fredag 7 december 2012

Is it possible to learn TGD?

Saturday, December 01, 2012



This is a blogpost directly from Matti Pitkänens blog. It seems that also Matti thinks that physics is only for physicists, and my efforts to give TGD lessons are in vain. I leave it for the readers to judge.
Matti also complains that the communication does not work, and I thought this would be one way to make things easier, not more difficult? Experts can go to Mattis blog, where they find the math and the physical phrases. I try to avoid them as far as possible here. I use more words, because words are my tool. The reader can determine if they form just a word-salat?

In an earlier blog discussion Hamed asked about some kind of program for learning TGD in roughly the same manner as I did it myself. I decided to write a brief summary about the basic steps leaving aside the worst side tracks since 35 years means too flat learning curve;-). 


I wrote a summary about the very first steps, that is the steps made during the four years before my thesis and related to classical dynamics mostly. I could not avoid mentioning and even briefly explaining notions like the "world of classical worlds" (WCW), quantum TGD, Kähler action, modified Dirac equation, zero energy ontology, etc... since I want to relate the problems that I encountered during the first years of TGD to their solutions which came much later, some of them even during this year. I hope that I find time to write similar summaries about later stages in the evolution of TGD and add them to this text.


This summary does not provide any Golden Road to TGD. I do not even know whether it is possible to learn TGD. And certainly it is much more difficult to passively assimilate ideas of others than to actively discover and develop ideas by one self. The authority of the original discoverer - such as that of Witten's - can help enormously but I do not possess this kind of authority so that I must trust only on the power of the ideas themselves.


Since the text consists of five pages it is more practical to give only a link to the pdf file containing it.

Comments:

Ulla said... I have stranded on the spacetime itself. I cannot decide which is the most easy way into TGD, and I think today it is wrong to start with introducing the classic concept of spacetime. There is clearly an interest in this, because my small 3 texts has got quite many visits. I have 30 texts written, but because of the uncertainty I have not published them yet.

Maybe the intro of some important problems would be a more logical way? As the three body problem?
Zero Energy Ontology etc. To link these to mainstream physics is also difficult for me.

Matti Pitkanen said...
The fact is that understanding of TGD requires understanding of basics of physics and mathematics. As a referee I have read so many unified theories by people who have read a couple of popular science books and got the impression that building a theory of everything requires just "creativity" that unified theories cannot be built in garage.

Physics and theoretical physics are disciplines, whose development has taken a about 500 hundred years, a life work of totally devoted brilliant people. Nowadays these 500 years can be compressed to 3-4 years in university classes. This is wonderful but during this time one of course gets only some important impressions, not much more. There is no hope of compressing 500 years to a couple of web articles. This would be however needed as a background to develop introduction to TGD for dummies;-).

Anyone can learn macro-economics but theoretical physics is a REALLY difficult discipline. Think only that the best mathematical brains have worked for 28 years in vain with superstring models. They did not get anywhere. We still have Einstein's theory as THE theory of gravitation.

The following old saying still applies. "God give me the wisdom to see what I cannot do and give strength to do what I can;-)". In my case this means that I cannot write a five page essay leading the reader to enlightment but I can improve endlessly the articulations of TGD so that who have the needed background can easily understand it when the Zeitgeist allows them to read an article about TGD in presence of colleagues.

Ulla said...
I did not talk of a 5 page essay. I talked about the basic questions leading to TGD. It is so enormously complex by itself. I have met so many questions now that need explanation in terms of mainstream thinking. The implicit part of TGD is one big obstacle. Also the different parts are so intwined in each other that it is almost impossible to start somewhere simple. This made me stop for a while, and now I have so little time for this. My aim is to continue, but I need advice what the best path would be. To simply repeat what you have said is nonsense. I need to UNDERSTAND it. As Hamed said, the most interesting part is the biology, but to reach there I need the physics first. Without university physics and most of the math :) I have only the words. And it is only an intro.

One thing that maybe went wrong is the Kaluza-Klein thinking about the cosmological constant? It led to string theory, but are there other ways out? Or is the try to mathematize the unknown wrong in itself?

