|Subject: gr-qc/0503022 v1
Date: Tue, 08 Mar 2005 21:05:58 +0200
From: Dimi Chakalov <email@example.com>
CC: firstname.lastname@example.org, Hermann.Nicolai@aei.mpg.de,
RE: Draft of review article
"(...) comments, corrections,
I believe "pure (2+1)-dimensional gravity" is a misnomer. As you put it (Sec. 5.3), "I believe it is fair to say that no one yet fully understands how to quantize the SL(2,R) WZW model."
I couldn't understand what kind of states you're counting, given the "new degrees of freedom at the conformal boundary" (Sec. 6). Which brings me to your question No. 7 (p. 38):
"7. Is the progress we have achieved unique to 2+1 dimensions, or can any of our results be extended to higher-dimensional spacetimes?"
I believe your progress and limitations pertain to 2+1 dimensions only,
As you suggested (p. 38), maybe we should be "doing something no one has yet thought of".
I'll be happy to elaborate, but will have non complaints if you don't care (I know that you live in a total socialism).
Subject: Quantum geometry: Under
Dear Professor Carlip,
I looked at your web site and noticed that Sec. Quantum geometry is still under construction,
My web site about Einstein is also under construction,
My efforts can be read at
In case you have received the beta version of my CD ROM "Physics of Human Intention", which I sent you last year, please disregard it. I'm working on a very different version for kids age 11-18,
Pritie amzanig huh?
[Ref. 1] Steve Carlip,
Conceptual problems in quantum gravity,
Why is quantum gravity hard? There are a lot of particular answers, but most, if not all, of them, have the same root.
According to general relativity, gravity is a characteristic of the structure of spacetime, so quantum gravity means quantizing spacetime itself. In a very basic sense, we have no idea what this means. For instance:
1. As a probabilistic theory, quantum
mechanics gives time a special role: we would like to say, for example,
that an electron has a total probability of one of being somewhere in the
Universe at a given time. But if spacetime is quantized, we don't know
what "at a given time" means.
Note: In the case of a relativistic "collapse" of an entangled state, as in the EPR argument, we don't know what 'at a given time' means either. An inanimate physical clock can read only, and exclusively only, the kind of time in classical mechanics (called here 'local mode of time'), in which all physical quantities have exact values at each and every "instantaneous" points from their continual trajectory.
Using this kind of time only, we cannot solve the problem explained by Steve Carlip above, since we have nothing to 'hold onto', as stressed many years ago by Lao-tzu: "If you realize that all things change, there is nothing you will try to hold onto." Abby Ashtekar was only able to say that this is a fascinating issue. See a detailed review of quantum gravity by Steve Carlip, gr-qc/0108040.
What did we miss, where, and why? Recall that, by calculating some "instantaneous" value at some "point" from the trajectory above, we inevitably obliterate the phenomenon of transience. As explained succinctly by David Bohm (Wholeness and the Implicate Order, Ark edition 1983, pp. 201-204):
"These all have to do with the image in which we represent time, as if it were a series of points along a line that are somehow present together, either to our conceptual gaze or perhaps that of God. Our actual experience is, however, that when a given moment, say t_2, is present and actual, an earlier moment, such as t_1 is past. That is to say, it is gone, non-existent, never to return. So, if we say that the velocity of a particular now (at t_2) is (x_2 - x_1) / (t_2 - t_1) we are trying to relate what is (i.e., x_2 and t_2) to what is not (i.e., x_1 and t_1). We can of course do this abstractly and symbolically (as is, indeed, the common practice in science and mathematics), but the further fact, not comprehended in this abstract symbolism, is that the velocity now is active now (e.g., it determines how a particle will act from now on, in itself, and in relation to other particles).
"How are we to understand the present activity of a position (x_1) now non-existent and gone for ever?
