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Author Topic:   Cosmic Background Radiation in Big Bang cosmology
Sylas
Member (Idle past 5260 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 1 of 6 (192837)
03-20-2005 3:40 PM


In Message 165, Lyndon Ashmore asks about inflation and spacetime geometry. Reminder; I spell my name with a "y". It's not important, but spelling it right helps me find posts I need to deal with.
He says:
I am sure that Silas is aware that he has dug himself into a hole here. For inflation (which Silas rightly says no one knows how it started they are only grateful that it explains the effects) one needs a ‘flat’ universe and indeed most now believe this to be the case.
However to explain where the energy went I believe that he needs space to be curved.
The two replies are mutually exclusive. One must be wrong!
The resolution is simple. Ashmore is wrong that curvature is required or has anything to do with an energy problem. Expansion explains the CMBR; not curvature.
Which one is it Silas? Can we have consistent answers to the two questions of the Horizon problem and the where did the energy go problem?
Already given in the post Message 153 in the other thread. It was off topic there; so I'll say it again here.
There are essentially two answers for where the energy goes to compensate for a loss of energy associated with the cosmological redshift. You can think of the loss as being compensated by a kind of gravitational potential energy bound up in the expansion of space. This means considering a kind of kinetic energy bound up the rate of expansion and a kind of potential energy in how far it has proceeded.
However, for a full understanding of the matter one really has to get to grips with the fact the energy conservation is not quite the same in general relativity and in special relativity.
In general relativity, you don't actually have a good handle on energy conservation except as a localized phenomenon. Put another way, it is crudely analogous to the energy loss in a Doppler shift. The energy "loss" in regular Doppler shift is simply a consequence of a Lorentz transformation between frames. Imagine then a non-inertial frame. There is no conservation of energy in such a frame.
GR does away with frames altogether. There is no single inertial frame for the universe; just local approximations at every point in spacetime. So you can think of the energy "loss" as a kind of artifact arising as a consequence of transport from one frame to another. But I'd love to get a more informed comment from others on this.
This matter of energy conservation is something that really worries people. But energy conservation is simply an abstraction to capture certain invariants in physics. We relate all kinds of diverse phenomena ... motions, placement in a field, mass, radiation, etc; with an quality called energy, and use the connection to express an invariant property. The invariant works out in a locally Euclidean geometry, but it becomes poorly defined over a non-Euclidean geometry.
A discussion of the issue in a lot more detail is available at Is Energy Conserved in General Relativity? by Michael Weiss and John Baez.
The CMBR in BB cosmology is radiation from the "surface of last scattering", which was some 380,000 years after the singularity, and long after any inflationary epoch. The homogeneity of the hot plasma from this epoch is explained in conventional cosmology by an inflationary epoch very very early in the universe's development, which homogenized the universe to well beyond the cosmological horizon. It also drove the universe to the point of a flat geometry, or at least incredibly close to it, to within many orders of magnitude.
Cheers -- Sylas

Replies to this message:
 Message 3 by JonF, posted 03-20-2005 7:10 PM Sylas has replied

  
AdminJar
Inactive Member


Message 2 of 6 (192839)
03-20-2005 3:47 PM


Thread moved here from the Proposed New Topics forum.

  
JonF
Member (Idle past 168 days)
Posts: 6174
Joined: 06-23-2003


Message 3 of 6 (192871)
03-20-2005 7:10 PM
Reply to: Message 1 by Sylas
03-20-2005 3:40 PM


In general relativity, you don't actually have a good handle on energy conservation except as a localized phenomenon. Put another way, it is crudely analogous to the energy loss in a Doppler shift. The energy "loss" in regular Doppler shift is simply a consequence of a Lorentz transformation between frames. Imagine then a non-inertial frame. There is no conservation of energy in such a frame.
GR does away with frames altogether.
In the first line of the quoted material, did you mean "special relativity" rather than "general relativity"? It doesn't seem to make sense as it stands, speaking first of frames in GR then the statement the GR gets rid of frames altogether.

This message is a reply to:
 Message 1 by Sylas, posted 03-20-2005 3:40 PM Sylas has replied

Replies to this message:
 Message 4 by Sylas, posted 03-20-2005 7:53 PM JonF has not replied

  
Sylas
Member (Idle past 5260 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 4 of 6 (192876)
03-20-2005 7:53 PM
Reply to: Message 3 by JonF
03-20-2005 7:10 PM


No, I meant GR in the first line. The wording is confusing; sorry about that.
GR does not use the notion of a "frame" except as a local approximation.
In special relativity, there is conservation of energy in an inertial frame; but the same photon has different energy for observers in different frames. We can convert between frames using a Lorentz transformation.
In general relativity, we don't actually use frames to cover the whole of space; but only as a local approximation.
The cosmic background radiation in conventional cosmology is radiation from 380,000 years after the singularity, when the plasma then filling the universe became neutral and transparent to its own thermal radiation. We see it now, but redshifted with a z factor of 1100. That is, we see photons with 1/1100 of the energy of the photons when they were emitted.
It is this loss of energy that Lyndon was asking about.
The problem is that the two measurements are made at widely separated positions in spacetime, and there is no "frame" to cover them both. If we use the normal notions of energy from special relativity, then the energy difference is not a loss so much as different perspectives by different observers. This is why I said it was very crudely analogous to the difference in energy of conventional Doppler shifts; it is an artifact of observers. (Don't take this analogy too far!)
You could only define a loss in the conventional special relativistic sense if you had a frame in which to express it; and we don't.
Now there are ways to get a more comprehensive notion of energy; in which there is energy bound up in the expansion of space. This can account for the energy loss, but the details are tricky and frankly beyond me. One problem is that the energy you have is no longer the energy showing up in the stress-energy tensor. So it will depend in part on what we mean by energy.
For a more complete treatment I refer you to the link in my original post.
Cheers -- Sylas

This message is a reply to:
 Message 3 by JonF, posted 03-20-2005 7:10 PM JonF has not replied

  
Diggo
Inactive Member


Message 5 of 6 (208329)
05-15-2005 9:22 AM


On the CBR note
Was wondering if anyone could help me with the following claim by AIG in their new book Refuting Compromise (pg 156-157), i am attempting a critique of it and would like some assistance:
The claim goes like this. Symmetry patterns such as octopole and quadrupole components are arranged in a straight line across the sky, along a kind of cosmic equator detected in the WMAP are given as evidence against the isotropy of the universe. It is however, seen as consistent with his theory that the matter in the cosmos is experiencing slow rotation, this would produce the quadrupole and octopole moments.
Anyone with some knowledge in this area that can shine some light on the issue for me would be greatly appreciated!
The heading of this section in this book from AIG is titled "CMB Patterns Indicate a Rotating Cosmos", he is trying to undermine the Cosmological principle by advocating this incoherence in the CBR manifested in the octopole and quadrupole components referred to above. I think the concept of a bounded and unbounded universe is key to his claim. I think since he has a bounded universe as proposed by Humphreys he would see the center of gravity at the center of the universe with the universe rotating as a black hole might rotate.
Would love to hear from those with some good understanding of the details to provide some input.

  
madarab
Inactive Member


Message 6 of 6 (208415)
05-15-2005 4:41 PM


A universe with a net rotation is not one in which it could be considered to have a consistant set of physical laws. All sorts of things, like global causality violations, would be possible. It simply wouldn't be meaningful to talk about cause and effect in such a universe.

  
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