Spin foam vacuum LQG versus false 'stringy theory'!

‘String theory has the remarkable property of predicting gravity’: false claim by Edward Witten in the April 1996 issue of Physics Today, repudiated by Roger Penrose on page 896 of his book The Road to Reality, 2004. String theory does not predict anything testable about gravity. - Comment on Peter Woit's blog

'... it is thus perhaps best to view spin foam models ... as a novel way of defining a (regularised) path integral in quantum gravity. Even without a clear-cut link to the canonical spin network quantisation programme, it is conceivable that spin foam models can be constructed which possess a proper semi-classical limit in which the relation to classical gravitational physics becomes clear. For this reason, it has even been suggested that spin foam models may provide a possible ‘way out’ if the difficulties with the conventional Hamiltonian approach should really prove insurmountable.' - http://arxiv.org/abs/hep-th/0601129

The spin foam vacuum of loop quantum gravity is the only consistent mathematical formulation of Feynman's path integrals that seems to have the potential of addressing the physical process by which the vacuum operates. The better known 'quantum gravity' is called string theory, and deals with particles as 10/11 dimensional loops. String theory suggests 10^500 different vacuum states, and although it could provide an empty framework for a (unobserved but speculated) spin-2 gauge boson (graviton speculation), it does not provide any dynamics or testable predictions after 20 years of intense funding and effort!

"An important part of all totalitarian systems is an efficient propaganda machine. ... to protect the 'official opinion' as the only opinion that one is effectively allowed to have." - STRING THEORIST Dr Lubos Motl: http://motls.blogspot.com/2006/01/power-of-propaganda.html

The quotation above shows how "string theorists" have been able to brain-wash many people with propaganda. Loop quantum gravity does not have that propaganda. So let's see a little recent work in Loop Quantum Gravity:

"... the spinfoam model of http://arxiv.org/hep-th/0512113. In that paper Freidel and Livine work out a model of 3D spacetime and matter which has QFT as the zero-gravity limit (as G -> 0) and General Relativity with some quantum corrections as the (semi)classical limit (as h-bar -> 0). In that paper I do not see other constants which can vary to give a large space of solutions. However they still have to extend their results to 4D spacetime and matter." - Woit blog.

http://arxiv.org/abs/hep-th/0601129: Loop and spin foam quantum gravity: a brief guide for beginners, by Hermann Nicolai, Kasper Peeters. This is a very nice brief (18 pages) review of 'loop quantum gravity and spin foam models at an introductory level, with special attention to questions frequently asked by non-specialists':

'In contrast to string theory, which posits that the Einstein-Hilbert action is only an effective low energy approximation to some other, more fundamental, underlying theory, loop and spin foam gravity take Einstein’s theory in four spacetime dimensions as the basic starting point, either with the conventional or with a (constrained) ‘BF-type’ formulation. These approaches are background independent in the sense that they do not presuppose the existence of a given background metric. In comparison to the older geometrodynamics approach (which is also formally background independent) they make use of many new conceptual and technical ingredients.

'A key role is played by the reformulation of gravity in terms of connections and holonomies. A related feature is the use of spin networks in three (for canonical formulations) and four (for spin foams) dimensions. These, in turn, require other mathematical ingredients, such as non-separable (‘polymer’) Hilbert spaces and representations of operators which are not weakly continuous. Undoubtedly, novel concepts and ingredients such as these will be necessary in order to circumvent the problems of perturbatively quantised gravity (that novel ingredients are necessary is, in any case, not just the point of view of LQG but also of most other approaches to quantum gravity). However, it is important not to lose track of the physical questions that one is trying to answer.

'... it is thus perhaps best to view spin foam models as models in their own right, and, in fact, as a novel way of defining a (regularised) path integral in quantum gravity. Even without a clear-cut link to the canonical spin network quantisation programme, it is conceivable that spin foam models can be constructed which possess a proper semi-classical limit in which the relation to classical gravitational physics becomes clear. For this reason, it has even been suggested that spin foam models may provide a possible ‘way out’ if the difficulties with the conventional Hamiltonian approach should really prove insurmountable.'

Christine Dantas points out that these authors are those of http://arxiv.org/abs/hep-th/0501114 which is a paper resubmitted to Classical and Quantum Gravity. There is always the prejudice question!

