|Subject: The third party
Date: Sat, 10 Apr 2004 02:45:11 +0300
From: Dimi Chakalov <email@example.com>
Dear Professor Nicolai,
You've been quoted by Mr. Rüdiger Vaas [Ref. 1], who suggested that "maybe even a third party is necessary."
I believe the third party could be Albert Einstein,
Hope to elaborate at GR17 in Dublin.
[Ref. 1] Rüdiger Vaas, The Duel: Strings versus Loops, physics/0403112
Hermann Nicolai: "I doubt that both approaches will finally mix harmoniously into a single theory since they start from diametrically opposite assumptions. It is not clear at all that in the end everybody will arrive at the same target. The purpose of our meeting was in fact to point out the differences and disputes."
Rüdiger Vaas: "It remains
to be seen who will toll the final sound -- or if maybe even a third party
Note 1: In order to compete with strings and loop hypotheses, a 'third party' should include the main features from both hypotheses, namely, it should provide some fixed background (the main explicit assumption in string hypothesis) and should enable a background-free evolution of quantum systems (the main wishful thinking in loop quantum gravity).
Done. We have a ubiquitous background and absolute reference frame (ether) in the global mode of spacetime, and a perfectly continuous, background-free evolution in the local mode of spacetime.
Also, we have some basic ideas about the mechanism producing spacetime per se: a spacetime "point" or 'event' is 'everything in the universe', although it is being stripped from its concrete physical content. Again, the initial idea stems from cognitive psychology, but we have to work a lot for elaborating a precise mechanism: the emergence of time and space is perhaps the most difficult task in quantum gravity. It is needed not only for completing the task of quantum gravity, but also for solving the utmost paradox of General Relativity: the 3-D space.
I thought that Prof. Hermann Nicolai, the Director of Albert Einstein Institute (Golm, Germany), would be interested. Perhaps it is very difficult to even consider the idea that every time we use differential calculus, we invoke a mathematical "point", which is nothing but God, plain and simple. Its concrete physical content is set to zero, while its Holon is covering absolutely everything: the ultimate Holon boson residing "inside" the instant 'now'.
We don't need "miracles", as advocated by the Holy Roman Catholic Church. We need to discover the quantum gravity of He Who Does Not Play Dice.
Perhaps a reply from the Vatican
is just as likely as a reply from Prof. Hermann Nicolai. If you challenge
their religion, they will reply only with a dark silence.
Note 2: I just turned off the TV, was watching a talk show with Prof. Dr. Hermann Nicolai on SAT 1. It's called News & Stories, and is intended for the general audience. He talked just about everything, and didn't miss the naked singularities which nobody has observed (12:04 AM), then went so far as to claim that the existence of black holes were almost confirmed (12:09 AM). He knows, of course, that the so-called black holes are fictitious objects, but since scientists have to explain the world to the general audience, he choose to offer some explanation, instead of saying on TV that we simply do not understand the physics of gravitational "collapse", if any. Besser ein Laus im Kraut als gar kein Fleisch.
The most interesting point was his statement (12:25 AM) that the quantum world is the true world from which the classical world emerges. Only he didn't say 'emerges to a good approximation', nor did he mention that the eigenvalue-eigenstate link is constructed by our free choice, on the basis of our knowledge and experimental setup, thus it says nothing about the quantum reality 'out there'. (There is a well-known speculation that quantum mechanics explains the success of classical mechanics because the mean values of quantum mechanical observables follow the classical equations of motion to a "good approximation"; see Albert Messiah, Quantum Mechanics, Vol. 1, North-Holland, Amsterdam, 1970, p. 215.)
How could this happen? The speculations suggested by Prof. Dr. Hermann Nicolai were based on Feynman path integral. That's the true story, according to the Director of Albert Einstein Institute. Our classical world is rooted on the 'sniffing' of all paths, "after" which the particle chooses one of the paths, etc.
Hermann Nicolai is a good story teller, only he didn't explain what is the proper "time" of the virtual sniffing of all possible trajectories, "after" which the particle takes one of the possible paths. He is an expert in gravitational physics, but I wonder if he can explain the proper "time" of the bi-directional talk between matter and geometry. How about the Gap of Zen?
That's philosophy. Hermann Nicolai
prefers math. Fine. See the references here.
ein Laus im Kraut als gar kein Fleisch.
Note 3: Let me offer some biased and unsolicited comments on a recent paper by Hermann Nicolai, Kasper Peeters, and Marija Zamaklar, entitled: "Loop quantum gravity: an outside view" (hep-th/0501114 v1, AEI-2004-129, January 14th, 2005, 50 pages, 11 figures). I will denote their paper with NPZ. Pay special attention to the discussion of the Hamiltonian constraint and "knowing the action of the Hamiltonian on all states of the ‘habitat’".
NPZ, Footnote 1: "there is no a priori notion of ‘time’ in quantum gravity"
NPZ, p. 3: "Structure of space(-time) at the smallest scales?
"how one can recover conventional
notions of continuity in this scheme."
2.1. You will inevitably wind up with a terribly ‘ill-behaved’ set anyway: the space of solutions of LQG is intrinsically non-separable, and the "solutions" to the quantum constraint equation form an uncountable infinity,
don't know if the exclusion of certain ‘ill-behaved’ sets, such as fractal
sets, can be justified on physical grounds. Probably not. See Tim Palmer,
"Quantum Reality, Complex Numbers and the Meteorological Butterfly Effect",
v2; main idea on p. 17.
"In full (3+1)-dimensional LQG, the
classical limit is, however, far from understood (so far only kinematical
coherent states are known [22, 23, 24, 25, 26, 27]). In particular, we
do not know how to derive or even only describe the classical Einstein
equations and their quantum corrections in this framework."
