| Subject: How to determine the semi-classical
regime in a background independent fashion?
Date: Wed, 26 Jan 2005 12:13:06 +0000 From: Dimi Chakalov <dimi@chakalov.net> To: Etera Livine <elivine@perimeterinstitute.ca> CC: r.loll@phys.uu.nl, kuchar@physics.utah.edu, Hermann.Nicolai@aei.mpg.de, lsmolin@perimeterinstitute.ca, odreyer@perimeterinstitute.ca, fotini@perimeterinstitute.ca, dgottesman@perimeterinstitute.ca, hburton@perimeterinstitute.ca, tthiemann@perimeterinstitute.ca, rmyers@perimeterinstitute.ca, lcrane@math.ist.utl.pt, ashtekar@gravity.phys.psu.edu BCC: [snip] Dear Etera, I read your recent "Some Remarks on the Semi-Classical Limit of Quantum Gravity", gr-qc/0501076 v1 [Ref. 1], and recalled a famous saying from Confucius: "The hardest thing of all is to find a black cat in a dark room, especially if there is no cat." Perhaps it will be a good idea if you prove the zeroeth hypothesis, which is that there is indeed a cat in the dark room. Which brings us to the question in the subject line. If you can prove that there is indeed a theoretical possibility to recover a smooth 3-D continuum, like the one at the scale of tables and chairs, I would say that there is indeed a cat in the dark room of loop quantum gravity, http://www.God-does-not-play-dice.net/Nicolai.html#note_3 To the best of my knowledge, the only semi-successful effort in this direction is that by Renate Loll and collaborators, hep-th/0404156 v4, http://www.God-does-not-play-dice.net/Kiefer.html#3D Lee Smolin, for example, wasn't successful at all: "One of the biggest mysteries is that we live in a world in which it is possible to look around, and see as far as we can" (Three Roads to Quantum Gravity, p. 205), while Abby Ashtekar is still wrestling with those intersecting knots in 3 dimensions ("To achieve this goal in 3+1 dimensions, one needs a much better understanding of the theory of (intersecting) knots in 3 dimensions"). Why don't you ask Karel Kuchar for advice? I believe he is uniquely qualified to help you in the following manner: In order to recover a smooth 3-D continuum from the quantum mesh of loop quantum gravity (hence making your hypothesis falsifiable, hopefully), you need to find solutions to [X], but in order to get these solutions, first of all you need to find some *observable* Perennial (the dark cat -- if any). Regarding [X], see the status of the Hamiltonian constraint, http://www.God-does-not-play-dice.net/Nicolai.html#C4 So, my suggestion is this: instead of waiting for another 50 years to develop a complete theory of quantum gravity, as suggested by Lee Smolin, ask Karel Kuchar to help you solve the the zeroeth hypothesis of Confucius 'there is a black cat in the dark room'. Kindest regards, Dimi
Reference [Ref. 1] Etera R. Livine, Some Remarks on the Semi-Classical Limit of Quantum Gravity, gr-qc/0501076 v1 "Finally, I will discuss the tools necessary in order
to understand the semi-classical regime, or more generally a macroscopic
regime, in full background independent quantum gravity such as loop quantum
gravity.
"We hope that such a study of semi-classical properties
of non-commutative spacetime can be extended to the four spacetime dimension
case (...).
"To conclude, the notion of semi-classicality is an important
issue in quantum gravity. In a background independent theory, either one
could introduce effective description of quantum gravity depending explicitly
on the observer and taking place in a (non-commutative) flat spacetime,
or one should introduce new ways to define the semi-classical regime in
a background independent fashion. I proposed to address the latter alternative
using tools of quantum information and developing the mathematical relation
between the quantum state of geometry and the corresponding renormalisation/coarse-graining
of geometrical objects."
Note: Etera Livine may sound like a beautiful graceful Italian girl, and one could expect that she would consider the arguments above. Wrong. This is a tall young man with
a long black hair, who is searching for the missing key under the lamp,
simply because it's brighter there. See also his friend and colleague Danielle
Oriti here. The latter keeps short black hair;
that's the sole difference IMHO.
D. Chakalov
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Subject: Why don't
you invite Karel Kuchar?
