MBH Readings

Reading
Sesana et. al. Dec 2004

This article is a more refined version of a similar paper published a few months prior. It seeks to calculate the number of Massive Black Hole (MBH) inspiral and coalescence signals observed by LISA in a three year observing period.
Key Concepts to refine:

• 'Generic' gravitational wave signals. Bursts, periodic signals, characteristic strain...
• 1/f noise
• Sensitivity. Is it S/N=Sensitivity*Signal?
• What is it mean to "Add in quadrature"
  

Keywords (words with ad-hoc or implicit definitions, related concepts)

• Hierarchy
• MBH formation

The statistics on page 8 seem ad-hoc. They give a single event count and explore the sensitivity to various priors by computing one or two other numbers. It would seem to me that the important prediction wouldnt be the number of events observed in three years but rather the dependence of that number on assumptions. The treatment of this question does not satisfy me.

I need a better understanding of the gravity waves. Why is the spectrum and time evolution the way it is? What is a "burst" and why can we treat it as a single wavelength pulse.

Is the loose estimate that the frequency 'bin' Df is the same size as f typical? This seems like an awfully large bin.

All this aside, this is much better than the first version of this article (Sesana et al, ApJ August 2004)

Evaluating Dark Energy Measurement Schemes

Several months ago I came across a video of a talk given by Carroll. I can't remember where it was but I was impressed by his compelling breakdown of the dependency of the "concordance" LCDM model on many poorly understood assumptions.
The talk centered around a theory flow chart that attempted to question every possible part of all the hypotheses on which the model is based. It was a very well written talk, in that he worked his way through the flow chart, adding to it as each question and possibility was addressed.
Now, in the white paper "Insights into Dark Energy: Interplay Between Theory and Observation" this diagram shows up again. I see this on the first page and I think, great a review paper that will go through that talk again except this time with details and references. My mouth waters.
Alas, tis but a shade of my desire. So many things in that flow chart are left completely unexplained. A short compendium:

1) Dust Reddening and\or Photon- axion mixing simulates acceleration

Axions are predicted to change to and from photons in the presence of strong magnetic fields, and this property is used for creating experiments to detect axions... Depending on their mass, axions could plausibly explain the dark matter problem of physical cosmology. --wp

I'd never heard this universe not actually accelerating thing before.

2) Strong Energy Condition violated required for a dark energy.

The strong energy condition stipulates that for every future-pointing timelike vector field , the trace of the tidal tensor measured by the corresponding observers is always non-negative:

--wp

Also, from Carroll's S&G we see that the SEC implies that "gravitation is attractive".

I don't know this is appropriate but I don't WANT the SEC violated. Feel the same way about violations of the Equivalence Principle. EP is one of the most beautiful thought experiment proofs ever! Who would be so cruel as to violate that?

DETF as a career counselor

Another wayside village on the road to the thesis topic is the previously mentioned Dark Energy Task Force report published on June 6 (6/6/06 for you doomsters). This "task force" was created as a combination of two science advisory counsels (like the ones who brought you the food pyramid) to report to the DOE, NASA ,and NSF on what they should do about figuring out Dark Energy. They are reporting mainly to scientists who now wear manager hats so they need a combination of good detective work for the ones who are still or recently were scientists and good beaurocratese for the ones who control the money.

Now, why should time and management be spent on a slight curvature of a nominally straight hubble flow graph? Because whatever makes that curve possible represents a very large departure from either the standard model, the particle physicists golden T-Shirt or the miraculas general relativity solution. A large departure from a well established theory seems to always earn us physicists a gold star, once its understood. Another reason the problem is so "vexing", to use the words of the Quarks to Cosmos top ten problems list, is that in the last thirty years the physics community has seen the creation of an entire new branch on their scale invarient tree. Some of the smartest most competitive minds in the physics world from places like theoretical gravity, so called "high energy" (particle physics), and plain old astronomers are now Cosmologists. This community occupies the central area of the physics Venn Diagram. In many cases these people have other interests and retain titular roles in their former areas but in reality compete mainly in the cosmology arena.

