| Subject:
gr-qc/0304074
Date: Tue, 22 Apr 2003 17:36:31 +0300 From: Dimi Chakalov <dchakalov@surfeu.at> To: Martin Bojowald <bojowald@gravity.phys.psu.edu>, Jerzy Lewandowski <lewand@gravity.phys.psu.edu> CC: tomasz.pawlowski@fuw.edu.pl, andrzej.okolow@fuw.edu.pl, mikolaj.korzynski@fuw.edu.pl, sahlmann@aei-potsdam.mpg.de Dear Colleagues, You and Prof. Ashtekar wrote: "In section IV we discussed the Hamiltonian constraint, i.e., quantum dynamics. Because there is no direct operator analog of c, we had to introduce the constraint operator C(µo) by an indirect construction." (...) "It is true that we simply promoted the classical Hamiltonian constraint function to an operator. However, because there is no direct operator analog of c, this 'quantization' is subtle and even on semiclassical (coherent) states, sharply peaked at classical configurations, the expectation value of the constraint operator equals the classical constraint function with small but very specific quantum corrections" (footnote 10, p. 25). I'm wondering if you or some of your colleagues can say something on the well-known problems of Ashtekar's quantization program, http://members.aon.at/chakalov/Ashtekar.html#NB Also, can you solve the inner product problem, given your "small but very specific quantum corrections"? Regards, Dimiter G. Chakalov
====== Subject: A cut-off for cosmological time?
Dear Dr. Bojowald, I my previous email of Tue, 22 Apr 2003 17:36:31 +0300, http://members.aon.at/chakalov/Bojowald.html I asked whether you or some of your colleagues can solve the inner product problem (also Hilbert space problem), given your "small but very specific quantum corrections", as mentioned in your gr-qc/0304074. I will highly appreciate your professional answer to this question. May I add another one, regarding your recent astro-ph/0309478 v1, "QUANTUM GRAVITY AND THE BIG BANG". I believe you would agree that quantum gravity is expected to provide not only a cut-off for curvatures, "which would otherwise diverge when a cosmological singularity is approached" (astro-ph/0309478 v1), but also a cut-off for cosmological time, as read by your clock, mine, and those of all readers of this email, both online and on my forthcoming CD ROM, in the next 300 years. If you or any of your colleagues are willing to talk about quantum gravity, I believe you should address all three issues: the inner product problem, the cut-off for curvatures, and the cut-off for the cosmological time. It's a package, isn't it? See the challenges at http://members.aon.at/chakalov/Shimony.html#Butterfield_Isham http://members.aon.at/chakalov/Schwarz.html I'm glad to see that you've moved to the Albert-Einstein-Institut in Potsdam/Golm, I believe you can find there many physicists who are preparing to celebrate Einstein's Annus Mirabilis, http://213.169.191.188/WYP_website/overview.html Let's make him a nice present, he certainly deserves it, http://members.aon.at/chakalov/faq.html#QM Regards, Dimi Chakalov
A. Einstein, Born-Einstein Letters, 29 April 1924 ======= Subject: The unknown physical inner
product
RE: Martin Bojowald, Kevin Vandersloot, Loop Quantum Cosmology and Boundary Proposals, gr-qc/0312103 v1 pp. 14-15: "From the discrete point of view, however,
there are many more solutions (infinitely many since µ is continuous)
with Planck scale oscillations. Their role and physical interpretation
are open issues, and it is expected that an understanding requires the
so far unknown physical inner product and the consideration of quantum
observables. Tentative ideas in this direction can be found in [43,44],
and further investigations are in progress.
"M. B. is grateful to C. Kiefer
for an invitation to a talk at the Xth Marcel Grossmann meeting, July 20-26,
2003, Rio de Janeiro, on which this paper is based."
Dear Dr. Vandersloot, I'm afraid you're wasting your time with M. Bojowald, he would never consider the possibility that the inner product problem cannot be solved, http://members.aon.at/chakalov/Bojowald.html#NB Perhaps it would be a better idea if you start from scratch and focus on the nature of gravity, http://members.aon.at/chakalov/Montesinos.html Then look at your brain, http://members.aon.at/chakalov/Beauregard.html#note and the solution to the problem by Mother Nature, http://members.aon.at/chakalov/Visser.html Kindest regards, Dimi Chakalov
http://members.aon.at/chakalov/faq.html Pritie amzanig huh?
Note: Martin Bojowald has not given up. He's pushing the so-called 'group averaging procedure' to crack the problem of internal time and coordinate time ("just a gauge coordinate") [Ref. 1]. He and his co-authors have obtained some "helpful intuitive understanding" but "the issue of the physical inner product and how to use the solution space to the Hamiltonian constraint are almost completely open in the full theory." Below are some excerpts, in which I highlighted my personal "intuitive understanding" with red. D.C.
[Ref. 1] Martin Bojowald, Parampreet Singh, and Aureliano Skirzewski, Time dependence in Quantum Gravity, gr-qc/0408094 v1, 30 August 2004 "A particularly striking difference between the classical and the quantum theory is the issue of time. A common understanding which works in both cases is that of relational time, where time is not an external, absolute parameter but encoded in the relative change between different degrees of freedom [20, 21, 22]. However, this concept is difficult to use explicitly, and so classically one employs the space-time picture where time is just a gauge coordinate. "Thus, this time coordinate has no
invariant physical meaning, but nevertheless provides a helpful intuitive
understanding of a given gravitational system. From the Hamiltonian point
of view, this time coordinate is the gauge parameter for orbits generated
by the Hamiltonian constraint.
"Whether or not we are using a self-adjoint
constraint operator has significance for the physical
inner product, which we are not considering here. (...) While the
averaging can be defined even for non-selfadjoint constraints, from the
numerical point of view self-adjointness of the constraint operator is
essential. Non-real eigenvalues would
imply exponentially growing modes in solutions to the differential equation
which lead to numerical instabilities. "The Gauss and diffeomorphism constraints can be solved by group averaging [26], but discussions about the correct Hamiltonian constraint are not settled yet [27, 30, 31]. Also the issue of the physical inner product and how to use the solution space to the Hamiltonian constraint are almost completely open in the full theory. "After reducing to symmetric models
[32], the Hamiltonian constraint simplifies and can often be treated explicitly.
Even in the simplest cosmological models the physical inner product is
not yet understood, but since the spatial
volume can be used as internal time in a cosmological situation the problem
of time does not play a role. In all these cases there is a Hamiltonian
constraint whose gauge parameter classically corresponds to coordinate
time, and it is our aim to discuss how such a parameter can appear with
this interpretation in quantum theory.
"V. CONCLUSIONS "Group averaging allows to introduce
a coordinate time parameter into quantum gravity, although only in an approximate
sense. Still, the resulting evolution equations are helpful in semiclassical
analysis and in providing intuitive pictures
of quantum effects.
"Thus, while the coordinate time
picture is well suited to justifying effective classical equations at non-vanishing
volume, the issue of the classical singularity can be understood only by
using the wave function directly and thus employing an
internal time to formulate evolution. Since the classical space-time
picture breaks down in this regime, there is no analog to coordinate time."
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