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


by marcus
Tags: analogy, balloon, effort
marcus
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Feb27-09, 12:35 PM
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Quote Quote by v2kkim View Post
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".
Chronos
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Feb28-09, 01:36 AM
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I politely disagree, marcus, most astronomers perceive redshift as a doppler effect,
v2kkim
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Feb28-09, 02:17 AM
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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
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Mar1-09, 02:57 AM
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Proper motion is insignificant in cosmological [ie, not in our galaxy] spectral studies.
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Mar1-09, 02:59 AM
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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
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Mar1-09, 10:01 AM
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Regarding the distance advanced by light in expanding universe , I did some calculation to get the result:

[tex]
D(T)\ = {c \over r} (\left( 1 + {r*dt} \right)^{T \over dt} -1)
[/tex]

Taking the limit dt going to 0,
[tex]
D(T)\ = {c \over r} (e^{rT} -1)
[/tex]
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
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Mar1-09, 04:33 PM
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Quote Quote by v2kkim View Post
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.

Quote Quote by v2kkim View Post
Regarding the distance advanced by light in expanding universe , I did some calculation to get the result:

[tex]
D(T)\ = {c \over r} (\left( 1 + {r*dt} \right)^{T \over dt} -1)
[/tex]

Taking the limit dt going to 0,
[tex]
D(T)\ = {c \over r} (e^{rT} -1)
[/tex]
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
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Mar3-09, 08:19 AM
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Quote Quote by marcus View Post

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..
Ich
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Mar3-09, 09:48 AM
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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 Quote by mintparasol View Post
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

[tex]1+z = \sqrt{\frac{1+\beta}{1-\beta}}[/tex]

The correct Doppler formula for light in special relativity. We would not use the formula appropriate for sound from moving source in still air, which by coincidence looks like the correct one for redshift if you interpret the scalefactor a(t) as distance between source and receiver.
When I think Doppler, I think the formula I wrote for you there.
It goes crazy when recession rates equal or exceed the speed of light. The Doppler formula (which is correct for actual motion) is completely different and completely wrong for redshift. (Only works as approx for nearby slow receding things.)
mintparasol
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Mar4-09, 06:40 AM
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Quote Quote by marcus View Post
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

[tex]1+z = \sqrt{\frac{1+\beta}{1-\beta}}[/tex]

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

Ok, well, the way I see it, the balloon analogy can be easily demonstrated in one dimension by marking a number line on a piece of elastic and stretching it. If we factor in time, we now have two dimensions and if we factor in two more spatial dimensions, we now have the four dimensional spacetime that we are all experiencing. The mathematics may become more complicated as we add more dimensions but it isn't any more difficult to visualise. Of course the maths need to be integrated for the expansion of the universe over time but this doesn't make the phenomenon more difficult to visualise, even for the lay person. To me, redshift is a phenomenon that is so analogous to the Doppler effect in sound waves that it can be called the Doppler effect when it occurs in light reaching us from distant parts of the universe. If the expansion history of the universe hasn't been uniform, isn't that what physicists all over the world are being paid to figure out? It doesn't change the nature of the basic phenomenon..
Ich
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Mar4-09, 09:39 AM
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Ich! I am glad to see you. My memory is unreliable but I have the notion (perhaps wrong) that you live somewhere in south Germany and know a fair bit of mathematics. I am glad that you sometimes glance at this thread. Thanks for any and all help!
Thanks for the nice welcome. Your memory seems quite reliable - except for the mathematics, which is not exactly my strong point. It's just enough to survive as a physicist.
Thanks also for this thread; it made me curious about what the dynamics on the balloon surface actually would be. I always felt uncomfortable about things being stuck on the surface and expanded by brute force, as this picture is not compatible with relativity.
This exercise helped my understanding of cosmology a lot. I will soon write more about some basic cosmological FAQs, maybe it is helpful for some of you as well.
Ike47
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#103
Mar26-09, 04:56 PM
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I just found this forum this morning, eventually got enough nerve to post a new thread in the relativity section, then came here when I saw this subforum because of questions I've long had about space, the universe, and cosmology. I've spent the last 4 or 5 hours reading this thread, with occasional breaks to read responses to my post in the relativity section, and to respond to them.

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

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

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

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

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

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

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

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

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

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

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

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

I apologize for being so verbose, but if I could get responses to my two questions, I think I'd be much more comfortable with my ability to conceptualize the universe than I have been in many years.
TalonD
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Mar26-09, 06:08 PM
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Ike, welcome. It's nice to see someone who reminds me of myself. Intelligent enough to get a grasp of this stuff but not a mathmetician or physicist, but with a keen interest in the subject.

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

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

Marcus is a good one to make much more educated comments on all this!
marcus
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Jun10-09, 03:19 PM
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I want this stuff on the sticky because I will need to refer to it. Numbers to have handy.

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

Sylas supplied the link to the Riess et al 2009 paper with the new Hubble rate.
http://physicsforums.com/showthread....28#post2231728

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

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

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

Near flatness then makes the dark energy fraction 0.75.

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

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

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

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

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

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

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

And it also tells you the distance to the CMB material was when it released the light, that is the angular size distance which the calculator says is 41.4 million lightyears. Again that is an actual or proper distance (the kind astronomers typically use) but referred to back when the light was emitted. The material was much closer then. 41.4 million and 45.2 billion should be about in the ratio 1090, the factor by which actual distances expanded while the light was in transit.



Oh, there is the Hubble distance c/H. By definition this is the actual presentday distance which is currently increasing at exactly rate c. You calculate it by putting "c/(74 km/s per megaparsec) in lightyears" into google. Google immediately tells you it is 13.2 billion lightyears.
What redshift does that correspond to?
Wright calculator tells you z = 1.4. Try putting that 1.4 into the calculator, primed with the new threesome, and you will get 13.2.
So the galaxies that come in with redshift 1.4 are the ones where the distance to them is increasing at rate c.
StandardsGuy
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Jun13-09, 11:27 PM
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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?
marcus
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Jun13-09, 11:41 PM
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Quote Quote by StandardsGuy View Post
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.
StandardsGuy
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Jun13-09, 11:52 PM
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Quote Quote by marcus View Post
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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