Can a Group Field Theory Approach Unify Quantum Gravity Approaches?

[jal]

How to build a universe.
1. Figure out how our universe is built
2. Determine if the data from CERN tell us that the smallest building blocks
are at 10^-18.
3. Figure out why #12 keeps cropping up in so many approaches.
4. Figure out the dynamics.
----------
For a more detail explanation, on how to build a universe, see:
http://arxiv.org/abs/0710.3276
Group field theory as the microscopic description of the quantum spacetime fluid: a new perspective on the continuum in quantum gravity
Authors: Daniele Oriti
(Submitted on 17 Oct 2007)
We introduce the group field theory (GFT) formalism for non-perturbative quantum gravity, and present it as a potential unifying framework for several other quantum gravity approaches, i.e. loop quantum gravity and simplicial quantum gravity ones. We then argue in favor of and present in detail what we believe is a new GFT perspective on the emergence of continuum spacetime from discrete quantum structures, based on the idea of quantum space as a condensed matter system.
In particular, group field theories can offer the context and the tools to realize explicitly the intriguing idea of spacetime as a condensate of fundamental building blocks and of continuum geometry as an emergent concept.
p.13
All this may be interesting and indeed it is intriguing to speculate of a unifying framework for all discrete quantum gravity approaches, that encompasses loop quantum gravity structures as well as simplicial quantum gravity ones. But is it useful?
p. 14
This exercise has two purposes. 1) It may help in acquiring a new understanding of the insights the different approaches provide, and in analyzing their mutual compatibility, and possibly also suggests ways in which what we have learned from one approach can contribute to solving presently open problems of another or common to all. 2) It is needed in order to check whether a single coherent picture of quantum gravity, patching together all these various insights and results, is possible, within the GFT setting. If it turns out that, indeed, it is possible, then we believe it would be arguably the best thing to use it and develop it further.
-------------
This is the approach which I can best understand since it is this concept that I have been advocating in my blog.
--------------
Daniele Oriti, and Tamer Tlas are using the fundamental building blocks of quantum space in their latest paper to find “dynamics”.
http://arxiv.org/abs/0710.2679
A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
Authors: Daniele Oriti, Tamer Tlas
(Submitted on 14 Oct 2007)
p. 11
Notice that there is almost nothing in the above choices that can select any specific dynamics of the geometric data (B variables and group elements, say) at the level of the individual Feynman diagram. The only dynamical ingredient above is the choice of a certain relation between them, but nothing seems to dictate, at the level of the GFT action, the individual dynamics of each set of variables.
p. 46
Our results, as we have discussed, support the view of GFTs as local and discrete 3rd quantizations of gravity, providing a nice field theoretic description of the quantum dynamics of the fundamental building blocks of quantum space.
Even more importantly, maybe, the new models, and possible modifications of the same, seem to provide the long sought for explicit unifying framework for spin foam/loop quantum gravity and simplicial quantum gravity approaches (quantum Regge calculus and dynamical triangulations). Looking at these different approaches from the proposed common GFT framework can offer, we hope, new possibilities for mutual enrichment and cross-fertilization between the various lines of research that are currently pursued as separate avenues toward a common goal, in particular regarding the outstanding issue of the continuum and semiclassical approximation of the discrete picture of quantum geometry they all seem to be based on.
-------------
jal

 

[Chronos]

It assumes there is such a thing as 'fundamental' building blocks of spacetime. I view that conjecture with skepticism. There is incompatible evidence.

 

[jal]

It assumes there is such a thing as 'fundamental' building blocks of spacetime. I view that conjecture with skepticism. There is incompatible evidence.

I think that the use of the term "building block" is ALL incompasing. Be it a wave, string, or ? Whatever, it is organized in a geometric pattern which we should be able to extract information by combining some of the tools learned in string, knots, spin foam, etc.
jal

 

[friend]

It assumes there is such a thing as 'fundamental' building blocks of spacetime. I view that conjecture with skepticism. There is incompatible evidence.

