Subject: The dead-end of Ashtekar's quantization program
Date: Thu, 24 Mar 2005 23:13:54 +0200
From: Dimi Chakalov <dchakalov@surfeu.at>
To: Karel Kuchar <kuchar@physics.utah.edu>
CC: Abhay Ashtekar <ashtekar@gravity.phys.psu.edu>,
     Chris Isham <c.isham@imperial.ac.uk>
 

Dear Professor Kuchar,

On Mon, 27 Jan 2003 15:13:51 -0700 (MST), you wrote:

> If you reread my paper which you quote, you will see that I
> never stated that Professor Ashtekar's quantization program
> is self-contradictory. One essential germ of truth is not
> to attribute to other people opinions based on superficial
> reading of what they actually said.

I believe have asked you to defend your insulting statement, by proving that I have been doing "superficial reading" of what you have actually said.

Instead, you chose to reply in a very vague way. Let me quote from your email from Tue, 28 Jan 2003 13:09:32 -0700 (MST):

"The sentence which you quote "the PROPOSAL AS IT STANDS is self-contradictory" refers to one specific preceding statement on the same page marked by a bullet. It is followed by a suggestion how `the proposal as it stands' can possibly be amended to remove the contradiction and what are the difficulties involved. What you claim in your letter to Professor Ashtekar is that I "stated that YOUR QUANTIZATION PROGRAM is self-contradictory". Different words mean different things and fortunately litera scripta manet."

My immediate reply (Wed, 29 Jan 2003 02:30:36 +0200):

"I take this as an introduction to your explanation of how the proposal referred to you as [39] can possibly be amended to remove the contradiction, and what are the difficulties involved.

"NB: Please send me your rigorous mathematical proof that this task can indeed be achieved."

Please note that I have not yet received any proof from you.

To avoid misunderstandings, let me write three points below.

1. Fact: The phrase 'the proposal as it stands' refers to Ashtekar's quantization program, Ch. 10 in his 1991 book,

http://www.God-does-not-play-dice.net/Ashtekar.html#Kuchar_1993

2. Fact: Your have not yet elaborated on your suggestions "how 'the proposal as it stands' can possibly be amended to remove the contradiction", firstly, and secondly -- "what are the difficulties involved".

3. Opinion: It is my understanding that your two suggestions above were clearly showing the DEAD-END of Ashtekar's quantization program. It is indeed self-contradictory, as you *hinted* in your gr-qc/9304012.

Again, I am respectfully urging you to defend your insulting statement by showing that I have indeed been doing "superficial reading" of what you and A. Ashtekar have actually said.

Again, please elaborate on your two suggestions (cf. (2) above) and demonstrate that my reading were indeed "superficial" (cf. (3) above).

Once I receive your rigorous explanation (cf. (2) above), I will do my very best to show you that "the difficulties involved" are totally insurmountable.

Again, please use math, not just words. As you said, different words mean different things, but if you use math to elaborate on your two suggestions (cf. (2) above), I am definitely positively sure that you will expose the dead-end of Ashtekar's quantization program.

Again, please be gentlemen and defend your insulting statement from Mon, 27 Jan 2003 15:13:51 -0700 (MST). This time with math, please.

Looking forward to hearing from you,

Yours faithfully,

D. Chakalov
--
http://www.God-does-not-play-dice.net
http://www.God-does-not-play-dice.net/download.html
 

Note: It goes without saying that in 1993 (see gr-qc/9304012 mentioned above) Prof. Karel Kuchar knew very well that "the difficulties involved" (see above) are indeed insurmountable. Otherwise he himself would have fixed the contradictions in Ashtekar's quantization program. This hasn't happened in the past twelve years, for reasons explained thirteen years ago: "classical geometrodynamics does not seem to possess a natural time variable, while standard quantum theory relies quite heavily on a preferred time."

