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

[geronimo]

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]

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)

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

 

[marcus]

...
I get that photons traveling 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:

* 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.

 

[marcus]

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 Omega_k 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 "Omega_curv" = -Omega_k. And then the 95% confidence interval for the private Omega_curv 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.

 

[Buckethead]

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 balloon analogy better then the raising loaf of raison bread as the balloon 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!

 

[marcus]

... 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 balloon 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.

 

[Carid]

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.

 

[marcus]

.. 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.

 

[v2kkim]

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.

 

[TalonD]

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 Earth's 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.

 

[v2kkim]

This is getting more towards a GR forum issue but...question..
since gravity is curved spacetime geometry. Does that mean a triangle outside the Earth's 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.

 

[TalonD]

actually I had something more abstract in mind, the geometry of space time rather than gravitational lensing or physical rulers.

 

[mintparasol]

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.

 

[mintparasol]

No one can explain this to me?

 

[marcus]

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 don't 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

 

[mintparasol]

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 don't 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..

 

[marcus]

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.

 

[mintparasol]

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:

 

[mintparasol]

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

 

[v2kkim]

So there are 2 kinds of doppler effect, one is from motion the other from space expansion.

 

[marcus]

So there are 2 kinds of doppler effect, one is from motion the other from space expansion.

not really, I think Mint is just kidding.
In the language of ordinary physics the Doppler effect is from motion
and therefore astronomers simply do not treat the cosmo redshift as a Doppler effect.

It can be so treated if you set up a chain of millions of little overlapping local coordinate patches between you and the thing and do some rather artificial mathematics. It is not the natural way to treat the redshift, but you can do a complicated Doppler analysis and get the right answer.

But a working astronomer would not go thru all that rigamarole. You treat the redshift not as a Doppler (motion) effect but as a distance expansion effect and the formula you use is not a Doppler formula (by any stretch ) but simply this:

wavelength(now)/wavelength(then) = distances(now)/distances(then)
or more formally:
1+z = a(t_rec)/a(t_em)

That is what you would see in a textbook. The two times are the time the light is emitted and the time the light is received. The a(t) function of time is the universe's scalefactor.

It is better to simply say, as most people do, that the redshift is not a Doppler effect, rather than to make up a private concept as Mint does and talk about "spacetime doppler".

 

[Chronos]

I politely disagree, marcus, most astronomers perceive redshift as a doppler effect,

 

[v2kkim]

I feel better in understanding universe and physics from this dialogue.
I have a new question:
Suppose that we got a new spectrum picture from a star, and that picture shows several dark lines with shift, and we speculate the object might be moving very fast but do not know the distance. Now from that shift pattern can we tell if it comes from space expansion or local motion ?

 

[Chronos]

Proper motion is insignificant in cosmological [ie, not in our galaxy] spectral studies.

 

[Chronos]

I should elaborate, in all fairness to marcus. Doppler shift as modified by gr is the normative reference. I believe that was his point.
.

 

[v2kkim]

Regarding the distance advanced by light in expanding universe , I did some calculation to get the result:

$$D(T)\ = {c \over r} (\left( 1 + {r*dt} \right)^{T \over dt} -1)$$

Taking the limit dt going to 0,
$$D(T)\ = {c \over r} (e^{rT} -1)$$
where
D(T): distance advanced by light during period T.
c: speed of light
T: time from emission to present.
r : space expansion rate 1/140 % per million.
dt: the arbitrary small time intervals in T.
** In case r goes to 0, D(T) goes to c*T as expected.

I got this formula by adding each light path segment advanced for each dt, that is after the last dt, the D1 (distance advanced of the last dt) is D1=c*dt*(1+r*dt), and the 2nd last one D2=c*(1+r*dt)^2, and so on .. Dn=c*(1+r*dt)^n. From summing D1 D2 ..Dn, I got above formula.
I do not want to use the word speed to avoid confusion, but it is just the distance of light advanced after a period T.

 

[marcus]

I feel better in understanding universe and physics from this dialogue.
I have a new question:
Suppose that we got a new spectrum picture from a star, and that picture shows several dark lines with shift, and we speculate the object might be moving very fast but do not know the distance. Now from that shift pattern can we tell if it comes from space expansion or local motion ?