Maybe not. I'm reading Lee Smolin's book, "The trouble with physics". He mentions how observation of spiral galaxies show that within a certain distance to the center the stars revolve around the center by laws given by Newtonian gravity. But outside that distance they revolve differently. The difference seems to be that there is a minimum acceleration. At further distances acceleration towards the center decreases until a certain point where it jumps to a higher than expected acceleration.

My point is quantized acceration equal quantized gravity by the equivalence principle. Thus there may be evidence of quantum gravity.

Perhaps more exact measurements will reveal a spectrum to these jumps in acceleration=gravity.

 

[Chronos]

I tend to agree with that conjecture, friend, but with reservations. Those types of observations tend to encourage the dark matter hypothesis, which I think is well founded. Quantum gravity might be a better candidate explanation, but I'm sticking with dark matter for now.

 

[Fra]

I'm not sure if I understand the suggested line of reasoning but how does an observer extrapolate any subjectively observed "quanta", to an objective (observer independent) existent quanta.

Is an apparent quanta a property of the "observational resolution" of the observer, an objective discreteness of what is observed and if so how would any observer distinguish between the two cases?

In the first case, one may wonder how the different subjective views relate to each other?

To consider building blocks of spacetime without mentioning an observer that can relate to the construct seems to me like something is missing, or is an arbitraty observer implicit in the reasoning and then the uniquenss of the description as communicated between observers is postponed for later in the research?

I apologize if I missed anything obvious.

/Fredrik

 

[jal]

arivero , I’m bring this over for discussion because I don’t want to litter your thread.

http://arxiv.org/abs/0710.3543
The significance of numerical coincidences in nature
Authors: Brandon Carter
(Submitted on 18 Oct 2007)

p. 9
They can be categorised as three coupling constants,
and three mass ratios, and their empirically determined numerical
values are approximately:12
gS .=4, e.=1/12, mN.=1/2× 10−10
The values of the coupling constants are rather more familiar in their
squared forms: thus we have the gravitational fine structure constant
… the ordinary (electromagnetic) fine structure constant, e2 .= 1/137, and …
I need explanation with e.=1/12 and , e2 .= 1/137
I always thought that 12X12=144 not 137
------------

arivero

Well, I guess he takes the nearest simple fraction to sqrt(137), and he chooses 1/12. So it really compares 12 against 11.7, arguably not so bad.

A peculiarity of this article is that a couple ways ago I have been told that the relationship between mass of electron and pion (!) had circulated as a conjecture in the sixties. I though it came from McGregor, but it is formula (6) in pg 11 of this paper.

"Figure out why #12 keeps cropping up in so many approaches."
Some relationship is being overlooked with e.=1/12 and , e2 .= 1/137.
e2 .= 1/137 is within the drip line. It is the strength of the interaction between electrons and photons. Dark energy in not within the drip line.
What would it be for photons and dark energy?
arivero , you have been doing a lot of thinking with the constants. Can you make a link to the number 12 and that tiny difference of 0.3?
-------------
Basic references
http://en.wikipedia.org/wiki/Fine-structure_constant
In the theory of quantum electrodynamics, the fine structure constant plays the role of a coupling constant, representing the strength of the interaction between electrons and photons. Its value cannot be predicted by the theory, and has to be inserted based on experimental results. In fact, it is one of the twenty-odd "external parameters" in the Standard Model of particle physics.
http://en.wikipedia.org/wiki/Coupling_constant
http://en.wikipedia.org/wiki/Dark_energy
http://2physics.blogspot.com/2007/07/changing-constants-dark-energy-and.html
Wednesday, July 25, 2007
"Changing Constants, Dark Energy and the Absorption of 21 cm Radiation" -- By Ben Wandelt
----------
jal

 

[friend]

I tend to agree with that conjecture, friend, but with reservations. Those types of observations tend to encourage the dark matter hypothesis, which I think is well founded. Quantum gravity might be a better candidate explanation, but I'm sticking with dark matter for now.

So the question is: What effect of Dark Matter can there be that cannot also be explained by a discrete spectrum of acceleration?