"It is commonly thought that this problem is resolved by the differential calculus. What is done here is to let the time interval, delta t = t_2 - t_1 become vanishingly small, along with delta x = x_2 - x_1. The velocity now is defined as the limit of the ration delta x / delta t as delta t approaches zero. It is then implied that the problem described above no longer arises, because x_2 and x_1 are in effect taken at the same time. They may thus be present together and related in an activity that depends on both.
"A little reflection shows, however, that this procedure is still as abstract and symbolic as was the original one in which the time interval was taken as finite. Thus one has no immediate experience of a time interval of zero length, nor can one see in terms of reflective thought what this could mean."
Yes, we do have an immediate and perfectly clear experience of a time interval of zero length. Only this experience is UNspeakable, and pertains to the global mode of spacetime inhabited by the Holon. It cannot be read by an inanimate physical clock.
Briefly, the reason why we cannot reconcile QM with STR, as explained by Erwin Schrödinger in 1931, is that the interference of probabilities leads to a cat-and-dog superposed state living in the Holon. An inanimate physical clock can read only the physical reality in the local mode of spacetime. It can record only, and exclusively only, a state of 'cat' that has been already explicated, and has been fixed in our past light cone, as a fact. A fact with total probability of one of being somewhere in the universe at a given time, as Steve Carlip stressed above. Or a state of a 'dog'. Again, with total probability of one of being somewhere in the universe at a given time, and in our past light cone, just as we observe the Sun.
So much about QM and the way it can be seen through the distorted glasses of classical mechanics. But how about another classical theory, Einstein's General Relativity? Read about the Holon state in GR here. The task is known since 1917. We use the so-called pseudo-tensors, not self-adjoint operator as in QM, but the same problem persists: due to Diff(M)-invariance, there is no uniquely defined energy density at more than one instantaneous "point" from any "trajectory" whatsoever. Every "next" point has to be re-calculated, since there is no absolute time parameter to fix two or more unique values of physical quantities along a continual trajectory, as in classical mechanics. Example: GR waves.
Again, the puzzle is well known since 1917. As explained eloquently by G. 't Hooft, "you automatically get the correct grav. contribution to the stress-energy from the Christoffel symbols in the covariant derivatives." Automatically -- yes, but for no more than one instantaneous frozen "point". And here comes the main issue: since there exists a global mode of spacetime, which enables the transition from one point to the nearest one, those instantaneous states can indeed be used to calculate a continuous trajectory, as in the case of the so-called gravitational waves. However, in order to have a perfect continuum in the local mode of spacetime, the global mode of spacetime has to be completely wiped out from the local mode of spacetime. We can only observe some blueprints from it, but cannot solve the main paradox of cosmological time, and are inevitably haunted by some smooth dark stuff that constitutes 96 per cent from the universe. This is the effect of the Holon pertaining to the whole universe. The "medium" in which the Holon "propagates" can be identified in both General Relativity and Quantum Mechanics.
The implications can hardly be overestimated; see Carlos Barcelo and Matt Visser, gr-qc/0205066. Regarding the energy conservation in GR, Michael Weiss and John Baez were very obscure, to say the least: "Indeed, the issue of energy in general relativity has a lot to do with the notorious "problem of time" in quantum gravity... but that's another can of worms."
Sure is. And a big one. Steve Carlip knows this 'can of worms' very well. Unlike many of his colleagues, he hasn't tried some "spin networks" or any other, seemingly "background-independent", approach to quantum gravity. Not surprisingly, the section on quantum geometry at his web page is still under construction.
Note a very symptomatic reason for his 'under construction' section: In 2+1 dimensions, the Einstein tensor is "fixed uniquely, through the Einstein field equations, by the distribution of matter. As a result, there are no propagating gravitational degrees of freedom - the geometry of spacetime at a point is (almost) entirely determined by the amount and type of matter at that point." The reference URL is here. In the physically realistic 3+1 case, however, the ambiguities in the bi-directional "talk" of matter and space change the case entirely. It's a brand new ball game with far too much freedom. What can we make of it? See a very interesting idea by Kevin Brown, which too is 'under construction'.
