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

by marcus
Tags: analogy, balloon, effort
Astronomy
PF Gold
P: 23,230
 Quote by Chilli ... 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, ... ... 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. ...
You are reminding me that an essential part of making intelligent use of analogies is to know when to get off one and move to the next. Realizing when an analogy has taught you most or all of what you can learn from it---sensing its limits.

In your post you mention several real limits, even liabilities, of the balloon analogy. I certainly agree it has its drawbacks.

One thing you made oblique reference to but didn't dwell on is the idea of being at rest relative to the CMB, or the matter that emitted it. Staying at the same longitude and latitude on the balloon surface provides something concrete corresponding to that. Helps assimilate the apparent paradox that things remain at rest while distances between them increase. I've highlighted a few things the balloon picture helps conceptualize.

In several instances I very much like your choice of words.

==================

So now let's say we've learned all we can from the balloon model and it is time to move on. Where do we go? For some people, a reasonable next step would involve trying stuff with the cosmology calculators. Others might get more out of imagining another material analog. You may be familiar with one or more ways of picturing 3D expansion. Basically carrying over features of the 2D balloon model into 3D. One hears about rising bread dough--specifically raisin bread dough. A few happy souls proceed directly from the balloon to the Friedmann equations.

BTW have you googled "wikipedia friedmann equations"? Curiously, visualizing Alexander Friedmann as he was around 1922 can be a step towards acquaintance with his equations
===================
I didn't see your latest post until just now. This is a valuable suggestion:
 Quote by Chilli * qualification of the analogy by noting what it isn't (perhaps the top five misconceptions).
You already listed some of the liabilities yourself! There may be nothing more to add.

I haven't woken up properly. I'll get some coffee and think about what we could do next. The thread doesn't need to focus solely on that one analogy. I'm wondering if there is a kind of bridge---a way to segue to the scalefactor a(t) and the differential equations that describe how it grows. If space actually were finite, and actually were the 3D cousin of a 2D balloonsurface then in a certain sense a(t) would be proportional to or somehow related to the radius of curvature, the radius in an imaginary extra dimension. Or should we not go there? Desparate for coffee.
 Astronomy Sci Advisor PF Gold P: 23,230 Chilli, Just to be sure everybody realizes: we don't yet know whether space is finite or infinite volume. Any analogy has limitations and a critical flaw of the balloon picture is that it gives people the impression that we know space has a finite volume. It might have, and space might be the 3D analog of the 2D balloon surface. Then if you could freeze expansion you could shine a lightray in any direction and after a long time it would circle around and come back. But space might also be infinite volume and even, if you overlook minor local irregularities, it might correspond to conventional Euclidean space---the jargon term is "flat". So there is a mental hurdle everyone has to hop over which is how to imagine infinite Euclidean 3D space expanding. Well it's not really much of a hurdle. It just means that the distances between stationary points are all increasing. To approach it gradually first try to picture the 2D Euclidean plane expanding, with a grid on it showing points at rest with respect to CMB. So it is like graph paper with the squares constantly getting bigger. The 2D Euclidean plane expanding is what you would see in the balloon model if the balloon was really vast, so big that the piece you were looking at seemed perfectly flat to you. ================= So the trick is to stay uncommitted mentally. Keep both images alive in your head. Because we don't know yet which one is closer to nature. The finiteness issue is closely related to curvature. Anyone who is interested can keep an eye on the current state of knowledge, which changes as new astronomical data comes in. (supernovae, galaxy and cluster surveys, CMB temperature map analysis...) There is a nasty sign convention where what they tabulate and report is the negative of what intuitively corresponds to curvature. They report Omegak where if it is zero then we are in the flat Euclidean case and if it is negative then we are in the spherical, positive curved case, with finite volume. So the 2008 data gave a 95% confidence interval of [-0.0179, 0.0081]. (table 2 in http://arxiv.org/pdf/0803.0547 ) The unintuitive sign reversal is an historical accident, a kink in the notation. My personal accommodation is to think of a private "Omegacurv" = -Omegak. And then the 95% confidence interval for the private Omegacurv is [-0.0081, 0.0179]. Which is roughly [-0.01, 0.02] So nature is somewhere in there, and future measurements will narrow it down some more (the Planck observatory is scheduled for launch in 2009) and if nature's number is zero then space is infinite volume and looks flat at large scale. And if it's positive then we're in the positive-curved finite volume case. It still looks nearly flat, because the radius of curvature is so large, but it is nevertheless finite. In neither case are there any edges or boundaries, the standard cosmo model is simple in that respect.
 PF Gold P: 222 Thanks for the interesting thread. There are some things that confuse me about the expanding universe. For one thing, dark energy is talked about as being the mechanism to explain the acceleration of the expansion of the universe, but if there's one thing that I'm getting from the expansion of the universe, it's that it's independant of matter and does not interact with it. If this were not so, then the expansion would be limited to sub-luminal expansion rates since nothing can travel faster than light. It can expand faster then light because it works outside the physical geometry (and all the matter it contains) of the physical universe. So how can "energy" as we know it (the energy as defined by e=mc^2) be used to explain the expansion of non-physical space. A good analogy is to imagine being a ghost and trying to interact with physical reality by moving a plate across a table for witnesses to observe. It can't happen because of the un-connected nature between physical energy and the (non-physical)expanding universe. Or is dark-energy by definition something that is outside our physical universe? The other thing that confuses me is how the wavelength of light can be affected by an expanding universe. According to quantum mechanics, light, once observed (as in a spectrograph while looking at red shift) collapses into photons. Not only that, but according to dual slit experiments that focus on delayed time anomolies, once observed, a wave not only collapses into a photon, but will suddenly always have been a photon throughout it's entire lifetime from the time it was released from it's source. Can an expanding universe have the ability to change the wavelength of a single photon? For a photon changing it's wavelength means changing it's energy, so this implies that an expanding universe has the ability to change the energy level of single photons. How is this explained? All very strange stuff indeed. BTW, I like the expanding ballon analogy better then the raising loaf of raison bread as the ballon easily demonstrates that nomatter where you are on the surface of the balloon, you can look in all directions and see the universe expand at the same rate from your point of view. Not so with the raising bread where looking toward the center of the bread will show a different rate of expansion then looking outward toward the surface of the bread. The balloon analogy is great!
Astronomy
PF Gold
P: 23,230
 Quote by Buckethead ... but if there's one thing that I'm getting from the expansion of the universe, it's that it's independant of matter and does not interact with it. If this were not so, then the expansion would be limited to sub-luminal expansion rates since nothing can travel faster than light...
Hi, I was just getting started but was interrupted. back in a minute. Back now. Cosmology is based on 1915 Einstein (general rel) which has dynamic geometry---distances change. I think you may have gotten yourself confused by reasoning from 1905 Einstein (special rel) which does not have dynamic geometry. One of the wonderful things about nature is that geometry DOES interact with matter. Distances between most pairs of galaxies do increase faster than c. We don't think of that as "traveling" (it doesn't get them anywhere it's just the distances increasing).

BTW I'm curious to know what of this thread you may have read. Has it gotten too long? Do I need to summarize and restate what was said in the first 5 or 10 posts?

 The other thing that confuses me is how the wavelength of light can be affected by an expanding universe. ... Can an expanding universe have the ability to change the wavelength of a single photon? For a photon changing it's wavelength means changing it's energy, so this implies that an expanding universe has the ability to change the energy level of single photons.
It certainly can! That is what cosmological redshift is. The wavelengths in the CMB are now about a thousand times longer than they were when the CMB was emitted. Because distances have expanded by a factor of about a thousand while they have been traveling. So the amount of energy in the CMB radiation has declined by a factor of about 1000, or more exactly 1090. You drew the right conclusion!

I'm not sure what you want explained. Whether I can explain depends on what it is. I think perhaps you are wondering how it is that "... an expanding universe [has] the ability to change the wavelength...?"

One way to think about it is it's just what happens with Maxwell's equations when the geometry is dynamic.
With a wave equation, each new cycle is determined by the E and B field geometry of the previous cycle, which has now been slightly extended. The effects of the slight expansion, the changing geometry, accumulate.

Expansion does not affect things that are bonded together like atoms in a crystal or a metal ruler, or which belong to bound systems like our solar system and local group of galaxies. But the wave crests of a wave propagating thru space are not bound together and they occur in the context of an an expanding geometry, so nothing prevents wavelengths from becoming extended.

