The balloon analogy (please critique)

[petm1]

FIRST: there is NO center. ONLY 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.

SECOND: 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.

THIRD: 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.

No edge, no center, and pennies don't expand, What proof does this analogy for an expanding universe give.

first; Every point on the surface of the balloon is just as much the center as any other point, no proof here of no center just that all points are equivalent centers.

second; Edges of the universe that we can see are the bound systems themselves, we may not be able to see an inner edge to the universe but we always see the outside edge.

third; If gavitationally bound systems don't expand and nothing inside of them expands then how can we see them?

 

[Calimero]

No edge, no center, and pennies don't expand, What proof does this analogy for an expanding universe give.

first; Every point on the surface of the balloon is just as much the center as any other point, no proof here of no center just that all points are equivalent centers.

First it doesn't offer any proofs. It is just analogy to help you better visualize metric expansion, which is obviously doing well even for skeptics like you, 'cause you justifiably conclude that all points are equivalent centers.

second; Edges of the universe that we can see are the bound systems themselves, we may not be able to see an inner edge to the universe but we always see the outside edge.

third; If gavitationally bound systems don't expand and nothing inside of them expands then how can we see them?

I have no idea what you mean with inner and outter edges. But we can see gravitationaly bound systems. What makes you think that we shouldn't be able too see them?

 

[Mark M]

No edge, no center, and pennies don't expand, What proof does this analogy for an expanding universe give.

Part of the goal of the balloon analogy is to show how thew universe can expand without boundaries. It would be nonsense to say the universe had some sort of edger or boundary. Spacetimes don't just abruptly 'end'. Perhaps you are confusing the comoving patch (the observable universe) with universe as a whole?

first; Every point on the surface of the balloon is just as much the center as any other point, no proof here of no center just that all points are equivalent centers.

That is the same exact statement as saying the universe has no center. When someone with no experience in cosmology hears about a center of the universe they instantly imagine some point from which all other expand from. To say there is no center is to say that there is no preferred direction to expansion.

second; Edges of the universe that we can see are the bound systems themselves, we may not be able to see an inner edge to the universe but we always see the outside edge.

The universe, once again, does not have an edge. Are you confusing the observable universe with the actual universe? The balloon analogy represents the universe as a whole.

third; If gavitationally bound systems don't expand and nothing inside of them expands then how can we see them?

What? Why would this preclude us from seeing them?

 

[petm1]

There IS no center to the universe.

First it doesn't offer any proofs. It is just analogy to help you better visualize metric expansion, which is obviously doing well even for skeptics like you, 'cause you justifiably conclude that all points are equivalent centers.

I am not a skeptic of the analogy, I just think that all points are equivalent centers, there may not be a preferred center but that is not the same a there is no center.

The universe, once again, does not have an edge. Are you confusing the observable universe with the actual universe? The balloon analogy represents the universe as a whole

Saying the universe once again does not have an edge is misleading, there are particles in my universe and they make up the edge of the world I walk on, we only see because this outside edge is where the interaction between photons and matter occurs. We always "see" the outside of the particles edge.

THIRD: 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.

If the pennies, don't change size and nothing inside of them expands how do you explain the photons we see, after all they are expanding from the inside of the gravitationally bound systems.

This is a good analogy for what we observe but making statements like there is no edge nor a center to me is misleading.

 

[phinds]

This is a good analogy for what we observe but making statements like there is no edge nor a center to me is misleading.

The balloon analogy is not supposed to prove those ideas but I present them WITH the balloon analogy for two reasons

1) because they are true
2) because the anaolgy sometimes leads to confusion on those two points (among others)

 

[Mark M]

Saying the universe once again does not have an edge is misleading, there are particles in my universe and they make up the edge of the world I walk on, we only see because this outside edge is where the interaction between photons and matter occurs. We always "see" the outside of the particles edge.

What? Are you referring to the particle horizon? If so, this is the boundary to the OBSERVABLE universe, NOT the universe as a whole.

I think you are misunderstanding my use of the words 'edge' and 'center'. Many people who aren't familiar with cosmology, when hearing about the big bang model, get this image of a bomb going off at some point in space, and identify this as the 'center of the universe'. When they hear that the universe is expanding, they get the idea there is some mysterious 'edge' that is growing. Neither of these are true, the point of the balloon analogy is to show what the big bang actually is, and that the universe can expand without having a boundary. Nothing is misleading there.

 

[GeorgeDishman]

The usual notion of distance ("proper distance") defined in this manner (measuring the distance along a curve of constant cosmological time) does not actually measure the distance along a straight line (or the equivalent of a straight line in a curved space-time, a space-like geodesic).

A curve of constant cosmological time [along which we would like to measure a proper distance’ ] connecting two points in a FRW universe is not a "straight line", i.e. it is not a geodesic.

It is however the distance that goes into the Hubble Law as explained here By Ned Wright:

http://www.astro.ucla.edu/~wright/cosmo_02.htm#MD

So for me, three key concepts from this thread which are not captured by the balloon analogy are that 'expanding space', balloon stretching, is misleading, distance increases are dependent on acceleration, not speed, characteristics, and distances are both model and coordinate dependent meaning, observer dependent.

The distances are dependent only on the scale factor.

edit: Depending on how far you wish to take all this, a short explanation of FLRW measures,conventions, assumptions, and how they compare with the balloon perspective could be helpful.

.. FLRW metric [distance measure] is an exact solution to the EFE but only approximates our universe because it assumes the universe is homogeneous and isotropic

One way to convey this is that the universe is more like the skin of an orange than a balloon.

superluminal expansion distances are are result of the FLRW model metric; those FLRW distances are NOT great circles nor geodesics on the balloon .. the most common distance measure ,comoving distance, defines the chosen connecting curve to be a curve of constant cosmological time and operationally, comoving distances cannot be directly measured by a single Earth-bound observer

If you are referring to Ned Wright's Java balloon, assuming the wiggles representing photons move at constant speed and in that case the great circle distances are the proper distance between the galaxies. Comoving distance is the proper distance divided by the scale factor.

http://www.astro.ucla.edu/~wright/Balloon2.html

If you imagine slicing the balloon through the centre, you get a graphic similar to this:

http://www.astro.ucla.edu/~wright/omega_2.gif

(It's from this page: http://www.astro.ucla.edu/~wright/cosmo_03.htm )

The radial lines are the worldlines of the comoving galaxies and the angle between two such lines is the comoving distance. In order to make surface distances the proper distance, the radial coordinate in Ned's balloon is the scale factor.

The light cones and red lines representing our past light cone of course assume the radial parameter is cosmological time so it isn't quite accurate.

Does the balloon analogy model the Hubble parameter accurately??: wiki mentions:

It's not easy to discern the Hubble Constant from the image.

"..the Hubble parameter seems to be decreasing with time, meaning that if we were to look at some fixed distance d and watch a series of different galaxies pass that distance, later galaxies would pass that distance at a smaller velocity than earlier ones..."

For the radiation and matter-dominated eras, the Hubble Constant is inversely proportional to cosmological time but in the energy-dominated era it reaches a minimum value as the expansion becomes exponential.

 

[GeorgeDishman]

Saying the universe once again does not have an edge is misleading, there are particles in my universe and they make up the edge of the world I walk on, we only see because this outside edge is where the interaction between photons and matter occurs. We always "see" the outside of the particles edge.

What? Are you referring to the particle horizon? If so, this is the boundary to the OBSERVABLE universe, NOT the universe as a whole.

Not if he is walking on it. He seems to be talking about looking down at the surface of the Earth.

 

[hitchiker]

metric expansion of space -When space expands, it does not claim previously unoccupied space from its surroundings. I've been gnawing on these concept for long,though i understand it... i can't take it to heart that this weird phenomenon is happening right now on universe

finally i give up balloon analogy and made one my own

☼ metric expansion happens ONLY in flat space between galaxies that are not gravitationally bound ☼

why can't we take for example movement of continents on our planet as expansion of space ? africa was once closer to asia but now distance between asia & africa has increased ppl in asia can say africa is receding from us though 2 continents are not expanding distance between 2 asian cities is same distance between 2 african cities is same but distance between asia and africa is increasing..and also we can compare dark energy to ocean

it works for me ...

 

[Whovian]

☼ metric expansion happens ONLY in flat space between galaxies that are not gravitationally bound ☼

But "flat space" doesn't exist.

Also, this suggests that there are regions of the Universe that are moving away from each other instead of just gravitationally bound systems, like the plates, which is rubbish. I might be taking the analogy too far here, though.

Another problem, which I am almost certainly not taking too far, is that at the same time, a North American city is getting closer to anyone Asian city. (Well, the Earth is round, so technically, in this case, it's moving further away, but that's taking it too far again.) So ... remember that in this analogy, things are also going to be getting closer together ...

 

[Ich]

distances are both model and coordinate dependent meaning, observer dependent.

The distances are dependent only on the scale factor.

I think you completely missed Naty1's point: the "cosmological proper distance" - which is only dependent on the scale factor for comoving objects - is just one of the infinitely many distances you may define in GR.
And, importantly, it is not consistent with the common definitions of distance we encounter outside cosmology.

 

[GeorgeDishman]

I think you completely missed Naty1's point: the "cosmological proper distance" - which is only dependent on the scale factor for comoving objects - is just one of the infinitely many distances you may define in GR.

Agreed, there are many distances used but that was not what Naty1 said, I'll comment on his post below to clarify.

More importantly the balloon analogy uses one specific definition. In particlular Ned Wright's balloon animations show "photons" crawling over the surface at constant speed relative to the local rubber which is great for explaining why superluminal rates of expansion don't violate SR. They're not the only balloon illustrations on the web of course but can be taken as representative, for a layman introduction we shouldn't need to be concerned about subtleties of distance definitions.

And, importantly, it is not consistent with the common definitions of distance we encounter outside cosmology.

If I am given two dots drawn on a sheet of paper and asked to find out the distance between them, I would place a ruler passing through the dots and read off the distance. The ruler is on the sheet for the duration of the measurement and I understand that to be a measurement made "now". Cosmological distance is defined as the sum of a set of rulers which happen to be laid exactly end to end at a particular cosmological time which directly corresponds to the ruler on a sheet of paper. I would suggest that is the most common understanding of distance you will find if you ask random members of the public.

On the other hand, if I send a radar pulse to a distant target and measure half the return time, I get "radar distance", the locations of the end points of the path are measured at different times. If you consider when the distance has the measured value, it was at the instant the signal was reflected, not "now" when it is received and the measurement is obtained.

In fact I inluded this graphic previously to illustrate the loci (past history worldlines) of comoving galaxies and photons on our past light cone:

http://www.astro.ucla.edu/~wright/omega_2.gif

The return path of a radar distance would be measured along the red line so obviously isn't the distance along the circumference of the balloon. One point Naty1 and others have made is that the distances are not measured along geodesics. The average person who is learning about cosmology from the balloon analogy probably has no idea what a geodesic is anyway. Just as for all light-like worldlines, the red line in the graph is a null geodesic.

Naty1 specifically said:

So for me, three key concepts from this thread which are not captured by the balloon analogy are that 'expanding space', balloon stretching, is misleading, distance increases are dependent on acceleration, not speed,

That is not true, the "acceleration" is only the rate of change of "speed" and "speed" is only sensibly defined as rate of change of distance anyway.

characteristics, and distances are both model and coordinate dependent meaning, observer dependent.

While it is true that they are model dependent, the balloon analogy is only illustrating one specific model, the Friedmann Equations or "FLRW model", just note how often Naty1 used "FLRW" in his reply, there were more in the sections I've omitted:

Here is a first draft list [in no particular order] : FLRW is the standard [cosmological] model; FLRW metric [distance measure] is an exact solution to the EFE but only approximates our universe because it assumes the universe is homogeneous and isotropic;

Obviously it is no use for say a steady-state model.

superluminal expansion distances are are result of the FLRW model metric; those FLRW distances are NOT great circles nor geodesics on the balloon,

Specifically they are great circle distances on the balloon. One of the positive features of the balloon analogy is that (in Ned's version at least) you can see how photons move over the surface, always at c while widely separated points can move apart faster thus illustrating how superluminal rates of increasing distance in the FLRW model do NOT contradict SR, a point that puzzles many laymen. You can also see how some photons moving towards a distant galaxy are failing to catch up to it, hence how there can be a horizon to our observable universe.

I kept my reply concise because I didn't want to focus on these few points, the majority of Naty1's reply was on the ball and IMO a very useful contribution but since you have raised the point, I've had to clarify what I was hinting at. Since this is being considered for a web page which may be viewed by many people for many years, and the author has had the courage to open his work to peer review, I think it is important that we should do our best to provide accurate and constructive criticism for him to consider.

 

[Naty1]

On the balloon analogy, Lineweaver and Davis:

A good analogy is to imagine that you are an ant living on
the surface of an inflating balloon. Your world is two-dimensional;
the only directions you know are left, right, forward
and backward. You have no idea what “up” and “down”
mean. One day you realize that your walk to milk your aphids
is taking longer than it used to: five minutes one day, six minutes
the next day, seven minutes the next. The time it takes to
walk to other familiar places is also increasing. You are sure
that you are not walking more slowly and that the aphids are
milling around randomly in groups, not systematically crawling
away from you.
This is the important point: the distances to the aphids are
increasing even though the aphids are not walking away. They
are just standing there, at rest with respect to the rubber of
the balloon, yet the distances to them and between them are
increasing. Noticing these facts, you conclude that the ground
beneath your feet is expanding. That is very strange because
you have walked around your world and found no edge or
“outside” for it to expand into.

edit: This approach avoids glued down versus floating pennies concerns and illustrates that galaxies [ants] move locally with respect to expansion while experiencing its effects. It also relates increasing distance measures to a conclusion of expansion.

 

[Ich]

for a layman introduction we shouldn't need to be concerned about subtleties of distance definitions.

No offense, but IMHO you're saying that because you're not aware of said subtleties. But I agree in this case, as I already said, the balloon analogy is not the right place to discuss them. In a general layman's introduction, it is necessary, though.

Cosmological distance is defined as the sum of a set of rulers which happen to be laid exactly end to end at a particular cosmological time which directly corresponds to the ruler on a sheet of paper. I would suggest that is the most common understanding of distance you will find if you ask random members of the public.

You forget the this ruler is made out of infinitely many segments which all have relative velocity wrt each other. Which is not exactly what you have in your household. And which leads to interesting, not widely known facts. For example, the so-called recession "velocity" is rather a rapidity, which goes quite naturally beyond c. This is important if one wishes to discuss "superluminal" recession "velocities", even in pop sci.
It's just that in the balloon analogy, the ruler looks much more natural than it really is, and therefore it makes no sense to discuss these subtleties here.

 

[Naty1]

George and Ich: interesting comments and I'll go back and think about them more.

...the author has had the courage to open his work to peer review, I think it is important that we should do our best to provide accurate and constructive criticism for him to consider.

yes,yes...well said!

I want to share an 'advanced version' of the balloon model...but one that has it's own issues. I think this illustration would be a good follow on for phinds to consder adding as a link to his balloon site.

[If you click on the illustration it will blow it up...necessry if you are old like me! ]


http://en.wikipedia.org/wiki/Metric_expansion#Understanding_the_expansion_of_Universe

The purple grid lines mark off cosmological time at intervals of one billion years from the big bang. The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day. The orange line shows the present-day distance between the quasar and the Earth, about 28 billion light years.

Note the orange line [present day distance] follows the purple grid curve of constant time.
Thats the arbitrary but convenient used to measure cosmological distance. You can see from this illustration there are many other curves we could pick...and each gives a different measurement. The orange [FLRW metric distance] line is not directly observable from Earth and that is why it doesn't compare closely in my opinion with the curved surface distance of the balloon analogy.

You experts on all this stuff can correct me on this but I did NOT think the orange distance a curve could possibly be the 'geodesic' light would follow...since light takes a finite time to travel.

I always pay close attention comments from ICH, but I don't think I get this one yet.

[me] those FLRW distances are NOT great circles nor geodesics on the balloon.

[Ich] They are. They are measured along geodesics of FRW-space. These are not geodesics of spacetime, though, which brings a lot of trouble if one doesn't appreciate this fact.

I don't see the first part right off since I thought we can pick space and time coordinates arbitrarily. And we are not moving with the expansion as we measure, but we can measure I guess at a fixed time...maybe that's the implication..

I agree on the last sentence and that is clearly a constraint of the balloon analogy. The Wikipedia illustration does better on the score since we can visulaize a fixed, universal, time coordinate.

To my way of thinking, so far, one could pick any number of curves on the balloon surface to measure penny separation distances. We would need to agree on a convention, and a great circle arc would be a natural. That does seem analogous to choosing a convention for a distance metric


Here is an issue I had not thought about before:
What about dips around pennies to illustrate local galaxy gravitational irregularities?? Maybe the idea of 'dip' is a non starter because the FLRW metric assumes homogeaneity so we skip those in our calculation. I dunno, but CMBR sure has to follow such dips when we measure redshift, right...but there is supposedly no expansion within galaxies, no distance increases, so no redshift, so no observational effect?
got to go. be back.

