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

[mysearch]

At some point, people get around to asking questions like:

o Is Hubble’s constant calculated or measured?
o Does a spatial flat universe require a critical density?
o How were the relative energy densities determined?

If so, I would recommend Marcus response in this post:
https://www.physicsforums.com/showpost.php?p=1973468&postcount=18

Is there a cosmology library section?
Maybe posts like this should be formalised into it?

 

[marcus]

Here's an outstanding set of 77 slides. They are for Ned Wright's 28 October 2008 UCLA Faculty Research Lecture, an annual event. It's a great introduction to cosmology.http://www.astro.ucla.edu/~wright/CMB-MN-03/FRL-28Oct08clean.pdf

Also not to be missed, Smoot's 20-minute TED talk given May 2008

http://video.ted.com/talks/podcast/GeorgeSmoot_2008P_480.mp4
Smoot's talk was illustrated by some remarkable animations of early universe structure formation, by Kravtsov
http://cosmicweb.uchicago.edu/filaments.html
http://cosmicweb.uchicago.edu/group.html
thx to Orion for pointing out Smoot's talk.

 

[marcus]

A famous Einstein quote about an important feature of General Relativity known as general covariance.
“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität."

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

source links here:
https://www.physicsforums.com/archive/index.php/t-166997.html

also see page 43 of
www.tc.umn.edu/~janss011/pdf%20files/Besso-memo.pdf[/URL]
==quote==
In a letter to Schlick, he again wrote about general covariance that
“thereby time and space lose the last vestige of physical reality” (“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität.” Einstein to Moritz Schlick, 14 December 1915 [CPAE 8, Doc. 165]).
==endquote==

 

[atyy]

not sure if this question belongs in this thread but... the expansion is just a pattern of increasing distance between us and distant galaxies, so there is no space/time substance that is stretching right? so in GR gravitation, what is it that is curved?

Spacetime (4D) is curved. However, there are usually "special" ways to split spacetime into "space" (3D) and "time" (1D). These are "special" splits because they don't simply pick an arbitrary coordinate as "time", but among other things they also ensure that the "time" direction at every "spatial location" points to the future and is the potential worldline of an observer. If you do this split in empty flat spacetime, two observers at "rest" in "space" don't find that the distance between them increases with "time". But when you do it in the matter-containing curved spacetime used to model our universe, two observers at "rest" in "space" do find that the "spatial distance" between them increases with "time". (Actually, you can do split flat spacetime so that "space" expands with "time", but then observers have to be massless and energyless, so that's not realistic. But it shows that one should remember that the description of curved 4D spacetime as expanding or being a pattern of distances that increases with time depends on a choice of 3+1D split that is permissible and convenient, but not unique.)

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

 

[TalonD]

A famous Einstein quote about an important feature of General Relativity known as general covariance.
“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität."

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

source links here:
https://www.physicsforums.com/archive/index.php/t-166997.html

also see page 43 of
www.tc.umn.edu/~janss011/pdf%20files/Besso-memo.pdf[/URL]
==quote==
In a letter to Schlick, he again wrote about general covariance that
“thereby time and space lose the last vestige of physical reality” (“Dadurch verlieren Zeit & Raum den letzter Rest von physikalischer Realität.” Einstein to Moritz Schlick, 14 December 1915 [CPAE 8, Doc. 165]).
==endquote==[/QUOTE]

[quote="atyy, post: 1994176"]Spacetime (4D) is curved. However, there are usually "special" ways to split spacetime into "space" (3D) and "time" (1D). These are "special" splits because they don't simply pick an arbitrary coordinate as "time", but among other things they also ensure that the "time" direction at every "spatial location" points to the future and is the potential worldline of an observer. If you do this split in empty flat spacetime, two observers at "rest" in "space" don't find that the distance between them increases with "time". But when you do it in the matter-containing curved spacetime used to model our universe, two observers at "rest" in "space" do find that the "spatial distance" between them increases with "time". (Actually, you can do split flat spacetime so that "space" expands with "time", but then observers have to be massless and energyless, so that's not realistic. But it shows that one should remember that the description of curved 4D spacetime as expanding or being a pattern of distances that increases with time depends on a choice of 3+1D split that is permissible and convenient, but not unique.)

Also, curvature is the distance between objects at different locations. If we use a piece of string and a protractor to measure distances between objects on a football, we will find the pythagorean theorem doesn't hold, so the football is curved. If we replace the football with spacetime, the piece of string with a ray of light, spatial distance with spacetime interval, and objects with events, we can find out if spacetime is curved.[/QUOTE]

Marcus, on the other hand... cogito ergo sum --Descartes

Atyy, as a non physisist layman, I find that kind of hard to follow, can you restate that in a simpler easier to understand way? I understand the football analogy but the previous paragraph was a little confusing.

