 

[Chronos]

The problem with science is it forces you to rely on the 'known' to explore the 'unknown'. We have no reliable way to test the 'known' aside from empirical evidence. Our 'knowns' currently appear pretty reliable given the vast body of empirical vetting they have managed to survive. That should not give us any false sense of confidence. No aspect of theoretical knoledge is invulnerable to future experimental results. We should, however, not abandon our hard fought knowledge without thoroughly well confirmed experimental evidence.

 

[Mordred]

Good job Phinds , Myself I would add that one function of the balloon analogy is to help students understand the Cosmological principle, then adding a brief description on the terms homogeneous and isotropic.

Another thing to consider is that the angles between any three points of measure also do not change.

Just a couple of points to consider adding.

 

[JDoolin]

The problem with science is it forces you to rely on the 'known' to explore the 'unknown'. We have no reliable way to test the 'known' aside from empirical evidence. Our 'knowns' currently appear pretty reliable given the vast body of empirical vetting they have managed to survive. That should not give us any false sense of confidence. No aspect of theoretical knoledge is invulnerable to future experimental results. We should, however, not abandon our hard fought knowledge without thoroughly well confirmed experimental evidence.

You can also use the "unknown" to explore the unknown.

Sometimes it makes sense to introduce a false or uncertain hypothesis for exploring the unknown.

For instance, we imagine what the world would really be like if the world were flat, and conclude that we should be able to see mountains thousands of miles away. We try to imagine a geocentric solar system and realize there is no mechanism which holds the planets or sun in orbit around the earth. But to my knowledge, this isn't done with "The Big Bang Theory." Instead of asking, honestly, at what a "real" Big Bang would imply, one is generally met with a chorus of "Everyone knows the Big Bang wasn't really a big bang."

It's like if we were discussing heliocentric vs. geocentric models of the solar system, but the heliocentric people insisted on calling their model "geocentric" then adding "geocentric isn't really geocentric."

Only after you give the ideas distinct names can you honestly make a comparison between them. Otherwise, you will have many different people all using the exact same words, and all having completely different meanings.

 

[Edriven]

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.

 

[PeterDonis]

What have the stars been doing? Are they not pushing away from one another?

No, they're not. They are in free fall; there is no thrust being applied to them.

 

[phinds]

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.

To the extent that there is any thrust created by stuff being ejected from stars, it averages out to being uniform over all directions so net thrust is zero. So no they are not, as Peter has already pointed out, thrusting away from each other.

 

[phinds]

Beautifully written.

Thanks.

It is a bad model.

I disagree. It is a limited analogy, not a bad model, and as long as you understand the limitations of the analogy it is quite a good one.

 

[phinds]

Good job Phinds , Myself I would add that one function of the balloon analogy is to help students understand the Cosmological principle, then adding a brief description on the terms homogeneous and isotropic.

Another thing to consider is that the angles between any three points of measure also do not change.

Just a couple of points to consider adding.

Yeah, I thought about it, but as I said in the article, there are just too many other things that could be brought into the discussion and it was already a bit longer than I would have liked.