Loop Quantum Gravity aims to
be a quantum theory of gravity alone, taking gravity to be
unique among the fundamental forces of nature. It is
non-perturbative (no graviton) and basically quantizes space
(not space-time) by “brute force,” with a smallest length,
smallest area and smallest volume. It has no extra
dimensions, does not require supersymmetry, and is
background-independent. Like string theory, LQG has
difficulty in making distinctive or characteristic predictions
that are verifiable experimentally. In my humble opinion,
the most serious problem with LQG is that it does not appear to
have Einstein's Theory of Gravity as its classical limit.
The other huge problem is an inability to identify the vacuum
state of the theory. Here
is an informed critique of the whole field of LQG.
{The entire field seems to have stagnated since it began in the
early 1980s, with some discoveries about Einstein's
Theory of Gravity, made by Amitaba
Sen, then a postdoc at the University of Maryland... and
grew dramatically for a few decades.} The basic idea is to
describe space as fundamentally quantum in nature (lengths,
areas and volumes, etc., are all quantized). It turns out that
this quantum description of quantized units of space has a
natural description in terms of a lattice or network, labelled
by quantities exactly like particle spins, hence such a system
is referred to as a spin network. The obvious problem is
that a quantum of space cannot be covariant.
 |
If you don't know what the
anthropic principle is, bless you, but you can click here.
|
[Comments by Andrew Z. Jones
and D. Robbins:] Many of the flaws in loop quantum gravity are
the same flaws [found] in string theory. The predictions
generally extend into realms that aren’t quite testable yet
(although LQG is a bit closer to being able to be
experimentally tested than string theory probably is). Also,
it’s not really clear that loop quantum gravity is any more
falsifiable than string theory. For example, the discovery of
supersymmetry or extra dimensions won’t disprove loop quantum
gravity any more than the [continuing] failure to detect them
will [eventually] disprove string theory. The only discovery
that I think LQG would have a hard time overcoming would be if
black holes [can be studied in extreme detail] and
Hawking radiation proves to be false, which would be a problem
for any quantum gravity theory, including string theory. The
biggest flaw in loop quantum gravity is that it has yet to
successfully show that you can take a quantized space and
extract a smooth space-time out of it. In fact, the entire
method of adding time into the LQG spin network seems somewhat
contrived to some critics, although whether it’s any more
contrived than the entirely background-dependent formulation
of string theory remains to be seen. The quantum theory of
space-time in standard LQG is really just a quantum theory of
space. The spin network described by the theory cannot yet
incorporate time.
One of the most important recent
developments in LQG is LQG
cosmology, which, when applied to the very early
universe, gives a very different picture of its origin and
earliest state than is provided by extrapolation of the
standard ΛCDM model. Also, it is not often pointed out
that LQG offers a way of solving the Wheeler-DeWitt
Equation.
LQG approaches, of which
there are now many, do not need supersymmetry or extra space
dimensions, but most versions must violate Lorentz Covariance.
The speed of light varies from place to place and depends on
frequency! LQG approaches famously also do not reduce in
the classical limit to Einstein's theory of gravity, and
generally do not use a 4-dimensional quantization; only space
is quantized. LQG makes no testable predictions that go
beyond the Standard Model. One of my former students
from years ago played a key role in launching LQG! He
is not responsible for its later evolution.
[Wikipedia Entry on LQG.] Over the years I have tried to
read a number of different introductory presentations of LQG,
and had to give up each time because the texts were just
presentations of one unjustifiable assumption after another,
with no motivation from physics. Just like string
theory, LQG lacks any underlying basic principle from which a
theoretical framework logically flows--- very, very unlike,
for instance, Einstein's theory of gravity, which is firmly
based on the Principle
of Equivalence. Anyway, here is a recent
review of LQG by one of its creators.
MY OVERALL VERDICT ON LQG: 
HAS LQG BEEN DISPROVED?
A Quantum Action for Gravity?
The Most Recent Approach to
Quantum Gravity is not Quantum
More on the Non-quantum Idea