Is this a misleading representation of boomerang results

[jerusalem]

hi,
is it misleading to write omega = 1.0000... for the ideally flat space?

 

[marcus]

I like the illustration. It communicates a lot graphically without too much possible misinterpretation.

A picture can never tell the whole story and needs words to make sure the viewer gets the right message, but for a picture without words this does a good job, I think.

Nowadays the 2010 confidence interval for Omega is different:

0.9916 < Omega < 1.0133

So you see by modern 2010 standards the Boomerang confidence interval is WRONG.
But that is what they got, say in 1998 using Balloons in Antarctica. Now we have spacecraft in their own orbits around the sun a million miles farther out from the sun than the Earth is. Of course we have better results than Boomerang. But it was an honorable well-executed attempt. And it is an excellent picture to communicate the idea.

 

[marcus]

The neat thing is that we know the actual sizes of those fluctuations, at least as a statistical distribution, how many of each various size. And we know how far away they were when they emitted the glow that we now see. So we can estimate what ANGULAR SIZES they should have, at least as a statistical distribution, which will depend on whether space is positive curved or zero or negative.

In a positive curved space the hot-cold fluctuation patches will look BIGGER, in angular size. Like looking thru a magnifying glass. Or looking at the patch of stars behind the sun, which appears spread out because of the "gravitational lens" effect of the sun's gravity curving the rays in towards us the viewers. Making parallel rays bend in and converge.

I've seen this graphic before but I don't have a link to it. Could you give us the link? I'd like to have it handy as an illustration.

Also I have a personal reason. I think that the importance of Andrew Lange's contribution to cosmology has not been fully appreciated. He was one of the main people in charge of BOOMERANG. The concept and instrumentation were elegant. The data was surprisingly high resolution for the time (1998).

 

[cepheid]

I don't think that the OP is questioning the veracity of the result from the BOOMERANG data (in the top panel).

It seems like the OP is asking if the Ω = 1.00000000.. statement in the lower left panel is misleading. My answer would be no, and I wonder why you think it might be. Ω is supposed to be exactly 1 for the flat case, given that you are talking the total density parameter.

 

[cepheid]

Hey marcus,

Found this on the BOOMERANG website:

http://cmb.phys.cwru.edu/boomerang/press_images/raw_images/model_maps.jpg

I never met Andrew Lange, but I felt the effects of his passing through the impact it had on colleagues, and through the vacuum it left behind in leadership and direction for a time.

 

[marcus]

Thanks!

I started a little CMB-observation history thread (Boomerang to WMAP, or could be to Planck) a while back. Anyone who knows any details of the history, of any sort, feel welcome to add. I will put your link on that thread.

 

[Chalnoth]

So you see by modern 2010 standards the Boomerang confidence interval is WRONG.

I wouldn't say that. The Boomerang confidence interval was fully consistent with the current value today. We can just do better today, with many other observations.

 

[marcus]

I wouldn't say that. The Boomerang confidence interval was fully consistent with the current value today. We can just do better today, with many other observations.

I'm glad you know what the interval was. Could you give a link and say what it was? This would save me having to dig it up.

The graphic which Jerusalem gave us says their estimate was [1.01, 1.13].

Is that right? Did Boomerang actually say [1.01, 1.13]?

Is that what you mean by fully consistent with the current value today, which I'm taking from WMAP7 to be [0.9916, 1.0133]?

 

[jerusalem]

I don't think that the OP is questioning the veracity of the result from the BOOMERANG data (in the top panel).

It seems like the OP is asking if the Ω = 1.00000000.. statement in the lower left panel is misleading. My answer would be no, and I wonder why you think it might be. Ω is supposed to be exactly 1 for the flat case, given that you are talking the total density parameter.

thank you cepheid,

quote: "I wonder why you think it might be"

I had an argument with some one who claimed that Ω = 1.000000.. gives a false impression about the precision of the instruments. I need to convince him that the statement in the lower left panel has nothing to do with the results of the experiment. it just states that Ω is supposed to be exactly 1 for the ideally flat space.

I'm glad you know what the interval was. Could you give a link and say what it was? This would save me having to dig it up.

The graphic which Jerusalem gave us says their estimate was [1.01, 1.13].

Is that right? Did Boomerang actually say [1.01, 1.13]?

