Penrose: WMAP Shows Evidence of ‘Activity’ Before Big Bang

[Chalnoth]

Very good. A clear indication that these plots are not convincing by itself, or at least that the 6-sigma claim came from wrong assumptions. However Gurzadyan and Penrose added a much more interesting claim.

Too bad there's so little flesh on the bones. Would you say this is true as well in your random realization of the CMB?

Well, I didn't explicitly look for low-variance circles. I just looked for low-temperature spots, and made plots like they made around them, then grabbed one that looked interesting.

But I don't think their analysis actually determines whether they are concentric or not. They just looked at a bunch of different centers and picked ones that looked interesting (presumably with some sort of search algorithm for finding interesting ones). It was, in other words, the same analysis I did on the simulated map (though I did limit mine to a mere 10 spots with low temperature centers).

 

[Lievo]

I don't think their analysis actually determines whether they are concentric or not.

I don't think either, but wouldn't be the smart move to do?

I did limit mine to a mere 10 spots with low temperature centers

Sure, they need to show more before one spend weeks on that. However, did your quick look reveals that any of these 10 plots that includes 1 maybe-concentric-thing also includes several?

You know, I see why one may expect to see something like that even in random reconstruction, but I don't see why one should expect to always see several when there is at least one. Or do you see a reason?

 

[Chalnoth]

I don't think either, but wouldn't be the smart move to do?

Sure, they need to show more before one spend weeks on that. However, did your quick look reveals that any of these 10 plots that includes 1 maybe-concentric-thing also includes several?

You know, I see why one may expect to see something like that even in random reconstruction, but I don't see why one should expect to always see several when there is at least one. Or do you see a reason?

Don't really see a reason, no.

Basically, I think it just comes down to the physics of the CMB. The most simple model for the CMB is that you have a bunch of waves on the sky, and each wave draws its amplitude from a random Gaussian distribution that only depends upon the wavelength.

In mathematical terms, it's the statement that:

P(a_{\ell m}) \propto e^{-a_{\ell m}a^*_{\ell m} \over 2C_\ell}So here's the question: if I have a random distribution where the variables are independent in harmonic space, what does that mean for real space?

Well, as long as C_\ell is non-constant, the real space distribution will also be Gaussian, but highly correlated. The covariance matrix becomes:

\sum_\ell {2\ell + 1 \over 4\pi} C_\ell P_\ell(\cos \theta_{ij})

Here P_\ell(\cos \theta) are the Legendre polynomials. I'm not sure it would be useful to go into detail about what these are, but the most important consideration is this: the entire covariance matrix is just a function of \theta_{ij}. What is this parameter?

This is the angle across the sky between pixel i and pixel j.

This means that different pixels on the sky are very highly correlated, and they are correlated by an amount that depends upon the angle of separation between them. Fundamentally this means that when you're binning up the pixels on the sky, the number of degrees of freedom is much smaller than the number of pixels in the bins. So with fewer random variables to average things out, you expect much larger variations from the expectation based just upon the number of pixels and assuming those pixels are independent.

Furthermore, by looking specifically at circles on the sky, which are a constant angle from some central point, you're exacerbating the visibility of any effect here because all pixels in each ring will have the same amount of correlation with the central pixel.

 

[Lievo]

Chalnoth, this is a very clear explanation of why the reported features could be by chance. But of course proving that there is truly nothing requieres some statistical testing. I was thinking at one test one could do (or that the authors could have done...), I wonder if you agree with the idea.

Suppose you count the number of 'concentric' features (min-max higher than, maybe, 10^-5K), automatically for each point of both real and randomly reconstructed CMB. Then you could plot the distribution of the points exhibiting more than 1, 2, ... n waves. If it's true that there is no anormality in the number of 'concentric' feature at some points in the CMB, then you could prove it by showing that real and sham distribution are the same even when considering the points with several 'concentric' features. What do you think?

 

[Chalnoth]

Chalnoth, this is a very clear explanation of why the reported features could be by chance. But of course proving that there is truly nothing requieres some statistical testing.