This field became largely popular with the discovery of the CMB and its variations but really exploded with the discovery of the problem of the "missing mass". Thus begins the perfectly exeptable practice of validating one theory (supersymmetry) with the postulates of another, Dark Matter = missing mass. Using one and other as crutches to prove theories otherwise unprovable at that time, theoretical astrophysicists and particle physicists founded a new Commonweal. Recall as well the rising popularity of so-called "multidisciplinary" work. This was an age where large "consortiums" of scientists struggled to add their thin veneer to the towering pile of paradigm built by their fathers and one monthly journal in the nineteenth century had become ten. The habits and traditions built then are bearing fruit today where thousands of papers a year are published electronically or in numerous and divers peer reviewed journals on possible configurations of alternative gravity, quantum fields, strings, branes, and on and on; all to solve this problem of why the hubble flow is curved.

This Task Force is a physicists response to this glut of theory by saying, "Hey wait, we're empiricists, lets measure this!" Of course no one ever really stopped measuring the universe, as evidenced by the "stage II" (now projects) listed in the report, but noone ever really sat down and thought about proving more than yes there is a problem.

What this paper draws out is a practical four part program for figuring out what is causing that curve. Each part is a different way of measuring properties of objects like their brightness, shape or size. Using this information one might be able to back out a "observed or intrinsic distance" and by looking at spectral features, might construe also a redshift z. To do this one needs models, as most astrophysics has been based on models for 60 years, this is exactly the way its always been done. A model is simply a way we think the thing (cluster, supernova, etc) works which provides a way to turn what we measure, (spectral features, light curves, etc) into what we want to know (intrinsic distance, velocity, growth factor etc). We then use another model to turn those distances and velocities into an estimate of the cosmological parameters, like the fraction of energy needed to close the universe and the number used by the DETF the "equation of state" parameter. In each case the model we use includes a number of steps where GR plays an important role. This I consider one of the cruxes of the problem. Those on the task force have taken what appears to be a very consensus building position by choosing the dominant model and "going with it", nominally a very sensible modern science decision, but in this case ignoring the fact that their entire empirical approach relies on a theoretical house of cards.

This is the landscape from a young physicist in the sticks. Lots of big fishes competing to be the first to solve the mystery, pushing for big projects and money but the possibility of something fundamental tugs at the mind.

wheresmysciencesoft? and the DETF

Well so much for free equation hosting. I just wish they had shared their scripts with someone. They were so much better than any equation place on the web. It doesnt really matter. The work I did with it didnt really mean anything anyway.
Newest project. Evaluating the Dark Energy Task Force report for career opportunities. This is interesting in that it is basicly astrophysics written for management types. Lots of repetition and very little science that makes sense beyond the "Figure of Merit" statistics. In places it seems like when they want to mention the basic physics they throw in the "scale factor" equation or something without actually explaining or using it.
But because it was written in this way I was able to see several new concepts without lots of clutter. The things I am wondering about now are:
1) growth factor. This has something to do with density perturbation evolution and compliments the scale factor as an observable. Never heard about this in 2 years of astrophysics.
2) Baryon Acoustic Oscillations. Acoustic waves which get frozen out during the epoch of recombination. My question is, if they are density rings in the CMB and beyond, why dont they show up in topology searches?
3) People dont really think dark energy will be the result of a GR modification. The way they've parameterized the problem in terms of equation of state and used one set of GR equations to model the results make me wonder how we'll be able to tell if it really isnt parameterized by w(a) = wo+(1-a)wa. So much model! Nerve wracking...
4) If one is predisposed to optimism weak lensing holds the most promise weighing in with a figure of merit above 13! This is for a Square Kilometer Array survey of galaxies and 21cm background. (Of course the pessimistic FOM is only 2.1. ) However, weak lensing holds the highest pessimistic possibilities in a space based mission. The cool thing about weak lensing is that its essentially a data mining project. The pictures can be taken for one purpose, say an optical survey of clusters, and then processed to get statistics about the shear of the background galaxies. The measurements of the clusters are important too because they help reduce the source location error.

