Lineweaver(May 2003)-web's best cosmology tutorial

[marcus]

Lineweaver(May 2003)--web's best cosmology tutorial

http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Lineweaver_contents.html


I've been using Ned Wright's (UCLA astronomy dept) cosmology tutorial and FAQ a lot, but this new one is even better for some
things---more up to date about accelerated expansion

Here's the arXiv address for the same thing. Printed out is is 34 pages. A lot of pictures: maps and diagrams which you can click on to get expanded views of.

http://arxiv.org/abs/astro-ph/0305179

 

[marcus]

Lineweaver, page 6 figure 1 caption

"In the immediate past our past lightcone is shaped like a cone. But as we follow it further into the past it curves in a makes a teardrop shape. This is a fundamental feature of the expanding universe; the furthest light that we can see now was receding from us for the first few billion years of its voyage."

 

[marcus]

There is a question contained here which I just posted in the Astronomy gamethread.

If you want to reply in the context of the game, please go to that thread. Responses here don't count in the game. Basically the story is I just understood something in Lineweaver's Figure 1. the first part of the diagram, up at the top and wanted to ask it as a question so as not to spoil it for people, because getting the insight could be a nice ahah moment.

If you go to the IPAC-Caltech site then you can enlarge the diagrams to fill the screen.

http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Lineweaver_contents.html

But its also nice to print it out which you can do from the Los Alamos archive site-----tho the diagrams are smaller printed out.

http://arxiv.org/abs/astro-ph/0305179

Either way, what you see in the figure is a tear-drop shaped lightcone

(elsewhere in the figure the lightcone is spread out and not teardrop shaped, but in the top diagram it is)

And also you see a curve showing the extent of the "HUBBLE SPHERE" which he explains what it is.

If you look very carefully you will see at a certain point the Hubble sphere crosses the side of the teardrop, I mean the lightcone.
Where the Hubble sphere intersects the lightcone is a special point. It comes at the widest point, like a point on the Earth's equator. Why?

At points below that intersection the teardrop is sloping outwards.
Why? What does that signify?

 

[marcus]

in Astronomy gamethread chroot mentioned the cosm. event horizon
the current distance to the farthest object we will ever be able to see even if we could wait forever for the light to get here

this paper by Davis Davies and Lineweaver compares the area and entropy of THAT horizon with those of another wellknown horizon----a black hole's.

some nice formulas that go back to Beckenstein 1973 about black holes and second law of thermodynmics entropy area and all.
must be deep because people have gotten a lot of mileage out of them, including Hawking---black hole temp and entropy has seeded a long line of development

so now these three in Sydney Australia who seem to be very good cosmologists are extending the second law of thermodynamics to this other horizon, and doing thought experiments like

...what happens to the total entropy as a black hole inside our ev. horiz sails out into the beyond, carrying all its great load of entropy?

analogous to the thought experiments Bekenstein did about things falling into black holes and asking what happens to the entropy

this is entertaining stuff. they get results.
I found the paper at the Penn State U website which lead me to a free online source of journal articles. Here's the abstract of the article, or part of it...

<<INSTITUTE OF PHYSICS PUBLISHING
CLASSICAL AND QUANTUM GRAVITY
Class. Quantum Grav. 20 (2003) 2753–2764 PII: S0264-9381(03)60278-9
Black hole versus cosmological horizon entropy
Tamara M Davis 1 ,PCWDavies 2 and Charles H Lineweaver 1
1 Department of Astrophysics, University of New South Wales, Sydney, Australia
2 Australian Centre for Astrobiology, Macquarie University, Sydney, Australia
Received 3 March 2003
Published 6 June 2003
Online at stacks.iop.org/CQG/20/2753

Abstract
The generalized second law of thermodynamics states that entropy always increases when all event horizons are attributed with an entropy proportional to their area. We test the generalized second law by investigating the change in entropy when dust, radiation and black holes cross a cosmological event horizon. We generalize for flat, open and closed Friedmann-Robertson–Walker universes by using numerical calculations to determine the cosmological horizon evolution. In most cases, the loss of entropy from within the cosmological horizon is more than balanced by an increase in cosmological event horizon entropy, maintaining the validity of the generalized second law of thermodynamics. However, an intriguing set of open universe models shows an apparent entropy decrease when black holes disappear over the cosmological event horizon. We anticipate that this apparent violation of the generalized second law will disappear when solutions are available for black holes embedded in arbitrary backgrounds.


1. Introduction

A significant advance in physical theory was made by Bekenstein with the suggestion (Bekenstein 1973)that the area of the event horizon of a black hole is a measure of its entropy. This hinted at a deep link between information, gravitation and quantum mechanics that remains tantalizingly unresolved today.

Bekenstein’s claim was bolstered by Hawking’s application of quantum field theory to black holes (Hawking 1975), from which he deduced that these objects emit thermal radiation with a characteristic temperature,...>>

a few thoughts of my own, on first seeing their journal article:

the math is remarkably easy here---first year calculus, mostly just a few simple integrals and some graphs

In the gamethread chroot was talking about the distance to the cosmological event horizon. According to Lineweaver's tutorial, it is currently 62 billion lightyears.

I wonder if it radiates. the way a bl. h. event horizon does.
It is a big sphere out there with radius 62 containing all we shall ever see. things that cross it into the outside can't ever send messages back... sorry for disordered thoughts----just looked at
this paper for the first time a few minutes ago

 

[r637h]

To Marcus:

Thank you for posting the Lineweaver lecture. It is the the best exposition of the subject matter I've seen in recent times.

Again, Bless You!

Rudi

 

[Imagine]

Originally posted by r637h
To Marcus:

Thank you for posting the Lineweaver lecture. It is the the best exposition of the subject matter I've seen in recent times.

Again, Bless You!

Rudi

To Marcus,

MERCI BEAUCOUP !

 

[marcus]

Originally posted by Imagine
To Marcus,

MERCI BEAUCOUP !

Dear Imagine and Rudi,
I am so delighted to hear that you liked Lineweaver's article!
Sorry not to have replied earlier, I somehow missed your posts
earlier and just now noticed them.

Lineweaver has some formulas and concepts that may need explanation----my impression is that basic differential and integral calculus would be sufficient to explain a lot of it---or even just more verbal/intuitive discussion at some points.

So if either of you find some places where you want clarification of something specific---please mention it with a page reference or quote and I or somebody else will try to respond.

(BTW someone was lazy with figure 4 on page 13, which should have been redrawn and the righthand y-axis relabeled, to make it more accurate, but making figures is a lot of work and so it was apparently left in a suggestive but confused state, so don't be surprised if you find that figure puzzling)

Anyway that is a favorite paper of mine so if anyone has questions or simply wants to talk about it I would be happy to reply.