The crux of the matter is solving the Hamiltonian constraint problem and the "reconstruction problem", namely, the problem of recovering a classical limit "with a nearly vanishing cosmological constant" (S. Carlip, Quantum gravity: a progress report, gr-qc/0108040 v1, 14 August 2001, p. 48). To quote again from S. Carlip's report (p. 33): "An original rationale for Ashtekar variables was that they simplified the Hamiltonian constraint. But this simplification requires the choice y = i, and thus a complex connection and problematic reality conditions." But the problem is of fundamental nature: there is a fundamental difference between gravity in 2+1-D and 3+1-D spacetime, and A. Ashtekar hasn't been able to reach the latter. More from S. Carlip (p. 24): "The Hamiltonian constraint does not merely constrain fields; it also generates transformations that leave physical states invariant, and these must somehow (Sic! - D.C.) be factored out when one forms an inner product." I believe Karel Kuchar holds an opinion on this issue (see the footnote on p. 24), and can elucidate the "observables" -- if any -- of Ashtekar's quantum gravity. Note that Kuchar's Perennials are time-independent and unobservable, and they cannot facilitate any dynamical evolution that can promote Ashtekar's purely kinematical model into a viable physical theory.

To sum up, the chain of tasks for A. Ashtekar is this: solve the Hamiltonian constraint, build a true physical Hilbert space, define an inner product, write down the observables, and check out if you have recovered a smooth 3-D space: look around, and see as far as you can.

I believe Karel Kuchar is uniquely qualified to make a 'reverse engineering' of Ashtekar's quantization program: start from a smooth 3-D space, get down to the requirements for solving the Hamiltonian constraint, and show A. Ashtekar that these requirements cannot be met in principle.

Karel Kuchar is optimist, as he stated above. I'm not. Recall that Ashtekar's hypothesis is explicitly background-independent, and thus he cannot recover the 3+1-D spacetime in principle. He would need to 'hold onto' Kuchar's Perennials to solve the "reconstruction problem" (cf. S. Carlip above), but there is no such option in his hypothesis, hence it is doomed to fail. This is my opinion, but maybe I'm wrong and Karel Kuchar has reasons to be optimistic, as he stated above.

Is this "superficial reading", Professor Kuchar? Just show me your math, please. Then I will do my best to elaborate on Ashtekar's "natural Hermitian inner product", from his 'Background independent quantum gravity: A status report', gr-qc/0404018 v2.

Meanwhile, see Ashtekar's recent effort to define "semi-classical" quantum state which is peaked at its classical state, by the so-called group averaging technique [Ref. 1]. Surely Karel Kuchar can comment on these issues, which he has studied back in 1971.
 

D.C.
March 24, 2005
Last update: April 13, 2005

[Ref. 1] Abhay Ashtekar, Luca Bombelli, and Alejandro Corichi, Semiclassical States for Constrained Systems, gr-qc/0504052 v1, 12 April 2005.

"In the standard Hamiltonian descriptions of fundamental interactions, the canonical variables are subject to constraints. Notable examples of systems of this type are gauge theories, general relativity and supergravity. In the gravitational case, a key question faced by any background-independent approach, such as loop quantum gravity, is whether specific constructions used to impose constraints in the quantization procedure lead to a theory with ‘a sufficient number of semi-classical states’. To analyze this issue one needs a framework which spells out the precise meaning of the term ‘semi-classical states’, introduces strategies to construct them and provides tools to analyze their properties. The purpose of this paper is to propose such a framework and illustrate its use with simple examples.
...

"However, our restriction excludes several important cases, most notably the Hamiltonian constraint of general relativity.
...

"First, the group averaging procedure [3] need not result in a state which has finite and positive norm. Second, even if it does, and therefore defines a state [psi]_phy in the physical Hilbert space H_phy, this state may not at all be semi-classical.
...

"Secondly, our goal here is not to provide a complete and exhaustive analysis of the application of the group averaging technique to construct candidate semi-classical physical states. We only wish to present a few simple examples in the hope that the explicit and rather intriguing results in these cases may stimulate further research."
...

The group averaging procedure, p. 5: "For a large class of physically interesting systems, the group averaging method provides a technique to extract physical states starting from kinematical ones. For a discussion of more general cases and a treatment of subtleties
and technical caveats see, e.g., Ref [3].
...

p. 6: "Our task is to spell out what we mean by a semi-classical quantum state which is ‘peaked at this classical state’.
...

p. 7: "The intended meaning is intuitively clear and, (...). However, such semi-classical states simply don’t exist unless the class of observables is greatly restricted.
...

"However, there is in fact an interesting situation in which the analogous observable is of direct physical interest. This is provided by the quantum theory of the Einstein-Rosen waves in 4-dimensional general relativity [6].
--
[6] Kuchar K 1971 Canonical quantization of cylindrical gravitational waves Phys. Rev. D 4 955.
...

