# Crossing The Desert-without h-bar

## Main Question or Discussion Point

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

As curvature has dimensions 1/L, L being length, such terms are dimensionless. To give them the dimension M�, M being mass, required from the action one has to multiply these terms by a dimensionfull parameter – the Planck constant ~. Thus, the terms in the quantum corrected action that are of second order in curvature have a multiple of ~ in front of them and thus are quantum corrections. This power of ~ agrees with the fact that these terms arise at one loop order of perturbation theory. Containing a prefactor of ~, these terms should be ignored when considering the classical gravity theory, as this is obtained via ~ → 0 limit.
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

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marcus
Gold Member
Dearly Missed
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]

$$\hbar$$

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marcus
Gold Member
Dearly Missed
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.

marcus
Gold Member
Dearly Missed
To get the Krasnov video, go here
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

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''.

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

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

marcus
Gold Member
Dearly Missed
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.

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

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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)
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
Gold Member
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.

Questioning everything??? Must lead to proposing an approach that should be investigated.
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 [Broken]
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

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Chronos
Gold Member
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.

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 [Broken]
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
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http://arxiv.org/PS_cache/gr-qc/pdf/0508/0508109.pdf [Broken]
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/graham/research-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.
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Do you have any link to recent papers that I could read?
jal

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Chronos
Gold Member
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.

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Hi Chronos!
My partiality to the causal set approach is admittedly showing here.

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'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.
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

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Chronos
Gold Member
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.

Hi 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.
hehehe…. We are all little pebbles …. Hehehe
We are all questioning …. And doing … what if??? …. Some people are more structured in their approaches and have more skills to apply to their postulates.
Example: Kirill Krasnov 01 March 2007
http://arxiv.org/PS_cache/gr-qc/pdf/0703/0703002.pdf [Broken]
Non-Metric Gravity I: Field Equations

(I don’t like to get into the para, meta domains since their postulates have not been advanced to being able to work with them.)
The following paper (from another thread) will surely motivate some skillful individuals to attack this approach or to try to develop this approach.
Like I’ve said, “It’s just as important to identify the dead ends as it is to forge new paths”.

http://arxiv.org/PS_cache/quant-ph/pdf/0604/0604064.pdf [Broken]
Relational EPR
Matteo Smerlak†, Carlo Rovelli‡
March 4, 2007
We study the EPR-type correlations from the perspective of the relational interpretation of quantum mechanics. We argue that these correlations do not entail any form of “non-locality”, when viewed in the context of this interpretation.
The abandonment of strict Einstein realism implied by the relational stance permits to reconcile quantum mechanics, completeness, (operationally defined) separability, and locality.
-----------------
When I say, “First Principle”, I am thinking of the opposite of random and chaos.
“Causal set” and Quantum Minimum Length Structure (QMLS)” are approaches that could end up as a dead end ..or …. Not.
jal

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Chronos
Gold Member
Looks like we are at the same lunch stand. Wondering how fine the line is between reality and imagination is an interesting excercise. On the other hand, I sometimes question if the line actually exists. More often I wonder if it is meaningful to make the attempt to draw one. It is an extension of the human condition and nature does not always respect that distinction.

My issues are with continuity between science and observation. I loathe unfalsifiable theories. I think that is an escape hatch. Did the universe have a 'beginning'? The question is inherently unfalsiable on the face of it. You can hardly justify its existence without a beginning. The only saving grace is causality ceases to be meaningful when you truly push the envelope. The chains of intellect are forged from a substance much tougher than steel - imagnination. That is what we lack. I suspect future historians will will characterize the 21st century as the 'gray age'.

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Hi Chronos!
I wonder if the "old guards" are paying attention to the work coming out of perimeter Institute. They cannot be accused of lack of imagination.
I'm sure that if they can accomodate a new idea in their approaches they would. How else can someone get "headlines" and "funding".
Do the "old guards" want to know about the dead ends and the new paths?
Does it really matter to them if the "Big Bang" is right or wrong? The people at CERN do not need a new interpretation to be able to do their experiments.
Even if SUSY is wrong, the experiments are capable of being performed.
So with cynicism aside ....
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http://arxiv.org/PS_cache/gr-qc/pdf/0703/0703027.pdf [Broken]
Conserved Quantities in Background Independent Theories
Fotini Markopoulou
05 march 2007
p. 8 In conclusion, our basic idea is that, if there is an effective theory, it is characterized by effective degrees of freedom which remain largely coherent, i.e., protected from the Planckian evolution and hence relevant for the low energy limit.

