“ We cannot even begin to fathom what riches an understanding
of the properties of geometry and matter, under the umbrella of
a theory of quantum gravity, will bring to our society and to the
world at large ”
presumed to be smooth and continuous. As such studying gravitons is analogous to studying the behaviour of perturbations of
a body of fluid. Studying the perturbations of a fluid will give us
the theory of waves but will not inform us of the nature of the
molecules and atoms which constitute the fluid. Similarly a study
of gravitons allows us to study perturbations of the gravitational
field but does not give us any indication of the “molecules” and
“atoms” from whose combinations the geometry - and therefore
the gravitational field - arises.
LQG advocates a different perspective. From the very beginning1 the notion of a smooth, continuous background geometry
is abandoned in favour of a discrete geometry which is built out
of elementary objects known as “simplices” - which is a complicated term for elementary geometric objects such as triangles and
tetrahedra. In much the same way that Lego blocks can be glued
together to build complicated structures, a collection of triangles or tetrahedra can be assembled to build a two-dimensional
or three-dimensional geometry respectively. LQG allows us to
calculate the quantized values of geometric attributes associated
with these simplices. It provides us with a framework for studying quanta of geometry - in the true sense of the phrase - and
to construct superpositions of different states of geometry.
However, there remain many shortcomings in the LQG approach.
Two significant obstacles are a) the lack of a grasp on how we can
obtain an (approximately) smooth, continuous spacetime by gluing
together our elementary simplices and b) a lack of understanding