NB: see p. 7, Footnote 2 (C. Rovelli).
...

p. 24: "However, in the general case, this canonical chart would not be adapted to the linearity of the phase space, whence it would be difficult to identify coherent states in this representation. Nonetheless, it should be possible to introduce some notion of kinematical semi-classical states [psi]_kin (q)."
 
 

===

Subject: Re: The dead-end of Ashtekar's quantization program
Date: Tue, 29 Mar 2005 00:19:40 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: Karel Kuchar <kuchar@physics.utah.edu>
CC: Abhay Ashtekar <ashtekar@gravity.phys.psu.edu>,
     Chris Isham <c.isham@imperial.ac.uk>

Dear Karel,

I don't know why you're keeping quiet. You were born in a communist country, and I believe you should really hate to keep quiet in a situation like Ashtekar's quantization program, also known as "Der Herr Der Quanten",

http://cgpg.gravity.psu.edu/people/Ashtekar/articles.html

I wonder what is your contribution to "100 Years of Relativity -
Space-time Structure: Einstein and Beyond", A. Ashtekar (Editor), World Scientific, Singapore, 2005.

Paddy and Alan Rendall were invited,

T. Padmanabhan, Understanding Our Universe
http://www.God-does-not-play-dice.net/Turok.html#5

Alan D. Rendall, The nature of spacetime singularities
http://www.God-does-not-play-dice.net/Turok.html#6

Recall Boetius: Si tacuisses, philosophus mansisses (wenn du geschwiegen hättest, so wärest du ein Philosoph geblieben).

Kindest regards,

Dimi

On Thu, 24 Mar 2005 23:21:49 +0200, Dimi Chakalov wrote:
>
> P.S. You can read my preceding email at
>
> http://www.God-does-not-play-dice.net/Kuchar.html
>
> Soon on CD ROM.
>
> D.C.

====

Note added on 28 March 2005: I just receive an email from The Eberly Professor of Physics and Director of the Institute for Gravitational Physics and Geometry at Penn State University A. Ashtekar! I've been trying to contact him since September 1998, and this is the first email from him ... well, not quite. See below.

D.C.
--

Subject: away from my mail
Date: Mon, 28 Mar 2005 16:20:40 -0500 (EST)
From: ashtekar@gravity.phys.psu.edu
To: dimi@chakalov.net

From 3/27/05 to 4/10/05 I will be away.

From Monday 28th March to Sunday 3rd April, in Pavia, Italy.
Conference: http://www.pv.infn.it/~spacetimeinaction/structure.html

From April 3rd to 9th, at the AEI conference:
http://www.aei.mpg.de/events/conference/

During this time I may not be able to access my e-mail.
In case of urgency, you can contact Ms Karen Brewster at (814) 863-9605, fax: (814) 863-9608; e-mail: Karen Brewster <kqb2@psu.edu>
--
 

====
Subject: It's all about Einstein
Date: Wed, 04 Feb 2004 04:17:51 +0200
From: Dimi Chakalov <dimi@chakalov.net>
To: Karel Kuchar <kuchar@physics.utah.edu>
CC: Abhay Ashtekar <ashtekar@gravity.phys.psu.edu>,
     carlo@rovelli.org

Dear Professor Kuchar,

I sincerely hope that you are well and in good health. One whole year I've been patiently waiting to hear from you regarding the quantization program of your colleague Prof. A. Ashtekar,

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

Please recall that I asked you to explain how the Hilbert space problem -- the problem of fixing the inner product in the Hilbert space of physical states by requiring that it is both invariant under Diff(M) and conserved in *time* -- can be resolved in Ashtekar's quantization program.

Ten years ago, your colleague was only able to say that this is a fascinating issue,

http://members.aon.at/chakalov/Shimony.html#Ashtekar

You were far less poetic, of course, and claimed that his quantization program is self-contradictory (Canonical Quantum Gravity, gr-qc/9304012, p. 25),

http://members.aon.at/chakalov/intro.html#Ashtekar_program

But one year ago, you suddenly decided to back off (please see the first URL above).

Let's be honest, okay?