We gave a simple example of a BI-I theory, evolving graphs of locally finite quantum systems.
p. 9 collective coherent excitations of the BI theory as a first step towards being able to describe such a transition.
Could someone explain the quoted phrases that I put in bold letters?
-------------------------
http://arxiv.org/PS_cache/gr-qc/pdf/0604/0604075.pdf [Broken]
Emergent General Relativity
Olaf Dreyer
18 April 2006
1.1 Introduction
This article wants to be two things. On the one hand it wants to review
a number of approaches to the problem of quantum gravity that are new
and have not been widely discussed so far. On the other hand it wants
to offer a new look at the problem of quantum gravity.

p.13 In recent years we have see a number of new approaches to the problem of quantum gravity come very close to the stated goal. Using methods and ideas foreign to the more traditional approaches they were able to make progress were others got stuck. Maybe we will soon have not
just one quantum theory of gravity but several ones to choose from. To
decide which one is the right one will then require recourse to experiment.
What an exciting possibility.
------------------
http://arxiv.org/PS_cache/hep-th/pdf/0604/0604120.pdf [Broken]
Towards Gravity from the Quantum
Fotini Markopoulou
18 April 2006
A spacetime emergent from a background independent theory raises is-
sues regarding emergent locality vs fundamental locality (section 1.6.2).
We are optimistic that this is not a problem but, rather, an opportunity
for quantum gravity phenomenology that is not tied to the Planck scale.
It also raises questions about the role of time which we discuss in section
1.6.3. Finally, in the speculative section 1.6.4, we conjecture that this
direction may provide a natural place and explanation for the Einstein
equations. We summarize in the Conclusions.

1) The emphasis on the effective coherent degrees of freedom addresses directly and in fact uses the dynamics. The dynamics is physically essential but almost impossible to deal with in other approaches.
2) A truly effective spacetime has novel phenomenological implications not tied to the Planck scale which can be tested and rejected if wrong.
3) A pre-spacetime back-ground independent quantum theory of gravity takes us away from the concept of a quantum superposition of spacetimes which can be easily written down formally but has been impossible to make sense of physically in any approach other than Causal Dynamical Triangulations.
Some of the more exciting possibilities we speculated on included solving the problem of time and deriving the Einstein equations. Clearly this direction is in its beginning, but the basic message is that taking the idea that general relativity is an effective theory seriously involves rethinking physics without spacetime and is likely to have large scale consequences.
This opens up a whole new set of possibilities and opportunities.
Jal

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Chronos
Gold Member
It might be the wrong approach, just my opinion.

I would not want you to think that trying to get away from the Planck Scale is unique to my approach.
Here are other approaches.

Is there a way to combine “Quantum Minimum Length Structure (QMLS)”, M-Theory and LQG?
There is an approach “minisuperspace”.

http://arxiv.org/PS_cache/gr-qc/pdf/0703/0703057.pdf [Broken]
Existence of generalized Kodama quantum states.
III. A new approach to finite, full quantum gravity.
Eyo Eyo Ita III
March 8, 2007
Also, check out Stefano Ansoldi to see more similarities when using “minisuperspace”.?

http://www-dft.ts.infn.it/~ansoldi/Research/PastResearchSummary.html
Past Research Activity of Stefano Ansoldi
In the first case, a great advantage of Eguchi's formulation of string dynamics is that it treats the extended object as a whole dynamical entity, without focusing on its constituents (points). The motion of the object can then be described in what is called loop space. In particular we worked on giving a path-integral formulation of string dynamics a la Eguchi [2], showing that the quantum dynamics can be described in terms of fractal properties of the world-sheet [6] and interpreting in terms of these aspects the small-scale space-time structure, whose microscopic constituents are branes, instead of points [7].

