What is Sean Carroll's Cosmology Primer?

[marcus]

Sean Carroll has posted a Cosmology Primer
explaining contemporary cosmology for general audience
It could be very handy for us to have at PF to refer to.

Here, for example, is the FAQ
http://pancake.uchicago.edu/~carroll/cfcp/primer/faq.html

for other sections, go to the TOC and click on something
what do you think?
too much for one person to read every section so
if you want, pick a section from the TOC and comment
so we get an overall idea of how we like it (the whole thing
not just the FAQ)

 

[meteor]

It's illuminating that he confess that there's no conservation of energy of the "stuff" of the universe. By stuff I mean dark energy, radiation, baryons,... He says that there's transfer of energy to the gravitational field, but "energy of the gravitational field" is not a well defined thing. Perhaps some future genius is able to define it

 

[Garth]

As he is talking about GR he is quite correct.
Garth

 

[marcus]

As he is talking about GR he is quite correct.
Garth

garth doesn't it strike you as weird that-----well, in rigid local coordinates there is hardly anything more basic than Energy Conservation----and yet GR is the best idea of space and time we have and in that context, no energy conservation law.

must have to do with time. in stiff local coordinates there is an absolute idea of time and universe evolves in time so that E is conserved.

but in extremesituations and very global situations E actually is not conserved as far as we know. nobody has ever given satisfactory expl. for where the energy in the CMB that has been lost by expansion/redshift has gone to.

nobody has given satisfactory expl. of where the energy comes from that is in the dark energy constantly being created by expansion

inflation, free lunch, all that stuff

now Ashtekar is talking about "deep Planck regime" at heart of black hole (where the singularity has been removed) and it sounds to me as if
in that regime there may be no proper idea of causality and there may also be no conservation of energy------or else the way it is conserved has not been elucidated. he is trying to say that only about half comes out in form of hawking radiation. ye gods.

I stand here clueless in bewilderment (hope you likewise)

 

[Loren Booda]

marcus,

doesnt it strike you as weird that-----well, in rigid local coordinates there is hardly anything more basic than Energy Conservation----and yet GR is the best idea of space and time we have and in that context, no energy conservation law

On the other hand, quantum mechanics within the Heisenberg uncertainty principle also appears to have no strict law of energy conservation.

 

[Garth]

garth doesn't it strike you as weird that-----well, in rigid local coordinates there is hardly anything more basic than Energy Conservation----and yet GR is the best idea of space and time we have and in that context, no energy conservation law.

What strikes me as weird is that not more is made of this in GR textbooks. After all we are told that Einstein was worried about it, so he thought it weird! Emmy Noether 'resolved' the problem by showing that GR belonged to a class of "improper energy theorems" in which energy is not expected to be conserved, so energy should not be conserved in GR but she did not answer the important question of whether energy, given its previous centrality should be conserved in the real world or not.
It is important to realize why energy is not conserved in GR, at least for a freely falling particle. Note that energy and momentum are both individually conserved in the observer's local inertial laboratory, in a local particle interaction for example. The problem arises when a particle is being observed from afar across space-time curvature. The energy is given by
E = - P_aU^a so to measure energy at two separate places along its freely falling geodesic you have to parallel transport the four momentum P_a to the new position, which cannot be done unless there is a time-like Killing vector (and there isn't in general), but it gets worse, the four-velocity U^a also changes even though no forces are acting on the particle, it accelerates simply because of spacetime curvature (the four-velocities of the particle and the observer diverge/converge in general).

must have to do with time. in stiff local coordinates there is an absolute idea of time and universe evolves in time so that E is conserved.

but in extremesituations and very global situations E actually is not conserved as far as we know. nobody has ever given satisfactory expl. for where the energy in the CMB that has been lost by expansion/redshift has gone to..

Its to do with the way four-momentum vectors 'lean over' because of space-time curvature, and that includes time! "nobody has ever given satisfactory expl" not quite! In the Jordan frame of SCC the CMB does not lose energy, particle masses gain it,
m = m₀exp(Ht).
Red shift is caused by the gain of mass by the apparatus. The universe is static and eternal, (cylindrical - conformally flat and yet finite) and rulers shrink and clocks speed up.

nobody has given satisfactory expl. of where the energy comes from that is in the dark energy constantly being created by expansion
inflation, free lunch, all that stuff

Again in SCC no need for DE or indeed DM - plenty of discussion about that on these forums.
- Garth

 

[selfAdjoint]

Hmmm. Global energy conservation is a legacy to us from 19th century physics. It has no more warrant than that. When you say energy is conserved in "the natural world" you mean the world where h and v/c go to zero, which is the world of 19th century physics. Quantum theory and GR have each their modern statements of energy behavior, and in both cases AFAIK the 19th century limit gives energy conservation.

To me, to repine because modern physics doesn't match the views of Clausius and Maxwell sounds just like the people who can't accept Lorentz transformations or superposition because those ideas disagree with Newton and Kelvin.

 

[Garth]

In the end of the day it comes down to competing testable theories; GR and SCC (and others) are being tested at the moment by the Gravity Probe B satellite, so we wait until the results are out in 2006. Until then it is good to understand the various issues underlying the theories.
- Garth

 

[Garth]

Hmmm. Global energy conservation is a legacy to us from 19th century physics. It has no more warrant than that. When you say energy is conserved in "the natural world" you mean the world where h and v/c go to zero, which is the world of 19th century physics. Quantum theory and GR have each their modern statements of energy behavior, and in both cases AFAIK the 19th century limit gives energy conservation.