Is that what you mean by fully consistent with the current value today, which I'm taking from WMAP7 to be [0.9916, 1.0133]?

check this marcus arxiv.org/pdf/astro-ph/0011469v1.pdf ,, Ω = (1.07 ± 0.06)

no doubt that WMAP confidence interval is far better than boomerang confidence interval.

but my question was about the lower left panel, I wrote Ω = exactly 1 with no margin of error, since it doesn't represent the result of the experiment.

 

[marcus]

...I need to convince him that the statement in the lower left panel has nothing to do with the results of the experiment. it just states that Ω is supposed to be exactly 1 for the ideally flat space.
...

You are quite right AFAICS. The aim of the graphic panel is to illustrate the ideally flat case where Omega is exactly 1.
At no time did I get any other impression, such as that you were saying something about the precision of the instruments.

The other person's objection does not seem reasonable or appropriate to me. I hope he can be convinced to see it in a better light.
=====================

But just as a stylistic matter you could change it to read Omega = 1
That can logically be taken to read "Omega = 1 exactly"

It communicates the essential point and it is cleaner than saying
"Omega = 1.0000000..."

When you first presented it, I did not realize that YOU had superimposed the equations on top of the Boomerang graphics. Now something you said makes me think you did, so you have control. I wonder what you are trying to get across to your audience by putting on all the zeros. Could it be communicated just as well by saying "Omega = 1 exactly"?

 

[jerusalem]

we were arguing about what Dr.Michio Kaku said here:

The inflation was so enormous, in fact, that the balloon seems flat in our vicinity, a fact that has been experimentally verified by the WMAP satellite. In the same way that the Earth appears flat to us because we are so small compared to the radius of Earth, the universe appears flat only because it is curved on a much larger scale.
books.google.ca/books?id=6rCw34JCLnsC&pg=PA13#v=onepage&q&f=false

Dr. Tom Murphy :

The universe looks pretty flat: it doesn’t deviate by more than 2% from being flat. But, the possibility exists that the universe is still curved on much larger scales. It’s just like the fact that the Earth looks flat locally, over small scales, but is curved on the whole. The universe could be closed into a sphere, but on a much larger scale than what we can see.
physics.ucsd.edu/~tmurphy/phys10/universe.pdf

ie: we should not rule out the possibility of a closed universe in a larger scale.
since we only mesure the observable universe:

So when we say "WMAP provides strong evidence that the universe is flat", we really mean "WMAP provides strong evidence that the observable universe is flat".
curious.astro.cornell.edu/question.php?number=171

 

[marcus]

Thanks for the clarification! I happen to agree with what you highlight in red.
As I recall from the WMAP5 report, they do not even claim the observable universe is flat. They use words like "nearly flat". The data is consistent (within uncertainty bounds) with the perfectly flat model. And also it is consistent with a overall slightly curved model.

The Cornell "Ask an astronomer" site is primarily for pre-college young people, I think. Some of the language is oversimplified or not carefully enough qualified, so you have to be cautious about taking it literally sometimes. What you quoted is a case of that:

So when we say "WMAP provides strong evidence that the universe is flat", we really mean "WMAP provides strong evidence that the observable universe is flat".
curious.astro.cornell.edu/question.php?number=171​

WMAP does NOT provide strong evidence that the observable universe is EXACTLY flat.
It provides wonderfully strong evidence that Omega is in the range
0.9916 < Omega < 1.0133 (talking about the universe as a whole, assuming uniformity)

And what that translates to, in the picture of a very large balloon that looks flat to creatures living on it, is that if the curvature is at the upper limit you have a circumference of 750 billion light years (again the universe as a whole.)

That is one way of gauging the "near flatness". When you say "nearly" you suppose some way of quantifying curvedness. Most people don't grok Omega. It doesn't do anything for them to say "within one percent of unity". So you can translate that into the large balloon picture and say that the most distant matter is AT LEAST 375 billion LY away (half the circumference).

The radius of the portion we can now observe is some 45 billion LY. So the whole balloon is AT LEAST ten times bigger than what we can see---in the vague way that 375 is bigger than 45. The most distant stuff is an order of magnitude (factor of 10) farther than the most distant stuff we can see.

Or you could talk in terms of the "RADIUS OF CURVATURE" of the local patch of universe we currently see. It is one way a mathematician might quantify curvedness. Divide the circumference of 750 by 2 pi. Is that about 120?