Watch this space! Maybe Steve Carlip will say something by 14 March 2004, Albert Einstein's 125th birthday. After all, it's all about Einstein and many kids who want to learn more about the universe. We certainly owe them a lot. It's not enough to say, after A. Ashtekar, that this is a fascinating issue. That's poetry. Can we do better?
"Whether you believe you can do a
thing or believe you can't, you are right", says Henry Ford.
Quantum geometry: Under construction
Dear Drs. Noui and Perez,
In your gr-qc/0402112 v1 of 25 February 2004, you wrote:
"We hope that the spin foam perspective, fully realized here in 2+1 gravity, can bring new breath to the problem of dynamics in 3+1 gravity. This is an issue that will be studied further."
I believe Ed Witten examined the case of 2+1 dimensional gravity back in 1988, and Steve Carlip wrote a whole book on this subject. I'm afraid it's hopeless,
Since I mentioned
Ed Witten, see The Official String Theory Web Site,
Q: How can the cosmological constant be so close to zero but not zero?
Ed Witten: I really don't know. It's very perplexing that astronomical observations seem to show that there is a cosmological constant. It's definitely the most troublesome, for my interests, definitely the most troublesome, observation in physics in my lifetime. In my career that is.
The way I see it, the crux of the problem is the nature of time at the scale of tables and chairs. It cannot be recovered from your approach,
Many people have tried and failed,
Should you and/or your colleagues have questions, please don't hesitate.
"To ask a question about a black hole in quantum gravity, one must restrict initial or boundary data to ensure that a black hole is actually present."
S. Carlip, Horizon Constraints and Black Hole Entropy, hep-th/0408123
How do we know that Father Christmas has a beard? We know it, because snow falls when he shakes his beard.
P.S. Steve Carlip banged back with "please remove me from your mailing list" (this was the only email from him received in the past three years), as if I was doing something wrong. I just wanted to help, since his Sec. "Quantum geometry" is still under construction, as of August 21, 2004.
I believe Steve Carlip's web site needs updating. He is referring us to an old paper by Abhay Ashtekar, "Quantum mechanics of Riemannian geometry'' (gr-qc/9901023 of 8 January 1999), which takes black hole thermodynamics as an illustrative application but says nothing new on the main problem stressed by A. Ashtekar and S. Carlip. Another very old reference suggested by S. Carlip is Carlo Rovelli's article in Living Reviews (C. Rovelli, Loop Quantum Gravity), dated 1 December 1997. Sad but true (21 August 2004).
Let me quote from the first paragraph of S. Carlip's hep-th/0408123:
"Suppose one wishes to ask a question about a quantum black hole. In a semiclassical theory, one can look at quantum fields and gravitational perturbations around a black hole background. In a full quantum theory of gravity, however, this is no longer possible: there is no fixed background, and the theory contains states with black holes and states without. One must therefore make one's question conditional: "If a black hole with property X is present..."
... there could be a naked singularity as well. The same "theory" (cf. Richard Feynman below) permits both misunderstandings, only the latter would have killed everything in the universe. Since Steve Carlip is alive and well, the theory is wrong.
No black holes nor naked singularities in the past 13.7 billion years, Steve. Have a nice summer.
Going back to the main issue raised by S. Carlip: if spacetime is quantized, we don't know what "at a given time" means. Where did we go wrong, and when? Just don't ask "why?", because you'll never hear from S. Carlip and his prominent colleagues.
Most importantly, never try to help
people with their own papers, such as "Quantum Gravity: A Progress Report",
because they will reply with "please remove me from your mailing list".
Is it not possible that perhaps gravitation
is due simply to the fact that we do not have the right coordinate system?
P.P.S. The reason why I quoted George Orwell can be explained with the latest version of John Baez' paper
John C. Baez and Emory F. Bunn (August 19, 2004), The Meaning of Einstein's Equation, gr-qc/0103044 v3
I'll replace the Greek letter 'epsilon' used in gr-qc/0103044 v3 with e .