3. There are actually two intermingled questions: (i) how does smooth space-time appear in the classical limit, and (ii) how does the smooth space appear with 3-D. See Renate Loll and Lee Smolin at
NPZ, p. 4: "Background independence?
"However, it must be emphasised that
‘background independence’ here, at least so far, refers only to spatial
backgrounds and spatial diffeomorphisms, and that, at the formal level,
this property might also be claimed for the conventional geometrodynamics
approach. The more challenging task is to make the formulation manifestly
independent of a particular space-time background. This is notoriously
difficult with any Hamiltonian approach."
["which makes us wonder what has really been gained in comparison with the old geometrodynamics approach"]
"With regard to the myriads of possibilities,
LQG proponents often express the view that these correspond to different
physics, and therefore the choice of the correct Hamiltonian is ultimately
a matter of physics (experiment?), and not mathematics. We disagree, because
we cannot believe that Nature will allow such a great degree of arbitrariness
at its most fundamental level.
4. Comments on "we have no reason to expect to be able to solve the theory exactly" and "we cannot believe that Nature will allow such a great degree of arbitrariness at its most fundamental level": Perhaps something essential is missing, such that LQG proponents encounter "great degree of arbitrariness at most fundamental level". To discover this missing element, try to figure out whether it is possible in principle to recover a 3-D space (cf. above).
Recall that LQG proponents claim
that 3-D space can be "pulverized" into some elementary objects (whatever
they call them) that can "sum up" to a volume of 3-D space of finite
dimensions, say, some 1099 "atoms of volume" in every cubic
centimeter of space (Lee Smolin). To test
this conjecture, and the whole loop quantum gravity (LQG), try to cover
a finite area of the walls in your bathroom with tiles, and make
sure there are no gaps whatsoever between the tiles (that's a classical
task, Roger Penrose tried it many years ago). If you can do this miracle
without fractals, please call me. Mind you, you'll
need an infinite time to get the job done. You will also need an infinite
time to count the "solutions" to the quantum constraint equation, since
they form an uncountable infinity, as mentioned above.
NPZ, p. 45: "These ambiguities
are most clearly visible in the discussion of the Hamiltonian constraint.
As we have stressed, it is this constraint which reflects the main problems
of quantum gravity, not only in the loop approach but also in geometrodynamics.
5. The discussion of the Hamiltonian constraint is based on an essentially incomplete notion of 'time' used by NPZ, as stressed above. NPZ clearly explain their notion of 'time':
NPZ, pp. 8-9: "A good way to visualise [Psi] is to think of it as a film reel; ‘time’ and the illusion that ‘something happens’ emerge only when the film is played.
"The substitution (2.12) turns the Hamiltonian constraint into a highly singular functional differential equation, which most likely cannot be made mathematically well defined in this form, even allowing for certain ‘renormalisations’."
What moves the film reel, then? You cannot explain the movement of the film with the frozen snapshots of [Psi] in "that damned equation..." (Wheeler-DeWitt equation; cf. footnote 4, p. 9). You need an Unmoved Mover, as Karel Kuchar explained here. I'm sure this sounds familiar, after Aristotle.
I bet neither Thomas Thiemann nor the authors of "Loop quantum gravity: an outside view" will pay any attention to my comments. They can put up with the criticism they exchange, as Thomas Thiemann does, but will never reply to my criticism, nor would allow me to take the stand and talk on these problems. Hermann Nicolai has never replied to my proposals, and Thomas Thiemann decided to bury my talk at GR17 into an evening poster session. That's their way to "put up" with my criticism.
To sum up, NPZ can reveal
the Perennials (K. Kuchar) of quantum gravity in 2-D spacetime only (footnote
14, p. 41). According to NPZ (p. 41), "hence it can serve as an
example of how quantisation should work" toward the full (3+1)-dimensional
quantum gravity. Only it can't.
Subject: Re: Uncountably infinite
P.S. Regarding the second point from
my preceding email (printed below),
"However, for a given [PSI], the limit e --> 0 of [XXX] does not exist on S, because wave functionals supported on the same network, but with an extra loop [XXX] attached to one of the vertices, are orthogonal to one another for different values of e by (4.7). For this reason, one must resort to a weaker notion of limit by transferring the action of the Hamiltonian to the dual space. (...) But let us repeat that there is no state in H_kin that could be interpreted as lim e ---> 0 [XXX].19"
Notice that footnote  refers to T. Thiemann's Phoenix project, the so-called Master constraint program for LQG.
The crux of the problem, the way I see it, is in the fact that the wave functionals supported on the same network, "with an extra loop [XXX] attached to one of the vertices, are orthogonal to one another for different values of e by (4.7)."
Your colleagues "resort to a weaker notion of limit", sweeping the garbage under the rug with the so-called group averaging method.
You cannot shrink the areas of loops to zero *in principle*, because such limit will ignore the quantum nature of geometry, i.e., "the fact that in full quantum geometry, the area operator has a minimum non-zero eigenvalue." The latter quote is from Ashtekar & Bojowald's gr-qc/0509075 v1, p. 24.
Can you suggest ANY (semi)classical limit by e --> 0 ?
Let me quote again from H. Nicolai et al., hep-th/0501114 v4, p. 44: "Not only will physical predictions depend on the choices made to fix these ambiguities, but these choices are important in order to determine whether or not the limit e --> 0 of (5.9) exists at all."
It is hopeless. Forget it. None of your colleagues have recalled the problems of (semi)classical limit exposed by Schrödinger in 1931. See the link in my preceding email below.
Should you have questions, please write me back.
On Mon, 19 Sep 2005 14:43:57 +0300,
Dimi Chakalov wrote: