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

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

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 Quote by mintparasol I'll have to go and have a study up on this, it's totally counter-intuitive. I don't understand how red shift is possible within this model. It seems that within this model that light speeds greater than c are directly proportional to the distance from source and my understanding of red shift as a measure of age and distance (probably wrong, I'm just a lay-nut) is that wavelengths stretch over distance because of increasing recession with distance, not despite it. Anyway I'll go look at the animation and see if it clicks with me..
One of the first things you learn in an introductory cosmo class is not to think of the redshift as a doppler effect. It is not the result of some particular speed.
The formula involves the entire factor by which distances have been expanded during the whole time the light has been traveling.

roughly speaking

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

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

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

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

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

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

Just another instance of pop-sci media damage that we are constantly having to recover from.

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

I'm not being deliberately difficult, I should probably stick to doing sound for bands :lol:

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

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

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

 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..

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 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.)

 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..

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