Ashtekar's quantization program is indeed self-contradictory. There is no background whatsoever, no metric, no fields, no nothing. Just a manifold,

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

NB: Neither you nor Ashtekar can fix any instant of *time* w.r.t.w. one can solve the Hilbert space problem,

http://members.aon.at/chakalov/Schwarz.html#2

No way.

There is a severe logical contradiction in Ashtekar's program: recall the Barber Paradox,

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

The Barber (Ashtekar) has to introduce some sort of *time* to his bare manifold, because the manifold itself cannot do this miracle (=barber's clients do not shave themselves).

Do you believe he can succeed?

To sum up, if you really and honestly believe that Ashtekar's quantization program is *not* self-contradictory, please provide the proof. With math, and with scrupulous intellectual honesty, as Carlo Rovelli used to say.

This was my request sent to you one year ago.

Alternatively, if you cannot defend Ashtekar's quantization program and stick to your previous opinion that this program is self-contradictory, please say it in plain flat English, and with scrupulous intellectual honesty, as Carlo Rovelli used to say.

Only please don't take all this personally. It's not about you and Ashtekar. It's all about Einstein, the nature of gravity, and the 3-D space,

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

I do hope to hear from you before 2005. Perhaps you can write a paper dedicated to Einstein's Annus Mirabilis, and elaborate on Ashtekar's quantization program and the Barber Paradox. Just a suggestion.

Yours sincerely,

Dimi Chakalov

P.S. Ceterum censeo Carthaginem delenda esse.
 
 

Note:  I just read the latest article by Martin Bojowald, in which he again talked about "work in progress" on the "fascinating issue" of his mentor Abby Ashtekar. Martin Bojowald knows Claus Kiefer, and is certainly aware of the problems encountered by Lee Smolin.

How is he going to solve the task of choosing one out of infinitely many "surplus solutions"?

Fuhgeddaboudit, Martin. You're a young guy, enjoy your life. Try to understand the nature of continuum. Example: the circumference of a circle, after Archimedes.
 

D. Chakalov
February 13, 2004

Martin Bojowald, Loop Quantum Cosmology: Recent Progress, gr-qc/0402053, Thu, 12 Feb 2004 10:13:47 GMT

"Work in progress includes a systematic derivation of perturbative corrections as well as approaches to find the physical inner product and observables.
...

"This representation has the same properties as observed before for loop quantum gravity in general [20]: There is a non-separable Hilbert space, only holonomies but not c  itself are promoted to well-defined operators, and the flux p  has a discrete spectrum. It is not possible to derive a c-operator because the holonomy operators are not continuous in µ at µ = 0 such that the derivative does not exist. The flux has a discrete spectrum in the sense that it has normalizable eigenstates  µi, even though the range of eigenvalues is continuous, the real line.
...

"One of the most important open issues conceptually is that of the physical inner product and quantum observables. (...) The meaning of the infinitely many surplus solutions, however, and the possible role of superselection can only be understood with the help of observables and the physical inner product."
 
 

=====

Subject: The Unmoved Mover
Date: Tue, 18 Feb 2003 00:28:08 +0200
From: Dimi Chakalov <dchakalov@surfeu.at>
To: Karel Kuchar <kuchar@physics.utah.edu>
CC: Abhay Ashtekar <ashtekar@gravity.phys.psu.edu>,
     Carlo Rovelli <carlo@rovelli.org>,
     Claus Kiefer <kiefer@thp.uni-koeln.de>,
     Steve Carlip <carlip@physics.ucdavis.edu>,
     Jim Hartle <hartle@big-g.physics.ucsb.edu>,
     Asher Peres <peres@photon.technion.ac.il>
 

Dear Professor Kuchar,

In your 1999 article "The Problem of Time In Quantum Geometrodynamics" [Ref. 1], you wrote:

"The profound message of general relativity is that spacetime does not have any fixed structure which is not dynamical but governs dynamics from outside as an unmoved mover. The problem of time is only one facet of the missing unmoved mover, and canonical quantization only a handy tool for laying bare the consequences. Unless the deep structure of the world reveals a hidden unmoved mover and thus overturns all expectations raised by general relativity, the quantum theory of the deep level is likely to encounter a problem similar to the problem of time, though in a different guise. If so, the problem of time in quantum geometrodynamics may be only a wind that precedes the storm.

"Saying that much as a physicist, I have missed my last chance to pretend to be a philosopher: Si tacuisses, philosophus mansisses."