 

[phinds]

I want to share an 'advanced version' of the balloon model...but one that has it's own issues. I think this illustration would be a good follow on for phinds to consder adding as a link to his balloon site.

[If you click on the illustration it will blow it up...necessry if you are old like me! ]


http://en.wikipedia.org/wiki/Metric_expansion#Understanding_the_expansion_of_Universe

The updated version already has this link

 

[Ich]

I don't see the first part right off since I thought we can pick space and time coordinates arbitrarily. And we are not moving with the expansion as we measure, but we can measure I guess at a fixed time...maybe that's the implication..

Yes, by fixing cosmological time you cut a three space out of 4D spacetime. It's similar to cutting the balloon surface out of 3D space.
In the balloon it is clear that the geodesics of the subspace - great circles - are not geodesics of the embedding space, which would be straight lines.
Same with FRW space, proper distance is measured along geodesics of the subspace, which are not geodesics of spacetime.

 

[GeorgeDishman]

No offense, but IMHO you're saying that because you're not aware of said subtleties.

By all means start another thread then, or feel free to message me if you feel it more appropriate, I am always keen to improve my understanding.

You forget the this ruler is made out of infinitely many segments which all have relative velocity wrt each other.

I didn't forget, that is why I included the highlighted qualifier:

Cosmological distance is defined as the sum of a set of rulers which happen to be laid exactly end to end at a particular cosmological time which directly corresponds to the ruler on a sheet of paper. ...​

Which is not exactly what you have in your household.

At that particular moment, it corresponds exactly IMHO, but please correct me if I have missed something.

 

[Naty1]

From post #49

Cosmological distance is defined as the sum of a set of rulers which happen to be laid exactly end to end at a particular cosmological time which directly corresponds to the ruler on a sheet of paper...

Ich

You forget the this ruler is made out of infinitely many segments which all have relative velocity wrt each other.

How can they have relative velocity if the cosmological moment in time is fixed?



Ich:

...the so-called recession "velocity" is rather a rapidity, which goes quite naturally beyond c. This is important if one wishes to discuss "superluminal" recession "velocities...

Of course! great point! Therefore, I shall continue to keep reading your stuff, Ich!

 

[Naty1]

pHinds
sorry for all this, discard what you like..my last comments!

Regarding your Balloon Analogy website
I like it! Well done...It should get put in FAQ in these forums


[1] Should the balloon analogy be linked to the FLRW model?? I'm unsure.

Ich seems to think in a post here it is. I think you should mention there are not precise measures of distance and time in cosmology...we use conventions to allow us to make agreed upon measures, standard comparisons. But overall, the arbitray split between space and time of different observers leads to 'ambiguity' [using a word in the wiki reference].


Under "third local effect" :

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.

Correct me, somebody, if I misinterpreted another thread discussion, but I thought that the FLRW model [homogeneous, isotropic] did NOT apply at galactic distances...too much lumpiness. In addition I thought nobody knows how to solve the EFE for representative galactic conditions...how to include the lumpiness in other words. So should we instead say something like 'gravitationally bound systems and things inside them are not thought to expand [or are generally not considered to exapnd] but we have no exact solution for such conditions. I'm not sure.

[3] In your description, Second Size shape:

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.

Last sentence: Should this be qualified to space versus spacetime. Or say that curvature in time is not represented in the balloon analogy. We believe the universe is pretty flat spacewise, right? Is it time that is mostly curving on cosmological scales...or not??


[4] Cosmological Time: How do we say in a sentence or two, and should we bother here, that

Cosmological time is the elapsed time since the Big Bang according to the clock of an observer comoving with the CMBR ...[we use the cosmological time parameter of comoving coordinates because it's convenient mathematically. There are other time measures that could also be used.] In the Wikipedia link above, cosmological time, the 'age of the universe', is the like the time of light transit along the red curve, about 13B years, not the transit time along today's orange curve distance which is about 28B years.