As I understand things, Dark Matter only interacts gravitationally, and by the equivalence principle gravitation is equivalent to acceleration. So if gravity is quantized, then acceleration is quantized. And there would be absolutely no way of distinquishing any Dark Matter effects from quantized acceleration effects. Does this make sense?

Sorry, Fra, I did not understand what you were trying to say.

 

[arivero]

arivero
arivero , you have been doing a lot of thinking with the constants. Can you make a link to the number 12 and that tiny difference of 0.3?

Nope. It is only that sqrt(137) is about 11.7 and he rounds off.

generically, 12 is a likely number. As mathematicians say, there is only a few low integers and a lot of relationships to meet, so it is not rare to find any low integer in a lot of places. In the case of 12, there was also a human endeavour: making lots. Old number systems, as well as monetary systems, are 12 based in order to be able to make lots between 2,3 or 4 persons. This was sophisticated to 60 in order to include 5. To put it in clear: four persons going dinner and paying under the old british system can always divide exactly the bill. Four persons paying under new british system, or under euro, can not. It is not physics and it is not even mathematics, it is just human bussiness.

In mathphys, it is easier to find 24, sometimes from 4!, sometimes from SO(8) triality.

 

[Phred101.2]

How about building a "wigglyverse" or a "Wverse"?

Imagine some space. This space has a lot of wiggly "things" in it. They wiggle a lot and bump into each other and sometimes end up turning into other kinds of "wigglys". They also "emit" and "absorb" a different, or a unique sort of wiggly that has a couple of strange properties., so it's called a "wiglet". Wiglets always "travel" (move around the space) at the same speed unless they are near a wiggly. They, like the wigglys can "wiggle" the same, but they can only get so big. Also if two of them bump into each other this sometimes ends up being no wiglets but a wiggly "instead". The reverse can happen too. After a "while" the space "expands" due to all the "wiggling" and the "wiglets" and they have a lot more room. There are also a couple of "strange" things about wigglys and the wigglyverse: the wigglys can "attract" each other through some innate "force" that acts like a field extending in all directions, and isn't at all related to how fast they are wiggling, another "force" that is "caused" by wigglys is that some of them have another property that acts a lot like the first but is related to wiglets. There is a third "force" or property of wigglys (and of course the special ones, the wiglets), that isn't at all like the others in that wigglys don't care about where they are in "space", but this one is also very unstable (unlike the first two), so it isn't very noticeable, unless you look carefully.

Anyone see where I'm going with this?

How can the wigglyverse end up with wigglys that "disappear" because of the first property they all have? If too many of them get together (now that there's all this room), get "attracted" together and can't make enough wiglets to prevent the attraction from making them all try to get into the same place, to "become" the same wiggly (no-space, like the third "force" seems to "work" in), they "collapse" into "somewhere" else than the wigglyverse, maybe. Something happens to all those wigglys and wiglets.

 

[jal]

HEHEH! A ROSE IS A ROSE BY ANY NAME.
Why don't you put your teeth into the following.
----------
The Schwarzschild radius of our universe is greater than the present size of our universe. It does not expand. It was always the same size. Changing the position of the particles inside the Scharzschild radius does not change the radius. What those particles are doing does not change the size of the radius. So, if you want to pretend that they all got together and made a big bang or that they all got together and bounced it still does not change the radius of the gravity. (Scharzschild radius)
What is important is how far away is another universe. After all, none of them have come crashing into our universe. (A black hole) There is no evidence that even one particle is falling into our universe. Or, ? is there? (Fred Hoyle would have liked to know.)
The universe is expanding into it’s Scharzschild radius and by black hole logic it cannot expand any farther.
If you want to use the logic of big bang then gravity cannot spread faster than the speed of light therefore, expansion, inflation cannot go faster than the speed of light. If it did then it would be equivalent to saying that something can get out of a black hole.
Maybe the “math kids” have already done the calculations. “Bouncing” is so much easier since the Scharzschild radius of the universe has already been created by the 10^80 particles.
Information going into a local black hole would not be lost since now we would be able to say that it is going to the Scharzschild radius of the universe. Nothing leaves the universe.
-------
Reference from David M. Harrison:
For a mass of 2.5 x 1053 kg, i.e. a 2 and a 5 followed by 52 zeroes kg, the Schwarzschild radius is about 17 billion light years. This huge mass is an estimate for the total mass of the universe. Also, given that the age of the universe is 15 billion years or so, 17 billion light years is awfully close to the size of the universe. Does this mean that the universe itself is a black hole?
-------
jal