Another vacuum picture: "Another possible “other approach” might be the emergent vacuum picture advocated by Laughlin and Chapline (popularly described in Laughlin’s book A Different Universe (Reinventing Physics from the Bottom Down)). Here is Susskind’s criticism of Laughlin’s approach:

“… Superfluid helium is an example of a material with special “emergent” properties … In a lot of ways, superfluids are similar to the Higgs fluid that fills space and gives particles their properties. Roughly speaking Laughlin’s view can be summarized by saying that we live in such a space-filling material. He might even say … space IS such an emergent material! Moreover, he believes that gravity is an emergent phenomenon. … There are two serious reasons to doubt that the laws of nature are similar to the laws of emergent materials. … The first … Laughlin himself …[argues]… that black holes (in his theory) cannot have properties, such as Hawking radiation, that practically everyone else believes them to have …[second]… insensitivity to the microscopic starting point is the thing that condensed-matter physicists like best about emergent systems. But the probability that … there should be one … endpoint … with the incredibly fine-tuned properties of our anthropic world is negligible. …”.

"It is sad to me that Susskind’s first criticism of Laughlin assumes that “practically everyone” believes that black holes have Hawking radiation, when, in fact, even Hawking himself has repudiated ( see his Dublin 2004 abstract at http://www.dcu.ie/~nolanb/gr17_plenary.htm#hawking ) information loss by Hawking radiation.

"It is also sad that Susskind’s second criticism of Laughlin assumes that the process of emergence CANNOT produce an “endpoint” with precisely the properties that our experiments observe.Perhaps a spin foam with J3(O) nodes might produce our observed universe,similar to the emergence of superfluid helium from helium atoms.Unless and until the physics community encourages research work along such lines, how will we know the answer?
- Tony Smith http://www.valdostamuseum.org/hamsmith/" - Woit blog.

UPDATE: yet another string hoax exposed to be misleading propaganda: http://www.math.columbia.edu/~woit/wordpress/?p=327

FROM WIKIPEDIA ENTRY ON LOOP QUANTUM GRAVITY (BIASED AGAINST LOOP QUANTUM GRAVITY, SINCE IT IS WRITTEN BY STRING THEORISTS IN PART):

Loop quantum gravity (LQG), also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the seemingly incompatible theories of quantum mechanics and general relativity. This theory is one of a family of theories called canonical quantum gravity. It was developed in parallel with loop quantization, a rigorous framework for nonperturbative quantization of diffeomorphism-invariant gauge theory. In plain English this is a quantum theory of gravity in which the very space that all other physics occurs in is quantized.

Loop quantum gravity (LQG) is a proposed theory of spacetime which is built from the ground up with the idea of spacetime quantization via the mathematically rigorous theory of loop quantization. It preserves many of the important features of general relativity, such as local Lorentz invariance, while at the same time employing quantization of both space and time at the Planck scale in the tradition of quantum mechanics.

This is not the most popular theory of quantum gravity; many physicists have philosophical problems with it. ...

LQG in itself was initially less ambitious than string theory, purporting only to be a quantum theory of gravity. ...

1) It is a nonperturbative quantization of 3-space geometry, with quantized area and volume operators
2) It includes a calculation of the entropy of black holes
3) It is a viable gravity-only alternative to string theory

However, these claims are not universally accepted. While many of the core results are rigorous mathematical physics, their physical interpretations remain speculative. LQG may or may not be viable as a refinement of either gravity or geometry. For example, entropy calculated in (2) is for a kind of hole which may or may not be a black hole.

The spin foam model proposed by Louis Crane, John Baez, et al, adds a time dimension to loop quantum gravity to accomodate relativistic spacetime.

The incompatibility between quantum mechanics and general relativity

Quantum field theory studied on curved (non-Minkowskian) backgrounds has shown that some of the core assumptions of quantum field theory cannot be carried over. In particular, the vacuum, when it exists, is shown to depend on the path of the observer through space-time (see Unruh effect).

Historically, there have been two reactions to the apparent inconsistency of quantum theories with the necessary background-independence of general relativity. The first is that the geometric interpretation of general relativity is not fundamental, but emergent. The other view is that background-independence is fundamental, and quantum mechanics needs to be generalized to settings where there is no a priori specified time.