I think I'm just repeating, but maybe that doesn't hurt. We don't have, in our common everyday language, good ways to talk about degrees of curvedness. But to give an honest account of what is known (WMAP and also BAO and SN data) we have to have a way. We can't just say "flat" and give the listener the idea of EXACTLY flat. We have to say nearly, and that supposed a concept of amount of flatness or curvedness.

If you like the idea of a "radius of curvature" then 2010 WMAP report says that RoC of the patch of universe we can see is, with 95% confidence, at least 120 billion LY

that is the radius of the fitting hypersphere, if the observable patch were laid on the 3D "surface" of a fitting 4D hypersphere.

 

[Chalnoth]

I'm glad you know what the interval was. Could you give a link and say what it was? This would save me having to dig it up.

The graphic which Jerusalem gave us says their estimate was [1.01, 1.13].

Is that right? Did Boomerang actually say [1.01, 1.13]?

Is that what you mean by fully consistent with the current value today, which I'm taking from WMAP7 to be [0.9916, 1.0133]?

Actually, I don't remember the specific parameters off the top of my head. I was, in part, going by the numbers posted earlier in this thread. I know, however, that no experiment to date has detected a statistically-significant deviation of spatial curvature from zero.

If you're curious, though, here is their paper on cosmological paramters for their latest flight (2003):
http://arxiv.org/pdf/astro-ph/0507503v1.pdf

There are multiple ways to combine the data, but the curvature always deviates from zero at less than two standard deviations.

 

[Chronos]

As I recall, boomerang allowed a generous range for omega - ranging from about 0.8 to 1.3. The 1.01+ thing was merely a best guesstimate.

 

[Chalnoth]

As I recall, boomerang allowed a generous range for omega - ranging from about 0.8 to 1.3. The 1.01+ thing was merely a best guesstimate.

Well, you generally don't get a very tight range using only CMB data. But combine Boomerang with other data and the constraints close to a couple percent (as shown in the paper I linked above).

Still that's rather old. We have better data today. Boomerang was just one experiment among a great many.

 

[cepheid]

As I recall, boomerang allowed a generous range for omega - ranging from about 0.8 to 1.3. The 1.01+ thing was merely a best guesstimate.

I don't think that is the case. I'm pretty sure that the constraints are somewhat tighter than that. As described here:

http://arxiv.org/abs/astro-ph/0104460

and in the paper they reference by Lange, 2001, they do a likelihood analysis, and the best estimate of the parameter is obtained from the peak of the likelihood function, with the uncertainties obtained by integrating over this function out to the 1-sigma limits. Maybe this is what you meant by best guesstimate, I don't know. They have values reported in table 5 such as 1.02 +/- 0.06, or 0.98 +0.04, -0.05, depending on their choice of prior.

 

[jerusalem]

I don't think that is the case. I'm pretty sure that the constraints are somewhat tighter than that. As described here:

arxiv.org/abs/astro-ph/0104460

and in the paper they reference by Lange, 2001, they do a likelihood analysis, and the best estimate of the parameter is obtained from the peak of the likelihood function, with the uncertainties obtained by integrating over this function out to the 1-sigma limits. Maybe this is what you meant by best guesstimate, I don't know. They have values reported in table 5 such as 1.02 +/- 0.06, or 0.98 +0.04, -0.05, depending on their choice of prior.

is there a degree of precision, if reached, we can say for sure that we are living in an infinite euclidean space?

WMAP does NOT provide strong evidence that the observable universe is EXACTLY flat.
It provides wonderfully strong evidence that Omega is in the range
0.9916 < Omega < 1.0133 (talking about the universe as a whole, assuming uniformity)

And what that translates to, in the picture of a very large balloon that looks flat to creatures living on it

well my interlocutor refused this possibility and claimed that (boomerang and wmap..) measure the shape of the ENTIRE universe because the photon we detect started its journey since the beginning (380000 after BB). Did you ever heard such interpretation ? In my opinion this make sense only if the speed of light is greater than the expansion of the universe.

 

[Chalnoth]

is there a degree of precision, if reached, we can say for sure that we are living in an infinite euclidean space?