There are other ways to think about how redshift happens, but they all amount to different ways of mathmatically parsing the same thing.

Just a side comment: conservation laws typically depend on the symmetries of a static geometry---one must be cautious about invoking them where they don't apply.

 ... BTW, I like the expanding ballon analogy better then the rising loaf of raisin bread ...
Me too
Probably the most important thing is it gives a visible analog to being at rest with respect to the CMB, or the expansion process itself. The dots representing clusters of galaxies stay at the same longitude and latitude, reminding us that they are stationary with respect to CMB. At rest with respect to the universe's expansion process, while distances between them nevertheless increase.
This is basically why the distances can increase at rates many times greater than c without anybody "traveling" faster than c.
Things at rest do not travel.
P: 282
 Cosmology is based on 1915 Einstein (general rel) which has dynamic geometry---distances change.
This thread is massive and I haven't gone through it all. I have a question however.

If my understanding is correct, GR speaks not of space or time but of spacetime. Is is spacetime which is expanding? If so, should not only distances be increasing, but also time intervals between events?

I have difficulty seeing the implications of this. And it is probably wrong but I'd like your help to explain to me my error. If any.
Astronomy
PF Gold
P: 23,230
 Quote by Carid .. GR speaks not of space or time but of spacetime.
Well, how do you picture an observer in GR? Almost anything can be an observer---a freely drifting galaxy, or star, or little guy in a spaceship.

The observer's own personal clock, the proper time of that particular observer, gives one possible timeline and slicing of spacetime into spatial slices.

So GR does after all speak of space, and does speak of time. As experienced by some given observer.

Cosmology involves some additional simplifying assumptions---uniformity---sameness in all directions---that make GR boil down to a couple of simple equations which Alex Friedmann got first, around 1923, so they are called the two Friedmann equations. But they are really the Einstein equation of GR radically simplified by assuming a kind of democracy. We are not in a privileged location, there is no privileged direction, all locations and directions are more or less equal.

In GR geometry is dynamic, geometric relations change. But without cosmology's additional assumptions you don't always necessarily get an overall pattern of expansion. All kind of changes can be happening depending on the distribution and movement of matter. The picture is simpler if you go over to cosmology.

It is cosmology where you have this approximately uniform overall pattern of largescale distances increasing a certain percentage each year, or each million years. The pattern is called Hubble Law. It doesn't affect smallscale distances like within our galaxy or between us and neighbor galaxies. It only applies on really large scale. The percentage rate is currently 1/140 of a percent every million years.
If you are talking about a really big distance, an increase of 1/140 of a percent can be quite sizable.

These are spatial distances that are increasing. The cosmic microwave background allows us to define a kind of standard observer's perspective, and an idea of being at rest. So in cosmology there is a standard idea of time. Hubble Law says distances between stationary objects increase with the passage of that standard time. It is understood we are talking space distances.

 Is is spacetime which is expanding?
No, Carid. It is hard for me to picture spacetime expanding, or to be sure what that would mean. Anyway that is not what is intended.

