Cosmological redshift: how much energy has gone missing?

marcus

I'm with you on this Nacho
It is simplistic to imagine that energy conservation holds
in contexts where it is not proven.

I dont have a copy of Mills book so I cannot tell exactly what
he is talking about----it may be in a context of Special Relativity---I'm not sure what the quantities are and can't comment specifically.

I had in mind a General Relativity context where space is expanding and there I believe it is simply a fact that energy is not conserved. I never heard of someone proving an energy conservation law for GR.

People seem to have tried and have apparently invented a formulary of "pseudo-tensors" in their attempts---but this is marginal, I understand, not generally accepted. In mainstream cosmology, according to my understanding, there is no energy conservation.

Alexander

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

marcus

this is a beautiful idea but it sounds like your own fantasy, Alex.

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? [8)]

Alexander

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

Nacho

[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 non-conservation 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.

schwarzchildradius

It is conserved. If you have some mass with grav energy GM²/r. Then explode it mv²/2 (=GM²/r). The small increase in m by factor gamma is paid for by whatever force exploded the mass in the form of a little extra acceleration needed to explode the mass.

marcus

This does not appear to be talking about global energy conservation, does it?

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 4-vector in the tangent space at a point x
to a 4-vector 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.

Nacho

You're right there .. it was on a section about Special Relativity. Also, as I said, one of the things that lead to the non-conversation is velocity, so it would have to be a particle, like an electron, that travels at less than the speed of light.

schwarzchildradius

I think you should check this.

Which integral?

marcus

Hello Schw.

Try this---its 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 ideas---they'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 red-shifted over billions of years. Each photon gets redder and redder. What happens to this energy? Cosmologists model the expanding universe with Friedmann-Robertson-Walker (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 pseudo-tensors 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 it---not 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.

schwarzchildradius

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.

marcus

Where are you getting this? Give a reference.
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

Dont you see the fallacy in what you are saying? This is covered in cosmology FAQ at Wright's site. Lots of the quasars we can see are at the present moment receding faster than c.
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.

This is covered at the Physics FAQ at Baez site. The simplest thing is to view the energy as lost---what do you mean "violate". It sounds as if you are under the misconception that there is a law of conservation of energy (in GR) to violate. Energy conservation laws are mathematical theorems which it is possible to prove in some contexts and and not in others.

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.

marcus

What website do you mean? I have posted several.

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 path----so 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

schwarzchildradius

he says that right on the web page.

marcus

Er....I will post the URL for the fifth time in a row.
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? [:D]

schwarzchildradius

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

marcus

My link was to page 2 because of the bearing on your question

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 one---he 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 web-pages is not workable in this case. For whatever reason---maybe 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 [:)]