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Interpreting the Supernova Data 
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#37
Sep1210, 01:43 AM

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You can attempt to get around this by proposing that the CMB doesn't come from the phase transition in the early universe from a plasma to a gas, but then this presents two problems: 1. Why is the frequency spectrum of the CMB nearly a perfect black body? A large collection of distant stars, for instance, will not produce a black body spectrum. 2. Why is the baryon acoustic oscillation effect visible at all? This effect is a correlation of an angular scale on the CMB with the typical separation between galaxies in the nearby universe. It isn't a trivial correlation, but instead a correlation that relies upon the physics that would have been active when our universe was still a plasma. If you want to get around saying that there was an early hot plasma state, you need to present a new model that predicts both of these effects (as well as others, such as the primordial helium abundance). If you don't, then the Milne cosmology is ruled out to hundreds of standard deviations, not even counting the obvious fact that there is matter in the universe, while the Milne cosmology assumes none. 


#38
Sep1210, 03:14 AM

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You could get really crazy and then reject GR and redshifts altogether, but at that point you've blown away the Milne model in addition to standard cosmologies. If you don't think that redshifts are caused by Hubble flow, that's interesting, but then you are rejecting all of the supernova and CMB data, at which point I don't see how looking at the details are going to be useful. It's generally considered rude to pick and choose what data you think is valid and which ones you think aren't, but the fun thing about this discussion is that even if you cherry pick data, you are going to find it difficult to get anywhere close to the Milne model. 


#39
Sep1210, 03:53 AM

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But this degeneracy isn't perfect, and more recent supernova experiments which have much more data rule out the Milne cosmology rather well. Of course, once you combine them with something like WMAP or BAO, the Milne cosmology becomes so far out of bounds of observation that the whole idea becomes patently absurd. 


#40
Sep1210, 10:25 AM

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The goal here is to find (cdt)^{2}  dx^{2}  dy^{2}  dz^2 in spherical coordinates. We must make the coordinate transformations of [tex] \begin{matrix} z=r cos(\theta)\\ x=r sin(\theta) cos(\phi)\\ y= r sin(\theta) sin(\phi)\\ \\ dz = cos(\theta) dr  r sin(\theta)d(\theta)\\ dx = sin(\theta)cos(\phi)dr + r cos(\theta)sin(\phi)d\theta  rsin(\theta)sin(\phi)d\phi\\ dy = sin(\theta)sin(\phi)dr + r cos(\theta)sin(\phi)d\theta + r sin(\theta)cos(\phi)d\phi \end{matrix} [/tex] I was thinking the calculation of dx^{2}+dy^{2}+dz^{2} was trivial and could be equated to dr^{2}. However, it is not so trivial as that. We have to multiply termbyterm, and combine like terms. [tex]\begin{tabular} {ccccc} \hline term & dz & dx & dy & total \\ \hline dr^2 & cos^2(\theta)& sin^2(\theta)cos^2(\theta) & sin^2(\theta)sin^2(\phi) & dr^2 \\ d\theta^2 & r^2 sin^2(\theta) & r^2 cos^2(\theta)cos^2(\phi) & r^2 cos^2(\theta)sin^2(\phi) & r^2 d\theta^2\\ d\phi^2 & 0 & r^2 sin^2(\theta)sin^2(\phi) & r^2 sin^2(\theta)cos^2(\phi)& r^2 sin^2(\theta)d\phi^2\\ dr d\theta & 2r sin(\theta)cos(\theta) & 2 r sin(\theta)cos(\theta)cos^2(\phi)&2rsin(\theta)cos(\theta)sin^2(\theta) &0 \\ dr d\phi & 0 & 2rsin^2(\theta)sin(\phi)cos(\phi)&2rsin^2(\theta)sin(\phi)cos(\phi) & 0\\ d\theta d\phi & 0 & 2r^2 sin(\theta)cos(\theta)sin(\phi)cos(\phi) & 2 r^2 sin(\theta)cos(\theta)sin(\phi)cos(\phi)&0\\ \hline \end{tabular}[/tex] Hence, the metric for the Milne model in spherical coordinates is [tex]ds^2=(c dt)^2  dr^2  r^2(d\theta^2 +sin^2(\theta)d\phi^2)[/tex] The equation given by the Wikipedia article for the Milne model has a hyperbolic sine function in it, and is clearly not appropriate for empty space or a gravityfree region. 


