========

Subject: arXiv:0709.4636v1 [gr-qc]
Date: Mon, 1 Oct 2007 15:01:07 +0300
From: "Dimi Chakalov" <dimi@chakalov.net>
To: "Benjamin Bahr" <bbahr@aei.mpg.de>
Cc: <tthiemann@perimeterinstitute.ca>

RE: "Also it may be that we overlooked some clever technique that allows to simplify the gauge integrals."

Hi Benjamin,

Perhaps you and Thomas have overlooked some well-known ideas from Aristotle

http://www.god-does-not-play-dice.net/Trautman.html

Recall Thomas' confession (hep-th/0608210 v1 p. 47): "We cannot even solve classical General Relativity completely and we will probably never be able to."

I'm afraid if you and Thomas find some "clever technique that allows to
simplify the gauge integrals", this won't help you solve GR completely,
hence the foundation of LQG will remain as shaky and murky as it has always been. Why waste your time and life?

Take care,

Dimi

============

Note: I haven't heard from Thomas Thiemann since July 2004, and will only post my brief comments on his latest effort, entitled: "Loop Quantum Gravity: An Inside View", Preprint AEI-2006-066, hep-th/0608210 v1,
29 August 2006. It is a response to a devastating paper by H. Nicolai, K. Peeters and M. Zamaklar (reference and comments here), which has been mentioned in T. Thiemann's hep-th/0608210 v1 as ref. [12],

[12] H. Nicolai, K. Peeters and M. Zamaklar. Loop quantum gravity: an outside view. Class. Quant. Grav. 22 (2005), R193. [hep-th/0501114]

Not only H. Nicolai, K. Peeters and M. Zamaklar failed to mention Thomas Thiemann's Master Constraint Programme in their hep-th/0501114, but were also puzzled "what has been gained in LQG as compared to the old
geometrodynamics approach".

So, their AEI colleague, Prof. Thomas Thiemann, decided to strike back.

First, he stated that "what we have in mind is to draw a more optimistic picture than [12] did, to hopefully resolve confusions that may have arisen from gaps in [12] and to give a more complete picture of all the research being done in LQG than [12] did. The discussion will be kept objectively, problems with the present formulation of LQG will not be swept under the rug but rather discussed in great detail together with their possible solutions."

My comments (denoted with C) follow the quoted text (denoted with Q):

Q1. Thomas Thiemann, pp. 7-8:

"The relational Ansatz solves the problem of time of canonical quantum gravity: By this one means that in generally covariant systems there is no Hamiltonian, there are only Hamiltonian constraints. Since the observables of the theory are the gauge invariant functions on phase space, that is, the Dirac observables, "nothing moves in canonical quantum gravity" because the Poisson brackets between the Hamiltonian constraints and the Observables vanishes (weakly) by construction.
...
"This has been achieved recently in [33] using suitable matter which supplies the clocks T_I with the required properties."
--
[33] T. Thiemann. Solving the problem of time in general relativity and cosmology with phantoms and k-essence. [astro-ph/0607380]

Three brief comments:

C.1.1. Had the problem of time of canonical quantum gravity been solved by the "relational Ansatz", we all would have learned about it from CNN Breaking News.

C.1.2. I personally am not aware of any confirmation of "Dirac observable" whatsoever, and haven't found any proof of its existence in T. Thiemann's paper either.

C.1.3. Ignotum per ignotius: If T. Thiemann wishes to solve the problem of time in general relativity and cosmology with phantoms and k-essence, he should first solve the generic problems of that "exotic matter", as explained here and here. First things first.
 

Q2. p. 31: "a physical inner product is currently missing"

p. 32: "As discussed, the most important open issues are the semiclassical limit and the physical inner product. These issues are overcome to a large extent by the Master Constraint Programme.
...
p. 39: "Certainly what is needed in the future is an approximation scheme with respect to which physical states, the physical inner product, Dirac observables and the physical Hamiltonian can be computed with sufficient detail. The semiclassical states [86] provide a possible avenue especially with respect to applications for which the quantum geometry can be regarded as almost classical.