Theres lots of fun stuff in this report. I like the idea of using data mining to solve problems. When I was an undergrad I wrote a proposal for a class that outlined the creation of a astrophysical data mining center. This would be an institute whos job was to archive astrophysical images and data. The focus would be using new and old data to find planets. Apparently such a thing has since been proposed and funded! To bad Van Romero wasnt a funding agency.


Question: Should I try to write in a more coherent fashion? This would be good for my writing but bad in terms of time usage. Also I am not a huge fan of the little tiny editing window so I would have to find a good plugin for an editor and an editor. Maybe googles beta blogger will solve this problem. Dear diary, I hope I get invited soon! Maybe a google guy will read this and invite me. Gosh I hope they'll add inline latex like mediawiki has. *Fingerscrossed*

Paper Overload

I need to serously review my reading strategy. I have written here before about how hard it is to keep track of all the current pubs I want to be reading. The basic problem is that when I read an old interesting paper I find that it cites papers located not in one or two specialized journals but maybe 5 or 6 locations. All of which mostly specialize in something completely different.

Therefore if I want to see the kind of things I am interested in I have to sift through ~100 articles to see one or two good things. Of course there is no problem that one cant solve with enough money. In this case a mac with DevonThink would do the trick. Total cost ~$2000.

Meanwhile my solution is Bloglines and their wholely inferior search feature. But its better than before. Above is the journals category after a typical weekend!

New Ideas, Worthless or Stolen

My wife says that when I post my ideas here in my obscure little corner of the web someone might "scoop" me. They might take my idea and make it better and do what I didnt with it.
Well isnt that what science is about? Plus I doubt my ideas are worth much yet except to the crackpot community since they are so vague and misconcieved. But I'm slowly becoming more discriminating.
Latest Readings:
After studying scattering problems in quantum wondered about Lensed gamma ray bursts as probes of black holes. Did quick arxiv search and found:

• "Gravitationaly Lensed Gamma-Ray Bursts as Probes of Dark Compact Objects", Marani et. al., 1998
  

Obviously the idea isnt new but these guys had some really crummy data to work with. The theory had been worked out to some degree by Nemiroff in 1980 (et al. at other times). They looked at BATSE and Ulysses data but since they arent really angularly resolved they had to look for temporal correllations. Overall this seems like a rush job to get a pub. The graphs are Awefull.
I couldnt help reading some of Milgrom's newest.

• "MOND as Modified Inertia", Milgrom 2005

Hes the inventor of Modified Newtonian Dynamics. He decided that he liked changing newtons 3rd law instead of adding Dark Matter. Most people dont take this too seriously mostly because it explains spiral galaxies really well but starts to become harder to justify in cases like lensing by invisible galaxies. (If theres no dark matter how can there be invisible galaxies?) Not that one cant think of explainations but our stunted imaginations get hurt after a while.

Also real quick before I have to go, I read

• "Conceptual Problems of the Standard Cosmological Model", Baryshev. 2005

An Ode to Me.

Inflation Readings

Read:
-Eternal Inflation and the Initial Singularity, A. Borde and A. Vilenkin PrL 72, 3305, 1994

Even eternal inflation must have had an initial singularity, but it might have been infinitely far into the past. Another kind of physics here; the study of "singularity theorems" and the most rigorous special relativity I've seen before. Some confusing definitions which seem to conflict. ie defining E by E= J-I but then "it can be shown that J=I". But E is a subset of I. The rest of the paper talks mostly in terms of I and E after that. Argh
Need to read "The Large Scale structure of Space-Time" by Hawking and Ellis. This is where this silliness comes from

-Is Inflation Natural, L. Jensen and J.A. Stein-Shabes PrD 35, 1146, 1987

The origin of Eternal Inflation? Maybe, it shows that for a large number of space-times, if Lambda is greater than zero inflation will occur. Add to this the measured fact that L is in fact positive (within a few z) does this imply inflation must be happening now? Here? I didnt really see anything in the proof that allowed the effect to be non-local. It was based on some manipulation of Einsteins equation. Which are differential, local and dont generally solve for steady state cosmologically (as stated in this paper).

