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#91
Aug3110, 12:24 PM

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#92
Aug3110, 12:30 PM

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2. These other physical processes in no way require a universal spacetime reference frame, but describing them is definitely more convenient in such a frame. 


#93
Aug3110, 02:52 PM

P: 40

However, assuming the existence of a "Universe" and consequently a universal reference frame that contains it and then applying the equations of GR to said "Universe" was indeed a "blunder" as you would have it. If you want claim this is a valid scientific approach then cite the empirical evidence supporting the assumption of this "Universality". Cite evidence that this issue was ever scientifically vetted. Show me where it was scientifically proven and not merely assumed that the cosmos constitutes a singular entity that you like to think of as the "Universe". If you are saying that the assumption was "simply a matter of convenience" I would have to agree. 2. I'm not saying that they require a universal spacetime reference frame. I'm saying that they constitute a universal spacetime reference frame. Calling them comoving coordinates is simply a semantic dodge. 


#94
Aug3110, 09:32 PM

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The question, then, is whether or not there actually is a reference frame for which our universe is approximately homogeneous and isotropic. The second part to that is, today, trivial to answer, just by looking at the CMB. The CMB is uniform to about one part in one thousand in each direction. Once we take out the dipole of the CMB (presumably due to our own motion with respect to it), the CMB is uniform to about one part in one hundred thousand. That is pretty darned isotropic. So, the only question remains, is the assumption that there exists a reference frame for which our universe is also homogeneous valid? First, the default answer to this would most definitely be yes, for the simple reason that a universe that appears isotropic, but isn't actually homogeneous, would indicate that we are extremely near the center of an extremely big universe. And that is something that is rather ridiculous on its face. However, can we test it? Indeed we can! You see, for a while some cosmologists thought that it was possible to explain the acceleration of our universe due to our universe being isotropic but not homogeneous. This would indicate that we live near the center of a very large, underdense region (a void). Well, this hypothesis does provide some definite predictions that don't line up with observation, as seen here: http://arxiv.org/abs/1007.3725 Thus, with all of the other observations that do make sense when we keep the assumption of homogeneity, we can be pretty darned confident that this assumption is accurate. And since there are no singularities in the coordinate system far from t=0, we don't have to worry about it giving us incorrect results due to picking a bad coordinate system. We should obviously be careful not to extrapolate it too far beyond our cosmological horizon, or too close to t=0. And we certainly wouldn't want to use these coordinates to attempt to describe behavior too close to overdense/underdense regions. But other than that it isn't a concern. 


#95
Sep110, 02:46 PM

P: 134

Not only that, there is a whole family of spacetimes (Stephani) that includes the FRW universes that also allows inhomogenous isotropic solutions. You call yourself "science advisor"?. Why do yo make such categorical assertions when they are not backed up by sound science? That shows either ignorance if you don't know or dishonesty if you choose to ignore those facts that disprove your arguments. 


#96
Sep110, 04:14 PM

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There may be some corrections we should apply to our equations for expansion that assume perfect homogeneity due to the fact that it's not really homogeneous on smaller scales, but there really isn't any question that the picture is approximately accurate. Unfortunately I don't feel like taking the time to search out the evidence for every forum post I make, but if we get into a solid disagreement I am willing to do so (though I will note: you also presented bald assertions without evidence, so please don't act selfrighteous here). 


#97
Sep210, 05:52 AM

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#98
Sep210, 09:23 AM

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When you look into the system in a bit more detail, and properly consider the fact that it isn't actually uniform, you end up with some interesting behavior: on very large scales, you get what is called "linear evolution of structure". This can be rather simply calculated, and you get that small inhomogeneities to start with become small inhomogeneities later on: you don't get, on large scales, very huge deviations from a homogeneous universe. But on smaller scales the picture is entirely different. Once the matter in a given region goes above a certain density relative to the surroundings, it starts to collapse in on itself. This is nonlinear evolution, and it can't be so easily computed, but must be simulated. From this you end up with the more dense places in the universe collapsing and forming galaxies, galaxy clusters, and superclusters, complete with interestinglooking structures visible on larger scales, but the statistical properties on even larger scales left undisturbed. The way this sort of thing works in a bit more detail is that they divide the matter in the universe up into small particles, and start with a slightly inhomogeneous distribution of said particles (based upon, for example, CMB data). They then run the simulation forward, calculating the gravitational attraction between the different particles at each step. Here's a video flythrough of the end result of one such simulation for how matter tends to clump: http://www.youtube.com/watch?v=y0ToCreO9fU 


#99
Sep410, 05:17 AM

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#100
Sep410, 05:51 AM

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#101
Sep610, 08:39 AM

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#102
Sep610, 08:45 AM

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One thing to bear in mind is that the way entropy interacts with gravitating systems is not simple, and cannot be directly related to the usual thermodynamic concepts we're used to. In fact, except in very special circumstances, we don't even know how to calculate the entropy of a gravitating system. 


#103
Sep710, 12:58 AM

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#104
Sep710, 01:05 AM

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P: 4,800

We don't currently know how to precisely define the value of the entropy in such a situation, but we can be very confident it increases. 


#105
Sep810, 11:19 AM

P: 40

The nature of my criticism can be summarized as follows: 1) The observed cosmos either comprises a singular entity or it does not. 2) Scientists have assumed the first option without ever properly vetting either. The problem with your posts is that you seem incapable of even grasping the conceptual distinction between the two possibilities. All of your responses consist of retreating into the shelter of your preferred model, pointing out its successes and discounting its failures and inconsistencies. But discounting inconvenient results is a mathematical strategy only, one that should have no place in science. 


#106
Sep810, 11:35 AM

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