I know you have the hierarchy.

http://www.scientificamerican.com/article.cfm?id=what-is-a-dimension-anyway

Matti Pitkanen said...

Unfortunately words are not enough when one is trying to talk about quantum physics or mathematics. In mathematics words are only a shorthand - program calls initiating processes in the brain of mathematician but not in brain of a layman. This mathematics is sometimes very simple but difficult to grasp without background. There is no concept so boringly simple as finite-D Hilbert space, but when you try to understand quantum theory without it you encounter mission impossible. Quantum superposition, quantum entanglement, and quantum jump: here are three notions whose understanding without Hilbert space is exceedingly difficult.

Complexity is very relative notion. Basic principles are simple but once you start to really develop and apply the theory, things become complex. So it is also with TGD: TGD is a TOE covering everything form CP_2 length scale to cosmology and one cannot expect simplicity at the level of implications.

The theory of von Neumann algebras is excellent example of this: the axioms look trivial but the mathematics generated by them looks formidable and fascinating at the same time.

If you look about text book about QED, something relatively simple by recent standards, you get absolutely scared by the complexity of the formulas. And they are only for electron-photon system!

I am sorry, but this is the situation. It is very very lonely here and also the air is very cold and thin;-). And it took 35 years to climb here;-). Maybe I should have thought twice.

Santeri Satama said...
Matti and Hamed, a learning strategy suggestion: to my knowledge there is no better way to learn a thing than to internalize it by trying to teach it to somebody else, "learn one thing, teach one other" as the saying goes; so if Hamed finds suitable "victim" at some stage of this process he could start trying to teach TGD - while simultaneously learning it with the help that Matti can can provide.

Good to see thins happening. The real test of TGD is can it be communicated to other theoreticians and even laymen, or will it remain the "Lonely God". ;)

PS: it's becoming almost impossible to post on this blog by passing the "not a robot" test. Which is both sad and funny.

 Matti Pitkanen said... To Santeri:

You are right about learning. Unfortunately too often only the teacher learns;-).

 11 said...
Dear Matti,

Did you think about future experiments to support or falsify your TGD?

 Matti Pitkanen said...

To 11:

Experimental tests are very important. TGD makes a lot of predictions. Many of them are acutally successfully tested already. Mention only p-adic mass calculations which are based on extremely general assumptions.

a) No standard SUSY is one prediction but no one takes this as interesting because standard SUSY is already excluded in practice.

b) My hope was that the absence of Higgs and identification of Higgs like state as pion of M_89 physics could provide a killer test. It however turned out that TGD is consistent with Higgslike state allowing at QFT limit effective description of particle masses: this follows more or less from the existence of QFT limit. Experimentally the situation is still unsettled. Decays in two-gamma channel and to fermion pairs are both decisive.

c) An excellent candidate for a breakthrough prediction is M_89 hadron physics. The prediction of entire new hadron physics is sensational. The recent observations from LHC (made for the first time already two yeas ago and commented also here) have simplest interpretation as decay of string like magnetic flux tubes to partons.

This kind of objects should not appear at ultra high energies since they relate to low energy hadron physics. The only possibility is that hadrons of new hadron physics with large mass scale are in question. M_89 hadron physics is of course the natural candidate for this hadron physics.
Already RHIC observed these events and QCD definitely does not predict them. Therefore the notion of color glass condensate was introduced to save the situation but it is not QCD prediction if we are honest. Quark gluon plasma is the prediction of QCD.

More generally fractal copies of hadron physics and also leptohadron physics predicting pion like states consisting of color octet charged leptons are predicted. These states have been observed for all lepton families but since they do not fit with standard model the observations have been put under the rug.

Also "infrared" Regge trajectories for ordinary hadrons are possible and there is recent evidence in case of ordinary hadrons for them: the scale of mass splittins is about 20-40 MeV.

d) TGD explains family replication in terms of the topology of partonic 2-surface and this also means predictions of new physics. Do gauge bosons have analog of family replication meaning an exotic octet of mesons besides singlet for dynamical symmetry SU(3) assigned to the 3 families? And how massive are the fermions corresponding to higher genus: here there is a good argument supporting the guess that they are massive.