Papers from Guth 2000

Key(?) papers from Guths review on eternal inflation:

Original Inflation
(3) S. Coleman, PrD 15, 292p (1977)
(6) A.D. Linde, PLett 108B, 389
(7) A. Albrecht et.al. PrLett 48, 1220 (1982)
(8) A.D. Linde 129B, 177 (1983)

Initial Singularity
(15) L.G Jensen et. al. PrD 35, 1146 (1987)

Eternal Inflation
(25) P.J. Steinhardt, in The Very Early Universe, proc of Nuffield Workshop Cambridge 1982
(26) A. Vilenkin, PrD 27, 2848 (1983)
(27) A. H. Guth et. al. PrD 32, 1899 (1985)

Phase Transitions
(28) S. Coleman et. al. PrD 21, 3305 (1980)
(29) V Vanchurinl, gr-qc/9905097
(30) M. Aryal PLett 199B, 351 (1987)

Initial Conditions
(42) A. Borde et. al. PrLett. 72, 3305 (1994)

Probabilities
(44) A. Linde PLett. B345, 203 (1995), hep-th/9411111

Creating Energy and Counter Speculations

Ok back to time.
My favorite astounding quote of the week

"Now in cosmology, energy is not conserved", P.C.W. Davies, 1983

Ok, so is energy conservation just a tool for doing simple physics that we naive youngins cherish blindly like some kind of constitution or Bible? The way he throws that out there bothers me almost as much as the fact that he says it all. Apparently this is the nature of the argument behind inflation. Some energy must have been created to power inflation. This energy enters in the form of "Dark Energy" (or "Dark Tension" or a positive cosmological constant or an equation of state parameter w<0). is not invarient under time translation because processes are not reversible. Does it then follow that energy is not necessarily conserved? Is the energy-time proof true in the negative sense? Is there some way to translate the question from time to entropy? So that I can find a new conserved quantity or perhaps a dynamical equation for the total energy?
...
Reading the Penrose 1979 and then immediately Penrose 1989 is very interesting. In 79 he made the argument that collapsing the wavefunction was a time reversable process then in 89 he argues the reverse. From my perspective I have to say that I never really believed that it was a time reversable process. Thats kind of the whole point isnt it? That once the wavefunction is collapsed and an observation is made then that particular aspect of the system behaves in a classical way.
For example, consider a two slit experiment. Let a beam of electrons pass through the two slits and one sees a diffraction pattern, decrease the particle rate to one and you can still predict that the particle is not very likely to hit at a null in the diffraction pattern. You can build a diffraction pattern one particle at a time, thus the particle is behaving like a wave. Now put a device at the slits which triggers when a particle passes through, perhaps by some E-field measurement. Now you dont get a diffraction pattern, not exactly sure what you do get though. Probably just one spot for each slit. In the time reverse experiment you evolve two beams of electrons backwards you measure the position as the particle passes through and you get two beams coming out definitely not the same.
The other thing I am thinking about recently is the initial correlations Page (Nature 1983) talks about as the assumption hidden in the "inflation exlains time asymmetry" argument. He says that assuming that each point in space was uncorrelated at the "beginning" assumes a much smaller parameter space than could be. (Which to me is another way of saying Penrose's "Creator with a pin in phase space" argument. (Penrose 1987) I guess parameter space is probably just a more general phase space. So I guess the way one goes about showing uncorrelation is by formulating the size of a points past light cone and the size of the universe in terms of the same parameter (time?) and then take the limit (t->0) and ask the question " "which goes to zero faster?" My guess is that maybe you get some space with a mathematical property which something like an infinite set of unconneted singularities. I guess I picture a spate-time foam prior to the planck time, take each on of those foam cells and contract it even further at the foam walls the light cones touch, as they contract further they seperate so they are no longer causal with each other and thus not connected.

