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

Time Asymmetry in a Nutshell

The follows is my first attempt at summarizing the search for the origins of the second law.

Entropy must start out small at beginning to observe non-equilibrium now. Given current observations, the universe did just this. Low entropy corresponds to a smooth universe in a system dominated by gravitation which we observe in the CMB. So the question we are asking is, how did it get this way? Is there a dynamical reason or just some initial condition?

Arguments usually center around coming up with some dynamics that allow generic initial conditions to evolve to what we see today.
One of the first proposed that inflation itself was responsible, simply flattening out all the inhomogenaities is its reason for existence anyway. But when gravity is repulsive, flattening inhomogenaities is still increasing entropy. (Albrecht and Guth)
One of the last arguments on the table is that the equilibrium state is actually unstable to inflation. Take a stable expanding universe, add an inflaton field and a zero point field and you can get thermally driven spontaneous inflation. This inflation can be "eternal" with "pockets" of reheating which look like big bang universes. (Carroll et al)

Need to read: Eternal inflation , inflaton fields, de Sitter space details.
Next time, more readings.

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.

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?

Some answers

Emergence, n. i-'m&r-j&n(t)s. A phenomenon where "simple" systems exhibit traits not "obviously suggested" by their initial definition. Wikipedia suggests that examples in physics are thermodynamic phenomena such as temperature, friction, and color.
Now that I am reminded, a host of examples come flooding back. I remember Wolframs blunt trauma murder weapon (e.g. Col. Mustard in the library with "A new kind of science"), I remember a colleages lectures on "Coherent Noise".

Coherent Noise is a term that describes the mechanism by which neural networks populated with random initial conditions appear to exhibit phenomena that are possibly analogous to physical properties. Its an approach that I like, creating what the universe is really like (just a bunch of events connected together by some rules), however I have to say that the methods employed do not appear to be widely accepted (or known). I am not comfortable with the method by which connections are made between the observed coherence and basic physics (like E&M). (Cf. Rappel and Karma 1996)

If a physicist coined the term and outlined the principle of emergence, he is probably kicking himself because Google searches imply that, like evolution, its one of those ideas latched onto by pseudo-science theoretists, creationists, philosophers, california crazies, and Michael Crichton.

Anthropic Priniciple n,(1973). An idea proposed by a cosmologist suggests that apparent fine tuning of fundamental properties is correlated to our existence. The same principle relates the difference between the way the universe is and the way we measure it to be. Related topics inlude quantum observation effects, EPR paradox, anthropomorphising, etc. Albrecht uses the term in the orginal context of early universe models. The more parameters we add to our system, the less it is relevant to reality.

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.

Times Arrow - In my thigh

How does one inspire undergrads? I thought I knew, but I guess its not what I thought.
This is the semester of Jackson so posts get shorter, more criptic.
Now I go home and chop wood. The arctic is coming down for a visit.

More Entropy

Today is not a good day for writing. Want to enslave self to writing habit. Will make better and cause learning of how words work. Have found good review of thermodynamic asymmetry in time by a philosopher at stanford. So my puzzlement at Albrecht's airieness about what Boltzmann taught us is justified -if I am to trust a philosopher.
B-Man posited what is known as the "Past Hypothesis" where initial conditions give rise to the one way street. However there appears to be much dissatisfaction with this idea. Mainly because:
A) it really doesnt explain thermodynamic behavior,
B) the same reason entropy increases -its likelyhood- makes this initial condition highly unlikely (a good example of physicists as contortionists),
C) One cannot generate a Law from this supposition because 1) the evidence is erased -except for the eraser- and 2) by definition, it is not repeatable
D) It is unsavory. (this is sort of my summary of the between the lines...)


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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.