These are just few predictions and related to particle physics. There are myriads of predictions in cosmology and astrophysics and also in biology. This because TGD Universe is fractal. Basic quantitative tool is p-adic length scale hypothesis predicting a hierarchy of length scales coming as powers of sqrt(2).

The problem is the communication barrier due to the extremely arrogant attitudes of the academic researcher. For this I cannot do much. It would be a job of psychiatrist.

Fractality said...
Matti: Noble attempt at helping us laymen out in cultivating understanding of TGD. It is much appreciated. Do you think you could do something similar for TGD theory of consciousness?
ThePeSla said... Matti,

This post is an excellent attempt at trying to communicate these frontier ideas. I downloaded it in hard copy of 8 pages and read it carefully. If you are interested in my impressions where we may share some evolution in our approaches I have stated it there.

Professors, like Hoyle when I had tea with him- well he said students are always coming to him to comment on their theories-of course we talked about other things, down to earth and I mentioned supporting him briefly if I did not have other directions but certainly not the new Big Bang cosmology.

Still feel free to comment on my system if I have in discussing yours made it a little easier- then you can get down to maybe something more useful from my own.

I mentioned the scientific american article ulla had posted in facebook- there was a time when I did break from just those two ways to apply and see dimensions and it was an awakening moment.

I think your more careful formal approach is much more difficult than freely allowing the intuition and poetic magic to flow.

But where you say you cannot understand some things even in the asking clearly that is an achievement and perhaps some things in the context were not an error (holographic stuff and surfaces for example) but the context is such an error.

As to why the advanced culture of Finnish science does not support your project that is like some form of economics it would take another Gauss to begin to phantom although I made meager suggestions.

All in all a great posting, thank you. I do wish I had the training in the exponential type notations but perhaps they slow us down.

Matti Pitkanen said...

To Fractality:

I hope I can find time and energy to continue the summaries, also about TGD inspired theory of consciousness and quantum biology.

Thanks for Pesla for encouraging comments.
Fractality said...
Matti: Excellent. You are inducing quantum jump to the order of Einstein ;) Have you ever theorized as to the roles of biologically active compounds like serotonin and certain tryptamine alkaloids?
Matti Pitkanen said...

Not seriously. Just some general ideas about what makes information molecule information molecule.

Santeri Satama said... Not sure how relevant this is to above questions, but watching this vid about psychological time and internal "clock" so far unexplained (http://www.youtube.com/watch?feature=player_embedded&v=DKPhPz5Hqqc)
gave the idea that internal clock or time-sense could be based on Shnoll effect. Through "information molecules"?.

Would that be the expectation of your general view about the relation of geometric times and psychological times?

Matti Pitkanen said...

Thank you for asking. I cannot answer without bringing in magnetic bodies.

One of their basic tasks is go generate EEG rhythms which define the ticks of clocks with different basic units of time. It has been observer that the period of EEG decomposes to two parts such that during first half there is coherence and second half non-coherence.

Maybe this means that during the first half period "alpha" subself with say average lifetime/wakeup time of .05 seconds wakes up and dies in the beginning of second half period (roughly). We ourselves would do the same in time scale of 12+12 hours. Wake-sleep cycle would define a universal clock.

In standard picture one tries to understand basic EEG rhythms in terms of various brain circuits. I see this as hopeless project as trying to find standard SUSY at LHC;-) but modern Big Science is full of this kind of desperate projects.

I have talked in http://matpitka.blogspot.fi/2012/11/quantum-dynamics-for-moduli-associated.html about the recent views concerning the generation of the arrow of time. I do not bother to type the recent view about time.

Perhaps it is enought to say that in zero energy ontology the analog of clock pendulum emerges at very abstract level. The state function reductions at upper and lower boundary of causal diamond take place alternatively. This has as an analog the motion of clock pendulum: the highest position at right- that at left- that at right-..... This would correspond at the level of self sleep-wake-up cycles which would be universal aspect of consciousness.

As always I think that the understanding is rather satisfactory now;-) . I must of course confess that the understanding of the arrow of time has been an Odysseia similar to the understanding of the nature of possibly existing Higgs in TGD Universe;-).

Ulla said...
Matti, fortunately I have absolutely no intention to make things more complex than they need to be. I only try to make some introduction, nothing else.

I have seen enough of nonsense to realize this is difficult, and that's why I usually ask. I WANT to do this because TGD is really a good way to understand things. But the details necessary are troublesome, and they force me to read lots and lots of articles. I don't write for experts, but for common people with common knowledge. For them words like math phrases are just garbage and say absolutely nothing. I have to 'translate' TGD.

Cold and thin air is good for the brain. Why on Earth did you have to come in my way? You should not have had, if things worked well, as T said. Dammit.

I have no problems with the test, which maybe says something about me?

 Ulla said...
Can I publish this discussion on my TGD Lessons?

Hamed said...
Dear Matti, and the readers,

When I see the posting I encounter with many comments. I know more of these persons are very interested to understand TGD, but there is a big problem for them that are a lot of physics and mathematics for those that don’t know about basic physics and mathematics.
I have some suggestions for the readers and I request from Matti if anything between them is wrong, he correct and complete it.

Generally learning science is a process that needs patient but it is very enjoyable ;-). About TGD this seems hard, because TGD is not only a theory but a program, a lot of mathematical and physical ideas and principles had evolved more than 30 years. Although learning TGD is hard but it is possible if one has enough patient.
I encourage everyone even laymen that are working in other fields of science to learn TGD. Because the worldview of TGD makes deep influence on their thinking and this leads to progress and evolution in other fields of science too.
How the laymen can learn TGD? I try to answer it.
in learning consciousness and biological parts of TGD, although at first it seems that these parts doesn’t need mathematics or physics but as I tried it, when one goes further and asks some whys in the bases of them, at end it will be Revealed that it needs understanding Quantum TGD. Similarly understanding the bases of Quantum TGD without classical TGD is impossible.
But for a beginner it is useful at first to understanding the definitions of concepts of TGD from classical to Quantum and after it to biology and consciousness at the introductory level without going further. For this the overview articles of TGD is very good.
After this, I encourage them to learn basic concepts of physics and mathematics. For laymen I think it is possible to learn them without calculations because it is enough for their purposes. Unfortunately it is not enough for me ;-). The book “The road to reality” of Penrose is very good for this purpose.(for example it gives some good mathematical intuitions about Hilbert space for learning Quantum too) The prerequisite for learning the book is physics and mathematics of high school. The physical intuitions in this book are very useful even for teachers in physics.

Santeri Satama suggested to me to teach for better understanding. Yes, It will be useful for my learning and I will try as I can. I remember the quoting of Einstein “You do not really understand something unless you can explain it to your grandmother.” ;-). I am certain that I can’t explain anything of physics to my grandmother ;-) but I think I can do it at least for the readers of the blog and request from Matti to correct it.

 Matti Pitkanen said... To Ulla:

Nothing against your proposal.


To Hamed:

Thank you for a perspective of a person who is really working hard to understand the ideas of TGD. It would be nice to have the "Road to Reality" in bookshelf. This kind of books are God's gifts to human kind. Maybe someone writes someday this kind of book explaining hyperfinite factors, Kac Moody algebras and all that stuff which makes me feel unpleasant;-).

I feel that technical side is not terribly important but maybe this is illusion: to learn the conceptual thinking one must perhaps learn first the basic techniques such as the mathematics learned in theoretical physical classes during first few years.


Maybe this relates to basic fact about language: words as such have no meaning, they only induce self-organization patterns giving rise to the experience of meaning. The meaning of the word is quite different for a person with and for a person without the adequate background. 

