Crossing The Desert-without h-bar

jal

Kirill Krasnov _
01 March 2007
http://arxiv.org/PS_cache/gr-qc/pdf/0703/0703002.pdf
Non-Metric Gravity I: Field Equations

Can it be done?
What will the slim down versions of h-bar look on this side of the desert?
This is another great step.
This is an approach to keep your eye on.
Jal

marcus

hello jal,

where you quote from Krasnov's paper he is using the symbol hbar
and it doesnt come thru in your quote

you would probably enjoy using TEX more so you can get those symbols
there is a sticky about it somewhere at PF.

there are two modes, ordinary tex on its own line
and inline tex where you use the symbol amongst the rest of what you have written in that line. To get these delimiters to work remove the *

[t*ex] and [/t*ex]

put the delimiters around \hbar

Maybe you know all this and have been using tex for years :-)

Remove the asterisks in this:
[t*ex] \hbar [/t*ex]

that may not look so good INLINE, so to make sure it works inline use the word ITEX instead of TEX and write the delimiters [it*ex] and [/it*ex]

Here is the ordinary version, where I removed the asterisks in
[t*ex] \hbar [/t*ex]

[tex] \hbar [/tex]

marcus

I can understand why you might be interested in Krasnov's paper. I was reading it last night.

the passage you quoted was the second paragraph of page 3.

HE IS NOT HOWEVER TALKING ABOUT DOING AWAY WITH HBAR. What he means by passing to the classical limit as hbar -> 0 is just what people have been doing for 70 or 80 years in quantum mechanics.

they set up some model with hbar in it and then they pass to the limit as hbar -> 0 to see what it looks like classically.
=============

Krasnov's paper is interesting and represents a new QG gambit.

Since you like this paper, you might like to watch him talking about it to Lee Smolin and friends on video----the video explains things in a more introductory way, and people ask questions.

Also Krasnov has an earlier paper about the same thing, from a month or two ago.

I will get some links.

marcus

To get the Krasnov video, go here
http://www.perimeterinstitute.ca/ind...113&Itemid=167
check the box "quantum gravity" and press "do search"
and scroll down to 0611 (November 2006)
and you will see

"PIRSA:06110041
Title: Renormalizable Non-Metric Quantum Gravity? ( Windows Media , Macromedia Flash , MP3 Audio , PDF)
Speaker(s): Kirill Krasnov - University of Nottingham
...
...
Date: 30/11/2006 - 1:30 pm
Series: Quantum Gravity
Location: 405
URL: http://pirsa.org/06110041/"

And maybe you can avoid all the preliminaries and simply use this link

http://pirsa.org/06110041/

Anyway what I pasted just now has "windows media" which you can click and watch the seminar. And the lecture note slides are available by clicking "PDF"
==================

I will get the arxiv preprint link too, for the earlier paper. It is the paper he is discussing in this seminar talk

http://arxiv.org/abs/hep-th/0611182
Renormalizable Non-Metric Quantum Gravity?
Authors: Kirill Krasnov
Comments: 5 pages, no figures

We argue that four-dimensional quantum gravity may be essentially renormalizable provided one relaxes the assumption of metricity of the theory. We work with Plebanski formulation of general relativity in which the metric (tetrad), the connection as well as the curvature are all independent variables and the usual relations among these quantities are only on-shell. One of the Euler-Lagrange equations of this theory guarantees its metricity. We show that quantum corrections generate a counterterm that destroys this metricity property, and that there are no other counterterms, at least at the one-loop level. There is a new coupling constant that controls the non-metric character of the theory. Its beta-function can be computed and is negative, which shows that the non-metricity becomes important in the infra red. The new IR-relevant term in the action is akin to a curvature dependent cosmological ``constant'' and may provide a mechanism for naturally small ``dark energy''.

jal

Thanks Marcus!
You're making it easier to learn.
jal

Chronos

This a really bad idea, IMO. Marcus is just trying to be nice. An anger management thing. The audacity is deafening.

marcus

When Albert Einstein was 5 years old they put him in a Roman Catholic kindergarten. I can see how you might interpret the rest of his creative life as anger management. It's a theory. But you still have to look at each new idea as it comes along.

Delighted by your image of two girls kissing under a waterfall. Gratuitously beautiful---inexplicable.
http://physicsforums.com/showthread....55#post1261855

jal

I'm alway looking for GOOD Ideas.
Don't be shy ... point me to your simple idea .... maybe I can learn something from your idea.
jal

marcus

Hi Jal,
two things to notice about Krasnov's paper.

He's really psyched up about this new approach to gravity, but at the same time he doesn't argue that it is the final answer to QG problem. If you read carefully you see where he is finding ample reasons to motivate investigating this non-metric formulation whether or not it ultimately turns out right.

he presents definite ideas of what can be learned by seeing how this re-formulation goes.

(that part was, to me, quite convincing---it is an innovative approach just in how it goes after classical gravity already---it virtually obvious to me that things of value will be learned whether or not he actually reaches the South Pole :-))

And here is the other thing to notice. On an average of about once per page, Krasnov mentions that this Roman Numeral I paper is part of a series of papers he is writing about this. The guy is heavy-duty motivated about this. It is a big project to un-earth this new version of classical gravity. We have to be prepared to be patient (unless one or two other researchers get interested and help speed it up, he is describing a several year project)

==========
EDIT I am replying here, since I can still edit and I don't want to cap yours with another merely to say *yes*
I strongly agree with what you say in the next post.

jal

Yes, Marcus. That is my take on his approach.
Once the others see the potential of this line of investigation, we could end up with a new path towards the understanding of the universe and how it works. Then again.... it could end up to be a dead end.
It is just as important to point out the dead ends as it is to find new paths.
jal

Chronos

No disagreement there Jal. That was never my intent. We probably got off on the wrong foot. I do not doubt your sincerity, just concepts. They don't make sense to me. It is my nature to question every assumption from every angle. That approach leads to surprising conclusions at times.

jal

Questioning everything??? Must lead to proposing an approach that should be investigated.
How about Casual Set
This paper does not have too much math. and should be understandable to the average readers.
http://arxiv.org/PS_cache/gr-qc/pdf/9706/9706002.pdf
FORKS IN THE ROAD, ON THE WAY TO QUANTUM GRAVITY*
Rafael D. Sorkin
01 June 1997
Abstract
In seeking to arrive at a theory of “quantum gravity”, one faces several choices among alternative approaches. I list some of these “forks in the road” and offer reasons for taking one alternative over the other. In particular, I advocate the following: the sum-over-histories framework for quantum dynamics over the “observable and state-vector” framework; relative probabilities over absolute ones; spacetime over space as the gravitational “substance” (4 over 3+1); a Lorentzian metric over a
Riemannian (“Euclidean”) one; a dynamical topology over an absolute one; degenerate metrics over closed timelike curves to mediate topology-change; “unimodular gravity” over the unrestricted functional integral; and taking a discrete underlying structure (the causal set) rather than the differentiable manifold as the basis of the theory.
In connection with these choices, I also mention some results from unimodular quantum cosmology, sketch an account of the origin of black hole entropy, summarize an argument that the quantum mechanical measurement scheme breaks down for quantum field theory, and offer a reason why the cosmological constant of the present epoch might have a magnitude of around 10−120 in natural units.

Another approach that tries to find out how the universe is made and how it works.
jal

Chronos

Interesting you should mention that paper. While more recent observations have constrained some of Sorkin's 'forks', this paper remains one of my personal favorites on QG. The causal set approach is irresistably logical to me.

jal

Hi Chronos!
I have been working on trying to make a blog with Casual set that would show how QMLS would fit in with this approach.
Now that h-bar has been set free...heheheh .... perhaps they will be able to combine the two approaches into one.
I do not have any recent links of what they have been doing.
Here is what I have that should interest others.

