Effort to get us all on the same page (balloon analogy)


by marcus
Tags: analogy, balloon, effort
TalonD
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Dec9-08, 09:00 AM
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Quote Quote by marcus View Post
A famous Einstein quote about an important feature of General Relativity known as general covariance.
“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realitšt."

“Thereby time and space lose the last vestige of physical reality”.

source links here:
http://www.physicsforums.com/archive.../t-166997.html

also see page 43 of
http://www.tc.umn.edu/~janss011/pdf%...Besso-memo.pdf
==quote==
In a letter to Schlick, he again wrote about general covariance that
“thereby time and space lose the last vestige of physical reality” (“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realitšt.” Einstein to Moritz Schlick, 14 December 1915 [CPAE 8, Doc. 165]).
==endquote==
Quote Quote by atyy View Post
Spacetime (4D) is curved. However, there are usually "special" ways to split spacetime into "space" (3D) and "time" (1D). These are "special" splits because they don't simply pick an arbitrary coordinate as "time", but among other things they also ensure that the "time" direction at every "spatial location" points to the future and is the potential worldline of an observer. If you do this split in empty flat spacetime, two observers at "rest" in "space" don't find that the distance between them increases with "time". But when you do it in the matter-containing curved spacetime used to model our universe, two observers at "rest" in "space" do find that the "spatial distance" between them increases with "time". (Actually, you can do split flat spacetime so that "space" expands with "time", but then observers have to be massless and energyless, so that's not realistic. But it shows that one should remember that the description of curved 4D spacetime as expanding or being a pattern of distances that increases with time depends on a choice of 3+1D split that is permissible and convenient, but not unique.)

Also, curvature is the distance between objects at different locations. If we use a piece of string and a protractor to measure distances between objects on a football, we will find the pythagorean theorem doesn't hold, so the football is curved. If we replace the football with spacetime, the piece of string with a ray of light, spatial distance with spacetime interval, and objects with events, we can find out if spacetime is curved.
Marcus, on the other hand... cogito ergo sum --Descartes

Atyy, as a non physisist layman, I find that kind of hard to follow, can you restate that in a simpler easier to understand way? I understand the football analogy but the previous paragraph was a little confusing.
TalonD
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Dec9-08, 10:09 AM
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I was just thinking that it is interesting that the baloon or flat rubber sheet analogy when used to explain gravity to the lay public would lead one to an obvious common sense conclusion that pressure has an effect on gravity. Yet without the analogy, for a physisist using mathmatics it might seem unexpected. I realise the analogy is not reality and that it's the math that counts (excuse the pun) but still, I thought that was interesting.
:P
atyy
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Dec9-08, 12:51 PM
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Quote Quote by TalonD View Post
Atyy, as a non physisist layman, I find that kind of hard to follow, can you restate that in a simpler easier to understand way? I understand the football analogy but the previous paragraph was a little confusing.
On the football (the spherical sort), if two observers start out at the north pole and follow straight lines of longitude, they find that the latitudinal distance between them increases, so their universe is "expanding". After they pass the equator, their universe starts to "contract".
TalonD
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Dec9-08, 01:52 PM
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Quote Quote by atyy View Post
On the football (the spherical sort), if two observers start out at the north pole and follow straight lines of longitude, they find that the latitudinal distance between them increases, so their universe is "expanding". After they pass the equator, their universe starts to "contract".
ok, I'm going to expose some of my ignorance in this question but here goes...

Thanks for the clarification. I still have some confusion though, maybe because I am trying to take the analogy too far. on a globe if you move along the lines of longitude it depends on whether you are moving toward or away from the equator as to whether you converge or diverge. So if our universe has a positve curvature rather than being flat. then would two objects traveling in paralel eventually converge no matter what direction they are traveling, but in an open universe they would eventually diverge right? The only problem I have with that concept is that it is easy enough to draw two paralel lines on a globe and make them stay paralel all the way around. but presumably in a univere with positive curvature you couldnt keep them paralel right? So since we know that on a large scale everything in our universe is diverging does that mean we are headed towards some kind of cosmic equator and when we pass it, everything will start to converge towards a big crunch? Could the question of continued expansion vs. a big cruch have to do with the ovearall geometry of the universe in adition to the critical density? well of course the geometry of the universe is dependent on the density so I guess that answers my own question.