 Ulla said...
Thanks Matti,

Hamed is right in the fact that consciousness needs the physical background to be right understood. Also every biological event need a physical explanation, and that is alone a huge task. We have as instance with Matti discussed the meaning of endorphins and serotonins, but without the physical background his explanations seems meaningless, even nonsensical. This is exactly what ordinary physicists encounter too, and this is why they say TGD is rubbish. They simply have not the patience to learn it from basics. Many times I feel I know more than them when I have tried to discuss things, but then again I have too many empty boxes of knowledge. The mainstream physicist have maybe what seems a coherent knowledge, but when I ask deep enough it turns out they too know very little. This is why I asked for a list of problems that show TGD as a possible solution.

Hamed is really very good for TGD. I hope time is ripe for it now, and he is not marginalized for it.

 Matti Pitkanen said...

To Ulla;

Every generation of scientists plays again the evergreen "Emperor's new clothes" by H. C. Andersen.



tisdag 24 januari 2012

Geometrodynamics.

Geometrodynamics from wikipedia (short variant here) generally denotes a program of reformulation and unification which was enthusiastically promoted by John Archibald Wheeler in the 1960s and is today rather loosely used as a synonym for GR, and some authors use the phrase Einstein's geometrodynamics to denote the initial value formulation. Spacetimes are sliced up into spatial hyperslices, and the vacuum Einstein field equation is reformulated as an evolution equation describing how, given the geometry of an initial hyperslice (the "initial value"), the geometry evolves over "time". This is also what distinguishes TGD and GR, in the big structure, says Matti.

As described by Wheeler in the early 1960s, geometrodynamics attempts to realize three catchy slogans
  • mass without mass,
  • charge without charge,
  • field without field.
Just LOOK. This is a pointing to thinking today?

"The vision of Clifford and Einstein can be summarized in a single phrase, 'a geometrodynamical universe': a world whose properties are described by geometry, and a geometry whose curvature changes with time – a dynamical geometry." The geometry of the Reissner-Nordström electrovacuum solution suggests that the symmetry between electric (which "end" in charges) and magnetic field lines (which never end) could be restored if the electric field lines do not actually end but only go through a wormhole to some distant location. He searched the momentum constraint in geometry and wanted to show that GR is emergent, like a logical necessity; he talked of spacetime foam; requres the Einstein-Yang-Mills-Dirac System."

Scattering and virtual particles are similar modern notions? A dynamic metric.

"Geometrodynamics also attracted attention from philosophers intrigued by the suggestion that geometrodynamics might eventually realize mathematically some of the ideas of Descartes and Spinoza concerning the nature of space."

Is this a bad way to say that Matti Pitkänens work is too spiritual? Not even the name mentioned. Still he is 'famous'. See Topological Geometrodynamics: What Might Be the Basic Principles.

Modern geometrodynamics.
Christopher Isham, (he got the Dirac medal 2011), Jeremy Butterfield, (his homepage here) + students have continued to develop quantum geometrodynamics.

Addendum: About the Dirac medal, se all Dirac Medal winners here, note the many famous names:
Professor Christopher Isham
Imperial College London
For his major contributions to the search for a consistent quantum theory of gravity and to the foundations of quantum mechanics.
Chris Isham is a worldwide authority in the fields of quantum gravity and the foundations of quantum theory. Few corners of these subjects have escaped his penetrating mathematical investigations and few workers in these areas have escaped the influence of his fundamental contributions. Isham was one of the first to put quantum field theory on a curved background into a proper mathematical form and his work on anti-de Sitter space is now part of the subject’s standard toolkit.
His early work on conformal anomalies has similarly gone from “breakthrough to calibration”, as all good physics does. He invented the concept of twisted fields which encode topological aspects of the spacetime into quantum theory, and which have found wide application. He did pioneering work on global aspects of quantum theory, developing a group-theoretic approach to quantization, now widely regarded as the “gold standard” of sophisticated quantization techniques. This work laid some of the foundations for the subsequent development of loop-space quantum gravity of Ashtekar and collaborators (the only well-developed possible alternative to string theory). He has also made significant contributions to quantum cosmology and especially the notoriously conceptually difficult “problem of time”.
On the foundations of quantum theory, Isham has made many contributions to the decoherent histories approach to quantum theory (of Gell-Mann and Hartle, Griffiths, Omnes and others), a natural extension of Copenhagen quantum mechanics which lessens dependence on notions of classicality and measurement in the quantum formalism. In particular, using a novel temporal form of quantum logic, he established the axiomatic underpinnings of the decoherent histories approach, crucial to its generalization and application to the quantization of gravity and cosmology.
His recent work has been concerned with the very innovative application of topos theory, a generalization of set theory, into theoretical physics. He showed how it could be used to give a new logical interpretation of standard quantum theory, and also to extend the notion of quantization, giving a firm footing to ideas such as “quantum topology” or “quantum causal sets”. Isham’s contributions to all of these areas, and in particular his continual striving to expose the underlying mathematical and conceptual structures, form an essential part of almost all approaches to quantum gravity.