Keep in mind that when people say "space expands" that is a verbal shorthand, a partly misleading way to put Hubble Law in words. What they are really talking about is some mathematics, a simple pattern of increasing largescale distances. It is the distances that are expanding. The expansion is not in a substance, but in geometry. In relationships.
GR teaches us that geometric relationships are dynamic and there is no reason to assume they are always the static orthodox ones of Euclid. Euclidean geometry is just one possible outcome allowed by GR, approximated in the limit when there is almost no matter in the universe. GR is the reason why Euclidean geometry (that maybe you learn in 10th grade) works, or almost works. It is the reason why, at this time in our history, the angles of a triangle add up to 180 degrees, or so close you can't tell the difference.
P: 103
 Quote by wolram To my mind the balloon analogy is a nuisance, gallaxies ect are not stuck to a surface, once one has read about the BA it takes some getting rid of.
- Galaxies move away in a same rate, roughly, from each other and it makes each galaxy the center of expansion, and in this sense galaxies are stuck to a certain frame like a balloon. However, general physical law continues, that is with universe expansion the gravitational law makes continuous adjustment of the galaxies motion to each other.
- However in very small scale like our body or atomic scale, it is different. Its expansion is extremely small in size and the distance of constituent components like molecules or atoms stays the same because the dominant physical law, electromagnetic and quantum physics, moves all back to stable position, so the tiny expansion is canceled out immediately. Thanks.
P: 177
 Quote by marcus Keep in mind that when people say "space expands" that is a verbal shorthand, a partly misleading way to put Hubble Law in words. What they are really talking about is some mathematics, a simple pattern of increasing largescale distances. It is the distances that are expanding. The expansion is not in a substance, but in geometry. In relationships. GR teaches us that geometric relationships are dynamic and there is no reason to assume they are always the static orthodox ones of Euclid. Euclidean geometry is just one possible outcome allowed by GR, approximated in the limit when there is almost no matter in the universe. GR is the reason why Euclidean geometry (that maybe you learn in 10th grade) works, or almost works. It is the reason why, at this time in our history, the angles of a triangle add up to 180 degrees, or so close you can't tell the difference.
This is getting more towards a GR forum issue but.....question..
since gravity is curved spacetime geometry. Does that mean a triangle outside the earths gravity would have angles that add up to 180 degrees, but they would add up to something other than 180 degrees in a strong gravitational field? would it be more or less than 180?
Also...
if you had a very long line segment rather than a triangle, would it be continuously getting longer in length because of the universe's expansion? In other words, is the expansion of the universe only a change in distance between galaxies or is it an actual change in the geometry of spacetime in the same sense that a gravitational field is a change in that geometry?
T.D.
P: 103
 Quote by TalonD This is getting more towards a GR forum issue but.....question.. since gravity is curved spacetime geometry. Does that mean a triangle outside the earths gravity would have angles that add up to 180 degrees, but they would add up to something other than 180 degrees in a strong gravitational field? would it be more or less than 180? Also... if you had a very long line segment rather than a triangle, would it be continuously getting longer in length because of the universe's expansion? In other words, is the expansion of the universe only a change in distance between galaxies or is it an actual change in the geometry of spacetime in the same sense that a gravitational field is a change in that geometry? T.D.
- The sum of triangle angles can be either way from 180deg, which is understandable considering gravitational lensing of lights from a very far object passing a cluster of galaxies. So the light can be bent to any direction depending on gravitation.
- In expanding universe the light wave length becomes longer. But a solid long ruler does not expand, because the ruler follows 2 main physical laws at the same time, the expansion and electric binding force to keep its shape, therefore as soon as there is an expansion it contracts back to original stable state resulting in no change of shape.
 P: 177 actually I had something more abstract in mind, the geometry of space time rather than gravitational lensing or physical rulers.
P: 78
 Quote by marcus So if you send a flash of light off in some direction, once the photons have gotten a substantial distance from you there will be a percentage rate of increase of distance (a recession speed) as well as the light's own standard speed of one inch per minute.
How is this possible? Nothing can travel faster than the speed of light so light cannot travel at the speed of light+a recession speed.
Also if what you say is true then red shift would be impossible as the recession speed the light gains would prevent the waveform from lengthening into the red end of the spectrum.
Please explain, I'm quite confused by this.
 P: 78 No one can explain this to me?
Astronomy
PF Gold
P: 23,230
 Quote by mintparasol How is this possible? Nothing can travel faster than the speed of light so light cannot travel at the speed of light+a recession speed. Also if what you say is true then red shift would be impossible as the recession speed the light gains would prevent the waveform from lengthening into the red end of the spectrum. Please explain, I'm quite confused by this.
Hello mint,
sorry, I didn't see your post until just now.
There are two Einstein Relativities. The 1905 one was SR (special) and the later extension to include curved and dynamically changing geometry is the 1915 (general) one.

Every man-made mathematical theory has limits to its applicability and cannot be pushed too far. As a student when you learn the math model of something you are also told the limits---how far you can trust its predictions, where it blows up and fails to compute meaningful numbers, or starts to diverge from reality.

A major fault of pop-sci journalism is it often fails to make this clear.

The 1905 special only applies locally in situations that are approximately uncurved and approximately non-expanding. It is only perfectly right in situations that dont exist, namely where space is perfectly uncurved, or flat, triangles always add up to 180 degrees, parallel lines...etc. etc. and that simply is never true. And locally means temporarily too, since we are talking spacetime.