Then there is gravity. I can understand that two objects traveling near each other in space would follow the curvature and converge. but why do to objects that are initially at rest relative to each other spontaneously start moving together?
atyy
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Dec9-08, 02:57 PM
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Quote Quote by TalonD View Post
Thanks for the clarification. I still have some confusion though, maybe because I am trying to take the analogy too far. on a globe if you move along the lines of longitude it depends on whether you are moving toward or away from the equator as to whether you converge or diverge. So if our universe has a positve curvature rather than being flat. then would two objects traveling in paralel eventually converge no matter what direction they are traveling, but in an open universe they would eventually diverge right? The only problem I have with that concept is that it is easy enough to draw two paralel lines on a globe and make them stay paralel all the way around. but presumably in a univere with positive curvature you couldnt keep them paralel right? So since we know that on a large scale everything in our universe is diverging does that mean we are headed towards some kind of cosmic equator and when we pass it, everything will start to converge towards a big crunch? Could the question of continued expansion vs. a big cruch have to do with the ovearall geometry of the universe in adition to the critical density? well of course the geometry of the universe is dependent on the density so I guess that answers my own question.
Yes, you've answered your question. But let me comment on not taking the analogy too far. On the spherical football, it is 2D spacetime which is curved. However, it does not make sense to say that each spatial slice has intrinsic curvature, because the spatial slices are 1D lines of latitude. In contrast, for the universe, each spatial slice is 3D, for which it does make sense to ask if it has intrinsic curvature. So one should distinguish between the curvature of 4D spacetime, and the curvature of 3D spatial slices.

Quote Quote by TalonD View Post
Then there is gravity. I can understand that two objects traveling near each other in space would follow the curvature and converge. but why do to objects that are initially at rest relative to each other spontaneously start moving together?
The objects themselves produce spacetime curvature. It is not possible to be at rest in time, so it is not possible to be at rest in spacetime, so the objects move together.
navneet023
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Dec12-08, 05:27 AM
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First of all, sincere apologies to everyone who feels offended by my post. But couldn't help posting, I had to!

I have come across the information that what we see(visible matter ) is just 4% of the mass of the universe. Rest is some DARK matter and energy.
I have a doubt. We have studied that light comes in the packets(quanta) and so does other forms of energy. Could it be possible that its like a sprinkler, which constantly changes its direction and comes to same direction after some time, hence causing temporary lack of water(or light, for that reason). So, matter is always there, only we can't see it due to lack of continuous radiation. Could it be logical by any means?

Just a point i want to make. Hope I haven't offended anyone. :)
marcus
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Dec19-08, 06:19 PM
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Navneet, you might enjoy this 20-minute talk by Nobelist George Smoot. Links here:
http://physicsforums.com/showthread.php?t=274265

This mp4 version is slow to download but higher resolution, I think.
http://video.ted.com/talks/podcast/G..._2008P_480.mp4
You click on it and go away and do something else for 5 or 10 minutes and then come back and start it.

Quote Quote by marcus View Post
Thanks also for these! The Kravtsov computer simulations are excellent. I like this especially:
http://cosmicweb.uchicago.edu/filaments.html
I see that Smoot used Kravtsov's movies in his TED talk.
This was a good one too:
http://cosmicweb.uchicago.edu/group.html
I watched the halfsize MP4 version of the movie because it is very easy to download, only about 2.4 MB.
Polter
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Dec19-08, 11:09 PM
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I was just wondering, if the galaxies are like coins on a balloon -- accelerating away from each other -- then how is the Milky Way-Andromeda Galaxy Collision possible?
marcus
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Dec19-08, 11:19 PM
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Quote Quote by Polter View Post
I was just wondering, if the galaxies are like coins on a balloon -- accelerating away from each other -- then how is the Milky Way-Andromeda Galaxy Collision possible?
That's another bad thing about the analogy.

Galaxies come in clusters. Galaxies within the same cluster interact, orbit each other, are bound together by their common gravity.

The balloon can't show this. It is a schematic oversimplified cartoon.

It is only widely separated galaxies---those not bound---that obey Hubble law, and act like the pennies of the model
thaddeus
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#64
Dec21-08, 06:04 AM
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If it is to be asserted that the Big-Bang was not of "point" origin then how is it justified in terms of -everything- expanding away from other items .. as though it were simply an outward expansion .