No. That would require infinite measurement accuracy, which is impossible (not just because building an infinitely-accurate measurement is impossible, but also because we can only see a fraction of the whole universe).

well my interlocutor refused this possibility and claimed that (boomerang and wmap..) measure the shape of the ENTIRE universe because the photon we detect started its journey since the beginning (380000 after BB). Did you ever heard such interpretation ? In my opinion this make sense only if the speed of light is greater than the expansion of the universe.

No, they only measure the shape of the visible portion of it. Extrapolating beyond the region which is visible to us is highly model-dependent.

 

[jerusalem]

Thank you guys for your replies

 

[Ibrahim64]

Hello
I was in discussion with Mr jerusalem about the universe did not require energy to form. I used Boomrang experiment since its results are freely available and can show the scientific result. I presented paper: http://arxiv.org/pdf/astro-ph/0011469v1.pdf, which shows that the results and made an estimate of Ω.
The experiment showed that the flat universe is in the confidence interval and I said that since the flat universe is in intersection between Boomrang experiment and Adams' Rees SN1a Measurement, then this experiment corroborate the hypotheses that the universe is flat. I told Mr jerusalem that, $Ω= 1$ is not real, but is a valid classical approximation because
paper: "the size and shape of the universe: The quest for the curvature of space" states that:$\frac{C^2}{R^2}=H^2(Ω-1)$
and a theory involves Quantum mechanics and general theory of relativity will remove the singularity at the begging of the universe and the infinite size of the universe.
The problem is:
1. Is it valid to take middle of the range? or if there is a theory predict a value we say that the experiment corroborate the hypotheses?
2. Is it valid to place 8 zeroes with experiment result that never claimed more than %15 accuracy...
These discussion has been for a while, Mr jerusalem tries to discredit me by making all of these misrepresentation of my actual saying. As you can see in the figure attached, Mr jerusalem took the value in middle and put it the actual result.
The figure under discussion was:

is this valid representation of Boomrang result or WMAP result?
Regards
Dr Ibrahim

 

[Ibrahim64]

I would like to mention the location of the discussion:

Regards

[edit]Link to non-English material removed by Mentor.[/edit]

 

[Ibrahim64]

is there a degree of precision, if reached, we can say for sure that we are living in an infinite euclidean space?

well my interlocutor refused this possibility and claimed that (boomerang and wmap..) measure the shape of the ENTIRE universe because the photon we detect started its journey since the beginning (380000 after BB). Did you ever heard such interpretation ? In my opinion this make sense only if the speed of light is greater than the expansion of the universe.

Another misrepresentation of my saying:
1. I said that if the universe is flat from 380,000 till now, that the total energy of the universe is zero.
2. I mentioned that R for the entire universe is estimated to be around 90 billion Light year, and so, if we have a theory that incorporate quantum mechanics and general relativity then this will make the universe have a finite size.
The talk was about the total energy of universe at the beginning and now, and boomrang experiment corroborated the hypotheses that the universe is made out of nothing...
Regards
Ibrahim

 

[el-fayoumi]

hello Mr ibrahim , some ppl who are following this topic understand well Arabic and know well what you said.
you have been asked: "can we say for sure and certain that the entire universe is flat or its only nearly flat locally?"
your answer was: "In fact the entire universe is flat, Radiation comes back since the beginning of the universe".
That's WRONG ! and I don't know how the age of the photon proved to you that wmap detected the shape of the entire universe?

Another misrepresentation of my saying:
1. I said that if the universe is flat from 380,000 till now, that the total energy of the universe is zero.
2. I mentioned that R for the entire universe is estimated to be around 90 billion Light year, and so, if we have a theory that incorporate quantum mechanics and general relativity then this will make the universe have a finite size.
The talk was about the total energy of universe at the beginning and now, and boomrang experiment corroborated the hypotheses that the universe is made out of nothing...

it wasn't a misrepresentation of your saying, the question was: " is there a degree of precision, if reached, we can say for sure that we are living in an infinite euclidean space? " the answer is NO. this refute your original claim that the results prove that the entire universe is flat. and again I know that you changed your mind later thanks to the debate. but remember you were talking about null hypothesis. choosing one of several possibilities is not "null hypothesis".

best regards,

 

[George Jones]

I would like to mention the location of the discussion:

Regards

[edit]Link to non-English material removed by Mentor.[/edit]

I have removed your link to non-English material. Physics Forums is a moderated set of forums, and, consequently, material has to be in a language that Mentors understand.