I'm glad to know you found it helpful!

The answer is no. One cannot tell just from the shift pattern whether it is Doppler from local motion or stretch-out redshift from the whole history of expansion during the light's travel time.

In fact one can do a complicated mathematical analysis involving a chain of overlapping patches---it's ridiculous but one can do it---so there might be a million observers between you and the object---and actually analyse cosmological redshift in terms of a million little Doppler shifts. But it is a clumsy and useless way to think about it.

Regarding the distance advanced by light in expanding universe , I did some calculation to get the result:

$$D(T)\ = {c \over r} (\left( 1 + {r*dt} \right)^{T \over dt} -1)$$

Taking the limit dt going to 0,
$$D(T)\ = {c \over r} (e^{rT} -1)$$
where
D(T): distance advanced by light during period T.
c: speed of light
T: time from emission to present.
r : space expansion rate 1/140 % per million.
dt: the arbitrary small time intervals in T.
** In case r goes to 0, D(T) goes to c*T as expected.

I got this formula by adding each light path segment advanced for each dt, that is after the last dt, the D0 (distance advanced of the last dt) is D1=c*dt*(1+r*dt), and the 2nd last one D2=c*(1+r*dt)^2, and so on .. Dn=c*(1+r*dt)^n. From summing D1 D2 ..Dn, I got above formula.
I do not want to use the word speed to avoid confusion, but it is just the distance of light advanced after a period T.

I'm impressed. I haven't examined this closely enough to guarantee it but I think it should give approximately right answers if it is used over short enough distances that the rate r does not change significantly during the light's travel time.

When I quote this figure of 1/140 of a percent, what I mean is that this is the current percentage rate of distance expansion. It has been larger in the past.
Vakkim, do you know the Hubble time? 1/H where H is the current value of the Hubble rate?

Have you ever calculated the Hubble time for yourself? I think you should, because you understand calculation, if you have not already.
What value of the Hubble rate do you like to use? I use 71 km/sec per Megaparsec.
Suppose I put this into google
"1/(71 km/s per megaparsec)"
What google gives me back is 13.772 billion years. I could round that off and say the Hubble time is 14 billion years.
Saying "1/140 of a percent per million years" is just a disguised form of this.

If the Hubble time (1/H) is 14 billion years, then the Hubble rate itself (H = 1/(1/H)) is 1/(14 billion years)
That is the same as 1/14 per billion years.
That is the same as 1/14000 per million years.
That is the same as 1/140 of one percent per million years.

In other words having calculated the Hubble time we could say the rate was "1/137.72 of a percent per million years", except that would be overly precise and we round off to two significant figures and say 1/140.

I expect this may be self-evident to you but want to make sure we know where the figure comes from, and that it gradually changes over time.

 

[mintparasol]

wavelength(now)/wavelength(then) = distances(now)/distances(then)
or more formally:
1+z = a(t_rec)/a(t_em)

I'm sorry marcus, the same basic equation can be used to calculate Doppler for sound waves. Why does so much of modern physics come across like the emperor's new clothes? I don't mean to be rude but I can't see anything in this that I'm not understanding..

 

[Ich]

I can't see anything in this that I'm not understanding

Then look again: what is the meaning of "a"?

 

[marcus]

the same basic equation can be used to calculate Doppler for sound waves.

Oh I see what you mean. What a(t) means here is the universe scale factor. You are drawing an analogy where a(t) is the distance between emitter and receiver, and the emitter is moving in still air.

Ich! I am glad to see you. My memory is unreliable but I have the notion (perhaps wrong) that you live somewhere in south Germany and know a fair bit of mathematics. I am glad that you sometimes glance at this thread. Thanks for any and all help!

Mint, if we were in a situation where Doppler applied, we would use

$$1+z = \sqrt{\frac{1+\beta}{1-\beta}}$$

The correct Doppler formula for light in special relativity. We would not use the formula appropriate for sound from moving source in still air, which by coincidence looks like the correct one for redshift if you interpret the scalefactor a(t) as distance between source and receiver.
When I think Doppler, I think the formula I wrote for you there.
It goes crazy when recession rates equal or exceed the speed of light. The Doppler formula (which is correct for actual motion) is completely different and completely wrong for redshift. (Only works as approx for nearby slow receding things.)

 

[mintparasol]

Oh I see what you mean. What a(t) means here is the universe scale factor. You are drawing an analogy where a(t) is the distance between emitter and receiver, and the emitter is moving in still air.

Ich! I am glad to see you. My memory is unreliable but I have the notion (perhaps wrong) that you live somewhere in south Germany and know a fair bit of mathematics. I am glad that you sometimes glance at this thread. Thanks for any and all help!

Mint, if we were in a situation where Doppler applied, we would use

$$1+z = \sqrt{\frac{1+\beta}{1-\beta}}$$

The correct Doppler formula for light in special relativity. We would not use the formula appropriate for sound from moving source in still air, which by coincidence looks like the correct one for redshift if you interpret the scalefactor a(t) as distance between source and receiver.
When I think Doppler, I think the formula I wrote for you there.
It goes crazy when recession rates equal or exceed the speed of light. The Doppler formula (which is correct for actual motion) is completely different and completely wrong for redshift. (Only works as approx for nearby slow receding things.)

Ok, well, the way I see it, the balloon analogy can be easily demonstrated in one dimension by marking a number line on a piece of elastic and stretching it. If we factor in time, we now have two dimensions and if we factor in two more spatial dimensions, we now have the four dimensional spacetime that we are all experiencing. The mathematics may become more complicated as we add more dimensions but it isn't any more difficult to visualise. Of course the maths need to be integrated for the expansion of the universe over time but this doesn't make the phenomenon more difficult to visualise, even for the lay person. To me, redshift is a phenomenon that is so analogous to the Doppler effect in sound waves that it can be called the Doppler effect when it occurs in light reaching us from distant parts of the universe. If the expansion history of the universe hasn't been uniform, isn't that what physicists all over the world are being paid to figure out? It doesn't change the nature of the basic phenomenon..

 

[Ich]

Ich! I am glad to see you. My memory is unreliable but I have the notion (perhaps wrong) that you live somewhere in south Germany and know a fair bit of mathematics. I am glad that you sometimes glance at this thread. Thanks for any and all help!

Thanks for the nice welcome. Your memory seems quite reliable - except for the mathematics, which is not exactly my strong point. It's just enough to survive as a physicist.
Thanks also for this thread; it made me curious about what the dynamics on the balloon surface actually would be. I always felt uncomfortable about things being stuck on the surface and expanded by brute force, as this picture is not compatible with relativity.
This exercise helped my understanding of cosmology a lot. I will soon write more about some basic cosmological FAQs, maybe it is helpful for some of you as well.

 

[Ike47]

I just found this forum this morning, eventually got enough nerve to post a new thread in the relativity section, then came here when I saw this subforum because of questions I've long had about space, the universe, and cosmology. I've spent the last 4 or 5 hours reading this thread, with occasional breaks to read responses to my post in the relativity section, and to respond to them.

So, anyway, first, thank you so much for this thread! It is an excellent introduction. I guess that at some point it would help to condense it into an FAQ of some sort, but I fear one would lose a lot of the insights available from reading through it all.

I have two questions to add, which have puzzled me for a long time. I think this thread has answered one of them, but I want to be sure. I haven't recognized any answer to the second question, but perhaps I've missed something. Given the time it has taken to read through the thread, I haven't gone through the additional 'exercises' recommended as of yet, except to read the SA article about misconceptions about the universe. If one of the other sources will answer either or both of my questions, please just point that out.

First a bit of background. Some aspects of the 'generally accepted' current understanding of the universe I have no problem conceptualizing. For example, that our 3D universe has no edge(s), that there doesn't have to be "something" outside of it to expand into, and that there doesn't have to be a 4th (spacial) dimension to expand 'into' (although there could be a 4th spatial dimension--I think: I am confused by the arguments that stable atoms, etc., cannot exist in more than 3 spatial dimensions).