 

[TalonD]

I was just thinking that it is interesting that the baloon or flat rubber sheet analogy when used to explain gravity to the lay public would lead one to an obvious common sense conclusion that pressure has an effect on gravity. Yet without the analogy, for a physisist using mathematics it might seem unexpected. I realize the analogy is not reality and that it's the math that counts (excuse the pun) but still, I thought that was interesting.
:P

 

[atyy]

Atyy, as a non physisist layman, I find that kind of hard to follow, can you restate that in a simpler easier to understand way? I understand the football analogy but the previous paragraph was a little confusing.

On the football (the spherical sort), if two observers start out at the north pole and follow straight lines of longitude, they find that the latitudinal distance between them increases, so their universe is "expanding". After they pass the equator, their universe starts to "contract".

 

[TalonD]

On the football (the spherical sort), if two observers start out at the north pole and follow straight lines of longitude, they find that the latitudinal distance between them increases, so their universe is "expanding". After they pass the equator, their universe starts to "contract".

ok, I'm going to expose some of my ignorance in this question but here goes...

Thanks for the clarification. I still have some confusion though, maybe because I am trying to take the analogy too far. on a globe if you move along the lines of longitude it depends on whether you are moving toward or away from the equator as to whether you converge or diverge. So if our universe has a positve curvature rather than being flat. then would two objects traveling in parallel eventually converge no matter what direction they are traveling, but in an open universe they would eventually diverge right? The only problem I have with that concept is that it is easy enough to draw two parallel lines on a globe and make them stay parallel all the way around. but presumably in a univere with positive curvature you couldn't keep them parallel right? So since we know that on a large scale everything in our universe is diverging does that mean we are headed towards some kind of cosmic equator and when we pass it, everything will start to converge towards a big crunch? Could the question of continued expansion vs. a big cruch have to do with the ovearall geometry of the universe in adition to the critical density? well of course the geometry of the universe is dependent on the density so I guess that answers my own question.

Then there is gravity. I can understand that two objects traveling near each other in space would follow the curvature and converge. but why do to objects that are initially at rest relative to each other spontaneously start moving together?

 

[atyy]

Thanks for the clarification. I still have some confusion though, maybe because I am trying to take the analogy too far. on a globe if you move along the lines of longitude it depends on whether you are moving toward or away from the equator as to whether you converge or diverge. So if our universe has a positve curvature rather than being flat. then would two objects traveling in parallel eventually converge no matter what direction they are traveling, but in an open universe they would eventually diverge right? The only problem I have with that concept is that it is easy enough to draw two parallel lines on a globe and make them stay parallel all the way around. but presumably in a univere with positive curvature you couldn't keep them parallel right? So since we know that on a large scale everything in our universe is diverging does that mean we are headed towards some kind of cosmic equator and when we pass it, everything will start to converge towards a big crunch? Could the question of continued expansion vs. a big cruch have to do with the ovearall geometry of the universe in adition to the critical density? well of course the geometry of the universe is dependent on the density so I guess that answers my own question.

Yes, you've answered your question. But let me comment on not taking the analogy too far. On the spherical football, it is 2D spacetime which is curved. However, it does not make sense to say that each spatial slice has intrinsic curvature, because the spatial slices are 1D lines of latitude. In contrast, for the universe, each spatial slice is 3D, for which it does make sense to ask if it has intrinsic curvature. So one should distinguish between the curvature of 4D spacetime, and the curvature of 3D spatial slices.

Then there is gravity. I can understand that two objects traveling near each other in space would follow the curvature and converge. but why do to objects that are initially at rest relative to each other spontaneously start moving together?

The objects themselves produce spacetime curvature. It is not possible to be at rest in time, so it is not possible to be at rest in spacetime, so the objects move together.

 

[navneet023]

First of all, sincere apologies to everyone who feels offended by my post. But couldn't help posting, I had to!

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

Just a point i want to make. Hope I haven't offended anyone. :)

 

[marcus]

Navneet, you might enjoy this 20-minute talk by Nobelist George Smoot. Links here:
https://www.physicsforums.com/showthread.php?t=274265

This mp4 version is slow to download but higher resolution, I think.
http://video.ted.com/talks/podcast/GeorgeSmoot_2008P_480.mp4
You click on it and go away and do something else for 5 or 10 minutes and then come back and start it.

Thanks also for these! The Kravtsov computer simulations are excellent. I like this especially:
http://cosmicweb.uchicago.edu/filaments.html
I see that Smoot used Kravtsov's movies in his TED talk.
This was a good one too:
http://cosmicweb.uchicago.edu/group.html
I watched the halfsize MP4 version of the movie because it is very easy to download, only about 2.4 MB.