Physics Forums Rules,

https://www.physicsforums.com/showthread.php?t=414380,

to which everyone agrees when they register, in part, state

All posts must be in English. Posts in other languages will be deleted.

 

[halifax12]

Hello
I was in discussion with Mr jerusalem about the universe did not require energy to form. I used Boomrang experiment since its results are freely available and can show the scientific result.

the result of wmap is also freely available.

$Ω= 1$ is not real

I guess an ideally flat universe must be infinite.

The problem is:
1. Is it valid to take middle of the range? or if there is a theory predict a value we say that the experiment corroborate the hypotheses?

theories can predict, but the experiments have the last word.

2. Is it valid to place 8 zeroes with experiment result that never claimed more than %15 accuracy...

I guess cepheid answered this question, you have 4 panels and you can place these zeroes in the lower left panel for an ideally flat universe that has nothing to do with the experiment result in the first panel.

The figure under discussion was:

what I understand from this drawing that there is a difference between a nearly flat universe and an ideally flat one. in a debate what count is the idea you are trying to prove, you don't have to draw a perfect picture for a slightly positive curve. you just can't draw the real universe in a debate, and you don't have to measure the spots to get the idea.

is this valid representation of Boomrang result or WMAP result?

well that's mean that Boomrang result is around 1.07 so its must be sometuing like Ω = 1.07 ± ε

 

[Ibrahim64]

hello Mr ibrahim , some ppl who are following this topic understand well Arabic and know well what you said.
you have been asked: "can we say for sure and certain that the entire universe is flat or its only nearly flat locally?"
your answer was: "In fact the entire universe is flat, Radiation comes back since the beginning of the universe".
That's WRONG ! and I don't know how the age of the photon proved to you that wmap detected the shape of the entire universe?

it wasn't a misrepresentation of your saying, the question was: " is there a degree of precision, if reached, we can say for sure that we are living in an infinite euclidean space? " the answer is NO. this refute your original claim that the results prove that the entire universe is flat. and again I know that you changed your mind later thanks to the debate. but remember you were talking about null hypothesis. choosing one of several possibilities is not "null hypothesis".

best regards,

It is very strange you using my surname, and only have only one post...
I said that, as a classical approximation, then $\Omega \approx 1$, and it is known that with a theory that take quantum and general relativity together, will solve the infinite value of the universe.
my understanding that, you claim that, this figure:

is a faithful representation of figure:

The images, are explained at: http://www.uAlberta.ca/~pogosyan/teaching/ASTRO_122/lect31/lecture31.html
the point of these images is that the spot, as far as the experiment can do, shows that the actual size of the spot is around 1 deg, which what you expect in a flat universe. This does not claim that the universe is ideally Euclidean, with $\Omega = 1$, integer 1, but that the universe began with $\Omega = 1$, and since it started with critical value, it remains very close to it.
The claim that we live in an infinite Euclidean space, was never done by me, I used it as a classical approximation...
I would like to also, clarify that, I did not say the whole universe is flat, when Abdel wahed (jerusalem ) sent me an email and ask, do you agree that the universe is "locally" flat, I told him, that I do not agree that it is locally flat, the radiation came from the beginning of the big bang and is a representation of the flatness of the visible universe. And also, I mentioned to him many times, beyond the visible universe, we have no way of finding so there is no need to talk about it... local mean solar system or galaxy i never thought he means visible universe...

Strange, you have the same surname as mine, do you mind if I ask when did you join?
Regards

 

[Ibrahim64]

the result of wmap is also freely available.

I guess an ideally flat universe must be infinite.

Hello
Yes, but we cannot be certain that our universe is ideally flat or curved, the inflationary universe, predicts that the $\Omega$ should be very close to the critical value of 1, but if the universe began with flat universe, it should remains so...

the result of wmap is also freely available.
theories can predict, but the experiments have the last word.

I quite agree, experiment can corroborate your hypotheses or falsify it...

the result of wmap is also freely available.
I guess cepheid answered this question, you have 4 panels and you can place these zeroes in the lower left panel for an ideally flat universe that has nothing to do with the experiment result in the first panel.