IF as positioned earlier the bigbang is not to be seen as a point radiation but as a whole universe instantaneous? radiation then stuff should be flying in all directions equally .. yes or no ?

And just because the claim is that there is no point origin of the big bang .. how can it be asserted logically that this means there is no center point to the universe ?

Maybe it would make more sense as a hypothesis that matter is shrinking lol .. sometimes feels that way mumble mumble .. .. :)
geronimo
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#65
Dec25-08, 06:28 AM
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Having ditched the balloon analogy as being too simplistic, I am visualising the mechanism as more like expanding gap-filling foam. This allows me a more realistic three dimensional picture and allows variations in local expansion caused by chaotic quantum anomalies, causing "lumpiness" on whatever scale you like. This model also allows the "bubble" to assume a non-regular shape eventually.

As for the singularity point of origin, this also becomes unecesary and indeed as a result of uneven expansion would not be definable.

I am becoming increasingly drawn to cyclic universe notions in which any debris from one cycle would affect the expansion and "lumpiness" of the next, or each expansion drives through the ghost of its predecessor. This in turn could mean that unexplained cosmological anomalies may not be caused by our present cycle on its own.

I could ramble on at length and dig myself into a hole because this model suggests to me many interesting scenarios. ( including a way to reconcile string and quantum theories) So I wont.

Perhaps Marcus would care to comment?

Merry Christmas to all.
Chilli
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Dec28-08, 03:06 AM
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On the balloon analogy and the Cosmic Microwave Background radiation ...

If a particle radiates from location A in the direction of location B, once it leaves location A it is no longer there, although A may remain the particle's apparent location from any number of viewing perspectives over time. What I don't understand in the balloon analogy is where are the "A" locations that are null of radiation? Does the CMB radiation just continuously criss-cross itself? If yes, why is the radiation still uniform? If no, where are CMB radiation source locations in the model?

Kind regards
marcus
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Dec28-08, 10:57 AM
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Quote Quote by geronimo View Post
Having ditched the balloon analogy as being too simplistic, I am visualising the mechanism as more like expanding gap-filling foam...
No special comment needed, I think. Neither balloon nor foam represent a mechanism.
The balloon image is intended to aid visualizing how distances between stationary points increase. And how they increase at a percentage rate, so that longer distances increase more. Meanwhile (if you recall Ned Wright's animations) wriggles of light slowly travel from one stationary point to another. So this says nothing about how the universe works, it is an key exercise in picturing changing distance relations---in visualizing Hubble law. If foam helps you assimilate Hubble law better than balloon, go with it! Of course neither provide a physical analog to the Friedmann equations, so neither teaches you any understanding of how geometry and matter actually work. Once you can visualize the pattern, if you want to explore the mechanism one way is to experiment with the online calculators which embody the Friedmann equations. I don't know any physical analog (like a balloon or whatnot) but the calculators are fun to play around with.

Quote Quote by Chilli View Post
On the balloon analogy and the Cosmic Microwave Background radiation ...

If a particle radiates from location A in the direction of location B, once it leaves location A it is no longer there, although A may remain the particle's apparent location from any number of viewing perspectives over time. What I don't understand in the balloon analogy is where are the "A" locations that are null of radiation? Does the CMB radiation just continuously criss-cross itself? If yes, why is the radiation still uniform? If no, where are CMB radiation source locations in the model?

Kind regards
Chilli, think of it this way: Everybody in the universe is currently receiving CMB radiation which was emitted by matter which is currently at a distance of 46 billion lightyears from them. And that matter has gone thru a lot of changes since it emitted the light that's now arriving.

In line with your example pick spots A and B on the balloon surface.
At a certain time (380,000 y) space is more or less uniformly filled with hot glowing stuff and it is turning transparent for the first time, as it cools below 3000 kelvin.
The balloon is small and A and B are close together (only 42 million ly)

All points including A and B send out light uniformly in all directions. Some of A's light heads towards B, some of B's light heads towards A.

The light doesn't get there right away, or any time soon, because of expansion of distances. The original distance of 42 million ly increases a thousand-fold while the light is traveling. More exactly by a factor of 1090. So today the distance between A and B is 46 billion ly, and this light has traveled 13.7 billion y and is just now arriving.