SR gives energy and momentum conservation and that was 20th century physics!

QT does give energy conservation but according to the principles of GR it requires a preferred foliation of space-time to do so, (Bell, Isham and Butterfield), thereby violating the principle of 'no preferred frames'. Herein lies a fundamental fault line between GR and QG.

So are we happy with GR's "modern statement of energy behaviour"?

As marcus has posted, "nobody has ever given satisfactory expl. for where the energy in the CMB that has been lost by expansion/redshift has gone to."
We could add that there isn't a satisfactory explanation of where the energy of a photon in ordinary gravitational red shift goes to. It is the same problem. (The photon is not losing potential energy as P.E. is a '19th century', not a 'modern', concept, it does not exist in GR. The photon is 'travelling' along its geodesic worldline with no forces acting, no work is being done, and yet it loses energy - neat!)

And he adds, "nobody has given satisfactory expl. of where the energy comes from that is in the dark energy constantly being created by expansion"
Could the problem of identifying DE in standard cosmology be a manifestation of this same problem of GR's "modern statement of energy behaviour"?

- Garth

 

[meteor]

Sean Carroll is going to publish a new multi Big Bang theory, accomodating his ideas about "infinite entropy"

The big bang could be a normal event in the natural evolution of the universe that will happen repeatedly over incredibly vast time scales as the universe expands, empties out and cools off, according to two University of Chicago physicists.
"We like to say that the big bang is nothing special in the history of our universe," said Sean Carroll, an Assistant Professor in Physics at the University of Chicago. Carroll and University of Chicago graduate student Jennifer Chen are scheduled to post a paper describing their ideas at http: //arxiv.org/ Thursday evening.

http://www.physorg.com/news1734.html

Voila!...the paper
http://arxiv.org/abs/hep-th/0410270

 

[Wave's_Hand_Particle]

And a fine bit of "over-enthusiastic" writing if ever I seen..Mentors should send it to TD instantly..if not then the double standerds of this site would be shameful!..just the mention of the theoretically insane smallest number ever devised in physics[P ∼ 10−101056]..should really delight some over-reactionary mentors?..not naming names.

 

[Garth]

I liked

We like to say that the big bang is nothing special in the history of our universe," said Sean Carroll

Do you think they forget birthdays as well?
Garth

 

[marcus]

I liked

"We like to say that the big bang is nothing special in the history of our universe," said Sean Carroll

Do you think they forget birthdays as well?
Garth

OK that does it. I'll have a look at the Carroll/Chen paper.
I was not going to bother with it because what he posted about it, in blog, didnt seem all that interesting. Limited awareness of alternatives, perhaps a bit silly.

I think Carroll's writing is mostly (at least 3/4 anyway) smart and fun, but that doesn't mean he can't have blind-spots.

There are the only two loop cosmology references and they are not particularly well-chosen (I suppose its possible Carroll may not have read them---his graduate student, Chen, may have provided some of the bibliography)
[100] M. Bojowald, “Quantum gravity and the big bang,” arXiv:astro-ph/0309478.
[101] M. Bojowald, R. Maartens and P. Singh, “Loop quantum gravity and the cyclic universe,” arXiv:hep-th/0407115.

In the acknowledgments, Carroll reports conversing with other pre-bang scenario folk such as Aguirre and Linde, but it does not appear that he talked with Bojowald, Ashtekar, or anyone else who might be supposed to know much about loop cosmology.

Here is what he says
--quote--
A number of other cosmological scenarios have been proposed in which the Big Bang is not a boundary to spacetime, but simply a phase through which the universe passes. These include the pre-Big-Bang scenario [94, 95], the ekpyrotic and cyclic universe scenarios [96, 97, 98], the Aguirre-Gratton scenario of eternal inflation [99], and Bojowald’s loop-quantum gravity cosmology [100, 101]. To the best of our understanding, each of these proposals invokes special low-entropy conditions on some Cauchy surface, either asymptotically in the far past or at some moment of minimum size for the universe. In our picture, on the other hand, there is a slice of spacetime on which the entropy is minimized, but that entropy can be arbitrarily large...
--end quote--

I would disagree with Carroll's generalization here. AFAIK there is no Cauchy surface or any 3D hypersurface corresponding to the former singularity because classical concepts don't apply there.
Conventional spacetime approximations only begin to apply a a few tens of Planck time units before and after the changeover.
I do not think the appropriate notion of entropy has so far been defined.
I do not think that one can say that the loop cosmology picture
"...invokes special low-entropy conditions on some Cauchy surface, ... at some moment of minimum size for the universe..." since
AFAIK such conditions have never been invoked by Bojowald or anyone doing similar research. And it is an open problem what such conditions would mean.

So what Carroll and Chen say, may in fact be true "to the best of their understanding" but I do not believe it is true in any more substantial sense than that.

This may seem like a small point. Carroll is promoting his own brand of inflation by faulting the alternatives----it is not a very effective argument and he spends little time on it. Instead, the bulk of the paper expounds his new Carrollian picture of inflation. I haven't had time to look at it----the summary put me off and made it seem extraordinarily far fetched.