[4] Under OTHER NOTES

How about a few sentences like this :

"Sending a light signal from one penny [galaxy] to another will take longer than if the pennies were stationary with respect to each other because the distances between them are increasing. [DUH!] Because the actual rate of expansion is not constant over all of cosmological time, the Hubble 'constant' varies over time since the big bang, and the actual transit time between pennies is different today than it was at earlier times. The current expansion of the universe proceeds in all directions as determined by the Hubble constant today, but it is a 'constant' in all directions of space not over time.

 

[phinds]

pHinds
sorry for all this, discard what you like..my last comments!

Regarding your Balloon Analogy website
I like it! Well done...It should get put in FAQ in these forums


[1] Should the balloon analogy be linked to the FLRW model?? I'm unsure.

Ich seems to think in a post here it is. I think you should mention there are not precise measures of distance and time in cosmology...we use conventions to allow us to make agreed upon measures, standard comparisons. But overall, the arbitray split between space and time of different observers leads to 'ambiguity' [using a word in the wiki reference].


Under "third local effect" :



Correct me, somebody, if I misinterpreted another thread discussion, but I thought that the FLRW model [homogeneous, isotropic] did NOT apply at galactic distances...too much lumpiness. In addition I thought nobody knows how to solve the EFE for representative galactic conditions...how to include the lumpiness in other words. So should we instead say something like 'gravitationally bound systems and things inside them are not thought to expand [or are generally not considered to exapnd] but we have no exact solution for such conditions. I'm not sure.

[3] In your description, Second Size shape:



Last sentence: Should this be qualified to space versus spacetime. Or say that curvature in time is not represented in the balloon analogy. We believe the universe is pretty flat spacewise, right? Is it time that is mostly curving on cosmological scales...or not??


[4] Cosmological Time: How do we say in a sentence or two, and should we bother here, that

Cosmological time is the elapsed time since the Big Bang according to the clock of an observer comoving with the CMBR ...[we use the cosmological time parameter of comoving coordinates because it's convenient mathematically. There are other time measures that could also be used.] In the Wikipedia link above, cosmological time, the 'age of the universe', is the like the time of light transit along the red curve, about 13B years, not the transit time along today's orange curve distance which is about 28B years.



[4] Under OTHER NOTES

How about a few sentences like this :

"Sending a light signal from one penny [galaxy] to another will take longer than if the pennies were stationary with respect to each other because the distances between them are increasing. [DUH!] Because the actual rate of expansion is not constant over all of cosmological time, the Hubble 'constant' varies over time since the big bang, and the actual transit time between pennies is different today than it was at earlier times. The current expansion of the universe proceeds in all directions as determined by the Hubble constant today, but it is a 'constant' in all directions of space not over time.

Good points. I've added a note at the bottom of the page that encompasses much of this (but without actually getting INTO any of it), for the reason stated in the note:

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 on this page are just that ... simplistic. My point here was to produce a fairly modest, but correct (with some simplifcations) analysis of the balloon analogy without, as I noted at the beginning, writing a text on cosmology.

EDIT: by the way, thanks again to all for the continued feedback.

Paul

 

[GeorgeDishman]

Note the orange line [present day distance] follows the purple grid curve of constant time. ... You can see from this illustration there are many other curves we could pick...and each gives a different measurement. The orange [FLRW metric distance] line is not directly observable from Earth and that is why it doesn't compare closely in my opinion with the curved surface distance of the balloon analogy.

First you need to imagine the sheet continued so the ends join up. That creates a picture like the one below with the galaxies etc.. Take the orange grid line (which is now a complete circle) and rotate it to create a sphere. That is your balloon.

You experts on all this stuff can correct me on this but I did NOT think the orange distance a curve could possibly be the 'geodesic' light would follow...since light takes a finite time to travel.

You are correct. The red line is a null geodesic which is the path that the light took to reach us from the quasar. As the page says, it crosses each grid line at 45 degrees. Any massive particle must travel more slowly hence must cross the cyan lines at less than 45 degrees.

To my way of thinking, so far, one could pick any number of curves on the balloon surface to measure penny separation distances. We would need to agree on a convention, and a great circle arc would be a natural.

If the balloon surface is uniform, distances between galaxies grow at a rate which is proportional to their separation. That is the Hubble Law and that law holds for comoving distances, the distance measured by the orange arc.

That does seem analogous to choosing a convention for a distance metric.

The balloon illustrates the FLRW metric.