"Namely we can consider kinematical semiclassical states which are peaked on the constraint surface and on the gauge cut defined by the clock variables. These states are then approximately annihilated by the Master constraint and the power series defining the Dirac Observables can be terminated after a few terms just like in perturbation theory."

p. 44: "We have indicated why non separable Hilbert spaces are no obstacle in LQG, they may even be welcome!

p. 49: "4. Does non-separability of the Hilbert space prevent the emergence of the continuum in the semiclassical limit?

"In [12] the authors point out the non separability of the kinematical Hilbert space which originates from the weak discontinuity of the holonomy operators. They call this the pulverisation of the continuum in the sense that all, even infinitesimally different, edges lead to orthogonal spin network states. The only topology on the set graphs with respect to which the scalar product is continuous is the discrete topology (every subset is open). They then ask whether the continuum can be recovered in the semiclassical limit.

"The answer is in the affirmative: The approximately physical states [86] (kinematical coherent states which are peaked on the constraint surface of the phase space) ... "
 

C2. I've highlighted the important text with red. In my opinion, all these "semiclassical states" and "semiclassical limit" are initially wrong approach toward recovery of the continuum. If you look at a table, you don't see some "semiclassical" table that is in cat states (or in some "self-similar structure (spiderweb) around each vertex", cf. below), some of which are "strongly peaked" around some definite value of the position of the table, say.

I can't see how T. Thiemann can recover the world of tables and chairs from those "semiclassical" approximations, for reasons explained here. Which brings us to the next quotation:

Q3. p. 3: "One of the reasons why LQG is gaining in its degree of popularity as compared to string theory is that LQG has "put its cards on the table". (...) In LQG one just tries to make quantum gravity and general relativity work together harmonically. However, in order to do so one must be ready to go beyond some of the mathematical structures that we got used to from ordinary QFT as we have explained."

p. 4: "It will be a common feature of all quantum gravity theories which preserve background independence. In such theories, the task is to construct a new type of QFT, namely a QFT on a differential manifold M rather than a QFT on a background spacetime (M, g₀). Since such a theory "quantises all backgrounds at once" in a coherent fashion, the additional task is then to show that for any background metric g₀ the theory contains a semiclassical sector which looks like ordinary QFT on (M, g₀). This is what LQG is designed to do, not more and not less."


p. 9: "All of this is of course difficult, if not impossible, to carry out exactly and in full completeness for General Relativity because, after all, one is dealing with a rather non-linear and highly interacting QFT. Hence, in praxis one will have to develop and rely on approximation schemes."


p. 21: "4.4 Quantum dynamics

"The quantum dynamics consists in two steps: 1. Reduction of the system with respect to the gauge transformations generated by the constraints and 2. Introduction of a notion of time with respect to which observables (gauge invariant operators) evolve."

p. 31: "6. Semiclassical limit

"The problem with demonstrating off-shell closure is that, in contrast to the first two, the third relation in (2.2) does not hold by inspection, not even modulo a diffeomorphism. (...) In order to make progress on this issue one would therefore like to probe the Dirac algebra with semiclassical states, the idea being that in expectation values with respect to semiclassical states the operators can be replaced by their corresponding classical functions and commutators by Poisson brackets, up to h~ corrections."

p. 31: "They are the first rigorous solutions ever constructed in canonical quantum gravity, have non zero volume and are labelled by fractal knot classes because the iterated action of the Hamiltonian constraint creates a self-similar structure (spiderweb) around each vertex. However, as in LQC these solutions are not systematically derived from a rigging map which is why a physical inner product is currently missing for those solutions."

[4.4.3 Dirac observables and physical Hamiltonian (p. 37):]

"In particular, h is itself a Dirac observable, namely the physical Hamiltonian that drives the physical time evolution of the Dirac observables.

"This holds for the classical theory. In quantum theory (4.48) should be replaced by

[XXX] (4.49)

"provided we can make sense out of h_x as a self-adjoint operator. This is work in progress."

p. 44: "...let us make a guess:

"Once a physical Hamiltonian such as the one of section 4.4.4 has been successfully quantised one can in principle define scattering theory in the textbook way, that is, one would compute transition amplitudes between initial and final physical states."
 

C3. Please hold your breath, and see C.1.1. and C.1.2 above.

Q4. p. 47: "It is true that not all questions have been answered in connection with the quantum dynamics and research on it will continue to occupy many researchers during many years to come. However, what is asked for in [12] is too much: Nobody expects that one can completely solve the theory. We cannot even solve classical General Relativity completely and we will probably never be able to."