 

[Phred101.2]

The wigglyverse also has a certain "background" wiggle that can "produce" wigglys somewhere but only for a very small time. And because some wigglys don't emit or aborb wiglets (and have very small "wiggles") they are "invisible" to them (wiglets). Maybe they "interact" with each other via the third property of the wigglyverse. (the third "force" which wigglys have to "work" with each other in the wigglyverse).

Wigglys, wiglets and wiggleons

Because some kinds of wigglys can get together (and this has largely happened since the wigglyverse got a lot bigger), wigglys can make up a stable wiggle together, two of these have very nearly the same wiggle (property) and they "condense" due to a certain interaction between the two which is related to one of them having the second property as well (as a wiggle), this means a third kind of wiggly, with a much smaller wiggle than the first two, can join this "condensed" state of wiggle, and these smaller wiggles then largely emit and receive wiglets. which make their wiggle change so they change their configuration with the other two. The two "heavy" wiggles stay together and the "light" wiggle wiggles around them, sending and receiving wiglets to other such combinations, or condensed wiggles. (maybe these could be labelled something like "wiggleons")

How am I doing so far?

 

[topovrs]

The Schwarzschild radius of our universe is greater than the present size of our universe.

This is not true. Although the universe may only be 13.8 billion years old, the comoving radius is about 46.5 billion ly. The estimated density of visible matter is far less than the critical density, leading to the need to postulate dark matter in order to account for the observed flatness of the universe. See http://en.wikipedia.org/wiki/Observable_universe.

topovrs

 

[jal]

What Is The Purpose Of You Posting In This Thread/here?

 

[Phred101.2]

"The Purpose"?
What is the "purpose" of a photon from a distant galaxy "causing" an electron in your eyeball to recoil? Or the "purpose" of your eyeball being there to ensure the electron was in just the right place?

 

[jal]

I guess that you have no teeth.
You should leave this thread to the "math kids"

 

[Phred101.2]

I guess that you have no teeth.
You should leave this thread to the "math kids"

I would guess that you may have something of a problem: arrogant attitudes to others who appear to you to be "ignorant", could well mean that you will end up toothless (at least in terms of the logic you seem to be so convinced you possess).
Whats a "math kid" btw?

 

[Chronos]

Restrain yourself, Phred, Jal is well intended. Agreement is not an issue, but civility is, so let's try to be civil. There will be plenty of observations to compare to conjectures over the next decade. In the mean time, be polite.

 

[jal]

Thanks Chronos!
I wish that I was a “math kid”. (The Schwarzschild radius is about 17 billion light years.)
I’ve tried to do the calculations and I keep getting my units and zeros mixed up.
The concept of our universe having an “edge”, (a 17 billion light years Schwarzschild radius.), is disturbing to me and is contrary to what I have been taught.
I have seen a lot of papers about the event horizon but there seem to be a total denial by the science community to investigate the implications of this 17 billion light years Schwarzschild radius.
The math says its there. The math and the logic for black holes has been studied. The Schwarzschild radius is a brick wall and nothing can get out. With no evidence of anything coming into our universe then we automatically get conservation of energy. This also implies that our local black holes are not consuming information but rather are a conduit of information flow to the 17 billion light years Schwarzschild radius.
If there are 10^500 other universes, they are irrelevant until one of them falls into our universe or we fall into that other universe.
We do have unexplained high energy produced by exploding stars. Could a possible explanation be that something came through the Schwarzschild radius and that “invisible connection”?
A “math kid” might be able to give an explanation of why we cannot seen the connection between that exploding star and the Schwarzschild radius that is 2 BLY farther than the event horizon.
The bounce rather than the bang becomes a lot more logical since there is a max. limit and min. limit for the particles to oscillate. Just like the gravity of the Earth does not change by the movement of matter in the interior of the Earth the gravity of the universe does not change by the movement of 10^80 particles. The Schwarzschild radius remains in its position.
I don’t relish all of those thoughts but that does not mean that they should not be investigated in a more formal setting.
I look forward to reading unbiased links or work in progress that you might have found.