 

[Polter]

I was just wondering, if the galaxies are like coins on a balloon -- accelerating away from each other -- then how is the Milky Way-Andromeda Galaxy Collision possible?

 

[marcus]

I was just wondering, if the galaxies are like coins on a balloon -- accelerating away from each other -- then how is the Milky Way-Andromeda Galaxy Collision possible?

That's another bad thing about the analogy.

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

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

It is only widely separated galaxies---those not bound---that obey Hubble law, and act like the pennies of the model

 

[thaddeus]

If it is to be asserted that the Big-Bang was not of "point" origin then how is it justified in terms of -everything- expanding away from other items .. as though it were simply an outward expansion .

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

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

Maybe it would make more sense as a hypothesis that matter is shrinking lol .. sometimes feels that way mumble mumble .. .. :)

 

[geronimo]

Having ditched the balloon analogy as being too simplistic, I am visualising the mechanism as more like expanding gap-filling foam. This allows me a more realistic three dimensional picture and allows variations in local expansion caused by chaotic quantum anomalies, causing "lumpiness" on whatever scale you like. This model also allows the "bubble" to assume a non-regular shape eventually.

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

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

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

Perhaps Marcus would care to comment?

Merry Christmas to all.

 

[Chilli]

On the balloon analogy and the Cosmic Microwave Background radiation ...

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

Kind regards

 

[marcus]

Having ditched the balloon analogy as being too simplistic, I am visualising the mechanism as more like expanding gap-filling foam...

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

On the balloon analogy and the Cosmic Microwave Background radiation ...

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

Kind regards

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

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

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

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

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

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

Does the CMB radiation just continuously criss-cross itself? If yes, why is the radiation still uniform?

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

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

==========
BTW Chilli is an excellent choice of name---reminds me of a favorite comic gangster movie. Looks like the above was your first post: welcome to the forums!

 

[Chilli]

Marcus, thank you for your explanation and for your kind welcome!

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

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

=========

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

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

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

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

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

I greatly appreciate your efforts to try to help beginners such as myself receive the analogy more correctly, Marcus!

 

[marcus]

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

Sounds like you are closer. But have you watched the short movie yet?
Google "wright balloon model". Ned Wright is a good teacher. his whole website is a useful resource. He usually has two balloon movies and its worth watching both.

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

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

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

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

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

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

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

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

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

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

At ordinary energies, beams of light that cross do not interact. Try it with two flashlights.
Positive and negative interference effects are something else, two beams of monochromatic light (both the same frequency) meeting on a projection screen. CMB is not monochromatic. It is a big mix of frequencies. Not to worry about interference.

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

That's right.

But, assuming the Inflationary Model is correct, the balloon became pretty large when it was still very young, which goes to the uniformity of the CMB in the first place. And this is where the powerful balloon analogy becomes intuitively confusing to me.

Like I already said. Inflation is relevant to the first second. Not part of the picture of what happened only after 380,000 years had gone by!

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

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

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

* Firstly, if a wriggle of light keeps traveling around a sphere, it’s going to end up back where it started.

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

* Secondly, since the coins themselves stopped emitting their original CMB radiation long ago, then I expect the timeline of a given location A to include periods in which there is no CMB.

At the time the CMB was emitted, space was entirely filled with a uniform glowing hot cloud. It only later began to condense into stars and galaxies. So the pennies are not a perfect representation of matter. They are sort of the right picture once matter condensed into clusters of galaxies. But it is still just an analogy, not accurate in detail.

So we have been receiving CMB radiation steadily for the whole 13.7 billion years. As time goes on, the glow emitted by more and more distant hot cloud comes in. Because the cloud was uniformly distributed. So the radiation would not have been sporadic.

 

[Chilli]

Sounds like you are closer. But have you watched the short movie yet?

Yes, but I don't have trouble picturing the expansion of distance between gravitationally sticky blobs.

BTW there is an issue with arithmetic. If you have 13.7 billion years and you take away one million years, what do you have? You have 13.7 billion years.

You do, indeed! (I did say my math was lacking.)

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

An optimistic prediction, but I say hold that dream!

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

Agreed.

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, and that they're destined to never exceed the speed of expansion, leading to an ultimately black and cold universe. What I was trying to do was point out challenges with the use of the balloon analogy.

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

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

Kind regards

 

[geronimo]

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:

<br /> D(T)\ = {c \over r} (\left( 1 + {r*dt} \right)^{T \over dt} -1)<br />

Taking the limit dt going to 0,
<br /> D(T)\ = {c \over r} (e^{rT} -1)<br />
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:

<br /> D(T)\ = {c \over r} (\left( 1 + {r*dt} \right)^{T \over dt} -1)<br />

Taking the limit dt going to 0,
<br /> D(T)\ = {c \over r} (e^{rT} -1)<br />
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.)