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

by marcus
Tags: analogy, balloon, effort
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P: 22,342
 Quote by v2kkim 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(trec)/a(tem)

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".
 PF Patron Sci Advisor P: 8,883 I politely disagree, marcus, most astronomers perceive redshift as a doppler effect,
 P: 103 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 ?
 PF Patron Sci Advisor P: 8,883 Proper motion is insignificant in cosmological [ie, not in our galaxy] spectral studies.
 PF Patron Sci Advisor P: 8,883 I should elaborate, in all fairness to marcus. Doppler shift as modified by gr is the normative reference. I believe that was his point. .
 P: 103 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.
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 Quote by 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 ?

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.

 Quote by 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 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.
P: 78
 Quote by marcus wavelength(now)/wavelength(then) = distances(now)/distances(then) or more formally: 1+z = a(trec)/a(tem)
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..
P: 1,883
 I can't see anything in this that I'm not understanding
Then look again: what is the meaning of "a"?
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 Quote by mintparasol 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.)
P: 78
 Quote by marcus 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..
P: 1,883
 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.
 P: 177 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!
 P: 59 Getting me on the same page may take some doing if it means that I will have the same opinons as everyone else. "To move on to the main course, here is Ned Wright's page with the balloon analogy animation" The thing that bothers me about this site is that he says the galaxies are not expanding. I have a problem with that as there is a lot of space inside of one. What evidence is there that they are "bound"? Is that opinion part of the "Standard model" that I am supposed to accept?
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 Quote by StandardsGuy What evidence is there that they are "bound"? Is that opinion part of the "Standard model" that I am supposed to accept?

Read the first 10 or 20 posts on this thread. I never say that space expands. Distances between widely separated observers each at rest relative to the Background do increase. That is Hubble law. It's about geometry, not about some substance called "space".

The solar system planets are in stable orbit around sun, no reason they should get farther.

The stars in Milky are in orbit around milky center. No reason for them to get farther.

Just because Milky has space in it is no reason for it to expand. Where do you get this idea? Could it maybe be popular science journalism ?

"Bound" which you put quotes around is a simple basic physics idea, it just means gravitationally bound, like in stable orbits, like planets and stars. Likw ir would take a big effort to drag them apart. It is not an opinion Guy. It is obvious from looking at these structures that they have gathered together into some semipermanent collective form.

 Getting me on the same page may take some doing if it means that I will have the same opinons as everyone else. "To move on to the main course, here is Ned Wright's page with the balloon analogy animation" The thing that bothers me about this site is that he says the galaxies are not expanding. I have a problem with that as there is a lot of space inside of one.
Ned Wright is telling you straight. There is no reason connected with Big Bang cosmology that the galaxies should expand. They don't expand. If you have the notion that they should then you are confused and need to dump that idea.

You don't have to adopt OPINIONS, Guy. We are talking fairly simple straightforward stuff. Once you dump some misconceptions you will be fine. Please to go watch Ned's animation. He is giving the straight dope and it's real helpful.
P: 59
 Quote by marcus The basic purpose of a thread like this would be achievable if new arrivals at the forum would read it (or a few posts containing a condensed version) before posting and would get free of some common misconceptions about the standard cosmology model. The standard should be like a home base point of reference. If you are going to explore alternatives at least first understand the common home ground from which you consciously deviate... We don't know whether universe is spatial finite or infinite but the balloon analogy is a good teacher in either case. Infinite means think of a much bigger balloon. Or of zooming in so close that the balloon you have looks flat, as it would to a very tiny observer. All the analogy is supposed to be is an approximation to help with visualizing, so the balloon's finiteness shouldn't be a problem... .
I am familiar with the LCDM model (standard model?), having made a 4-part summary of it on another forum. I must disagree with the second paragraph above. If the universe is infinite, then the balloon analogy fails, because then (as I see it) all points in the universe would not be equal to each other like the surface of a balloon, in fact it would be flat. The philosophical differences are huge.

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