#41
Sep1210, 11:31 AM

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Yes, it is a pain to get the details right. And yes, the devil is in the details, because the details are hard to get right. The worst details are the ambiguous details; the "not even wrong" variety. For instance, you claim that the Milne model and the standard model handle electron recombination in the same way. Of course they do! However, why is the frequency of the light redshifted? Why is it that this light can still be seen? In the standard model, the the events happened long ago, (the plane of last scattering is no longer happening anywhere in the universe) but the light is just now reaching us. But in the Milne model the redshift is entirely due to the recession velocity of the plane of lastscattering. And the fact that this plane can still be seen is due to timedilation. The events are still happening; the plane of lastscattering is still there, moving away from us at nearly the speed of light. On your other detail, you are asking "Can the Milne model predict the lumpiness." Of course not! We can see it, and perhaps hope to find an explanation for it, but the idea that you could or should predict the lumpiness of the CMBR from a metric is mere conceit. It is analogous to asking a man to "predict" the shape of the mountains and valleys on an unseen planet, using only the Pythagorean theorem. What you can do, though, if you have a map , then you can begin forming real theories. In the case of a planetary map, you can develop theories about tectonic plate motion, volcanic activity, sedimentary action, etc. If you have a map, you can develop a real theory: With WMAP and COBE, for instance, they could see that the light was a thermal spectrum, and then they were able to come up with a phenomenon that caused it. Other than using the idea of redshift, the standard model neither helped nor hindered them in figuring out that the process must be caused by recombination. Jonathan 


#42
Sep1210, 12:13 PM

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Jonathan 


#43
Sep1210, 04:25 PM

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[tex]r \to t \sinh r[/tex] [tex]t \to t \cosh r[/tex] ...and you will have the Milne metric. 


#44
Sep1210, 04:34 PM

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And as for the lumpiness, at the time COBE was launched, there were two major competing theories that predicted its statistical properties: cosmic strings, and inflation. Inflation won out. This was apparent with COBE plus balloon data, but became blatantly and wildly obvious with WMAP. 


#45
Sep1210, 04:35 PM

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#46
Sep1210, 05:21 PM

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The key word is model. You're able to model the CMBR, but you aren't predicting anything, and it you're not explaining anything. You just have an equation that fits the data. 


#47
Sep1210, 05:27 PM

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#48
Sep1210, 06:34 PM

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I don't want to lose the main question of my original post.
So far, noone has given me an answer to the questions of my original post. I hoped I could find someone who knew how to obtain the following data about the supernovae . a) right ascension b) declination c) luminosity distance d) redshift But meanwhile... For instance For instance, in the Milne model, inflation arises very naturally from acceleration. You take a sphere expanding at the speed of light, and perform a Lorentz Transformation around any event after the Big Bang. All you need is collisions or explosions to get the necessary Delta V. If you accelerate toward the center, it will expand the universe. If Milne was correct, and all particles are attracted to the center, then this phenomenon would go on forever, accelerating toward a receding center would make inflation continue forever. 


#49
Sep1210, 06:49 PM

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It is the proper age of particles that are traveling away from you that are going to be aging slower, and the actual distance between particles that are going to be closer together. The metric does not change when the particles are moving away from one another. The Minkowski metric and the Milne metric are the same. You just have to go back to "Relativity, Gravitation, and World Structure" to find out. 


#50
Sep1210, 07:00 PM

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1. Normal matter density. 2. Dark matter density (assumed to be zerotemperature). 3. Cosmological constant value. 4. Scalar spectral index (an inflation parameter). 5. Optical distance to the surface of last scattering. 6. Hubble constant. Some other parameters are also input from other observations, such as the CMB temperature and the Helium fraction. With these parameters, this is the simplest CMB model, and it fits the data very precisely. Of crucial importance is that with any combination of these parameters, a rather specific sort of power spectrum of the CMB is predicted. The parameters themselves change various ways in which this power spectrum can appear, but the overall pattern is set by these parameters alone. The second point is that once you measure these parameters, the prediction is that other experiments will measure the same values for the same parameters, to within the experimental error. And they do. It is true that this simplest CMB model is expected to be a bit wrong. The scalar spectral index, for example, isn't expected to be exactly constant, with the exact behavior depending upon the precise model of inflation (with some inflation models already ruled out by WMAP). Similarly, the dark matter isn't expected to be zerotemperature for many models, but is expected to have some finite, measurable temperature that can, in principle, be measured. The optical distance to the surface of last scattering is also a simplification, as this depends upon precisely how the universe reionized when the stars started turning on. But the point is this: the simplest model is valid to within experimental errors, and these other issues will require extremely precise measurements of the CMB, as well as other measurements, in order to nail them down further. b) Models are explanations. 


#51
Sep1210, 07:02 PM

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#52
Sep1210, 07:16 PM

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#53
Sep1210, 07:21 PM

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These values are typically listed for each supernova when a supernova experiment's results are reported. For instance, here is the SNLS firstyear release: http://xxx.lanl.gov/abs/astroph/0510447 The table including the supernovae is at the end. The redshift of each supernova is measured by careful measurement of its spectrum. The magnitudes of each supernova are also listed, and the relationship to the luminosity distance is described in the paper. Look, you can't just say, "Hey, look, in this model the words I use make it sound sort of like it works like this other model! Therefore they're the same!" This isn't the way science works. You have to dig into the details of the model and see what it actually says, not just look at superficial behavior. 


#54
Sep1210, 07:29 PM

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In the case that you have a model with these six parameters, then I have to admit that is more interesting. 


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