QFT then Inertia

Reading QFT in a nutshell, by Zee. 5 sections into the first chapter he says im not supposed to go on until I understand series expansion which relates to Feynman diagrams. The math is kind of obscure to me now but the expansion seems obvious enough, a particles existence is characterized by an infinite number of creations and destructions... sort of. Ok, I'll try the math.
I have been digging through that reading list below. Went to the library over the break last week and got all the Nature Letters, "Einstein Centenary", "Emperors New Mind", and "Gravitation and Inertia" (Ciufolini and Wheeler) which I just grabbed on a lark. They use a lot of funny words for things in that one. They frame the Mach principle "mass here makes inertia there" but I'm not sure what that really means. Somehow this is a restatement of the equivalence principle -"cant tell the difference between 1g space-ship acceleration and resting on the ground" but how? Inertia is the resistance to acceleration and is physically quantified by mass. If the equivalence principle can be restated as "the inertial mass is exactly equal to the gravitional charge" then that may be the key. Thus perhaps I can reframe the Mach principle as "mass here influences the mass there". They write in "Poor Mans Language" (in which I am fluent) that inertia is the "grip" of spacetime on mass here.
I've thought about this before when I read about vacuum energy and how it might give rise to inertia. But I didnt really understand then how that worked either. It has to do with the local curvature observed in an accelerating reference frame. The energy density of the vacuum in an accelerated reference frame might be an effective pressure in the direction opposite the acceleration. I think this is called Unruh radiation. But I think that it was the wrong strength, plus I would expect inertia to be proportional to the mass not the acceleration.
Maybe I dont understand at all. All of the GR I know has to do with gravitating objects. We use the equivalence principle to get from the rocket to the planet and then just go crazy fooling with black holes and such. How does one do the reverse and ask about physics in accelerated reference frames? What happens to a matter field, say, when you "transform" to an accelerated reference frame? I am still hopefull that Wheeler and Ciufolini will help me understand. However if I have to write a page of blog for every two I read it will take a while. Maybe I should read the book from a rocket travelling at 0.9c.

More Reading

Cross-Correlation between several exhaustive bibliographies has yielded this partial list of paradigm building primary sources in cosmological time asymmetry.

• R. Penrose, The Emporer's New Mind, Oxford, 1989
• ibid, "Singularities and Time-Asymmetry", In Hawking and Israel (1979): p604
  
• P.C.W. Davies The Physics of Time Asymmetry. London: Surrey Press
• ibid, "Inflation and Time Asymmetry: Or What Wound Up the Universe?," Nature 301, 398 (1983)
• D. N. Page, "Inflation Does Not Explain Time Asymmetry," Nature 304, 39 (1983)
• 
  
• A.D Linde, "Eternal Chaotic Inflation," Mod. Phys. Lett. A 1, 81 (1986)
• A. D. Linde, "Eternally Existing Selfreproducing Chaotic Inflationary Universe," Phys. Lett. B 175, 398 (1986)
• H. Price, "A Point on the Arrow of Time", Nature 340, 181

I need to reexamine my current subcriptions. I thought I got one free online journal with APS membership but I see nothing about that on their website. huh. A lot of the popular citations come from Nature, so I guess I should be paying closer attention to Nature. What else?

No Apologies (Just lets not mention this unfortunateness).

Well, lets put that ugliness behind us.
I guess its obvious to everyone but I that being a new graduate student with vague goals leaves one open to all kinds of unpleaseantness.