Loop quantum gravity is an effort to formulate a background-independent quantum theory. Topological quantum field theory is a background-independent quantum theory, but it lacks causally-propagating local degrees of freedom needed for 3 + 1 dimensional gravity.
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History of LQG

In 1986, Abhay Ashtekar reformulated Einstein's field equations of general relativity using what have come to be known as Ashtekar variables, a particular flavor of Einstein-Cartan theory with a complex connection. He was able to quantize gravity using gauge field theory. In the Ashtekar formulation, the fundamental objects are a rule for parallel transport (technically, a connection) and a coordinate frame (called a vierbein) at each point. Because the Ashtekar formulation was background-independent, it was possible to use Wilson loops as the basis for a nonperturbative quantization of gravity. Explicit (spatial) diffeomorphism invariance of the vacuum state plays an essential role in the regularization of the Wilson loop states.

Around 1990, Carlo Rovelli and Lee Smolin obtained an explicit basis of states of quantum geometry, which turned out to be labelled by Penrose's spin networks. In this context, spin networks arose as a generalization of Wilson loops necessary to deal with mutually intersecting loops. Mathematically, spin networks are related to group representation theory and can be used to construct knot invariants such as the Jones polynomial.

Being closely related to topological quantum field theory and group representation theory, LQG is mostly established at the level of rigour of mathematical physics.

The ingredients of loop quantum gravity

Loop quantization

At the core of loop quantum gravity is a framework for nonperturbative quantization of diffeomorphism-invariant gauge theories, which one might call loop quantization. While originally developed in order to quantize vacuum general relativity in 3+1 dimensions, the formalism can accommodate arbitrary spacetime dimensionalities, fermions (John Baez and Kirill Krasnov), an arbitrary gauge group (or even quantum group), and supersymmetry (Smolin), and results in a quantization of the kinematics of the corresponding diffeomorphism-invariant gauge theory. Much work remains to be done on the dynamics, the classical limit and the correspondence principle, all of which are necessary in one way or another to make contact with experiment.

In a nutshell, loop quantization is the result of applying C*-algebraic quantization to a non-canonical algebra of gauge-invariant classical observables. Non-canonical means that the basic observables quantized are not generalized coordinates and their conjugate momenta. Instead, the algebra generated by spin network observables (built from holonomies) and field strength fluxes is used.

Loop quantization techniques are particularly successful in dealing with topological quantum field theories, where they give rise to state-sum/spin-foam models such as the Turaev-Viro model of 2+1 dimensional general relativity. A much studied topological quantum field theory is the so-called BF theory in 3+1 dimensions. Since classical general relativity can be formulated as a BF theory with constraints, scientists hope that a consistent quantization of gravity may arise from the perturbation theory of BF spin-foam models.

Lorentz invariance

For detailed discussion see the Lorentz covariance page.
LQG is a quantization of a classical Lagrangian field theory which is equivalent to the usual Einstein-Cartan theory in that it leads to the same equations of motion describing general relativity with torsion. As such, it can be argued that LQG respects local Lorentz invariance. Global Lorentz invariance is broken in LQG just as in general relativity. A positive cosmological constant can be realized in LQG by replacing the Lorentz group with the corresponding quantum group.

Diffeomorphism invariance and background independence

General covariance, also known as diffeomorphism invariance, is the invariance of physical laws under arbitrary coordinate transformations. A good example of this are the equations of general relativity, where this symmetry is one of the defining features of the theory. LQG preserves this symmetry by requiring that the physical states remain invariant under the generators of diffeomorphisms. The interpretation of this condition is well understood for purely spatial diffemorphisms. However, the understanding of diffeomorphisms involving time (the Hamiltonian constraint) is more subtle because it is related to dynamics and the so-called problem of time in general relativity. A generally accepted calculational framework to account for this constraint is yet to be found.

