Dynamical coherent states and physical solutions of quantum cosmological bounces

[jal]

http://arxiv.org/PS_cache/gr-qc/pdf/0703/0703144.pdf
Dynamical coherent states and physical solutions of quantum cosmological bounces
Martin Bojowald_
29 march 2007

…As an exactly solvable model even at the quantum level, it illustrates properties of dynamical coherent states and provides the basis for a systematic perturbation theory of loop quantum gravity….
…We will see that the coherent state structure of the model is much richer than that of unsqueezed Gaussian states, with squeezing influencing the general behavior significantly….

I could ask a lot of question ... however, one for now
What does he mean by "squeezing"?
jal

 

[marcus]

What does he mean by "squeezing"?
jal

A squeezed coherent state is one where there is the LEAST amount of uncertainty allowed by the uncertainty principle.

the H.U.P. says there always has to be a certain amount of uncertainty, but sloppy states can have more uncertainty than Heisenberg requires.
a squeezed state is constructed to be as crisp as possible so for a given amount of uncertainty in the position there isn't any more uncertainty than absolutely necessary about the momentum.

that's my two-bits maybe someone else would like to elaborate. It's an interesting topic.
here's a wikipedia on it with neat PICTURES!

http://en.wikipedia.org/wiki/Squeezed_state

 

[marcus]

Jal, this paper is definitely going to be on the Second Quarter MIP forecast poll!

bojowald is into a major line of investigation here.

Basically the idea is to extend something good in LQC to the full LQG.

LQC ( loop q. cosmol.) is a simplified version of LQG where you simplify the way cosmologists always do by assuming the universe is uniform (largescale homogeneous isotropic---looks approx the same from wherever and in whatever direction)

when you assume that kind of uniformity (sometimes called a "symetry reduction" because you reduce the complexity by assuming uniformity)

when you assume that much uniformity then describing the universe comes down to just a few numbers so that is what cosmologists do (they work with the Friedmann equation which is a symetry reduced version of the full Gen Rel Einstein equation)

and that is what QUANTUM cosmologists do, they use quantized versions of the Friedmann equation and they are quantizing just a few numbers instead of the whole shebang.

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so LQC, which Bojo invented, is SIMPLER and it has been known for some years to have a very good classical limit. After the big bang it goes very rapidly to the standard classical behavior, within a few Planck times. It homes in on classical gravity incredibly fast!

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What Bojo is trying to do essentially here is to BOOTSTRAP a correct classical behavior for a relevant sector of LQG, using what he already has about LQC.

he has already had some success at this last year. Now this paper that you flagged is pushing the investigation further.

 

[marcus]

The paper last year was
http://arxiv.org/gr-qc/0611112
Effective constraints of loop quantum gravity
Martin Bojowald, Hector Hernandez, Mikhail Kagan, Aureliano Skirzewski"Within a perturbative cosmological regime of loop quantum gravity corrections to effective constraints are computed. This takes into account all inhomogeneous degrees of freedom relevant for scalar metric modes around flat space and results in explicit expressions for modified coefficients and of higher order terms. It also illustrates the role of different scales determining the relative magnitude of corrections. Our results demonstrate that loop quantum gravity has the correct classical limit, at least in its sector of cosmological perturbations around flat space, in the sense of perturbative effective theory."

You can already see signs of the good classical LQG limit in the abstract. The LQG-critics are very likely to scream a lot about these two papers of Bojowald because for some reason (I'm not entirely sure why) they cannot stand the idea that LQG might have a good classical limit.

or that some sector might. or that some variant that the LQG-community is working on might, even if it is not the standard 1995 version of LQG but something evolved from it.

anything the LQG-community is working on, they can't stand to hear that it might have an OK classical limit---and copy familiar gravity at large scale and in low-curvature regimes.
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the potential usefulness of QG is in small scale and high-curvature regimes (like pit of BH or like bigbang) and there are interesting developments there too----singularity removal.
but it also has to copy familiar gravity in low-curvature situations. and that is what this Bojo work that you flagged is about
===============

the key word is both these papers is PERTURBATIVE.
you get a good solution to a narrow problem (like LQC) and then you expand the solution to a broader range of problems by fuzzing around the narrow solution

you perturb around LQC to prove some good behavior about LQG---that is the direction Bojo is going