 

[Phred101.2]

BTW are "we" going to be in this universe?

“...the complex question of how the brain and its constituent parts produce mental activity (specifically consciousness) is, as usual, based mainly on the temporal and spatial analogy that exists between what are believed to be the properties of the conscious mind and those of the electromagnetic fields of the brain. Reasoning by analogies of this kind is, ...widely appreciated in philosophical circles to be a flawed road to understanding.
We have learned that in the modern world of information processing machines and Turing's theorems that symbolic representation is an entirely plausible way to represent even the most intangible of concepts or personal experiences. The idea that isomorphic encoding (i.e. spatiotemporal congruence) has any priority over symbolic representation that flies in the face of our ability to encode such parameters as the hue of a 700nm light or the aroma of a flower... [T]he assumption ...that the information content of the EM fieldand the states of the neurons are identical, as McFadden puts it[:] ...'”...The brain's EM field holds precisely the same information as neuron firing patterns...”'.
...Einstein was speaking of matter-energy equivalence and not information equivalence. ...[M]ore specifically, the essence of Einstein's equation is the bidirectionality of the equal sign. Mass could be converted to energy [and back again]. There is no such bidirectionality possible between the EM wave and ...neurons." -William Uttal

 

[jal]

Keeping the Schwarzschild radius in mind... the following paper might give new insight on minimum length and maximum length and possible observations.
http://arxiv.org/abs/hep-th/0610064
Scale Dependent Metric and Minimal Length in QEG
Authors: Martin Reuter, Jan-Markus Schwindt
(Submitted on 5 Oct 2006)
Abstract: The possibility of a minimal physical length in quantum gravity is discussed within the asymptotic safety approach. Using a specific mathematical model for length measurements ("COM microscope") it is shown that the spacetimes of Quantum Einstein Gravity (QEG) based upon a special class of renormalization group trajectories are "fuzzy" in the sense that there is a minimal coordinate separation below which two points cannot be resolved.

 

[jal]

I have been able to find
http://eprintweb.org/S/authors/All/my/Y_Myung/10
Black hole and holographic dark energy
Yun Soo Myung

Received. 06 February 2007 Last updated. 11 April 2007
Abstract. We discuss the connection between black hole and holographic dark energy. We examine the issue of the equation of state (EOS) for holographic energy density as a candidate for the dark energy carefully. This is closely related to the EOS for black hole, because the holographic dark energy comes from the black hole energy density. In order to derive the EOS of a black hole, we may use its dual (quantum) systems. Finally, a regular black hole without the singularity is introduced to describe an accelerating universe inside the cosmological horizon. Inspired by this, we show that the holographic energy density with the cosmological horizon as the IR cutoff leads to the dark energy-dominated universe with $ømega_{ m Lambda}=-1$.
------------
I would assume that, eventually, that there will be calculations made which include the bounce model.
If you "click" on his name you will get 106 papers.
-----------------
http://www.math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html
Is the big bang a black hole?
One of the most exciting possibilities was considered by C. Hellaby, in 1987 who envisaged the Universe being created as a string of beads of isolated while holes that explode independently and coalesce into one Universe at a certain moment. This is all described by a single exact solution of general relativity.
-----------
This would in effect be saying that we exist in a Schwarzschild universe and that the expansion of the universe is due to “more matter”, (another black hole) being added to our Schwarzschild universe black hole. It sounds like a good way to eliminate the “inflaton” and the massless scalar field.
(Hey! Don’t knock this approach. It’s similar to having the Earth bombarded by meteorites in its early formation and having the Earth “sweeping” up the dust in its path.)
I have not been able to find this paper. It’s probably because it is under a title which I could not recognize.
http://www.mth.uct.ac.za/~cwh/mypub.html
Charles Hellaby's Publications
--------
-------------------

