
#1
Sep810, 07:31 AM

PF Gold
P: 706

I have been arguing the case that the universe may be a modified Milne model. Let me ask my questions first.
First, I am asking about graphs and data presented here: http://www.astro.ucla.edu/~wright/sne_cosmology.html Questions 1) The "binned data" appear to be points with constant redshift (yaxis), but with errorbars in the luminosity distance. (xaxis). How many supernovae make up each of the "bins." Better yet, is there a similar graph that simply shows one dot per datapoint? 2) The remaining graphs on the page all refer to [itex]\DELTA D M[/itex]. What is this quantity? 3) I believe this data appear in table 11 here. Is there a copy of this data anywhere in spreadsheet format? 4) Also, what are z, m(max B), s, c, mu? Are these sufficient to find Right Ascension, Declination, Luminosity Distance, and Redshift? Now, if you're curious about the modified Milne model: In the Milne model, all of the universe explodes from a single event. A fixed "point" in space is stationary in only one reference frame. On the other hand, a fixed event can be the center of an expanding sphere in any and every reference frame. The particles in the Milne universe are least dense in the center, and much more dense on the outside. Any observer in the Milne universe will be comoving (but not necessarily colocated) with the center, in his own reference frame. There is some argument that the Milne model can only represent an empty universe. I acknowledge that I have never understood this argument. Milne's own analysis was that there had to be an infinite amount of matter in the causally connected portion of the universe. The density of particles increases towards infinity at the outside edges. The reason I wish to modify the Milne model is to add two or three major events. These events are sudden accelerations of our galaxy or explosions of the matter around our galaxy, while the universe was still very dense, well before our galaxy actually spread out into stars. I found that an analysis of the outliers in the supernova data seemed consistent with this modified Milne Model. 



#2
Sep910, 02:25 AM

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#3
Sep910, 07:00 AM

P: 2,068

No comment on your other questions, but DM refers to Distance Modulus, which is the difference between the apparent and absolute magnitudes.




#4
Sep910, 07:11 AM

PF Gold
P: 706

Interpreting the Supernova Data 



#5
Sep910, 07:36 AM

PF Gold
P: 706

But, the analysis I'm doing so far is for an object undergoing constant acceleration, (or sitting on the ground). To understand this, I gather, you'd have to do a related analysis for an object in freefall. Is your idea of "curvature" a description of the gravitational potential through space? 



#6
Sep910, 07:44 AM

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[tex]G_{\mu\nu} = T_{\mu\nu}[/tex] The right hand side of this equation is all about matter. Specifically, it's a tensor which includes contributions from energy density, momentum density, pressure, and shear of matter fields (shear is a twisting force). The left hand side of this equation is all about the curvature of spacetime. When you write down something like the Milne cosmology, what you're doing is specifying the format of the left hand side of this equation. But particular cosmology only works if you set the right hand side to zero, which means no matter (no energy, no momentum, no pressure). Does that help any? By the way, I'd also like to point out that you can exclude the Milne cosmology very easily by combining supernova observations with other cosmological observations. 



#7
Sep910, 07:51 AM

Mentor
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http://www.physicsforums.com/showthr...34#post1757634. 



#8
Sep910, 07:56 AM

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#9
Sep910, 08:14 AM

Mentor
P: 6,038

For another similar example, use standard spherical coordinates for Minkowski space. Holding t and r constant results in a constant intrinsic curvature 2dimensional surface in Minkowski spacetime, a sphere. 



#10
Sep910, 08:16 AM

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#11
Sep910, 11:22 AM

PF Gold
P: 706

Not really. What do the matrices [tex]G_{\mu\nu} = T_{\mu\nu}[/tex] operate on? Do they input and output events, or do they input and output momentum vectors? What is the transform between? Transforming between what and what? The view from afar vs. the view nearby? The view in freefall vs. the view from the ground? Ostensibly the matrices are fourbyfour with either numbers or functions in each of the 16 positions, and should operate on explicit 1 by 4 vectors, which are also explicitly determined quantities. I really can't fathom what the tensors are for, at all. The big question is, do they operate on momentum and energy of individual particles, or do they operate on the coordinate positions of events in space? 



#12
Sep910, 11:34 AM

PF Gold
P: 706

As a hint, Milne claimed, a particle at rest (v=0) in this reference frame would be pulled toward the center. I do not recall how he reasoned this out, though. It was not entirely clear. I would have expected there to be no pull in either direction. Because a particle in the same position, but with v=r/t would be in the center, in its own reference frame, so would feel no such pull. 



#13
Sep910, 12:53 PM

PF Gold
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#14
Sep910, 03:26 PM

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P: 4,721

Thus, by the Einstein field equations, [tex]G_{\mu\nu} = T_{\mu\nu}[/tex] [tex]0 = T_{\mu\nu}[/tex] This means that every component of the stressenergy tensor is necessarily zero. Since the stressenergy tensor contains components related to energy density, momentum density, pressure, and stress, this means that energy density is zero, pressure is zero, momentum density is zero, and stress is zero. In other words, it's an empty universe. If you want to get a slightly better idea of how you compute particle paths in a space time, what you need to understand is that the Einstein tensor [itex]G_{\mu\nu}[/itex] is a function of what is known as the metric, [itex]g_{\mu\nu}[/itex]. The metric is a way of encoding the spacetime distance along a path, and the motion of any particle is always the shortest spacetime distance between its starting point and time and its ending point and time. For instance, if I consider a three dimensional metric with just one's along its diagonal, then this represents flat space (no time for now). This is equivalent to the equation: [tex]ds^2 = dx^2 + dy^2 + dz^2[/tex] I can then use this metric to find the distance between any two points in flat space, and lo and behold, when I compute the shortest distance between any two points, I get a straight line. 



#15
Sep1010, 12:52 AM

P: 6,863

I'm not sure that the data will be useful to you. If you are looking for supernova *counts* rather than using them as standard candles, then I think the data will be useless since you can't easily remove the effects of stellar evolution or selection biases.
For example, you could have a lot of supernova at a certain distance because that happens to be the distance at which the first generation of stars blow up. Or not. 



#16
Sep1010, 12:59 AM

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#17
Sep1010, 05:32 AM

P: 2,890

To get the Minkowski spacetime you actually have to make the Riemannian tensor vanish, not just the Einstein tensor. 



#18
Sep1010, 07:38 AM

PF Gold
P: 706

http://en.wikipedia.org/wiki/Edward_Arthur_Milne Click on the fullsized image, (Direct Link) and you'll see, in the very last line "The particles near the boundary tend toward invisibility as seen by the central observer, and fade into a continuous background of finite intensity." Milne actually predicted a continuous background of finite intensity. He did not know precisely what wavelength it would be at. He did not know if we would ever have instruments sensitive enough to detect it. I imagine that to him, this prediction was actually an inconvenience, since it predicted something that had never been detected. You're saying that the WMAP data rules out the Milne model, but to the contrary, the WMAP data resoundingly supports the Milne model. It is a long awaited vindication of the Milne model. 


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