The balloon is 1090 times bigger now than it was. Some of A's light is arriving at B and some of B's (that didn't go in other directions) is arriving at A.

By now both A and B have matured in the sense that they are no longer hot glowing gas---the gas has condensed into stars and galaxies and some stars have planets and some planets may have life and so on. So each of A and B could have creatures that construct antennas and receive the light----whose wavelengths are now longer by a factor of 1090.

Does the CMB radiation just continuously criss-cross itself? If yes, why is the radiation still uniform?
I'm not sure what you have in mind by continuously criss-crossing, but I think yes it does because there is uniform radiation going in all directions at every spot at all times. It is almost perfectly uniform because the whole shebang that emitted it was approximately uniform---all space filled about evenly with hot partly ionized hydrogen etc. all at about the same temperature and all turning transparent at the same time. There is no way that a lot of non-uniformity could arise. Some perhaps, but not a lot.

Remember that in the balloon analogy, all existence is concentrated in the 2D surface of the balloon and there are no directions off the surface. So if radiation starts out uniform it will always remain so.

==========
BTW Chilli is an excellent choice of name---reminds me of a favorite comic gangster movie. Looks like the above was your first post: welcome to the forums!
Chilli
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Dec28-08, 07:03 PM
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Marcus, thank you for your explanation and for your kind welcome!

Let’s see if I’m getting any closer … Setting aside post-inflationary expansion (because I really don’t have the math), say I am at location B, and it’s 13.7 billion years o’clock. I am receiving CMB radiation that was emitted in the year 380,000 from a location A that is presently 46 billion lightyears away. Location A was only 42 million lightyears away in the early universe, but a particular wriggle of light didn’t take the whole 46 billion years to reach me at location B because the expansion itself carried (stretched?) A’s particle wave to within 13.4 billion lightyears of B (yes/no?).

With my question about whether the CMB radiation criss-crosses itself, I meant to ask: when individual light waves hit each other, might they cancel or strengthen each other?

=========

Given this thread is to identify things that help or hinder intuition with regard to the balloon analogy, for what it’s worth, here’s some feedback from a clueless newbie.

When you say the balloon is now 1090 times bigger than it was, I reflexively picture the expansion as a slow and steady inflation, analogous to me blowing up a party balloon. And this lets me picture how the ‘coins on the surface of the balloon’ get further away from each other, and also lets me picture the timeline of the balloon, equating small to young, large to old (with us being old). But, assuming the Inflationary Model is correct, the balloon became pretty large when it was still very young, which goes to the uniformity of the CMB in the first place. And this is where the powerful balloon analogy becomes intuitively confusing to me.

For me, picturing all the coins on the surface of the balloon as radiating wriggling cosmic microwaves turns the surface of the balloon into a seething mass of tiny worms. Which might actually work in imagining a uniform distribution, but a spherical balloon also conjures some less helpful tangents.

* Firstly, if a wriggle of light keeps travelling around a sphere, it’s going to end up back where it started. Given the Earth is a sphere, it feels perfectly logical to imagine that the universe is also spherical, and thus a layman like myself automatically connects the balloon analogy with the shape of the universe. Of course, what we really need is a good homespun image to grab onto for the shape of space-time. (Pringles just don’t cut it.) If there was a big bang from a high-pressured source with no particular obstacles to free motion, then intuition says the universe is a big round thing with a definite (if empty) centre. Without an alternative, the balloon analogy is the best ‘big round thing’ image on offer from Cosmology, so, it is destined to be used in—creative—ways.

* Secondly, since the coins themselves stopped emitting their original CMB radiation long ago, then I expect the timeline of a given location A to include periods in which there is no CMB. Ie, the time period after emission and before reception of the first waves of radiation from other sources, and the time period after all radiation waves have passed by. But this idea isn’t compatible with the balloon analogy because the radiation simply circles around the balloon forever.