Regarding the Riemann curvature tensor, John C. Baez and Emory F. Bunn wrote (gr-qc/0103044, p. 13):
"The limit [Eq. 5] is well-defined, and it measures the curvature of spacetime at the point p ."
How is this so-called curvature of spacetime "well-defined"? By instructing e to approach asymptotically zero.
What is e ? The infinitesimal displacement in time. That is, the infinitesimal "movement" in time. In order to define the equivalence principle in Einstein's GR, we have to operate with some idiosyncratic idea of "points" obtained with a totally unrealistic requirement e --> 0. Since we have no other choice, the only possible way to get these "points" is the global mode of spacetime. John Baez has had the chance to learn it since January 14, 2002. Needless to say, the problem is widely known: the paradox of transience is insoluble in Einstein's GR, since 'empty space' is forbidden (cf. the hole argument). Not surprisingly, we encounter the cosmological constant problem: the immense force which drives the expansion of spacetime with constant acceleration operates in the complete absence of matter and radiation. That is, in empty space. The "explanation" provided by John Baez (p. 10): "Here pressure effects dominate because there are more dimensions of space than of time!" I decline to comment.
Next quote (p. 13): "Now let us wait a short while. Both particles trace out geodesics as time passes (emphasis mine - D.C.), and at time e they will be at new points, say p' and q'. The point p' is displaced from p by an amount ev , so we get a little parallelogram, exactly as in the definition of the Riemann curvature."
The whole bundle of issues in 'parallel transport', 'geodesic' ("the closest thing there is to a straight line in curved spacetime", p. 3), and 'geodesic deviation equation' (p. 13) are based on e being instructed to approach asymptotically zero.
"Our curved spacetime need not be embedded in some higher-dimensional flat spacetime for us to understand its curvature, or the concept of tangent vector. The mathematics of tensor calculus is designed to let us handle these concepts 'intrinsically' -- i.e., working solely within the 4-dimensional spacetime in which we find ourselves."
It's not about some "higher-dimensional flat spacetime", however. It's all about some 'global mode of spacetime'. It is the only possible logical solution to the paradox of continuum. You can try it with your brain, too.
Then the above-mentioned physicists wrote (p. 6): "Gravitational waves have not been directly observed, but there are a number of projects underway to detect them."
Then comes dead silence about that nice word "directly". More from Hermann Weyl here; details here. What if these are empty waves "traveling" on a null-plane only? The problem is known from T. Levi-Civita since 1917. See also my comment on Penrose's 'isolated system' here.
Final quote (p. 2): "This article is mainly aimed at those who teach relativity, but except for the last section, we have tried to make it accessible to students, as a sketch of how the subject might be introduced."
Our students are kids. They have the right to know everything we know. We mush never 'sweep the garbage under the carpet'.
John Baez knows exactly what I mean. Regrettably, to see what is in front of one's nose requires a constant struggle, as pointed out by George Orwell. Not surprisingly, on Monday, 14 January 2002, John Baez warned me not to send him email:
"I've repeatedly requested that you not send me email. You can save both of us some trouble by taking me off your list."
It seems to me that John Baez is
one of those prominent physicists who
just don't care. The list of such people
is very long, unfortunately. More in my forthcoming
CD ROM "Physics of Human Intention".
v1, Sec V, What Can We Still Learn?
You wrote: "comments, criticisms, additions, missing references welcome".
I don't think you can understand the limitations of (2+1)-dimensional gravity as a test bed unless you understand the nature of the "energy" of spacetime geometry in Einstein's GR. To be specific (p. 41):
"Perhaps the most important lesson of (2+1)-dimensional quantum gravity is that general relativity can, in fact, be quantized."
It's not a *fact*, and it cannot be a *fact*, for the simple reason that we don't know how to represent the "energy" of the geometry, after H. Weyl,
It's a big can of worms,
If you need references, please write me back.