To the best of my knowledge, the last sentence belongs to Boetius (Anicius Manlius Severinus Boethius), and could be translated roughly as "Should you have kept quiet, you would have stayed a philosopher".

If so, why are you keeping quiet like a philosopher?

I believe have sent you three very polite email messages on Fri, 27 Dec 2002 05:22:47 +0200, Fri, 27 Dec 2002 15:08:25 +0200, and Tue, 21 Jan 2003 04:34:32 +0200. The subject was "Request for opinion". I haven't heard from you regarding my request, so please see my explanatory note of Thursday, January 29, 2003 at

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

The Unmoved Mover which you mentioned three times in your article [Ref. 1] could be the Holon of Arthur Koestler,

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

It seems to me that the task we need to solve is the nature of 3-D space. Please see again my note at

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

and my guess about the nature of 3-D space at

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

Please correct me if I'm wrong.

And, most importantly, please do not keep quiet, like a philosopher. I'm sure you can say much more on the Unmoved Mover of Aristotle and your Perennials. [Ref. 2]

I very much hope to hear from you as a physicist. The opinion of your colleagues will be highly appreciated, too.
 

With kindest regards,

Dimi Chakalov
http://members.aon.at/chakalov
 

References

[Ref. 1] Karel Kuchar, "The Problem of Time In Quantum Geometrodynamics", in "The Arguments of Time", ed. by Jeremy Butterfield, Oxford University Press, Oxford, 1999, p. 193.
 

[Ref. 2] Karel Kuchar (1993). Canonical Quantum Gravity.
http://xxx.lanl.gov/abs/gr-qc/9304012

"Our space is three-dimensional and a theory which makes an effective use of this fact is not to be blamed.
...

"No perennial ever changes along a dynamical trajectory."
 
 

===========

Subject: It's about the 3-D space, not H[Psi]=0
Date: Tue, 18 Feb 2003 11:42:52 +0200
From: Dimi Chakalov <dchakalov@surfeu.at>
To: William G Unruh <unruh@physics.ubc.ca>,
E I Guendelman <guendel@bgumail.bgu.ac.il>,
A B Kaganovich <alexk@bgumail.bgu.ac.il>,
Grigori Volovik <volovik@boojum.hut.fi>,
Alejandro Perez <perez@gravity.psu.edu>,
Sean A Hartnoll <s.a.hartnoll@damtp.cam.ac.uk>,
Rafael A Porto <rafael@fisica.edu.uy>,
Rodolfo Gambini <rgambini@fisica.edu.uy>,
Jorge Pullin <pullin@rouge.phys.lsu.edu>,
Don N Page <don@phys.ualberta.ca>,
Carlos Barcelo <carlos.barcelo@port.ac.uk>,
Matt Visser <matt.visser@mcs.vuw.ac.nz>,
Adam Helfer <adam@math.missouri.edu>,
Julian Barbour <jbarbour@online.rednet.co.uk>,
Joy Christian <joy.christian@wolfson.ox.ac.uk>
 
 

Dear Colleagues,

I think the "mysterious time" introduced by Bill Unruh in 1988 strikes back as the mystery of 3-D space,

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

I will appreciate your critical comments. Will keep them private and confidential.

Regards,

Dimi Chakalov
http://members.aon.at/chakalov
--
Dead matter makes quantum jumps; the living-and-quantum matter is smarter.
 

===========

Subject: Re: Addendum
Date: Tue, 26 Oct 2004 06:19:15 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: Karel Kuchar <kuchar@physics.utah.edu>
CC: Chris Isham <c.isham@imperial.ac.uk>

P.S. I heard that you've been working on the consistent histories approach to quantum gravity, and some thoughts on your "Time and interpretations of quantum gravity" emerged, in some coarse-grained way, at

http://God-does-not-play-dice.net/Giachetta.html#addendum

D.C.

On Sat, 23 Oct 2004 07:54:34 +0300, Dimi Chakalov wrote:
>
> Dear Professor Kuchar,
>
> I discussed your gr-qc/9304012 at
>
> http://God-does-not-play-dice.net/Ashtekar.html#addendum
>
> Sincerely,
>
> Dimi Chakalov
 
 

Note: If you follow the two links above, in my email to K. Kuchar from Tuesday, 26 October 2004, you might be lost in the jungle of present-day research in quantum gravity. Let me try to keep you focused on the main issues, by referring to Karel Kuchar's article "The Problem of Time In Quantum Geometrodynamics" [Ref. 1].
 