I greatly appreciate your efforts to try to help beginners such as myself receive the analogy more correctly, Marcus!
marcus
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Dec28-08, 10:10 PM
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Quote Quote by Chilli View Post
Letís see if Iím getting any closer Ö Setting aside post-inflationary expansion (because I really donít have the math), say I am at location B, and itís 13.7 billion years oíclock. I am receiving CMB radiation that was emitted in the year 380,000 from a location A that is presently 46 billion lightyears away. Location A was only 42 million lightyears away in the early universe, but a particular wriggle of light didnít take the whole 46 billion years to reach me at location B because the expansion itself carried (stretched?) Aís particle wave to within 13.4 billion lightyears of B (yes/no?).
Sounds like you are closer. But have you watched the short movie yet?
Google "wright balloon model". Ned Wright is a good teacher. his whole website is a useful resource. He usually has two balloon movies and its worth watching both.

All this stuff we are talking about is post-inflation expansion. If inflation happened it was by some exotic not-understood mechanism way early, like in the first second.

We are talking about stuff beginning at year 380,000 which is LONG past the end of inflation.

BTW there is an issue with arithmetic. If you have 13.7 billion years and you take away one million years, what do you have? You have 13.7 billion years.
That is, actually 13.699 but it rounds off to 13.7.

Likewise 13.7 billion minus 380,000 is still 13.7 billion. Even more true this time because 380,000 is less than a million.

So we are talking about an episode in history lasting from year 380,000 to year 13.7 billion, during which distances gradually increased only about 1000-fold, more precisely 1090-fold.

That period lasted about 13.7 billion years and I predict that if you watch the Ned Wright movies several times you will easily understand how at the end of 13.7 billion years a photon can find itself 46 billion lightyears from its point of origin.

Expansion makes the distance that the photon has already traveled grow like money you put in the bank, in your savings account, at a percentage rate. The rate actually changes over time but that is of secondary importance to what I'm saying.

You can see this happening in the movies. The photon travels a certain ways on its own, at the usual speed of light (say one millimeter per second on the balloon model). But because of expansion after a while it is a long long ways from where it started.

I think you are getting this, or have already gotten. It has nothing to do with inflation.


With my question about whether the CMB radiation criss-crosses itself, I meant to ask: when individual light waves hit each other, might they cancel or strengthen each other?
At ordinary energies, beams of light that cross do not interact. Try it with two flashlights.
Positive and negative interference effects are something else, two beams of monochromatic light (both the same frequency) meeting on a projection screen. CMB is not monochromatic. It is a big mix of frequencies. Not to worry about interference.


When you say the balloon is now 1090 times bigger than it was, I reflexively picture the expansion as a slow and steady inflation, analogous to me blowing up a party balloon. And this lets me picture how the Ďcoins on the surface of the ballooní get further away from each other, and also lets me picture the timeline of the balloon, equating small to young, large to old (with us being old).
That's right.

But, assuming the Inflationary Model is correct, the balloon became pretty large when it was still very young, which goes to the uniformity of the CMB in the first place. And this is where the powerful balloon analogy becomes intuitively confusing to me.
Like I already said. Inflation is relevant to the first second. Not part of the picture of what happened only after 380,000 years had gone by!

Maybe inflation expanded some portion of the universe from the size of an atomic nucleus (say 10^-15 meter) to 100 million kilometers. That is the expansion factor the inflation scenario-makers typically attribute to an inflation episode. That still is not even the radius of the earth's orbit!

After inflation, what is now the observable universe (radius about 46 billion ly) is still not very large. Inflation, if it happened, would have increased size by a large factor, typically they use a figure of e^60. But if you start with something very small to begin with, a large factor doesn't mean the result is necessarily large in absolute terms.

I wouldn't bother trying to include inflation in your visual picture. Just start some time after the universe has attained some reasonable size----like for example on the order of 42 million ly.

* Firstly, if a wriggle of light keeps travelling around a sphere, itís going to end up back where it started.
Nah. Watch the movies. In the case he shows where it keeps expanding, they never make it around. Say you are a caterpillar traveling 1 mm per second on the balloon surface and the circumference of the balloon is increasing 10 mm per second, and this rate is accelerating. How are you ever going to make it around? We can do this with numbers, but it is almost as good to do it visually-intuitively with Ned Wright's animations.

* Secondly, since the coins themselves stopped emitting their original CMB radiation long ago, then I expect the timeline of a given location A to include periods in which there is no CMB.
At the time the CMB was emitted, space was entirely filled with a uniform glowing hot cloud. It only later began to condense into stars and galaxies. So the pennies are not a perfect representation of matter. They are sort of the right picture once matter condensed into clusters of galaxies. But it is still just an analogy, not accurate in detail.