C4. T. Thiemann rightly acknowledges that we haven't yet solved classical General Relativity. We also know very well that haven't solved the clash of QM with STR either, as demonstrated with the measurement problem here.

Thus, the first off task of his Master Constraint Programme should be elucidating the pitfalls in LQG, which are produced by our incomplete knowledge of GR and QM. If you're building a house on shaky grounds, make sure you know its limitations. First things first.

T. Thiemann has chosen an entirely different approach (p. 9) : "Hence, in praxis one will have to develop and rely on approximation schemes."

But you cannot solve the initial problems of GR and QM by approximation schemes. That's 'sweeping the garbage under the rug', hoping that it might not show up in your alleged "quantum dynamics" and "physical inner product". "This is what LQG is designed to do, not more and not less" (p. 4).

If you wish to build on rocks, solve the dynamics of GR and find the proper math. Thomas Thiemann isn't interested in my math, however. Neither he nor any of his AEI colleagues have responded to my proposals. Obviously, they aren't interested.

Meanwhile, "a physical inner product is currently missing" (p. 31).

How can you expect to find a physical inner product, ever? Would it point to some approximately semiclassical states?

You're surely joking, Mr. Thiemann. Or maybe you have problems with your neocortex. Or both.
 

D. Chakalov
August 31, 2006

===================

From: Dimi Chakalov <dimi@chakalov.net>
To: Thomas Thiemann <tthiemann@perimeterinstitute.ca>
Cc: <odreyer@perimeterinstitute.ca>, <fotini@perimeterinstitute.ca>,
<dgottesman@perimeterinstitute.ca>, <hburton@perimeterinstitute.ca>,
<rmyers@perimeterinstitute.ca>, <david.delphenich@uwrf.edu>,
<gleiser@dartmouth.edu>, <jb56@cus.cam.ac.uk>, <leecl@physics.ucla.edu>, <box@peter-ostermann.de>, <Dominik.Schwarz@cern.ch>, <deser@brandeis.edu>, <israel@uvphys.phys.uvic.ca>, <shapiro@astro.physics.uiuc.edu>, <saul@astro.cornell.edu>
Subject: The cosmological constant problem
Date: Tue, 27 Jan 2004 13:00:49 -0000
 

Dear Dr. Thiemann,

In your recent hep-th/0401172, you stated that "these new representations could solve some of the major puzzles of string theory such as the cosmological constant problem."

According to Feynman, the cosmological constant problem tell us that there could be something profound about gravity, which we still don't know,

http://members.aon.at/chakalov/Schwarz.html#1

http://members.aon.at/chakalov/Sarkar.html

Going back to an old debate of 1917, it seems to me that both Levi-Civita and Einstein were undoubtedly right [Ref. 1]. More at

http://members.aon.at/chakalov/Montesinos.html#1

http://members.aon.at/chakalov/Loinger.html

How could Levi-Civita and Einstein be right? I'm wondering if you or any of your colleagues would agree that there is an incredible puzzle about the nature of gravity.

Regards,

Dimi Chakalov
35 Sutherland St
London SW1V 4JU
http://members.aon.at/chakalov
 

Reference

[Ref. 1] Angelo Loinger, Non-existence of gravitational waves. The stages of the theoretical discovery (1917-2003),
http://arxiv.org/abs/physics/0312149

"This result has an unquestionable logical soundness, as it was finally admitted by Einstein himself. Of course, it implies the rejection of the various pseudo (false) energy tensors of the gravitational field proposed by Einstein and by other authors: a false tensor cannot have a true physical meaning!

"Einstein objected that in such a way the total energy-momentum of a closed system would always be equal to zero -- and this fact would not imply the further existence of the system under whatever form. However, from the standpoint of the coherence of the formalism, Levi-Civita -- and Lorentz [1] --  were undoubtedly right."
 
 

Note: If we adopt the solution to the paradox of continuum and the generic quantization of spacetime, we should keep the global mode of spacetime as the 'perennial' (Karel Kuchar) mode of all quantum systems. In this global mode, quantum systems do not work as a physical clock, because their local time, as read by a clock, is frozen. Zero. Just as if you were riding a photon.

