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Cosmological redshift: how much energy has gone missing? 
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#19
May1803, 02:19 PM

P: n/a

Of course, there is. Flatness of universe is the consequence of energy of universe conservation.



#20
May1803, 02:24 PM

Astronomy
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PF Gold
P: 23,117

If it is not just your own imaginings, please cite an online reference where some expert is asserting this. The CMB is distributed roughly uniformly throughout space and the loss from it (by expansion) is occurring as we speak uniformly throughout space where is the energy going, where is the gravitational potential, in your picture, in what direction does the field point? I understand the conversion of energy in a supernova explosion from kinetic (outward motion) to potential (distance from center). but in the expansion of space there is no center. It is not a useful analogy as far as I can see. Or would you like to explain? 


#21
May1803, 02:55 PM

P: n/a

Marcus, everybody knows that gravitational potential energy is icreasing with spread. Gravity is attractive, dude.



#22
May1803, 03:38 PM

P: 170

[quote]I'm with you on this Nacho
It is simplistic to imagine that energy conservation holds in contexts where it is not proven.] Yabut, as I said, a minor point. From what I can get out of what I read (I'm not a real good mathmatician), one thing that leads to nonconservation of energy is velocity. But we are talking here about particles that travel only at the speed of light .. so the velocity is a constant, and in essense is not a factor in transformation. 


#23
May1903, 12:38 AM

P: 179




#24
May1903, 09:48 AM

Astronomy
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PF Gold
P: 23,117

One fundamental reason often cited for why GR has no energy conservation law is that you DO have conservation at a single point but to get global energy you have to do an integral and the integral is not defined. People have constructed concrete counterexamples to conservation in GR. Adding a 4vector in the tangent space at a point x to a 4vector in the tangent space at a different point y is like adding apples to oranges. So the process of integration does not work and the usual method of proof breaks down. I dont have Mills so I cant say what the context is. But it seems likely that he is not talking about global energy cons in GR. Otherwise he wouldnt quibble about energy and momentum getting mixed. In GR the problem with defining it goes much deeper than that. 


#25
May1903, 09:17 PM

P: 170




#27
May2003, 12:14 AM

Astronomy
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PF Gold
P: 23,117

Hello Schw.
Try thisits a page from Baez introduction to his tutorial on GR http://math.ucr.edu/home/baez/einstein/node2.html The picture might help. If it doesnt help heres a kind of rumination on my part. Im summarizing here what I get from reading what experts have to say about the failure of energy conservation in GR. Do you ever go to Usenet? Its a good place to learn stuff John Baez is the moderator on sci.physics.research which is kind of the best from my point of view. they have discussions about why no energy cons in GR and give reasons like no way to integrate globally cant add tangent vectors in two different tangent spaces (apples and oranges idea) Also Usenet has a physic FAQ and one of the FAQ is about this very thing. You have to find access at a level you understand. I summarize expert mainstream views that I gather and if you don't trust my boiling it down and giving you my take on it then you have to go to the horse's mouth. These are not my pet ideasthey're what I get from the smartest people I can find who have something to say about it. I dont have a stake in it either way. I'd be delighted if it DID have an energy conservation theorem that somebody could prove. Einsteins GR does not have energy conservation as it stands but it could always be modified someday with some new mathematical gizmo and the new theory could have a mathematical proof of a conservation theorem and then they would test the new theory experimentally and MAYBE it would be more accurate and people would gradually accept it. But as it stands the plain vanilla GR does not have it. "pseudotensors" which have problems and turn many people off are a gizmo invented to get energy conservation but so far not generally accepted as workable. A QUOTE FROM PHYSICS FAQ at Baez site": "The Cosmic Background Radiation (CBR) has redshifted over billions of years. Each photon gets redder and redder. What happens to this energy? Cosmologists model the expanding universe with FriedmannRobertsonWalker (FRW) spacetimes. (The familiar "expanding balloon speckled with galaxies" belongs to this class of models.) The FRW spacetimes are neither static nor asymptotically flat. Those who harbor no qualms about pseudotensors will say that radiant energy becomes gravitational energy. Others will say that the energy is simply lost." they are standing around scratching their heads and saying how can we fix it so there will be energy conservation, what extra assumptions do we need, what tools must we invent etc etc. I believe to understand the tangent spaces on a differential manifold and the ambiguity of transporting vectors from one point to another you need a course in differential geometry. But someone may be able to explain itnot I tho. http://math.ucr.edu/home/baez/einstein/node2.html Baez draws The Picture that goes with the explanation in his GR tutorial at his website, maybe that would help. But maybe it wouldnt. 


#28
May2003, 02:15 AM

P: 179

Don't take offense. That's a nice web site you posted. I read through it but didn't see the problems that you're talking about. The only major problem they mentioned was the condition that t=0, physics breaks down, because you have possibly infinite density in zero space.
The FAQ is not maintained by Dr. Baez. 


