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Loop Quantum Gravity
Loop quantum gravity
Loop quantum gravity (LQG) is a proposed
quantum theory of
spacetime which blends together the seemingly incompatible theories (see
below) of
quantum mechanics and
general relativity. As a theory of
quantum gravity, it is the main competitor of
string theory, although stringy people outnumber loopy
people by a factor of roughly 10:1. The main successes of Loop Quantum Gravity
are: a
nonperturbative
quantization of 3-space geometry, with quantized area and volume operators;
a calculation of the
entropy of physical
black holes; and a proof by example that it is not necessary to have a
theory of everything in order to have a sensible candidate for a quantum
theory of gravity. Its main shortcomings are: not yet having a picture of
dynamics but only of kinematics; not yet able to incorporate particle physics;
not yet able to recover the classical limit.
The fundamental lesson of general relativity is that there is
no fixed spacetime background, as found in
Newtonian mechanics and
special relativity. While easy to grasp in principle, this is the hardest
idea to understand about General Relativity, and its consequences are profound
and not fully understood, even at the classical level. To a certain extent,
general relativity can be seen to be a completely relational theory, in which
the only physically relevant information is the relationship between different
events in space-time.
On the other hand, quantum mechanics since its invention has
depended on a fixed background (non-dynamical) structure. In the case of quantum
mechanics, it is
time
that is given and not dynamical, just as in Newtonian classical mechanics. In
relativistic quantum field theory, just as in classical field theory,
Minkowski spacetime is the fixed background of the theory. Finally, string
theory started out as a generalization of quantum field theory where instead of
point particles, string-like objects propagate in a fixed spacetime background.
No attempt will be made to describe
string theory/M-theory
in more depth in this article, since it wouldn't be possible to do it justice.
Quantum field theory on curved (non-Minkowskian) backgrounds,
while not a quantum theory of gravity, has shown that some of the core
assumptions of quantum field theory cannot be carried over to curved spacetime,
let alone to full-blown quantum gravity. In particular, the vacuum, when it
exists, is shown to depend on the path of the observer though space-time. Also,
the field concept is seen to be fundamental over the particle concept (which
arises as a convenient way to describe localized interactions).
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 just an emergent quality of some
background-dependent theory. This is explicitly stated, for example, in Steven
Weinberg's classic Gravitation and Cosmology textbook. The opposing
view is that background-independence is fundamental, and quantum mechanics needs
to be generalized to settings where there is no a-priori specified time. The
geometric point of view is expounded in the classic text Gravitation,
by Misner, Wheeler and Thorne. It is interesting that two books by giants of
theoretical physics expressing completely opposite views of the meaning of
gravitation were published almost simultaneously in the early 1970's. The reason
was that an impasse had been reached. Since then, though, progress was rapid on
both fronts, leading ultimately to String Theory and Loop Quantum Gravity.
Loop quantum gravity is the fruit of the effort to formulate
a background-independent quantum theory. Topological quantum field theory
provided an example of background-independent quantum theory, but with no local
degrees of freedom, and only finitely many degrees of freedom globally. This is
inadequate to describe gravity, which even in vacuum has local degrees of
freedom according to general relativity.
In LQG, the fabric of spacetime is a foamy network of
interacting loops mathematically described by
spin networks. These loops are about 10-35 meters in size, called
the
Planck scale. The loops knot together forming edges, surfaces, and vertices,
much as do
soap bubbles joined together. In other words, spacetime itself is
quantized. Any attempt to divide a loop would, if successful, cause it to
divide into two loops each with the original size. In LQG, spin networks
represent the
quantum states of the geometry of relative spacetime. Looked at another way,
Einstein's theory of general relativity is (as Einstein predicted) a
classical approximation of a quantized geometry.
An important principle in quantum cosmology that LQG adheres
to is that there are no observers outside the
universe. All observers must be a part of the universe they are observing.
However, because
light cones limit the information that is available to any observer, the
Platonic idea of absolute truths does not exist in a LQG universe. Instead,
there exists a consistency of truths in that every observer will report
consistent (not necessarily the same) results if truthful.
Another important principle is the issue of the cosmological
constant, which is the energy density inherent in a vaccuum. Because string
theory/m-theory makes use of supersymmetry, the physics implies a negative or a
zero comsological constant. This is in apparent contradiction to observation,
which observes a positive, but very close to zero, cosmological constant.
However, the ground state in LQG is positive, although very small; LQG, unlike
its rival string theory/m-theory, apparently incorporates a positive
cosmological constant in agreement with observation.
Unlike
string theory and
M-theory, LQG makes experimentally testable hypotheses.
The path taken by a photon through a discrete spacetime
geometry would be different from the path taken by the same photon through
continuous spacetime. Normally, such differences should be insignificant, but
Giovanni Amelino-Camelia points out that photons which have travelled from
distant galaxies may reveal the structure of spacetime. LQG predicts that more
energetic photons should travel ever so slightly faster than less energetic
photons. This effect would be too small to observe within our galaxy. However,
light reaching us from
gamma ray bursts in other galaxies should manifest a varying
spectral shift over time. In other words, distant gamma ray bursts should
appear to start off more bluish and end more reddish. LQG physcists anxiously
await results from space-based gamma-ray spectrometry experiments -- a mission
set to launch in September, 2006.
The recent result that
gravity propagates at the speed of light is consistent with LQG. However,
the result significantly constrains
string theory and probably
M-theory because large numbers of dimensions would allow gravity to
propagate along extra dimensions. This result does not by itself rule out all
forms of
string theory.
Loop quantum gravity theorists:
-
Popular books:
-
Julian Barbour,
The End of Time.
-
Lee Smolin,
Three Roads to Quantum Gravity
-
Introductory/expository works:
-
John Baez and
Javier Perez de Muniain,
Gauge Fields, Knots and Quantum Gravity, World Scientific (1994),
ISBN 9810220340
-
Carlo Rovelli, A Dialog on Quantum Gravity,
preprint available as
hep-th/0310077
-
Advanced books, reports, conference proceedings:
-
Robert M. Wald, Quantum Field Theory in Curved
Spacetime and Black Hole Thermodynamics, Chicago University Press
(1994),
ISBN 0226-87027-8
-
Robert M. Wald, General Relativity, Chicago
University Press,
ISBN 0-226-87033-2
-
Steven Weinberg, Gravitation and Cosmology:
principles and applications of the general theory of relativity, Wiley
(1972),
ISBN 0-471-92567-5
-
Misner, Thorne and Wheeler, Gravitation,
Freeman, (1973),
ISBN 0-7167-0344-0
-
A. Ashtekar, Lectures on Non-Perturbative Canonical
Gravity, World Scientific (1991)
-
Rodolfo Gambini and
Jorge Pullin,
Loops, Knots, Gauge Theories and Quantum Gravity
-
John Baez (ed.),
Knots and Quantum Gravity
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