So, first, the question I think you've answered. Does the universe expand everywhere equally, and in particular, "here"? I have read in rather unreliable other places that there is no expansion where matter is present in substantial quantities, such as within our galaxy. If I have understood this thread properly, however, the correct answer is that the universe, or 'space', whatever that may be, is expanding everywhere, but that locally (anywhere) binding forces continuously bring back matter to its previous size, be that matter individual atoms, or, for example, our bodies, our solar system, or our galaxy itself. Do I have that right? If so, does that 'rule' also apply to our Local Group, or are the galaxies that make it up too far separated for the gravitational forces among them to cause the whole Local Group to continuously 'spring back'?

Or, in other words, for example, does the Andromeda Galaxy approach us at a speed based precisely on the gravitational attraction (and momentum) of it and the Milky Way galaxy, or is the speed slightly reduced by the expansion of space, although not enough to make a practical difference?

More generally, at what point does the strength of gravity become too weak to cause matter to 'spring back' to the shape it had at any given point before the current moment's spatial expansion? (I have no idea if I've phrased that question accurately or even meaningfully.) Or, let me ask it another way: although all galaxies are gravitationally attracted to all other galaxies, obviously most of them are too far separated to overcome the expansion of space, or else there would be no expansion. But how far is too far? Between any two galaxies? Between Local Groups? Between Super Clusters? Or perhaps we don't know?

I'm not happy at all with how I tried to phrase my first question. Let's see if I can do any better on my second. I think it's a tougher question, but more easily asked. Most simply, if the universe is closed (finite), mustn't it have a center? We may not be able to locate it, it may not be within our 3 spatial dimensions, but doesn't it have to exist somewhere?

I understand that if the universe is open/infinite, then the concept of a 'center' is meaningless. I also understand that there is a distinct possibility that the universe is open (even if intuitively, I don't like the idea, and find the idea of a finite universe much more satisfying).

Yet everything I've read states (with insufficient proof, it seems to me) that the universe has no center. Since the universe is larger, presumably much larger, that that portion of it we can see within our horizon dictated by the speed of light (and expansion, etc.), I understand that we presumably have no way of identifying where the center of the universe is. But unless there's some aspect of solid geometry I don't understand (which may be true, of course), a finite universe still has to have a center, no?

Again, that center might be in a 4th, or higher, spatial dimension, if such dimension/s exist/s. Just as the center of the balloon in the balloon analogy is not findable by the folks on the balloon surface, since the center is in the 3rd dimension.

[One side comment: I suggested the center could be in the 4th or 'a higher' spatial dimension because of an analogy from the balloon ultimately. Let us consider a one dimensional world by taking just one line drawn on the balloon... a great circle initially for convenience. This one-dimensional world would have its center in the second dimension, namely at the center of the balloon, but along the plane which bisects the balloon along the great circle. So the center is just 'one dimension' beyond the world itself. But now, take that great circle and make it irregularly wavy along the surface of the balloon. It is still one dimensional (a line), but it's center could only be found in the 3rd spatial dimension, somewhere offcenter of the balloon.

Well, I don't know if my analogy is accurate, but I thought I'd toss it out as well, just to find out.]

I apologize for being so verbose, but if I could get responses to my two questions, I think I'd be much more comfortable with my ability to conceptualize the universe than I have been in many years.

 

[TalonD]

Ike, welcome. It's nice to see someone who reminds me of myself. Intelligent enough to get a grasp of this stuff but not a mathmetician or physicist, but with a keen interest in the subject.

Your Andromeda question is a good one and I'd like to hear the answer. Is it's aproaching speed slowed by the expansion of the universe. For me this also brings up another deeper question dealing with GR and geometry, but one I'm not sure I am articulate enough to ask so I will leave it for now.

As for your question about a center of the universe. This is hard to imagine but if you can accept the kind of counterintuitive concepts that you seem to be able to accept, then think of it this way. Imagine the balloon analogy. think of the 2 dimensional surface as the only thing that exists. A sphere with no inside, only a surface. If you can imagine a sphere with no outside, only a surface, then the next step to.. no inside, should be easy.