Here is an issue I had not thought about before:
What about dips around pennies to illustrate local galaxy gravitational irregularities?? Maybe the idea of 'dip' is a non starter because the FLRW metric assumes homogeaneity so we skip those in our calculation.

The surface looks smooth at large scales but closer up it looks like the skin of an orange.

I dunno, but CMBR sure has to follow such dips when we measure redshift, right...but there is supposedly no expansion within galaxies, no distance increases, so no redshift, so no observational effect?

The dip extends beyond the galaxy, that's what creates gravitational lensing:

http://apod.nasa.gov/apod/ap090921.html

See also the Integrated Sachs-Wolfe Effect:

http://en.wikipedia.org/wiki/Sachs–Wolfe_effect#Integrated_Sachs.E2.80.93Wolfe_effect

 

[Naty1]

On distance analogy:
I have three [oops, four] perspectives that I am trying to sort thru regarding the appropriatness [accuracy] of the balloon analogy to FLRW metric.

Ich
Which is not exactly what you have in your household.

George:
At that particular moment, it corresponds exactly IMHO, but please correct me if I have missed something.

George, Thats my perspective, so far, as well. It's what I questioned in my post #49. I also feel like I might be missing something.

A second related point is this which I already posted:

The orange [FLRW metric distance] line is not directly observable from Earth and that is why it doesn't compare closely in my opinion with the curved surface distance of the balloon analogy.

[George noted:

The red line is a null geodesic which is the path that the light took to reach us from the quasar. As the page says, it crosses each grid line at 45 degrees.

Of course! I did see that then forgot!...That's a really nice reference especially if phinds is aiming his Site at beginners: It ties the Wiki diagram to the traditional lightcone used with Minkowski spacetime. The connection is not so obvious for those starting out! Such visual links between concepts can really cement new concepts in place.


#3: I happened to be rereading LineWeaver and Davis since I haven't in a long time and they make this interesting statement:

The microwave background radiation fills the universe and defines a universal
reference frame, analogous to the rubber of the balloon, with respect to which motion can be measured

I had this same thought earlier and forgot to post it. I consider it a useful analogy. Seeing this analogy several years ago would have made me realize that in the balloon model we are observing the 'universe' from the outside and that can't be done in the 'real world' ! We are stuck on the surface and this statement begins to define the FLRW metric distance convention.

#4: My last issue is the earlier posted point from Wallace regarding acceleration not velocity [or rapidity if your prefer] as the determining factor in separation. The balloon analogy does NOT capture that but how to explain in simple terms why is not yet clear to me...

 

[Naty1]

George:

If the balloon surface is uniform, distances between galaxies grow at a rate which is proportional to their separation. That is the Hubble Law and that law holds for comoving distances, the distance measured by the orange arc.

That's a nice observation regarding CURRENT distance measures...since the Hubble constant varies over time. It's obvious, but I did not think of it...thanks!



me:

I dunno, but CMBR sure has to follow such dips when we measure redshift, right...but there is supposedly no expansion within galaxies, no distance increases, so no redshift, so no observational effect?

George:

The dip extends beyond the galaxy, that's what creates gravitational lensing

See also the Integrated Sachs-Wolfe Effect:

http://en.wikipedia.org/wiki/Sachs%E...93Wolfe_effect

I read that for the first time a few weeks ago and never got around to posting my basic question about it. Wikie says

Accelerated expansion due to dark energy causes even strong large-scale potential wells (superclusters) and hills (voids) to decay over the time it takes a photon to travel through them. A photon gets a kick of energy going into a potential well (a supercluster), and it keeps some of that energy after it exits, after the well has been stretched out and shallowed. Similarly, a photon has to expend energy entering a supervoid, but will not get all of it back upon exiting the slightly squashed potential hill.

What I wondered in the article is whether such potential well 'detours' of CMBR photons require or deserve any correction in CMBR observations??

 

[GeorgeDishman]

#4: My last issue is the earlier posted point from Wallace regarding acceleration not velocity [or rapidity if your prefer] as the determining factor in separation. The balloon analogy does NOT capture that but how to explain in simple terms why is not yet clear to me...

Think of Lineweaver's ants and aphids. Suppose an ant gets tired of walking ever farther and ties a rope to an aphid. By the time he gets home, the rope is slipping through his hand if he stands still. He puts on roller skates and grabs the rope. Now he is moving across the rubber. If the inflation rate of the balloon falls, the rope goes slack and he coasts back to the aphids, no effort involved ;-)

That is however very different to saying the rate of increase of distance between his home and the aphids only depends on the acceleration.

