Quantum gravity is an open problem that has been investigated for
over seventy years now. When one contemplates two deep problems,
one is tempted to believe that they are related. In the history
of physics, there are surprising examples of two deep problems
solved by one stroke (the unification of electricity and
magnetism and the nature of light, for instance); but also many
examples in which a great hope to solve more than one problem at
once was disappointed (finding the theory of strong interactions
and getting rid of quantum field theory infinities, for
instance). Quantum gravity has been asked, at one time or
another, to address almost every deep open problem in theoretical
physics (and beyond). Here is a list of problems that have been
connected to quantum gravity in the past, but about which loop
quantum gravity has little to say:

Interpretation of quantum mechanics.
 Loop quantum gravity is a standard quantum (field) theory.
Pick your favorite interpretation of quantum mechanics, and use
it for interpreting the quantum aspects of the theory. I will
refer to two such interpretations below: When discussing the
quantization of area and volume, I will use the relation
between eigenvalues and outcomes of measurements performed with
classical physical apparatusses; when discussing evolution, I
will refer to the histories interpretation. The peculiar way of
describing time evolution in a general relativistic theory may
require some appropriate variants of standard interpretations,
such as generalized canonical quantum theory [166,
168,
165] or Hartle's generalized quantum mechanics [103]. But loop quantum gravity has no help to offer the scientists
who have speculated that quantum gravity will solve the
measurement problem. On the other hand, the spacetime
formulation of loop quantum gravity that has recently been
developed (see Section
6.10) is naturally interpreted in terms of histories
interpretations [103,
119,
120,
123,
122]. Furthermore, I think that solving the problem of the
interpretation of quantum mechanics might require relational
ideas connected with the relational nature of spacetime
revealed by general relativity [179,
180].

Quantum cosmology.
 There is widespread confusion between quantum cosmology and
quantum gravity. Quantum cosmology is the theory of the entire
universe as a quantum system without external observer [102]: With or without gravity, makes no difference. Quantum
gravity is the theory of one dynamical entity: the quantum
gravitational field (or the spacetime metric), just one field
among the many. Precisely as for the theory of the quantum
electromagnetic field, we can always assume that we have a
classical observer with classical measuring apparatusses
measuring gravitational phenomena, and therefore study quantum
gravity disregarding quantum cosmology. For instance, the
physics of a Planck size small cube is governed by quantum
gravity and, presumably, has no cosmological implications.

Unifications of all interactions
 or
``Theory of Everything''
. A common criticism of loop quantum gravity is that it does
not unify all interactions. But the idea that quantum gravity
can be understood
only
in conjunction with other fields is an interesting hypothesis,
not an established truth.

Mass of the elementary particles.
 As far as I see, nothing in loop quantum gravity suggests
that one could compute masses from quantum gravity.

Origin of the Universe.
 It is likely that a sound quantum theory of gravity will be
needed to understand the physics of the Big Bang. The converse
is probably not true: We should be able to understand the small
scale structure of spacetime even if we do not understand the
origin of the Universe.

Arrow of time.
 Roger Penrose has argued for some time that it should be
possible to trace the time asymmetry in the observable Universe
to quantum gravity.

Physics of the mind.
 Penrose has also speculated that quantum gravity is
responsible for the wave function collapse, and, indirectly,
governs the physics of the mind [155].
A problem that has been repeatedly tied to quantum gravity,
and which loop quantum gravity
might
be able to address, is the problem of the ultraviolet infinities
in quantum field theory. The very peculiar nonperturbative short
scale structure of loop quantum gravity introduces a physical
cutoff. Since physical spacetime itself comes in quanta in the
theory, there is literally no space in the theory for the very
high momentum integrations that originate from the ultraviolet
divergences. Lacking a complete and detailed calculation scheme,
however, one cannot yet claim with confidence that the
divergences, chased from the door, will not reenter from the
window.

Loop Quantum Gravity
Carlo Rovelli
http://www.livingreviews.org/lrr19981
© MaxPlanckGesellschaft. ISSN 14338351
Problems/Comments to
livrev@aeipotsdam.mpg.de