http://www-dft.ts.infn.it/~ansoldi/Research/LoopQuantumMechanics/HTML/index.html
Loop Quantum Mechanics and the Fractal Structure of Quantum Spacetime
5.1 Correspondence Principle, Uncertainty Principle and the Fractalization of Quantum Spacetime
If spacetime is a derived concept, then is seems natural to ask, what is the main property of the fuzzy stuff, let us call it quantum spacetime, that replaces the smoothness of the classical spacetime manifold, and what is the scale of distance at which the transition takes place?''. Remarkably, the celebrated Planck length represents a very near miss as far as the scale of distance is concerned. The new source of fuzziness comes from string theory, specifically from the introduction of the new fundamental constant which determines the tension of the string. Thus, at scales comparable to , spacetime becomes fuzzy, even in the absence of conventional quantum effects ( ). While the exact nature of this fuzziness is unclear, it manifests itself in a new form of Heisenberg's principle, which now depends on both and . Thus, in Witten's words, while a proper theoretical framework for the [new] uncertainty principle has not yet emerged, ...the natural framework of the [string] theory may eventually prove to be inherently quantum mechanical.''.
That new quantum mechanical framework may well constitute the core of the yet undiscovered -Theory, and the non perturbative functional quantum mechanics of string loops that we have developed in recent years may well represent a first step on the long road toward a matrix formulation of it. If this is the case, a challenging testing ground is provided by the central issue of the structure of quantum spacetime. This question was analyzed in Ref. [6] and we limit ourselves, in the remainder of this subsection, to a brief elaboration of the arguments presented there.
The main point to keep in mind, is the already mentioned analogy between loop quantum mechanics'' and the ordinary quantum mechanics of point particles. That analogy is especially evident in terms of the new areal variables, namely, the spacelike area enclosed by the string loop, given by Eq. (18), and the timelike, proper area of the string manifold, given by Eq. (4). With that choice of dynamical variables, the reparametrized formulation of the Schild action principle leads to the classical energy per unit length conservation . Then, the loop wave equation can be immediately written down by translating this conservation law in the quantum language through the Correspondence Principle
….we insist in maintaining the wholeness'' of the string and consider exact solutions in loop space, or adopt a minisuperspace approximation quantizing only one, or few oscillation modes, freezing all the other (infinite) ones. In the first case, it is possible to get exact free'' solutions, such as the plane wave.

The central result that follows from the above equations, is that the classical world-sheet of a string, a smooth manifold of topological dimension two, turns into a fractal object with Hausdorff dimension three as a consequence of the quantum areal fluctuations of the string loop [6].

Hence, quantum string dynamics can be described in terms of a fluctuating Riemannian -surface only when the observing apparatus is characterized by a low resolution power. As smaller and smaller areas are approached, the graininess of the world-sheet becomes manifest. Then a sort of de-compactification occurs, in the sense that the thickness of the string history comes into play, and the world-surface'' is literally fuzzy to the extent that its Hausdorff dimension can be anything between its topological value of two and its limiting fractal value of three.

5.2 Superconductivity and Quantum Spacetime
Quantum strings, or more generally branes of various kind, are currently viewed as the fundamental constituents of everything: not only every matter particle or gauge boson must be derived from the string vibration spectrum, but spacetime itself is built out of them.
At the same time, the functional approach leads to a precise interpretation of the fuzziness of the underlying quantum spacetime in the following sense: when the resolution of the detecting apparatus is smaller than a particle DeBroglie wavelength, then the particle quantum trajectory behaves as a fractal curve of Hausdorff dimension . Similarly we have concluded on the basis of the shape uncertainty principle'' that the Hausdorff dimension of a quantum string world-sheet is , and that two distinct phases (smooth and fractal phase) exist above and below the loop DeBroglie area. Now, if particle world-lines and string world-sheets behave as fractal objects at small scales of distance, so does the world-history of a generic -brane including spacetime itself [19], and we are led to the general expectation that a new kind of fractal geometry may provide an effective dynamical arena for physical phenomena near the string or Planck scale in the same way that a smooth Riemannian geometry provides an effective dynamical arena or physical phenomena at large distance scales.
------------
I'll be trying to include these points in my blog.
jal

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Chronos
Gold Member
Personally, I like information theory and entropy as a background. Scaling factors, while permitted, have no meaningful local consequences. It might be science, but is not very useful.

Hi Chronos!
I would like to hear you decription of what a system that has no entropy and no degree of freedom would look like.
From that point, what would need to change to obtain our perceived universe.
Jal

Chronos