Point #1. The difference between the intrinsic and extrinsic properties of a curved surface is based on the presumption that neither the ribs nor the fabric of the umbrella are being "appreciably stretched"; see Fig. 7.1 in [Ref. 1, p. 171].

Perhaps this seemingly innocent expression "appreciably stretched" contains too much poetry.

Why can we ignore the obvious stretching? This whole web site is about replacing the simple "flat Euclidean space" in which the umbrella can bend on a windy day [Ref. 1, p. 170] with a new 'reference fluid' called 'global mode of spacetime'. Yes, we can ignore the stretching of the umbrella, because the ordering of "points" on the continuum of the local mode of spacetime is facilitated by the global mode of spacetime, as explained here. The "stretching" occurs only in the global mode.
 

Point #2. The intrinsic metric and extrinsic curvature are not localized at a single spot, but "distributed along a three-dimensional hypersurface" [Ref. 1, p. 179]. If we toss a ball, we can imagine that at some "point" from its trajectory the ball will have a single time value, instantaneous velocity, well-defined energy, etc.

In canonical gravity, we substitute this instantaneous snapshot with a whole three-dimensional hypersurface, and the laws of this instant are drastically different: we run into the famous many-fingered time. The energy conjugated to this brand new many-fingered time is the "energy density and its flux at all points" of the three-dimensional hypersurface [Ref. 1, p. 179]. However, to "draw such a hypersurface" we must specify where each of these infinitely many points lies in a four-dimensional spacetime [ibid.], which in turns requires fixing the error with applying double standards in treating space and time in GR, as explained here. Otherwise we cannot even begin to "draw" the picture of many-fingered time.

We must not do "grave injustice to space-time covariance that underlies general relativity", as did A. Ashtekar. The intrinsic properties of 3-D space are 'inside' and 'outside', but they are excluded from the basic principle of general covariance, hence present-day geometrodynamics incorporates a Newtonian notion of 3-D space but operates with a many-fingered time. Hence we have 'the problem of time' but not a 'problem of 3-D space', as if the intrinsic properties of 3-D space could be immune to the basic rules of reparametrization invariance of GR.

To fix this crucial error, I believe we need to extend the rules of active diffeomorphism invariance to include a new symmetry group called 'space invariance'. It should eliminate the notion of some absolute 3-D space with forever-fixed spatial relations 'inside and outside' from Newtonian mechanics, just as we have eliminated the notion of absolute time and have replaced it with the many-fingered time.

This is a whole new ball game, however. The fundamental object that can encode the dynamics in GR -- the elementary increment of the universal Heraclitian time called instant -- has to be placed in the global mode of spacetime, where it can not only "wiggle up and down" along its T-invariant many-fingered time, but can also "wiggle inside and outside" along a fourth spacelike "direction", as explained here. Note that this forth spacelike "direction" corresponds to the so-called imaginary time. All this is needed for the next two steps, Point #3 and Point #4 below, because we need to expand the phase space of potential states to include all possible "unphysical" states from which one physical 4-D instant will be actualized, along the universal Heraclitian time. One-at-a-time.

Going back to the question of where each of these infinitely many points lies in a four-dimensional spacetime [Ref. 1, p. 179], I believe we could answer it by providing a new "holder" of these potential states in the many-fingered time: the global mode of spacetime.
 

Point #3. Karel Kuchar doesn't like the so-called negative energy densities and negative probabilities, because the latter would imply that a particle "would not be found anywhere at all" [Ref. 1, p. 184].