So we have been receiving CMB radiation steadily for the whole 13.7 billion years. As time goes on, the glow emitted by more and more distant hot cloud comes in. Because the cloud was uniformly distributed. So the radiation would not have been sporadic.
Chilli
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Dec30-08, 03:41 AM
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Quote Quote by marcus View Post
Sounds like you are closer. But have you watched the short movie yet?
Yes, but I don't have trouble picturing the expansion of distance between gravitationally sticky blobs.

Quote Quote by marcus View Post
BTW there is an issue with arithmetic. If you have 13.7 billion years and you take away one million years, what do you have? You have 13.7 billion years.
You do, indeed! (I did say my math was lacking.)

Quote Quote by marcus View Post
I predict that if you watch the Ned Wright movies several times you will easily understand how at the end of 13.7 billion years a photon can find itself 46 billion lightyears from its point of origin.
An optimistic prediction, but I say hold that dream!

Quote Quote by marcus View Post
I think you are getting this, or have already gotten. It has nothing to do with inflation.
Agreed.

I get that photons travelling at the speed of light can find themselves at a distance from their point of origin which, due to expansion, is further away than lightspeed alone could have achieved, and that they're destined to never exceed the speed of expansion, leading to an ultimately black and cold universe. What I was trying to do was point out challenges with the use of the balloon analogy.

Firstly, in offering a 2D construct in the form of the surface of a balloon, that surface can be misinterpreted as an expanding boundary to the universe, undermining all sorts of unbounded models. And then, of course, balloons don't expand forever; they burst, so, in looking at Wright's animation, or even just a static drawing, the balloon will (perhaps subliminally) be perceived as somehow finite in its expansion. And if expansion is finite, and light keeps travelling, light will eventually circle the balloon. I'm not saying such thoughts are of any use; quite the contrary, they merely muddy things.

Balloons tap into the layman's wealth of experience with birthday parties, sore lungs, and aching fingertips. It's why people look at the balloon as being the shape of the universe and then, quite logically and incorrectly, see the centre of the balloon as the centre of the universe. And I circle back to my earlier point that what is needed (what I need) is a proper analogy for the shape of space-time. Something that will let the balloon analogy be used purely to convey the concept of swelling distances between big things that are more or less at rest.

Kind regards
geronimo
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#71
Dec30-08, 05:12 AM
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Those who take Ned Wrights tutorial as gospel will not take kindly to ditching his balloon model, even if some see its limitations.

I got short shrift when suggesting a more versatile model/analogy for which I was chastisd for calling a mechanism (though in my book even an expanding balloon is a mechanism).

If you take expanding foam as a more versatile analogy and you still want to think in 2D terms, simply take a slice through it; and the foam won't burst like a balloon!
Chilli
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#72
Dec30-08, 06:27 AM
P: 4
Hello Geronimo,

I've no desire to ditch the balloon analogy. The stated objective of this thread is to: "...simply discuss the balloon analogy. Get clear on it. Find out any problems people have with it, if there are some." (refer quote below)

Quote Quote by marcus View Post
In my experience many of the misconceptions people have [about the balloon analogy] when they first come to this forum stem from misunderstanding what that analogy is intended to teach us. And a lot of the confusion we occasionally experience comes from getting that analogy somehow crossed up. So in this thread what I propose we do is, at least for starters, simply discuss the balloon analogy. Get clear on it. Find out any problems people have with it, if there are some.
I think Marcus is being sincere and helpful (thanks, Marcus!), but the focus in most of the posts to date mostly seem to be in asserting the validity of the balloon analogy for describing expansion, not so much on the problems in using a balloon to describe expansion. For me, I'm interested in targeting which natural, intuitive leaps are leading people (including me) in the wrong directions.

Maybe what we need to end up with is:

* a clear statement of what the analogy is (which several of the early posts have already done);
* a few pertinent elaborations (eg, someone already noted that inside the balloon was the past and outside the future)); and then
* qualification of the analogy by noting what it isn't (perhaps the top five misconceptions). Of course, the pursuit of precision necessitates no such thing, but you need to ask yourself: when drawing an analogy, do you want to be precise or do you want to be understood?

Kind regards


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