 

[jal]

The folowing paper should have been in the first post, for anyone who want to build an universe.
http://arxiv.org/abs/0711.0077
Dark Energy and Dark Gravity
Authors: Ruth Durrer, Roy Maartens
(Submitted on 1 Nov 2007)
Observations provide increasingly strong evidence that the universe is accelerating. This revolutionary advance in cosmological observations confronts theoretical cosmology with a tremendous challenge, which it has so far failed to meet. Explanations of cosmic acceleration within the framework of general relativity are plagued by difficulties. General relativistic models are nearly all based on a dark energy field with fine-tuned, unnatural properties. There is a great variety of models, but all share one feature in common -- an inability to account for the gravitational properties of the vacuum energy. Speculative ideas from string theory may hold some promise, but it is fair to say that no convincing model has yet been proposed. An alternative to dark energy is that gravity itself may behave differently from general relativity on the largest scales, in such a way as to produce acceleration. The alternative approach of modified gravity (or dark gravity) provides a new angle on the problem, but also faces serious difficulties, including in all known cases severe fine-tuning and the problem of explaining why the vacuum energy does not gravitate. The lack of an adequate theoretical framework for the late-time acceleration of the universe represents a deep crisis for theory -- but also an exciting challenge for theorists. It seems likely that an entirely new paradigm is required to resolve this crisis.

 

[jal]

In a short paper (27 pages) they have managed to summarize where we are and are proposing experiments that could be done in space that would extend our knowledge.
http://arxiv.org/abs/0711.0150
Space-based research in fundamental physics and quantum technologies
(Submitted on 1 Nov 2007)
Abstract: Space-based experiments today can uniquely address important questions related to the fundamental laws of Nature. In particular, high-accuracy physics experiments in space can test relativistic gravity and probe the physics beyond the Standard Model; they can perform direct detection of gravitational waves and are naturally suited for precision investigations in cosmology and astroparticle physics. In addition, atomic physics has recently shown substantial progress in the development of optical clocks and atom interferometers. If placed in space, these instruments could turn into powerful high-resolution quantum sensors greatly benefiting fundamental physics.

 

[Phred101.2]

(The top-down approach)

How to build a universe.
1. Figure out how our universe is built
2. Determine if the data from CERN tell us that the smallest building blocks
are at 10^-18.
3. Figure out why #12 keeps cropping up in so many approaches.
4. Figure out the dynamics.

Is there a "bottom-up" version of this? Are we going to find the bottom quark that will nail this (large) 'map' to some wall...?

 

[jal]

Hi Phred101.2!
As far as I can deduct from reading all the published papers, there is only one approach and only one tool that is being used.

Mathematics ===> symmetry ===> minimum length ===> two possible patterns
There are only two patterns that preserve volume.
Cubic pattern
For example see
http://arxiv.org/abs/0711.0273
The Emergence of Spacetime, or, Quantum Gravity on Your Desktop
R. Loll

hex. pattern
for example see
http://arxiv.org/abs/0711.0146
LQG vertex with finite Immirzi parameter
Authors: Jonathan Engle, Etera Livine, Roberto Pereira, Carlo Rovelli
-----------
Both approaches are yielding secrets.
When combining the mathematics/logic that has been developed in the study of black holes with what has been learned in the study of what makes patterns in a cavity then, in my opinion, CERN will discover that the smallest patterns are at 10^-18.
---------
Corrections, inputs, will accelerate my learning curve.
jal

 

[jal]

Ansari is proposing a formula that would be able to analyze a mini black hole. It would also determine if the minimum length has been reached by CERN.
http://arxiv.org/abs/0711.1879
Area, ladder symmetry, degeneracy and fluctuations of a horizon
Authors: Mohammad H. Ansari
(Submitted on 13 Nov 2007)
A few of harmonic modes appear to be extremely amplified on top of the Hawking's radiation. They are expected to form a few brightest lines with the wavelength not larger than the black hole size.
Maybe you are aware of other ways/formulas that could identify and analyse black holes.