Some reading notes:
Many references in "Double Standard" to Hawkings popular science "Brief History of Time". So I read it. Not quite as good as the other giants, Sagan (who wrote the forward), Gamow, and Feynman but mostly readable. Picked up some new pieces of history about the development of inflationary cosmology. Apparently I need to pick up Penroses time arrow book. Most of the interesting citations to him (likelihood of low S initial conditions, etc) are not in papers which I can download, but in his book (books?).

Weakness

Some recent reads.

• The Rise and Fall of the Cosmic String Theory for Cosmological Perturbations, L. Perivolaropoulos, U of Ioannina.
• Cosmic Strings Reborn?, T. Kibble
• Stationary Black Holes, R. Beig and P. Chrusciel
• Spontaneous Lorentz and the Long-Range Gravitational Preferred-Frame Effect, M. Graesser, A. Jenkins, and M. Wise

Need a field theory book for the last guy. I like the 3d pictures of the string networks. But basicly 2 weeks of nothing. Maybe some summaries in a couple of days.

Chewing on S and ICs

Finished "Cosmic Inflation and the Arrow of Time", (Albrecht, 2003). He's at Davis, I wonder if Sara knows him.
I am still struggling with the origins and meaning of a common statement in "time" cosmology,

"The origin of the Second Law is traced back to initial conditions: the early universe had an extremely low entropy, allowing it to continue to increase thereafter." (Carroll et. al. 2004)

After lots of reading I still fail to see how this "ultimate initial condition" is elevated to explanans for the monotomic increasing state function that is the entropy, as if the initial condition causes the law. I think that maybe there is a subtle confusion of wording here, or at least reading. We observe that any system with an arrow of time must begin in an "abnormal" state, that is, of lower entropy than the state which we consider to be macro-equilibrium. Ok, so what they really mean is that we need the right ICs.
I am thinking about what the measurement of entropy entails, what kind of information we need to get a number for "S". We need to know not only the state of the system, but also all the other available micro-states, or rather what the system can do. In the case of the gas in the box, this is equivalent to knowing the equilibrium macro-state. Only most consider the chance that the Universe is finite and bounded unlikely. So to treat the question of entropy we have to understand both limits of evolution of the system. This appears to be an open and contentious question. Albrecht lists ten theories of initial conditions; theories of available states (or t->inf evolution) are even more plentiful.
I think I will take this time to hand out the award for most readable paper in the past 5 or so to Andreas Albrecht. His examples were simple and insightful. His definition of the thermodynamic arrow is clear and well illustrated. I finally understand the inner workings of inflation and the definition of a deSitter space. Now when someone says "slow roll" I have a picture to think about.
New things I need to understand.

• the anthropic principle (has something to do with number of parameters in a theory)
• potential dominance (how does the inflaton field couple to matter?)
• emergent things (what does it mean?

Leftovers from Price

• No Boundary Condition (wavefunction of the universe)
• Weyl curvature
  
• how can one use the word "obtain"? eg "Notice here that there are two possible models of the connections that might obtain between the products of two low entropy boundary condtions..."
• Cf. (Does it mean, "refer to"?)
• bilking argument
• pre-emption

Seeing the Light

I finished Price, "Cosmology, Time's Arrow, and That Old Double Standard". The double standard basicly says that if you use fine tuning (far from likely conditions) to get inflation and smoothness but later argue that times arrow is the direction of most statisticly likely evolution you are guilty of holding a double standard.
A fun quote:
"For present purposes the latter issue -that as to why the universe is not less homogeneous- is the more pressing"
Just a transitionary sentence of no real merit, except as an example of the kind of double-talk that obscures the issues. Science writing is full of bombast like this and worse. On multiple occasions I found myself counting off the conjoined negatives on my fingers. I guess if I was critiquing Hawking I would probably obfuscate a little out of nervousness.
My perspective on the issue of the closed universe, entropy, and time is still clouded.
Huw says that in a Gold universe entropy decreases close to any singularity, eg wacky physics near black holes. But isnt there a difference between the radius from a black hole and the fiducial cosmological size scale measure (a)? But I guess I always expected wacky thermodynamics near black holes anyway because with any kind of horizon, all microstates are not accessable, which I was taught is a key assumption for the statistical definition of entropy.