Dear Lee, I believe you've been working on Loop Quantum Gravity (LQG) since February 1986 [Ref. 1], and are aware of the devastating criticism by Hermann Nicolai, Kasper Peeters, and Marija Zamaklar, in "Loop quantum gravity: an outside view" (hep-th/0501114 v1). Regarding the status of the Hamiltonian constraint, your colleagues even wonder "what has really been gained in comparison with the old geometrodynamics approach", http://www.God-does-not-play-dice.net/Nicolai.html#C3 Perhaps it would be a good idea if you ask Karel Kuchar for advice. I already suggested to Etera Livine to contact Prof. Kuchar who is definitely qualified to help you sort out "the black cat in the dark room" of LQG, http://www.God-does-not-play-dice.net/Etera.html I believe Prof. Kuchar can shed light on the following question: What should be the solution to the Hamiltonian constraint problem in LQG in order to recover a smooth 3-D continuum at the scale of tables and chairs? Perhaps it is impossible to obtain such solution *in principle*, and I suppose Prof. Kuchar can demonstrate you the inevitable contradictions from such hypothetical solution (reductio ad absurdum). I looked at the web site of Perimeter Institute, and found out that you've had 109 visitors in 2002, 184 in 2003, 42 in 2004, and will host another 50 visitors until October 16, 2005. Couldn't find Karel Kuchar though. I think it would be great if you invite Prof. Karel Kuchar, I believe he has been working on canonical quantum gravity many years before you discovered "an infinite number of absolutely genuine solutions to the real equations of quantum gravity" in February 1986 [Ref. 1]. Please don't take this personally. Mike Lazaridis and his friends have invested $120 million (Canadian) in the Perimeter Institute, http://www.phys.lsu.edu/mog/mog19/node7.html http://www.perimeterinstitute.ca/about/history.cfm After six years, perhaps they are expecting some real results. You can read this email also at http://www.God-does-not-play-dice.net/Etera.html#Lee Regards, Dimi
Confucius
References [Ref. 1] Lee Smolin, Three Roads to Quantum Gravity, Phoenix, London, 2001, pp. 40-41. "One day in February 1986, .... (...)
(W)e had obtained an infinite number of absolutely genuine solutions to
the real equations of quantum gravity."
Suppose that the spacetime can be modeled as some smooth, connected, paracompact, and Hausdorff manifold. What is missing here is the very mechanism that generates that smooth, connected, paracompact, and Hausdorff manifold. In order to obtain one point from this manifold, to which you attach some point-like number (e.g., by calculating the circumference of a circle, after Archimedes), you need two things: first, an infinite and uncountable "number" of steps to reach this "final" infinitesimal beast, and secondly -- the phenomenon of actual infinity to get it for you. The first process goes in the local mode of spacetime, while the second is facilitated by the global mode of spacetime. You need both the local and the global mode to describe the mechanism of creating "points". It's a package. To explain this, recall a question posed by J. von Neumann (emphasis mine - D.C.): "... one should expect that 2. would suffice to describe the intervention caused by a measurement. Indeed, a physical intervention can be nothing else than the temporary insertion of a certain energy coupling into the observed system, i.e., the introduction of an appropriate time dependency of H (prescribed by the observer). Why then do we need the special process 1. for the measurement?" (The Mathematical Foundations of Quantum Mechanics, Princeton University Press: Princeton, 1955, p. 352). We need that "special process 1." because we have to convert the global mode of the quantum system into the local mode, by "the introduction of an appropriate time dependency of H (prescribed by the observer)." The real fun begins when you don't have a classical world to introduce "an appropriate time dependency of H", as in quantum cosmology. More here and here. Now, in loop quantum gravity (LQG), you have an uncountable "solutions" to what you call "points" at the scale of tables and chairs. These "solutions" are not distinguishable but resemble the amplitude density in QFT. It's something like a non-separable continuous "dough" of classical alternatives, which is not smooth and isotropic, because some "parts" from it have higher "density". What you don't have in LQG is the action of the phenomenon of actual infinity, which would select one classical solution from this dough, elevate it at the scale of tables and chairs, and make you calculate the circumference of a circle, after Archimedes. Two months ago, I stated that the math is available upon request. Nobody replied (see an incomplete list of physicists here). Two years ago, I wrote to Prof. Karel Kuchar, but no reply has reached me so far. Obviously, people are not interested in my work, and I sincerely hope that Prof. Karel Kuchar will be invited at the Perimeter Institute. Then they will sort out this whole mess in an "open atmosphere where anybody can criticize anybody, honestly and directly", and also in a "supportive atmosphere, where people are generous and sympathetic about difficulties and failures." This is what the Perimeter Institute is supposed to be. Do you like the tranquilizing philosophy - or religion? - of loop quantum gravity? Do you like the tranquilizing philosophy - or religion? - of the decoherence mechanism? Do you like the tranquilizing philosophy
- or religion? - of the linearized approximation
of Einstein's GR?
D. Chakalov
A. Einstein
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