http://arxiv.org/PS_cache/gr-qc/pdf/0507/0507078.pdf
Structure, Individuality and Quantum Gravity
John Stachel∗
12 July 2005
First I look at the effective field theory and asymptotic quantization approaches to general relativity, and then at string theory. Then a discussion of some issues common to all approaches to quantum gravity based on the full general theory of relativity argues that processes, rather than states should be taken as fundamental in any such theory.

p. 20 Fay Dowker states: Most physicists believe that in any final theory of quantum gravity, space-time itself will be quantized and grainy in nature. .... So the smallest possible volume in four-dimensional space-time, the Planck volume, is 10-42 cubic centimeter seconds. If we assume that each of these volumes counts a single space-time quantum, this provides a direct quantification of the bulk ([15], pp. 38
---------------
http://arxiv.org/PS_cache/gr-qc/pdf/0508/0508109.pdf
Causal sets and the deep structure of spacetime
Fay Dowker
Blackett Laboratory, Imperial College, London, SW7 2AZ, UK.
May 19, 2006
--------------
http://www.maths.lse.ac.uk/Personal/...arch-appl.html
Causal Sets
The hope is that an appropriate model can be found, which on large scales approximates the classical structure of the universe, but on small scales gives rise to "quantum" effects. Of particular interest is the case where the causal set has a unique minimal element.
---------------
http://uk.arxiv.org/PS_cache/gr-qc/pdf/0309/0309009.pdf
Notes for the Valdivia Summer School, Jan. 2002
Rafael D. Sorkin
01 Sept 2003
For the purposes Causal Sets: Discrete Gravity
of quantum gravity, a causal set is, of course, meant to be the deep structure of spacetime
. Or to say this another way, the basic hypothesis is that spacetime
ceases to exist on sufficiently small scales and is superseded by an ordered discrete structure to which the continuum is only a coarse-grained, macroscopic approximation.

… one might anticipate that the entropy of a black hole is effectively counting suitably defined “molecules” of its horizon. With this possibility in mind, one can ask whether any simply definable sub-structures of the causets associated with a given geometry could serve as candidates for such “horizon molecules” in the sense that counting them would approximately measure the “information content” of the black hole.
----------
Do you have any link to recent papers that I could read?
jal

Chronos

Stefan Zohren has published a number of related papers in the past year
[including one in collaboration with Ambjorn]. This most recent entry is very good, IMO:

Counting entropy in causal set quantum gravity
Authors: D. Rideout, S. Zohren
Comments: 5 pages, 1 figure. Talk given by S. Zohren at the Eleventh Marcel Grossmann Meeting on General Relativity at the Freie U. Berlin, July 23 - 29, 2006

The finiteness of black hole entropy suggest that spacetime is fundamentally discrete, and hints at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered, but should manifest itself in a theory of quantum gravity. We review recent attempts to define a microscopic measure for black hole entropy and for the maximum entropy of spherically symmetric spacelike regions, within the causal set approach to quantum gravity.

My partiality to the causal set approach is admittedly showing here. Any approach that does not include causal sets is, IMO, fundamentally incomplete. I'm not happy with the 'grainy space' hypothesis. There is observational evidence that does not set well with that proposition - an issue I find very troubling. High energy gamma ray photons should exhibit more scattering than is observed.

jal

Hi Chronos!

If different approaches yields similar results, then, it should be possible to said that "the results" arise from "First Principle".
By examining the "unexplained" "taken for granted", "presumptions" and "assumptions" of the different approaches, It should be possible to arrive at some "First Principle".
Therefore, all of the approaches which use "Minimum length", "Planck Scale", "grainy space", should end up with a "structure", "casual set".
I would search, for the assumptions and presumptions that have been made, in process of going from 'grainy space' to 'observational evidence'.

I think that the fun is in the search.
The answer will probably be "in our face" and prove to be very dull.
jal

Chronos

Well [nudging pebble with toe], I'm not entirely happy with 'First Principle' concepts. They tend to let time dependency sneak into the backdoor without a pass. I'm not convinced this is necessarily valid.