My favorite part is the examination of time sense when observing between positive and negative entropy gradients. The telescope cools when you point it at a reverse galaxy. Speaking of which, what is the "bilking argument"? Besides the loud discussion with my MCI representive. The funny stuff gets funnier when the discussion turns to the apparent paradox of time direction and radiation. There should be a whole bunch of radiation from the reverse universe right now (since the time goes backwards and is passing us in the opposite direction as we speak) Huw says we dont see this cause we have to look backwards to see reverse radiation and we can only see forwards. I wonder if he wrote this stuff with a straight face... But I say to him, what about scattering? I guess it doesnt matter because its still reverse scattering... arg!

I still like my donut theory.
Ah, the sillyness of time cosmology.

Boltzmann I Never Knew Ye'

Well apparently there is quite a bit which I either failed to pick up on during Thermo last year or lots of stuff was glossed over.
The entropy I knew and loved was simply the logarithm of the multiplicity of a state, or (if an ideal gas) some derivatives of internal energy and temperature. A closed system's entropy tends to increase -the system evolves towards equilibrium- because all microstates are equally accessable. These rules are all talked about in terms of simple isolated dankenexperiments like einstein solids (bricks) or gas filled pistons.
Now apparently, after figuring all of this out -which was where I left the story-, Boltzmann went on to worry about why adding probability + mechanics removes detirmanism. eg Gasses are just molecules running into each other, this is a reversable process, so why cant I get the air back in my tire? In his paper, "Cosmic Inflation and the Arrow of Time", Andreas Albrecht writes,

...Boltzmann taught us that the thermodynamic arrow of time
arises from very non-generic ("low entropy") initial conditions.

Well, Boltzmann didnt teach ME this.
So first I google "boltzmann low entropy initial conditions". From Soshichi Uchii at Kyoto U I have my first hit . She has an essay on reductionism (one theory "reduces" to another) with thermo as the example. She talks about Boltzmann's fight to reconcile mechanics with probability and the irreversability probability adds, finally ending with his "Ergodic Hypothesis". She is a little unclear about its other meanings besides all microstates are equally accessable. According to Laura Cupple's old website at Davidson, another reading of the hypothesis is:

The Ergodic Hypothesis states that the dynamical probability of finding a physical system in a particular state (X) is
T(X)/T = Omega(X)/Omega
T(X) is the fraction of time (out of total time T) spent in state X.
Omega(X) is X's fraction of the number of states (out of the total number Omega).

Thus Boltzmann defines probability in terms of dynamical properties in an attempt to justify additional probabilistic assumptions.
This short essay by Astri Kleppe in Norway is also very good. However still noone is mentioning initial conditions. Well so much for the google quick fix. I have walked ALL the way down to the computer lab from office to print,

• "Cosmology, Time's Arrow and That Old Double Standard", Huw Price 1994
• "Cosmic Inflation and the Arrow of Time", Andreas Albrecht

These are references 1 and 2 from Carroll's "Arrow". Maybe I will feel less indignant after reading more than Albrecht's abstract.

Thoughts about entropy

Still plowing through "time's arrow". I think I came in at the middle of the movie. I Realize that to appreciate what's going on I must pick my way through the citations. However I think I should take stock.
I should remind myself that I'm reading and trying to understand almost at random the most recent "interesting" looking material (mostly from the "new" section of gr-qc on the LANL archive). For this reason I'm always "doing" new and sometimes weird things and am being forced to act not only as partially educated reader but also discriminating reviewer. How easy is it to publish something there?
Ok, so the back story to time's uni-directionality goes something like, "In the beginning there were very few states (low entropy). Therefore, the number of states accessible to any closed system existing in this universe must always increase."
I feel I should be shocked by the second sentence. I can recall no qualifiers about initial conditions in the laws of thermodynamics. At the same time I feel giant gaps where math and mechanics have shovied Clausius and Kelvin aside over the past 6 months. So I go home to find my trusted Fermi reader to guide me out of this wilderness.