Bingo! This is exactly what we need to make all states in the the many-fingered time (global mode of spacetime) potential. I believe we should explore again the hints from the complex Klein-Gordon state and discover the 'alter ego' of positive mass solutions, hence recovering the whole set of potential states. Their dynamics has been truncated by eliminating the additional field degrees of freedom called 'polarization' [Ref. 1, p. 186]. We have to recover these additional filed degrees of freedom that pertain exclusively to 4-D spacetime; see S. Carlip here. This is yet another grave injustice to Einstein's GR, which we must undo as soon as possible. We know from STR that luxons (photons are the only known example of this specie) do not have an alter ego [Ref. 1, p. 184], and only luxons can safely "separate" the material and tachyonic worlds, and the "proper time" of this luxonic world would be zero, if read by a physical clock. Hence the global mode of spacetime could be physically manifested on a null-plane only. It is indeed an "instant". But "before" it becomes an instant, all potential states in the global mode of spacetime should be generated by the proposed extended rules of active diffeomorphism invariance, which should include a new symmetry group called 'space invariance'. Namely, in the global mode of spacetime, the material and tachyonic worlds should freely "wiggle" by conflating three spatial dimensions with one temporal. I believe something similar happens in the Kruskal-Szekeres diagram. Here I can only offer my hunch that, by making a maximum extended space of potential states in the global mode of spacetime, we might see some possibility for 'sum-over-whatever', which would eliminate all ambiguities in the present-day approaches to quantum gravity. I see these ambiguities as 'richness', and my gut feeling is that we should make our global mode of spacetime 'as rich as possible', and then this additional richness would hopefully help us nail down an "instant" of fixed, already-actualized 4-D spacetime in the local mode of spacetime, one-at-a-time.
 

Point #4. We should keep in mind the issue of actualization of the potential states, which is also known as 'the emergence of time and space' in quantum gravity; see C. Isham and J. Butterfield here. I believe we should upgrade Einstein's GR with suitable "dynamics", in the global mode of spacetime, of two worlds with inverted spacetime basis, and look for some analog of the Born rule, as outlined here and here. Instead of some "projection postulate", we need a brand new 'cancellation mechanism' that would cancel all unneeded potential states and allow only one set of states to be actualized in an "instant", thus creating a 4-D spacetime "instant", one-at-a time. The rest are kept safe in the global mode of spacetime (resembling the memory of our brain), ready to be actualized if such need occurs. The "need" for particular "instant" comes from our relational reality. It is the ultimate "chooser", and is a genuine Perennial, since it "governs the dynamics from outside as an unmoved mover" [Ref. 1, p. 193].
 

Point #5. Finally, let me quote again Karel Kuchar [Ref. 1, p. 178]: "I hope that any reader who has got this far feels cheated. (...) So the people who tried to quantize geometry surely made some slip, and they are misleading laymen and possibly themselves by the combined trickery of general relativity and quantum theory. I will try to explain here where the slip may be and what remedies have been proposed to avoid it. The problem is that none of them quite works (Kuchar, 1992)."

I fully agree. The first slip may be in our understanding of the "dynamics" in quantum theory. If so, the remedy has been proposed here. I tried to follow strictly the path of Karel Kuchar: "classical geometrodynamics does not seem to possess a natural time variable, while standard quantum theory relies quite heavily on a preferred time" (Kuchar, 1992). It's a bundle, and I believe its solution will require new physics. Mind you, 96 per cent from the stuff around us is made of some "dark" mass and "dark" energy, so we better get used to new ideas.
 

It is a great pleasure to read Karel Kuchar. I think he and Chris Isham have developed schools in general relativity and quantum gravity. All we have to do is to study their schools and zoom on some subtle "poetic" details, such as the phrase "appreciably stretched" above.

Regrettably, I cannot produce anything but poetryand cannot offer anything substantial. Just a bunch of speculations and gut feelings about some 'virtual geodesic path' formulation of Einstein's GR. Besides, I'm not a physicist but psychologist, and am old and biased.

If you, my dear reader, are psychologist or neuroscientist, you may be baffled by the current situation in quantum gravity research. 'Die gegenwärtige Situation' looks quite murky, and you may ask a very simple question: Why would a fish need a bicycle? Well, I believe we need quantum gravity to understand how the brain works, which in turns requires understanding quantum mechanics. I haven't been able to understand quantum mechanics nor Einstein's GR, and my only hope is that we can model the universe as a human brain and develop a 'virtual geodesic path' formulation of Einstein's GR, the ultimate theory of He Who Does Not Play Dice.

Only don't expect any help from the established theoretical physics community. There is too much money and politics involved with the current projects of "gravitational wave astronomy" and "the God particle", and nobody really cares about Einstein's legacy. As Max Planck stated, the future belongs to youth. If you want to win, you have to fight. Your main "weapon" is differential geometry and topology.

Praise The Lord and pass the ammunition!
 

D. Chakalov
October 28, 2004
Last update: October 29, 2004