Ok, the point of this figure was that, the actual angle of the spots are around 1 deg...
http://img823.imageshack.us/img823/8872/spotsn.png
so the experimental results agrees with a flat universe, or very close to it, and cannot distinguish from flat universe...
To explain: http://www.uAlberta.ca/~pogosyan/teaching/ASTRO_122/lect31/lecture31.html

the result of wmap is also freely available.
what I understand from this drawing that there is a difference between a nearly flat universe and an ideally flat one. in a debate what count is the idea you are trying to prove, you don't have to draw a perfect picture for a slightly positive curve. you just can't draw the real universe in a debate, and you don't have to measure the spots to get the idea.

The problem is:
WMAP according to the wiki, used to claim: $\Omega = 1.00 \pm 0.02$ so Mr jerusalem took the value in the middle and placed them in the graph with 8 zeroes for the flat universe, do you think this is proper way? The actual figure never claimed values for different sizes of the spots. Just to show that boomrang results, matches one of flat universe...

the result of wmap is also freely available.
well that's mean that Boomrang result is around 1.07 so its must be sometuing like Ω = 1.07 ± ε

The point I was trying to conceive that, The universe total energy was zero at the beginning and now.. do you agree with that?
Also, I was using paper: http://arxiv.org/pdf/astro-ph/0011469v1.pdf, which states:
http://img717.imageshack.us/img717/2356/boomrang.png
Regards

 

[halifax12]

It is very strange you using my surname, and only have only one post...

don't worry Mr.ibrahim no one will think that you are arguing with yourself or your surname.

I said that, as a classical appropriation, then Ω≈1, and it is known that with a theory that take quantum and general relativity together, will solve the infinite value of the universe.
The claim that we live in an infinite Euclidean space, was never done by me

flat universe means euclidean and by definition is an infinite space.
if its not infinite then its a closed universe.

Yes, but we cannot be certain that our universe is ideally flat or curved, the inflationary universe, predicts that the Ω should be very close to the critical value of 1, but if the universe began with flat universe, it should remains so...

as marcus said:

WMAP does NOT provide strong evidence that the observable universe is EXACTLY flat.
It provides wonderfully strong evidence that Omega is in the range
0.9916 < Omega < 1.0133 (talking about the universe as a whole, assuming uniformity)
And what that translates to, in the picture of a very large balloon that looks flat to creatures living on it

so even if you are close to the critical value you still have the possibility of a closed universe.

my understanding that, you claim that, this figure:

is a faithful representation of figure:

faithful in what sense? none of them is precisely accurate, its just explain the general idea how the spots change. NASA never claimed that you can get the value of Ω by measuring the spots of this cartoon style small figure.

The problem is:
WMAP according to the wiki, used to claim: Ω=1.00±0.02 so Mr jerusalem took the value in the middle and placed them in the graph with 8 zeroes for the flat universe, do you think this is proper way? The actual figure never claimed values for different sizes of the spots. Just to show that boomrang results, matches one of flat universe...

I guess you mean Ω=1.02±0.02 not Ω=1.00±0.02 . any way even if the figure never claimed values for different sizes of the spots, " Ω is supposed to be exactly 1 for the flat case " as Mr. cepheid said.

Also, I was using paper: http://arxiv.org/pdf/astro-ph/0011469v1.pdf, which states:
http://img717.imageshack.us/img717/2356/boomrang.png

the data is also consistent with a slightly curved model.

The data is consistent (within uncertainty bounds) with the perfectly flat model. And also it is consistent with a overall slightly curved model.

...

so the experimental results agrees with a flat universe, or very close to it, and cannot distinguish from flat universe...

if you are talking about the observable universe.

The point I was trying to conceive that, The universe total energy was zero at the begging and now.. do you agree with that?

well I can not say that as a fact, but if the universe total energy is zero, you still need a non-null positive and negative energy in order to have the capacity to perform work.

http://img823.imageshack.us/img823/8872/spotsn.png

if this is your measuring, how you know that you are comparing the same spots?
best regards,

 

[Ibrahim64]

don't worry Mr.ibrahim no one will think that you are arguing
if you are talking about the observable universe.
well I can not say that as a fact, but if the universe total energy is zero, you still need a non-null positive and negative energy in order to have the capacity to perform work.