Basically, 1915 general trumps 1905 special. But as a rule nature deviates from static flat geometry so slightly and slowly that 1905 works admirably well! It is only over very long distances and time periods that deviation is pronouced enough to be intrusive.

Be sure you have watched Wright's balloon model, the animated film. Better watch several times.
A galaxy (the white spiral whirls) is at rest with respect to the microwave background if it stays at the same longitude latitude on the balloon. All the galaxies are at rest. The distances between them increase.

We have this rule that information cannot travel faster than c.

Think about two galaxies, both sitting still relative to background, and the distance between them increasing. Neither is going anywhere, no information is being transmitted from one place to another, by the mere fact that the distance between is increasing.

Neither of the galaxies could overtake and pass a photon!

The speed law only applies to motion within a given approximately flat frame of reference, where SR applies.

So two things can sit still, and the distance between them can be increasing at 4 or 5 times the speed of light, and nobody is breaking any rules.

You can see that in the balloon animation. The wiggles that change color and have lengtheningwavelengths represent photons. They move at a standard speed like one millimeter per second. But if you watch alertly you will see that after a photon has left the neighborhood of some galaxy the separation between it and the galaxy will begin to grow faster than c, and after a while will be several times c. It's remoteness is increasing several times the rate it can travel on its own.

http://www.astro.ucla.edu/~wright/Balloon2.html
P: 78
 Quote by marcus Hello mint, sorry, I didn't see your post until just now. There are two Einstein Relativities. The 1905 one was SR (special) and the later extension to include curved and dynamically changing geometry is the 1915 (general) one. Every man-made mathematical theory has limits to its applicability and cannot be pushed too far. As a student when you learn the math model of something you are also told the limits---how far you can trust its predictions, where it blows up and fails to compute meaningful numbers, or starts to diverge from reality. A major fault of pop-sci journalism is it often fails to make this clear. The 1905 special only applies locally in situations that are approximately uncurved and approximately non-expanding. It is only perfectly right in situations that dont exist, namely where space is perfectly uncurved, or flat, triangles always add up to 180 degrees, parallel lines...etc. etc. and that simply is never true. And locally means temporarily too, since we are talking spacetime. Basically, 1915 general trumps 1905 special. But as a rule nature deviates from static flat geometry so slightly and slowly that 1905 works admirably well! It is only over very long distances and time periods that deviation is pronouced enough to be intrusive. Be sure you have watched Wright's balloon model, the animated film. Better watch several times. A galaxy (the white spiral whirls) is at rest with respect to the microwave background if it stays at the same longitude latitude on the balloon. All the galaxies are at rest. The distances between them increase. We have this rule that information cannot travel faster than c. Think about two galaxies, both sitting still relative to background, and the distance between them increasing. Neither is going anywhere, no information is being transmitted from one place to another, by the mere fact that the distance between is increasing. Neither of the galaxies could overtake and pass a photon! The speed law only applies to motion within a given approximately flat frame of reference, where SR applies. So two things can sit still, and the distance between them can be increasing at 4 or 5 times the speed of light, and nobody is breaking any rules. You can see that in the balloon animation. The wiggles that change color and have lengtheningwavelengths represent photons. They move at a standard speed like one millimeter per second. But if you watch alertly you will see that after a photon has left the neighborhood of some galaxy the separation between it and the galaxy will begin to grow faster than c, and after a while will be several times c. It's remoteness is increasing several times the rate it can travel on its own. http://www.astro.ucla.edu/~wright/Balloon2.html
I'll have to go and have a study up on this, it's totally counter-intuitive. I don't understand how red shift is possible within this model. It seems that within this model that light speeds greater than c are directly proportional to the distance from source and my understanding of red shift as a measure of age and distance (probably wrong, I'm just a lay-nut) is that wavelengths stretch over distance because of increasing recession with distance, not despite it.
Anyway I'll go look at the animation and see if it clicks with me..
Astronomy
PF Gold
P: 23,230
 Quote by mintparasol I'll have to go and have a study up on this, it's totally counter-intuitive. I don't understand how red shift is possible within this model. It seems that within this model that light speeds greater than c are directly proportional to the distance from source and my understanding of red shift as a measure of age and distance (probably wrong, I'm just a lay-nut) is that wavelengths stretch over distance because of increasing recession with distance, not despite it. Anyway I'll go look at the animation and see if it clicks with me..
One of the first things you learn in an introductory cosmo class is not to think of the redshift as a doppler effect. It is not the result of some particular speed.
The formula involves the entire factor by which distances have been expanded during the whole time the light has been traveling.