 

[GeorgeDishman]

If the balloon surface is uniform, distances between galaxies grow at a rate which is proportional to their separation. That is the Hubble Law and that law holds for comoving distances, the distance measured by the orange arc.

That's a nice observation regarding CURRENT distance measures...since the Hubble constant varies over time. It's obvious, but I did not think of it...thanks!

That's not quite the point. For any given cosmological time, the Hubble Law is a linear relationship, rate of recession equals the constant times a distance. That is also true of separations measured on the surface of the balloon. If you use other distance measures (luminosity distance, angular size distance, etc.) for the analogy, the relationship will not be linear so it would no longer match the balloon.

What I wondered in the article is whether such potential well 'detours' of CMBR photons require or deserve any correction in CMBR observations??

The EM emissions from the galaxies themselves are generally greater so "foreground features" have to be removed. However, we can use the effect to learn about the galaxies since the CMBR is so well defined.

 

[Ich]

#4: My last issue is the earlier posted point from Wallace regarding acceleration not velocity [or rapidity if your prefer] as the determining factor in separation. The balloon analogy does NOT capture that but how to explain in simple terms why is not yet clear to me...

What he meant by "velocity" is $\dot a$, the time derivative of the scale factor. It corresponds to the radial velocity of the balloon surface. (It is its proper velocity rather, not bounded by c therefore.)
The acceleration is $\ddot a$, here the proper radial acceleration of the balloon surface.

Now if you put two dots at rest wrt each other on the surface (i.e. not comoving), their relative acceleration is proportional to $\ddot a$, not $\dot a$. That holds in FRW coordinates as well as in the analogy.

I'll open another thread for the distance definition subtleties, that doesn't belong here.

 

[Naty1]

Ich, George,,,thanks for the feedback...appreciate it...

will reread your explanations tomorrow and be back then...

But not until I walk my Yorkies...after all, this is JUST science...!

Idea of a separate discussion on distance is good... look forward to that!

 

[Naty1]

George's Ned Wright link posted above did not 'click' for me after an initial reading so I was doing some background reading and came across this Wikipedia discussion which seems to support my own incorrect interpretation... not what George claimed for Wright...but in all honestly, Wright's explanation link and this one below are not really clear to me yet:

http://en.wikipedia.org/wiki/Comoving_distance#Uses_of_the_proper_distance

...It is important to the definition of both comoving distance and proper distance in the cosmological sense (as opposed to proper length in special relativity) that all observers have the same cosmological age. For instance, if one measured the distance along a straight line or spacelike geodesic between the two points, observers situated between the two points would have different cosmological ages when the geodesic path crossed their own world lines, so in calculating the distance along this geodesic one would not be correctly measuring comoving distance or cosmological proper distance. Comoving and proper distances are not the same concept of distance as the concept of distance in special relativity. This can be seen by considering the hypothetical case of a universe empty of mass, where both sorts of distance can be measured. When the density of mass in the FLRW metric is set to zero (an empty 'Milne universe'), then the cosmological coordinate system used to write this metric becomes a non-inertial coordinate system in the flat Minkowski spacetime of special relativity, one where surfaces of constant time-coordinate appear as hyperbolas when drawn in a Minkowski diagram from the perspective of an inertial frame of reference.[4] In this case, for two events which are simultaneous according the cosmological time coordinate, the value of the cosmological proper distance is not equal to the value of the proper length between these same events,(Wright) which would just be the distance along a straight line between the events in a Minkowski diagram (and a straight line is a geodesic in flat Minkowski spacetime), or the coordinate distance between the events in the inertial frame where they are simultaneous...[/QUOTE

Maybe this is better saved for a subsequent discussion on distance...I did want to post it for future reference.

I assume I am the one that is 'mixed up' and will continue background reading...

 

[Ich]

Sorry for the delay, I'll start the other thread tomorrow (I hope). Again, it will go along the line of Ned Wright's arguments.
For the time being: a spacelike geodesic is not the same as a geodesic of space. The former is a geodesic of spacetime which is, well, spacelike. The latter is a curve of extremal distance in some subspace of spacetime, which is necessarily spacelike but not necessarily also a geodesic of spacetime.