Hello halifax12
it is just strange, same surname, joined just after I replied, is strange...
I guess that you agree to talk a value in the middle of the experimental result and place it in a figure with another simulated picture that claim that it is accurate to 8 decimal places, I actually find that pretty strange.
There are many papers about forming the universe from quantum bubble...

if this is your measuring, how you know that you are comparing the same spots?
best regards,

The point of this figure was that the area in the spot with the same density cannot make more than one degree, more than that, means that the ends never been in contact (they separated by speed more than the speed of light) and so it does not matter if they are the same spot... I think this figure makes it clear...

This figure is in the same paper I mentioned...
you can see the first peak is at one degree...
This site explains the boomrang result, I recommend you have a look...
http://www.uAlberta.ca/~pogosyan/teaching/ASTRO_122/lect31/lecture31.html
So you think calling Ω=1 as a classical approximation, is not valid? Given that we do not know the actual value, and we do not have a theory that have general relativity and quantum mechanics?
Kind regard

 

[el-fayoumi]

It is very strange you using my surname, and only have only one post...

its my surname !

I would like to also, clarify that, I did not say the whole universe is flat

you said that
you have been asked: "can we say for sure and certain that the entire universe is flat or its only nearly flat locally?"
your answer was: "In fact the entire universe is flat, Radiation comes back since the beginning of the universe".

you changed your mind after your interlocutor posted several quotes from well known Physicists.

 

[Ibrahim64]

its my surname !

you said that
you have been asked: "can we say for sure and certain that the entire universe is flat or its only nearly flat locally?"
your answer was: "In fact the entire universe is flat, Radiation comes back since the beginning of the universe".

you changed your mind after your interlocutor posted several quotes from well known Physicists.

Where did I said that?
I said 'I never agreed that the universe is "locally" flat'...
In fact, it may be flat, but as I explained many many many many many many times to mr jerusalem that beyond the visible universe there is no mean of knowing, it could be that the universe is infinite and flat, we have no way of knowing...
Do you agree with attributing the visible universe as "local"?
Regards

 

[el-fayoumi]

Where did I said that?

noname asked you: "can we say for sure and certain that the entire universe is flat or its only nearly flat locally?"
your answer was: "In fact the entire universe is flat, Radiation comes back since the beginning of the universe".

I said I never agreed that the universe is "locally" flat...
Do you agree with attributing the visible universe as "local"?

you never agreed that the universe is "locally" flat
because you were trying to prove that the universe is "entirely" flat.

 

[Ibrahim64]

man you are weird ! you said it in eltwhed several times!
noname asked you: "can we say for sure and certain that the entire universe is flat or its only nearly flat locally?"
your answer was: "In fact the entire universe is flat, Radiation comes back since the beginning of the universe".

you never agreed that the universe is "locally" flat
because you were trying to prove that the universe is "entirely" flat.

If we can quote what I said (In Arabic), I said there is no way of knowing what after the Hubble horizon. In my post number 4 I mentioned that the observable universe has radius of 90 billion years (estimated) and read in my post number: 17 I told him that Ω cannot be integer 1, because there is no physical constant to be integer. Also, I mentioned to him that I objected to placing 6 zeroes with an experiment that never claimed more than %15 accuracy... and In post 26 I quoted:size and shape of the Universe: the quest for the curvature of space...

http://img864.imageshack.us/img864/4237/paperz.png
What else can I say...
Please watch you language...
Regards

 

[Chalnoth]

If we can quote what I said (In Arabic), I said there is no way of knowing what after the Hubble horizon. In my post number 4 I mentioned that the observable universe has radius of 90 billion years (estimated) and read in my post number: 17 I told him that Ω cannot be integer 1, because there is no physical constant to be integer. Also, I mentioned to him that I objected to placing 6 zeroes with an experiment that never claimed more than %15 accuracy... and In post 26 I quoted:size and shape of the Universe: the quest for the curvature of space...

http://img864.imageshack.us/img864/4237/paperz.png
What else can I say...
Please watch you language...
Regards

The radius is about half that. The diameter is approximately 90 billion light years.

As for why the universe is so flat, well, cosmic inflation drives the universe exponentially close to $\Omega = 1$ in a remarkably short time.

 

[Ibrahim64]

The radius is about half that. The diameter is approximately 90 billion light years.

As for why the universe is so flat, well, cosmic inflation drives the universe exponentially close to $\Omega = 1$ in a remarkably short time.

Thank you for correction, I actually said in the post "Diameter", but from keep repeating and repeating...