Yes, absolutely. I just don't see much of any reason to do that. His theoretical justification for this sort of feature is flimsy at best, and the default assumption is just that it isn't there. If he really believes it, let him do the work. I spent one morning on it, not really willing to spend much more.

The real difficulty here that mucks things up tremendously is instrument noise. Basically, it is currently impossible on most machines to store the instrumental noise covariance matrix for the whole sky at the resolutions of interest (these are nside=512 maps, where the instrument noise covariance stored in single precision would be 36 Terabytes).

It may be possible to compute and store only the instrument noise covariance for the patch of interest, but that would require some mapmaking, and mapmaking is not my strong suit.

Without pursuing the full noise covariance matrix in addition to the CMB covariance, we will never know for sure whether any deviation we do detect from normal CMB behavior (if any) is actually just instrument noise or some real deviation.

There's also the additional problem of the foreground signals, which will contaminate things and nobody knows how to simulate properly.

These are relatively small details, mind you, but they would all have to be taken into account to ensure that what deviations are seen (which there probably would be some) are real.

 

[Lievo]

If he really believes it, let him do the work.

Sure

The real difficulty here that mucks things up tremendously is instrument noise.

Oh? So it's not true, as they suggest, that finding the same features in both the maps of WMAP and of BOOMERanG’s excludes that instrumental noise can account for the result?

 

[Chalnoth]

Oh? So it's not true, as they suggest, that finding the same features in both the maps of WMAP and of BOOMERanG’s excludes that instrumental noise can account for the result?

Well, it does show that the general shape isn't due to the instrument noise. The difficulty is that when you want to talk about the statistical significance of the result, you have to look at things much more carefully than just considering the general shape. I fully expect the instrument noise to be a very subdominant effect here, but nevertheless necessary to get the right answer for the statistical significance of the effect. Same with foregrounds (but in that case, looking at another instrument doesn't help you much).

 

[Lievo]

Well here I would respectfully disagree. It's an extraordinary claim in need for a clear cut result. So to me the exact sigma doesn't matter to much: 6-10 sigma would be good enough, 2-4 won't. To me the present result is questionnable not because the sigma could be slightly different, but because it could be completely different, and we don't have enough information to assess it except by redoing the job they should have shown.

Anyway, thank you for your insights.

 

[twofish-quant]

Chalnoth, this is a very clear explanation of why the reported features could be by chance. But of course proving that there is truly nothing requieres some statistical testing. I was thinking at one test one could do (or that the authors could have done...), I wonder if you agree with the idea.

Statistical testing is something has a lot of gotchas.

If it's true that there is no anormality in the number of 'concentric' feature at some points in the CMB, then you could prove it by showing that real and sham distribution are the same even when considering the points with several 'concentric' features. What do you think?

Part of the hard part of statistics is to decide when something is the "same" or not. It's much more difficult than it first appears. There's also a problem in that there is a huge difference in looking at the probability of an anomaly in a specific place rather than an anomaly *somewhere*. The odds that you will find an anomaly somewhere is considerably higher than finding an anomaly at a specific location.

 

[twofish-quant]

Oh? So it's not true, as they suggest, that finding the same features in both the maps of WMAP and of BOOMERanG’s excludes that instrumental noise can account for the result?

Also you have to realize that you have the same sort of detectors so you could have the same sort of instrumental noise.

 

[Coin]

It seems like a problem unto itself that Penrose has stated his claim so vaguely that someone trying to refute it has to start by trying to guess at what he was even trying to say :|

 

[Lievo]

proving that there is truly nothing requieres some statistical testing.

Here it is.

http://arxiv.org/PS_cache/arxiv/pdf/1012/1012.1268v1.pdf
http://arxiv.org/PS_cache/arxiv/pdf/1012/1012.1305v1.pdf

 

[Chalnoth]

Here it is.

http://arxiv.org/PS_cache/arxiv/pdf/1012/1012.1268v1.pdf
http://arxiv.org/PS_cache/arxiv/pdf/1012/1012.1305v1.pdf

Haha, two papers on the same day, I am amused :)

I know some of the guys in these papers. Really great guys on this sort of thing.

 

[Lievo]

Haha, two papers on the same day, I am amused :)

Birthday unparadox