River Model and Reviews

Recent readings include:
The river model of black holes. By Andrew Hamilton and Jason Lisle.
They review how one can rewrite the Schwartzchild metric to represent a river of space flowing through a "flat" background. The points of the paper are: it is a good model to explain black holes to non-expert and it can be generalized to include rotating/charged black holes.

In this model space is basically flowing into the black hole like a river. At the event horizon it flows at the speed of light, the photons are like fishes which cant swim faster than c. (There's even a picture fishes swimming upstream.)

Unrecognized terms\phrases included.

• Kerr-Newman geometry does not admit conformally flat slices
  
• ADM formalism
  
• tetrad
  
• Doran-Cartesian coordinates
  
• Jacobi Identity
• vierbein
  

The Kerr metric and the ADM formalism I was able to remind myself about from past GR studies. Still not exactly sure what the difference between a tetrad and a coordinate system is. Googling Doran-Cartesian coordinates gets only this paper back again. According to the references Doran was one of the first river type metric for a black hole guy. I looked up the Jacobi identity but already forgot. Vierbein in context appears to be some kind of transform, between the normal metric and the Doran-Cartesian(?) river metric. It is also German for four legs/legged.

Comments: I cant resist wondering where the space is going? Is it being dissipated inside the black hole? Is it just building up? Is it just taking the analogy too far?

---

Also read.

• Quantum fields and "Big Rip" expansion singularities. Bill Hiscock and Hector Calderon
  Saw Hector's talk, had to read the paper.
  
• From COBE to WMAP: A Decade of Data Under Scrutiny. Louise M. Ord
  Reading lots of reviews.
  
• Does Chaotic Mixing Facilitate Omega Cornish et. al.
  Shortest abstract ever.
• Spontaneous Inflation and the Origin of the Arrow of Time Sean Carroll and Jennifer Chen
  Still reading but Apparently though they might not have needed the Cauchy surface.
  

Cosmology Book

I finished Scott Dodelson's "Modern Cosmology" the other day. By finished I of course mean switched from reading the text to reading bold words, headings, figures and final equations.

It is a detailed look at the physics of the standard post big-bang model. Early universe physics appears to be rife with perturbation theory.
eg Let there be some first order scalar or tensor perturbations. What do they do to the stuff? (stuff includes matter, dark matter, and photons)
OR
Let there be some perturbation in the stuff. What does that do to the curvature?
I actually read half of the book, very nearly word for word. Doing this I did learn a couple of things including that scalar and tensor perturbations are completely independent.

The most important lesson I take away from this is that "Cosmology" really is a word without meaning. Or really is that it has a different meaning for everyone.

What I wanted to learn, but didn't was how CMB anisotropies "prove" the existence of Dark Matter. All I found was that if you suppose some non-interacting substance you get lots of smaller perturbations because they can't coalesce via your everyday radiation processes. This is what we see in the angular size spectrum of the CMB, lots more small clumps than matter would make. My naive perspective is that if gravity works differently at large scales a similar situation would arise.
My greatest challenge in becoming a good theorist will be to avoid ad-hoc or lay-sounding "theories". I must learn enough to know what can and cant reasonably be proposed. For example, I don't know enough about current ideas in quantum gravity to avoid thinking that maybe the gravity quanta have a decay lifetime, so that if there are large distances between the attractors the quanta could decay into somethings that interact differently. This would explain the sharp diversion point from Newtonian physics in the rotational curves of many spiral galaxies.