#29
May2003, 10:19 AM

Astronomy
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PF Gold
P: 23,117

On Usenet people get laughed at for saying this about the Hubble law v. It is a confusion between SR and GR. In SR there is indeed a doppler formula for z according to which v=c corresponds to infinite z. But that is not the same v as in the Hubble law What is the "by definition" you are talking about? We see the quasar at a moment a long time ago when it was not receding so fast. I dont like arguing about generally accepted matters, even with people who have Hitchcock sigs and believe the US is governed by a Kleptocracy. Please bring your viewpoint up to date. 


#30
May2003, 10:38 AM

Astronomy
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PF Gold
P: 23,117

In the my post immediately preceding yours there was a link to an essay by Baez himself. http://math.ucr.edu/home/baez/einstein/node2.html I know that the Physics FAQ is not maintained by Baez and each article is signed. He writes some of them. But the FAQ is just a small part of what is at Baez site. he has a lot of his own essays. the one I referred you to was one of this. It addresses the "apples and oranges" problem (incomparability of tangent vectors at different points on manifold) which tends to stymie global theorems. The picture is there on the page. It is a ball. It shows parallel transport of a vector from one point to another depends on pathso the correspondence is not uniquely defined. This is why in GR stuff can recede at greater than light speed. (velocities only compare rigorously at a single point, or less rigorously in a small neighborhood of a single point) I don't recall seeing anything there about "t=0" and the beginning of the universe and "physics breaking down" I will repost the link http://math.ucr.edu/home/baez/einstein/node2.html 


#32
May2003, 05:28 PM

Astronomy
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PF Gold
P: 23,117

There are ten paragraphs on the page and a picture which gives the key to why energy conservation is not proven in GR. It's a sphere showing parallel transport of tangent vectors. There is nothing on the page about "t=0" and "physics breaking down". What I believe I'm testing is what happens when you ask a question and request a link, and then I give you a link bearing on the question. The issue is trolldom, I believe. Here is the link again: http://math.ucr.edu/home/baez/einstein/node2.html In which of the ten paragraphs does it talk about "t=0" and "physics breaking down"? We two are certainly burning up the wires with all this communication aren't we? 


#33
May2003, 05:51 PM

P: 179

Now a miracle occurs...
so, true it doesn't say the words "physics breaks down." 


#34
May2103, 09:50 AM

Astronomy
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PF Gold
P: 23,117

http://math.ucr.edu/home/baez/einstein/node2.html Your link is to page 7 http://math.ucr.edu/home/baez/einstein/node7.html On page 7 Baez says: [[...Now a miracle occurs. By all rights, this equation should only hold at t = 0 for a small ball of initially comoving particles in free fall. However, in the special situation we are considering, it holds at all times for arbitrarily large ball of galaxies, even though the galaxies are not comoving! I wish I knew a simple reason why this works...]] He is not saying "the physics breaks down" but that the model continues (fortunately and unexpectedly) to hold for all time than only around a specific moment t = 0. What he is doing is deriving a form of the first Friedmann equation from the simplified GR equation that he started with. The whole essay is "GR made simple" and at some point one wants to get the Friedmann equation from the main Einstein onehe is doing this and saying "the physics works here remarkably well and I can't explain why it does in a simple way but just take it on faith that the equation works for all time under assumptions of homog and isotropy." I don't think one can understand this out of context. Indeed you have misunderstood the passage with a complete 180 degree twist! Although it says Big Bang in the title on page 7 this does not mean that t = 0 refers to the very beginning of the universe and he is saying that the equation does NOT break down. At issue for me is I need to learn what happens when you ask a question and I find something on web that bears on it and give you a link to a specific page (in this case with a specific picture). Then is it likely to happen that you get to talking about something that is not on the page and misinterpreting other stuff on the wrong page and, as in this case, making up "physics breaks down" phrases that arent even there and arent part of the authors meaning even on the wrong page! If that happens it means discussion by means of shared webpages is not workable in this case. For whatever reasonmaybe you don't like me, or you are feeling ornery or whatever. It doesnt matter what the reason is, the point is I should not try to share web pages and discuss them with you cause it doesnt work. No hard feelings however 


#35
May2303, 10:05 PM

P: 179

as long as you have no problems with infinite energy existing in an infinitely small volume, then physics has no problem describing the conditions of t=0.



#36
May2403, 12:39 AM

Astronomy
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PF Gold
P: 23,117

"the Meaning of Einstein's Equation"? http://math.ucr.edu/home/baez/einstein/einstein.html It has 9 pages linked together and he calls it "a brief introduction to General Relativity." I still go back over certain pages from time to time because it is a masterful job of making an honest presentation of the mathematics short and understandable. I suggested you look at page 2 , "Preliminaries". I cant tell what you are discussing. It does not seem to be page 2. On many of the pages (not page 2 but others) he uses "t=0" to stand for some normal reference time, like the present, after the universe is well on its way and evolving normally. Think of it as noon GMT on March 1some arbitrary time zero. In no case does he use "t=0" to refer to a singularity. Nothing in the essay concern infinite densities. So it has been four days now since I suggested the essay to you and it clearly has not helped you. I'm not clear about why. But probably means I shouldnt recommend online physics links to you. 


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