 

[marcus]

I had better copy the abstract of the paper you flagged in your initial post, for clarity.
http://arxiv.org/abs/gr-qc/0703144
Dynamical coherent states and physical solutions of quantum cosmological bounces
Authors: Martin Bojowald
30 pages, 3 figures
IGPG-07/3-5, NSF-KITP-07-55

"A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As an exactly solvable model even at the quantum level, it illustrates properties of dynamical coherent states and provides the basis for a systematic perturbation theory of loop quantum gravity. The detailed analysis is remarkably different from what is known for harmonic oscillator coherent states. Results are evaluated with regard to their implications in cosmology, including a demonstration that in general quantum fluctuations before and after the bounce are unrelated. Thus, even within this solvable model the condition of classicality at late times does not imply classicality at early times before the bounce without further assumptions. Nevertheless, the quantum state does evolve deterministically through the bounce."

LQC is the thing that has the demonstrated correct largescale limit.
LQG is the thing which doesn't yet have it.
perturbation is the bridge to get results from one to the other

or you can think bootstrapping from a simpler model to a more complex model

I think there may be some hostile attempts to drown out with other discussion, which may make it exciting to talk about the new Bojo papers :-)
But don't get your hopes up. They could be pointedly ignored too. Life is funny.

 

[jal]

marcus
A squeezed coherent state is one where there is the LEAST amount of uncertainty allowed by the uncertainty principle.

the H.U.P. says there always has to be a certain amount of uncertainty, but sloppy states can have more than Heisenberg requires.
a squeezed state is constructed to be as crisp as possible so for a given amount of uncertainty in the position there isn't any more uncertainty than absolutely necessary about the momentum.

I get it.
heheh ... sorry... I usually look up what I don't understand ... I thought that squeezed was a special expression that I would not be able to find a definition/explanation.

Like you... I see promisses in this approach.
Even strings have got to have a minimum "state".
Therefore, I would expect that the "right" minimum model will end up producing the "right" dynamics.


jal

 

[jal]

I understand, “Squeezed”, as another approach to try to understand minimum length, (QMLS) and enter it in my blog as another reference.
jal

 

[marcus]

. I usually look up what I don't understand ...

that's good. but it also seems OK sometimes to not look up and instead to ask.
(I don't always know but someone else might---and I don't mind having to say I don't know the answer when that happens.)

there's a fair amount that's over my head in these two recent Bojo papers:
the one you flagged and the pre-quel to it.

BTW Bojo is now producing PhDs----he is "replicating" himself at Uni Berlin.
this is a really important development
he cites the 2006 PhD thesis of Aureliano Skirzewski--that is his reference [7] in the paper you mentioned.

he also co-authored a paper with Aureliano---he cites both these to make a key point.

the power to make change in academia comes in part from this replication process---you have to have postdocs to fill positions when they start asking for people to do your kind of research!
if there is only one person they get spread too thin to have effective influence.

another interesting fact is the KITP address (along with Penn State) in Bojo's byline.

he has PhD students in Berlin that he is fostering, he is at Penn State, he has this puzzling SantaBarbara KITP address----this is where the amoeba is too much in demand and is getting stretched thin and needs to replicate.

We need another Bojo for the program to continue to succeed. Maybe Aureliano will be that other Bojo.
=================

Jal, I am glad to see you are pushing ahead with your minimal length ideas in your journal and incorporating some of these research papers. right now it takes all I've got to try to follow developments in the LQG-community, but at some time I may feel able and at liberty to react.

there is a fair amount of literature on the minimal length idea, with the newest stuff being in the DSR area (they want the minimal length to look the same to all observers so there is a considerable buzz about DSR because it allows for that)