From Wikipedia cont. "Topological ideas in the realm of gravity date back to Riemann, Clifford and Weyl and found a more concrete realization in the wormholes of Wheeler characterized by the Euler-Poincare invariant. They result from attaching handles to black holes.
Observationally, Einstein's general relativity (GR) is rather well established for the solar system and double pulsars. However, in GR the metric plays a double role: Measuring distances in spacetime and serving as a gravitational potential for the Christoffel connection. This dichotomy seems to be one of the main obstacles for quantizing gravity. Eddington suggested already 1924 in his book `The Mathematical Theory of Relativity' (2nd Edition) to regard the connection as the basic field and the metric merely as a derived concept.
Consequently, the primordial action in four dimensions should be constructed from a metric-free topological action such as the Pontrjagin invariant of the corresponding gauge connection. Similarly as in the Yang-Mills theory, a quantization can be achieved by amending the definition of curvature and the Bianchi identities via topological ghosts. In such a graded Cartan formalism, the nilpotency of the ghost operators is on par with the Poincare lemma for the exterior derivative. Using a BRST antifield formalism with a duality gauge fixing, a consistent quantization in spaces of double dual curvature is obtained. The constraint imposes instanton type solutions on the curvature-squared `Yang-Mielke theory' of gravity, proposed in its affine form already by Weyl 1919 and by Yang in 1974. However, these exact solutions exhibit a `vacuum degeneracy'. One needs to modify the double duality of the curvature via scale breaking terms, in order to retain Einstein's equations with an induced cosmological constant of partially topological origin as the unique macroscopic `background'.
Such scale breaking terms arise more naturally in a constraint formalism, the so-called BF scheme, in which the gauge curvature is denoted by F. In the case of gravity, it departs from the meta-linear group SL(5,R) in four dimensions, thus generalizing (Anti-)de Sitter gauge theories of gravity. After applying spontaneous symmetry breaking to the corresponding topological BF theory, again Einstein spaces emerge with a tiny cosmological constant related to the scale of symmetry breaking. Here the `background' metric is induced via a Higgs-like mechanism. The finiteness of such a deformed topological scheme may convert into asymptotic safeness after quantization of the spontaneously broken model."

LinkAddendum, Wheeler in wikipedia:
During the 1950s, Wheeler formulated geometrodynamics, a program of physical and ontological reduction of every physical phenomenon, such as gravitation and electromagnetism, to the geometrical properties of a curved space-time. Aiming at a systematical identification of matter with space, geometrodynamics was often characterized as a continuation of the philosophy of nature as conceived by Descartes and Spinoza. Wheeler's geometrodynamics, however, failed to explain some important physical phenomena, such as the existence of fermions (electrons, muons, etc.) or that of gravitational singularities. Wheeler therefore abandoned his theory as somewhat fruitless during the early 1970s.
Maybe he used the wrong concept for the unification? Why are forces making qubits?