roughly speaking

1+z = size(now)/size(then)

Technically the index of size used is called the "scalefactor" usually written a(t) as a function of universal time. Intuitively it is just a handle on the size of the universe or (if that is too vague and undefined) the average distance between galaxies. The exact definition involves a differential equation modeling the growth of a(t), the expansion history of the universe.

So you get taught that
1+z = a(now)/a(then)
the factor by which distances have increased from the moment the light was emitted until the moment it reached our telescope.

Since z is the fractional increase in wavelength, that is the amount added to it, it must be that 1+z is the ratio by which wavelength(now) is bigger than wavelength(then).

So wavelengths have increased by the same factor that large astronomical distances have, during the same time interval.

==================
Pop-sci journalism often misleads readers by presenting the redshift z as a Doppler effect.
Presumably the Doppler shift due to some particular recession speed at one moment in history. But it is not. It is the integrated stretch due to the whole history of expansion during the light's transit.

Just another instance of pop-sci media damage that we are constantly having to recover from.
P: 78
 Quote by marcus One of the first things you learn in an introductory cosmo class is not to think of the redshift as a doppler effect. It is not the result of some particular speed. The formula involves the entire factor by which distances have been expanded during the whole time the light has been traveling. roughly speaking 1+z = size(now)/size(then) Technically the index of size used is called the "scalefactor" usually written a(t) as a function of universal time. Intuitively it is just a handle on the size of the universe or (if that is too vague and undefined) the average distance between galaxies. The exact definition involves a differential equation modeling the growth of a(t), the expansion history of the universe. So you get taught that 1+z = a(now)/a(then) the factor by which distances have increased from the moment the light was emitted until the moment it reached our telescope. Since z is the fractional increase in wavelength, that is the amount added to it, it must be that 1+z is the ratio by which wavelength(now) is bigger than wavelength(then). So wavelengths have increased by the same factor that large astronomical distances have, during the same time interval. ================== Pop-sci journalism often misleads readers by presenting the redshift z as a Doppler effect. Presumably the Doppler shift due to some particular recession speed at one moment in history. But it is not. It is the integrated stretch due to the whole history of expansion during the light's transit. Just another instance of pop-sci media damage that we are constantly having to recover from.
Hmm, sounds like spacetime Doppler to me!!

I'm not being deliberately difficult, I should probably stick to doing sound for bands :lol:
P: 78
 Quote by marcus One of the first things you learn in an introductory cosmo class is not to think of the redshift as a doppler effect. It is not the result of some particular speed. The formula involves the entire factor by which distances have been expanded during the whole time the light has been traveling. roughly speaking 1+z = size(now)/size(then) Technically the index of size used is called the "scalefactor" usually written a(t) as a function of universal time. Intuitively it is just a handle on the size of the universe or (if that is too vague and undefined) the average distance between galaxies. The exact definition involves a differential equation modeling the growth of a(t), the expansion history of the universe. So you get taught that 1+z = a(now)/a(then) the factor by which distances have increased from the moment the light was emitted until the moment it reached our telescope. Since z is the fractional increase in wavelength, that is the amount added to it, it must be that 1+z is the ratio by which wavelength(now) is bigger than wavelength(then). So wavelengths have increased by the same factor that large astronomical distances have, during the same time interval. ================== Pop-sci journalism often misleads readers by presenting the redshift z as a Doppler effect. Presumably the Doppler shift due to some particular recession speed at one moment in history. But it is not. It is the integrated stretch due to the whole history of expansion during the light's transit. Just another instance of pop-sci media damage that we are constantly having to recover from.
Hmm, sounds like spacetime Doppler to me!!

I'm not being deliberately difficult, I should probably stick to doing sound for bands
 P: 103 So there are 2 kinds of doppler effect, one is from motion the other from space expansion.

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