Instead of exploring the perennial or global mode of spacetime, as a unique and crucial feature of gravity, physicists are frantically trying to eliminate it. See, for example, the 'consistent discrete canonical formulation of general relativity' by Rodolfo Gambini, Rafael Porto, and Jorge Pullin, gr-qc/0302064 and gr-qc/0305098. I very much respect Jorge Pullin and his colleagues, but I'm afraid their efforts are based on the so-called relational interpretation of quantum mechanics, which takes for granted that reality is relational in sense that an object is real only in relation to another object that it is interacting with. By resorting to this highly constrained view on reality, we can never solve the puzzle of relativistic "collapse" of an entangled state.

The problem is known since 1935. The solution is simple: extend the notion of reality by including the perennial or global mode of spacetime, in which quantum systems exist in a holistic, UNspeakable mode. You might get a perfectly hidden absolute reference frame which cannot be detected in any inertial frame and by any physical clock, since it is placed "between" any two successive points from the local -- and perfectly continual -- mode of spacetime.

Then you might find the answer to the 1917 question above: How could Levi-Civita and Einstein be right?

Also, you might find an answer to the central mystery of quantum mechanics: the self-interference of quantum particles (R. Feynman, QED, The Strange Theory of Light and Matter, New Jersey: Princeton Science Library, 1985, p. 80). They can be "in two places at the same time" (Omar Yepez, physics/0401153), just like the human brain.

Only the 4-D torus intersecting the 3-D space (Ibid.) has to be immersed in the global mode of spacetime in such a way that the quantum particle in its Holon state could be theoretically in many places "at the same time". How many places? Infinitely many. I mean, actual infinity. Otherwise we cannot obtain any finite value of any observable, say, the circumference of a circle. That's Quantum Geometry 101.

However, the task is by no means trivial. See, for example, Simone Mercuri and Giovanni Montani, gr-qc/0312077 and gr-qc/0401127: an evolutive canonical quantum gravity dynamics would require a special reference fluid which "never approaches a test system and, in view of the super-Hamiltonian structure (the supermetric has no definite sign), its energy density is not always positive."

Bingo! We might need a tiny little piece of "exotic matter" to explain the so-called dark energy and inflation. The idea stems from a paper by Sir Hermann Bondi, published in 1957, and from the atom of Lucterius (Titus Lucretius Carus, 96 BC - 55 BC, Book I, Character of the Atoms), as explained some 2060 years ago.

To sum up, the theory of quantum gravity requires a pre-geometrical formulation. Otherwise we cannot understand the very existence of 3-D space. As eloquently stated by Lee Smolin, "one of the biggest mysteries is that we live in a world in which it is possible to look around, as see as far as we like" (Three Roads to Quantum Gravity, p. 205).

Needles to say, I will be happy to elaborate. I would begin with the human brain. It provides invariant knowledge in any reference frame and can correlate at least 10¹⁴ events per second (Matthew Donald, quant-ph/0208033). Perhaps this could be the right way to approach the cosmological constant problem and the nature of gravity, and to avoid the tantalizing question of the number of angels on the head of a pin.
 

D. Chakalov
January 30, 2004
Last update: February 2, 2004

===

Subject: It's all about Einstein
Date: Wed, 04 Feb 2004 17:29:01 +0200
Message-ID: <40210FBD.334E0599@chakalov.net>
From: Dimi Chakalov <dimi@chakalov.net>
To: Curt.Cutler@aei.mpg.de, Hermann.Nicolai@aei.mpg.de,
     Kirill.Krasnov@aei.mpg.de, bernard.schutz@aei.mpg.de,
     Gerhard.Huisken@aei.mpg.de, Bernd.Schmidt@aei.mpg.de,
     tthiemann@perimeterinstitute.ca, loc@gr17.com,
     cmw@wuphys.wustl.edu, marc@usal.es, lewand@fuw.edu.pl,
     jim@newton.uoregon.edu, misao@yukawa.kyoto-u.ac.jp,
     frieman@fnal.gov, varun@iucaa.ernet.in, gary@physics.ucsb.edu
BCC: [snip]
 

Dear Colleagues,

Perhaps you may be interested to see

http://members.aon.at/chakalov/Kuchar.html

http://members.aon.at/chakalov/Thiemann.html#note

http://members.aon.at/chakalov/Loinger.html

Your feedback will be highly appreciated, and will be kept strictly private.

Regards,

Dimi Chakalov