Addendum: Wikipedia, the talk page for discussing improvements to the John Archibald Wheeler article.

information regarding geometrodynamics is not accurate

This is a good article on J.A. Wheeler. However, the information regarding geometrodynamics is not accurate, especially the following statement: "Wheeler abandoned it as fruitless in the 1970s".As a matter of fact, Wheeler kept using the term "geometrodynamics" to describe Einstein's theory of general relativity till his last days. For example, in Gravitation and Inertia, a book written with the Italian physicist I.Ciufolini in 1995(and which was missing from the bibliography), the authors keep referring to "Einstein Geometrodynamics"(the title of Chapter 2) throughout the the book: Chapter 3 is entitled " Tests of Einstein Geometrodynamics", Chapter 5 is "The Initial-Value Problem in Einstein Geometrodynamics" and Chapter 7:"Some Highlights of the past and a Summary of Geometrodynamics and Inertia".This proves that Wheeler did not abandon the concept at all in the 1970s! 
John A. Wheeler, 1990, "Information, physics, quantum: The search for links" in W. Zurek (ed.) Complexity, Entropy, and the Physics of Information. Redwood City, CA: Addison-Wesley.
Addendum about quantum geometrodynamics, hard linked to time and quantum gravity: Claus Kiefer, 2008. Quantum geometrodynamics: whence, whither? Total search here. Abstract:
Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler--DeWitt equation. Here I give an overview of the status of this approach. The issues discussed include the problem of time, the relation to the covariant theory, the semiclassical approximation as well as applications to black holes and cosmology. I conclude that quantum geometrodynamics is still a viable approach and provides insights into both the conceptual and technical aspects of quantum gravity.
And this is actually published; Gen.Rel.Grav.41:877-901, 2009 DOI:10.1007/s10714-008-0750-1
See also: Interpretation of the triad orientations in loop quantum cosmology
Scalar perturbations in cosmological models with dark energy - dark matter interaction

Look: Does time exist in quantum gravity?
Comments: 10 pages, second prize of the FQXi "The Nature of Time" essay contest

Cosmological constant as result of decoherence. This means non-commutative geometry?

An earlier article (Adrian P. Gentle, Nathan D. George, Arkady Kheyfets, Warner A. Millerfrom 2004; Constraints in quantum geometrodynamics, http://arxiv.org/abs/gr-qc/0302044

And about time and geometrodynamics, by the same authors
http://arxiv.org/abs/gr-qc/0302051
http://arxiv.org/abs/gr-qc/0006001
http://arxiv.org/abs/gr-qc/9412037
http://arxiv.org/abs/gr-qc/9409058

A geometric construction of the Riemann scalar curvature in Regge calculus. Jonathan R. McDonald, Warner A. Miller http://arxiv.org/abs/0805.2411

and
A Discrete Representation of Einstein's Geometric Theory of Gravitation: The Fundamental Role of Dual Tessellations in Regge Calculus http://arxiv.org/abs/0804.0279

Quantum Geometrodynamics of the Bianchi IX cosmological model
Arkady Kheyfets, Warner A. Miller, Ruslan Vaulin 2006 http://arxiv.org/abs/gr-qc/0512040

and from 1995,
Quantum Geometrodynamics I: Quantum-Driven Many-Fingered Time
Arkady Kheyfets, Warner A. Miller http://arxiv.org/abs/gr-qc/9406031

All actually published.


References:
  • Anderson, E. (2004). "Geometrodynamics: Spacetime or Space?". arXiv:gr-qc/0409123 [gr-qc]. This Ph.D. thesis offers a readable account of the long development of the notion of "geometrodynamics". University of London, Examined in June by Prof Chris Isham and Prof James Vickers. 226 pages including 21 figures. 396 cit.
    This thesis concerns the split of Einstein's field equations (EFE's) with respect to nowhere null hypersurfaces. Areas covered include A) the foundations of relativity, deriving geometrodynamics from relational first principles and showing that this form accommodates a sufficient set of fundamental matter fields to be classically realistic, alternative theories of gravity that arise from similar use of conformal mathematics. B) GR Initial value problem (IVP) methods, the badness of timelike splits of the EFE's and studying braneworlds under guidance from GR IVP and Cauchy problem methods.