Whether or not Lorentz invariance is broken in the low-energy limit of LQG, the theory is formally background independent. The equations of LQG are not embedded in, or presuppose, space and time, except for its invariant topology. Instead, they are expected to give rise to space and time at distances which are large compared to the Planck length. At present, it remains unproven that LQG's description of spacetime at the Planckian scale has the right continuum limit, described by general relativity with possible quantum corrections.
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Problems

As of December 2005, there is not a single experiment which verifies or refutes any aspect of LQG. This problem plagues most current theories of quantum gravity. LQG is affected especially, because it applies on a small scale to the weakest forces in nature. There is no work around for this problem, as it is the biggest problem any scientific theory can have; theory without experiment is just faith. The second problem is that a crucial free parameter in the theory known as the Immirzi parameter can only be computed by demanding agreement with Bekenstein and Hawking's calculation of the black hole entropy. Loop quantum gravity predicts that the entropy of a black hole is proportional to the area of the event horizon, but does not obtain the Bekenstein-Hawking formula S = A/4 unless the Immirzi parameter is chosen to give this value.

Finally, LQG has gained limited support in the physics community, perhaps because of its limited scope. So far, it seeks to describe a quantum theory including gravity and more or less arbitrary other forces and forms of matter. String theory and M-theory are more ambitious, since they seek a more or less unique theory which predicts not only the behavior of gravity but also the detailed behavior of elementary particles and the forces besides gravity. While they have not succeeded in doing so yet, the general feeling is that these competing theories are more potent. Loop theorists disagree, because they believe that we need a proper theory of quantum gravity as a prerequisite for any theory of everything. Only time and experimentation can decide the matter.

Bibliography
Popular books:
Julian Barbour, The End of Time
Lee Smolin, Three Roads to Quantum Gravity
Magazine articles:
Lee Smolin, "Atoms in Space and Time," Scientific American, January 2004
Easier introductory/expository works:
Abhay Ashtekar, Gravity and the quantum, e-print available as gr-qc/0410054
John C. Baez and Javier Perez de Muniain, Gauge Fields, Knots and Quantum Gravity, World Scientific (1994)
Carlo Rovelli, A Dialog on Quantum Gravity, e-print available as hep-th/0310077
More advanced introductory/expository works:
Abhay Ashtekar, New Perspectives in Canonical Gravity, Bibliopolis (1988).
Abhay Ashtekar, Lectures on Non-Perturbative Canonical Gravity, World Scientific (1991)
Abhay Ashtekar and Jerzy Lewandowski, Background independent quantum gravity: a status report, e-print available as gr-qc/0404018
Rodolfo Gambini and Jorge Pullin, Loops, Knots, Gauge Theories and Quantum Gravity, Cambridge University Press (1996)
Hermann Nicolai, Kasper Peeters, Marija Zamaklar, Loop quantum gravity: an outside view, e-print available as hep-th/0501114
Carlo Rovelli, Loop Quantum Gravity, Living Reviews in Relativity 1, (1998), 1, online article, 2001 15 August version
Carlo Rovelli, che cos'è il tempo, che cos'è lo spazio, Di Renzo Editore, Roma, 2004
Carlo Rovelli, Quantum Gravity, Cambridge University Press (2004); draft available online
Thomas Thiemann, Introduction to modern canonical quantum general relativity, e-print available as gr-qc/0110034
Thomas Thiemann, Lectures on loop quantum gravity, e-print available as gr-qc/0210094
Conference proceedings:
John C. Baez (ed.), Knots and Quantum Gravity
Fundamental research papers:
Abhay Ashtekar, New variables for classical and quantum gravity, Phys. Rev. Lett., 57, 2244-2247, 1986
Abhay Ashtekar, New Hamiltonian formulation of general relativity, Phys. Rev. D36, 1587-1602, 1987
Roger Penrose, Angular momentum: an approach to combinatorial space-time in Quantum Theory and Beyond, ed. Ted Bastin, Cambridge University Press, 1971
Carlo Rovelli and Lee Smolin, Loop space representation of quantum general relativity, Nuclear Physics B331 (1990) 80-152
Carlo Rovelli and Lee Smolin, Discreteness of area and volume in quantum gravity, Nucl. Phys., B442 (1995) 593-622, e-print available as gr-qc/9411005
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External links
Quantum Gravity, Physics, and Philosophy: http://www.qgravity.org/
Resources for LQG and spin foams: http://jdc.math.uwo.ca/spin-foams/
Gamma-ray Large Area Space Telescope: http://glast.gsfc.nasa.gov/
Zeno meets modern science. Article from Acta Physica Polonica B by Z.K. Silagadze.