Marcus is a good one to make much more educated comments on all this!

 

[marcus]

I want this stuff on the sticky because I will need to refer to it. Numbers to have handy.

The Hubble value of 71 km/s per megaparsec was what Wendy Freedman's group gave us in 1998 based on HST (hubble space telescope) observations up to that time. And we have been it as a default for about 10 years. Finally Adam Riess's team has boiled down 10 more years of HST observations and provided a new number of 74 with tighter bounds. It is consistent with Wendy, just that Wendy's figure had wide bounds. They do the best they can. Things just got better. So we need to adjust.

Sylas supplied the link to the Riess et al 2009 paper with the new Hubble rate.
https://www.physicsforums.com/showthread.php?p=2231728#post2231728

To do standard model cosmology (LCDM assumes w = -1) it usually suffices to have handy the matter fraction, dark energy fraction, and the Hubble rate. For some years we have been using .27, .73, and 71 for these. For example in Ned Wright's calculator those values are the default. If you want anything else you have to type it in.

Now we have to type in .25, .75, 74. I will explain this. It will turn out that the Age is now 13.4 billion years, for example. So we have to stop saying 13.7, or 14.
What about the particle horizon---the radius of the observable? It will turn out to be about 46.0, so we have to stop saying 46.5.

The point is that the critical density goes as the square of H, so whatever it was before it is now (74/71)^2 times that. Keeping the same actual matter density means that the matter fraction is now smaller. The denominator is bigger so instead of 0.27 the matter fraction is now 0.27*(71/74)^2 = 0.25.

Near flatness then makes the dark energy fraction 0.75.

So to avoid unnecessary noise in the numberchannels, we need to stop saying
(.27, .73, 71) and start saying (.25, .75, 74)

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

You might want to get some of the new numbers for yourself rather than just looking them up. Here is how to get the expansion age and the particle horizon (current radius of the observable.) Just google "wright calculator" and put in the new threesome in place of the default threesome, and try z = 10000. You could also use z = 100000. It won't make any appreciable difference. You will get that the particle horizon is about 46.0 (call it 46) billion lightyears from here. Actual now distance.

That is how far the galaxies are where the people could now be receiving signals from our matter at the very earliest times, before our material condensed to form any structures. I don't know what of signals those could be. Ordinary light from before year 380,000 gets wiped by the glare. It's just the theoretical max. And it slowly increases as the universe gets older. The same distance limit applies to us getting signals or particles from their matter. The material that eventually became galaxies and stuff. It's the present day distance to the farthest stuff we can see.

AND at the same time the calculator will give you the age of the universe is 13.39 billion years. Call it 13.4 billion.
We should not say 13.7 any more. The new age of 13.4 reflects the new parameters (.25, .75, 74).

Now what about the distance to last scattering? The distance to the material that sent us the microwave background light that we are now receiving with the WMAP spacecraft and will soon be receiving with the new Planck spacecraft .

Well, again you prime the calculator with the new threesome and try z = 1090. And you get 45.2 billion lightyears. It says the usual thing: the age of expansion is 13.4 billion years, the light was released in year 380,000. Which is nothing compared with 13.4 billion, so the CMB light travel time was 13.4 billion years.

And it also tells you the distance to the CMB material was when it released the light, that is the angular size distance which the calculator says is 41.4 million lightyears. Again that is an actual or proper distance (the kind astronomers typically use) but referred to back when the light was emitted. The material was much closer then. 41.4 million and 45.2 billion should be about in the ratio 1090, the factor by which actual distances expanded while the light was in transit.
Oh, there is the Hubble distance c/H. By definition this is the actual presentday distance which is currently increasing at exactly rate c. You calculate it by putting "c/(74 km/s per megaparsec) in lightyears" into google. Google immediately tells you it is 13.2 billion lightyears.
What redshift does that correspond to?
Wright calculator tells you z = 1.4. Try putting that 1.4 into the calculator, primed with the new threesome, and you will get 13.2.
So the galaxies that come in with redshift 1.4 are the ones where the distance to them is increasing at rate c.