Abstract
The work in this thesis concerns the split of Einstein field equations (EFE’s) with respect to nowhere-null hypersurfaces, the GR Cauchy and Initial Value problems (CP and IVP), the Canonical formulation of GR and its interpretation, and the Foundations of Relativity. I address Wheeler’s question about the why of the form of the GR Hamiltonian constraint “from plausible first principles”. I consider Hojman–Kuchar–Teitelboim’s spacetime-based first principles, and especially the new 3-space approach (TSA) first principles studied by Barbour, Foster, ´O Murchadha and myself. The latter are relational, and assume less structure, but from these Dirac’s procedure picks out GR as one of a few consistent possibilities. The alternative possibilities are Strong gravity theories and some new Conformal theories. The latter have privileged slicings similar to the maximal and constant mean curvature slicings of the Conformal IVP method.
The plausibility of the TSA first principles are tested by coupling to fundamental matter. Yang–Mills theory works. I criticize the original form of the TSA since I find that tacit assumptions remain and Dirac fields are not permitted. However, comparison with Kuchaˇr’s hypersurface formalism allows me to argue that all the known fundamental matter fields can be incorporated into the TSA. The spacetime picture appears to possess more kinematics than strictly necessary for building Lagrangians for physically-realized fundamental matter fields. I debate whether space may be regarded as primary rather than spacetime. The emergence (or not) of the Special Relativity Principles and 4-d General Covariance in the various TSA alternatives is investigated, as is the Equivalence Principle, and the Problem of Time in Quantum Gravity.
Further results concern Elimination versus Conformal IVP methods, the badness of the timelike split of the EFE’s, and reinterpreting Embeddings and Braneworlds guided by CP and IVP knowledge.
Mielke, Eckehard W. (2010, July 15). Einsteinian gravity from a topological action. SciTopics. Retrieved January 17, 2012, from http://www.scitopics.com/Einsteinian_gravity_from_a_topological_action.html
Topological ideas in the realm of gravity date back to Riemann, Clifford and Weyl and found a more concrete realization in the wormholes of Wheeler characterized by the Euler-Poincare invariant. They result from attaching handles to black holes.
Observationally, Einstein's general relativity (GR) is rather well established for the solar system and double pulsars. However, in GR the metric plays a double role: Measuring distances in spacetime and serving as a gravitational potential for the Christoffel connection. This dichotomy seems to be one of the main obstacles for quantizing gravity. Eddington suggested already 1924 in his book `The Mathematical Theory of Relativity' (2nd Edition) to regard the connection as the basic field and the metric merely as a derived concept.
Consequently, the primordial action in four dimensions should be constructed from a metric-free topological action such as the Pontrjagin invariant of the corresponding gauge connection. Similarly as in the Yang-Mills theory, a quantization can be achieved by amending the definition of curvature and the Bianchi identities via topological ghosts. In such a graded Cartan formalism, the nilpotency of the ghost operators is on par with the Poincare lemma for the exterior derivative. Using a BRST antifield formalism with a duality gauge fixing, a consistent quantization in spaces of double dual curvature is obtained. The constraint imposes instanton type solutions on the curvature-squared `Yang-Mielke theory' of gravity, proposed in its affine form already by Weyl 1919 and by Yang in 1974. However, these exact solutions exhibit a `vacuum degeneracy'. One needs to modify the double duality of the curvature via scale breaking terms, in order to retain Einstein's equations with an induced cosmological constant of partially topological origin as the unique macroscopic `background'.
Such scale breaking terms arise more naturally in a constraint formalism, the so-called BF scheme, in which the gauge curvature is denoted by F. In the case of gravity, it departs from the meta-linear group SL(5,R) in four dimensions, thus generalizing (Anti-)de Sitter gauge theories of gravity. After applying spontaneous symmetry breaking to the corresponding topological BF theory, again Einstein spaces emerge with a tiny cosmological constant related to the scale of symmetry breaking. Here the `background' metric is induced via a Higgs-like mechanism. The finiteness of such a deformed topological scheme may convert into asymptotic safeness after quantization of the spontaneously broken model.
Although many details remain to be seen, topological actions are prospective in being renormalizable and, after symmetry breaking, are inducing general relativity as an "emergent phenomenon" for macroscopic spacetime.
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GEOMETRODYNAMICS IS NOT DEAD YET!