Page 24 - Perimeter Institute 2012 Annual Report

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Spinning up spacetime
Quantum theory and the modern theory of gravity, Einstein’s
general relativity, don’t fit easily together. There are many reasons
why, but here’s one: relativity radically changed classical notions
about space and time, while quantum theory largely preserves
those notions. It’s fitting, therefore, that one of the approaches to
combining quantum theory with gravity, loop quantum gravity or
LQG, would fundamentally change our picture of space and time.
Initially developed in the early 1980s, LQG has progressed to
the point where it can provide a detailed – albeit still untested
– physical and mathematical picture of quantum spacetime.
Specifically, LQG proposes that, at the smallest scale, space looks
like a fine fabric woven of closed loops. These networks of loops
are called spin networks.
Spin networks provide a language to describe the quantum
geometry of space. To describe the evolution of such a network
– to describe not space but spacetime – requires a formalism
called spin foams. The development of spin foams allowed loop
quantum gravity to address such matters as causality, light cones,
and the like – to begin to give sensible answers about the nature
of space and time on the shortest possible scales.
Spin foams were pioneered by several people, including
Perimeter
Faculty member Laurent Freidel
. It was Freidel (collaborating
with Perimeter visitor Kirill Krasnov) who first wrote down a spin
foam model that corresponds to four-dimensional quantum
gravity. The seminal work answered many questions and was the
first to describe the relationship between the quantum and the
classical in a satisfying way.
Freidel’s discovery was too technical to receive much attention at
the time, but it turned out to be very useful. The model he created
continues to be the most widely used spin foam model, the basis
of most of the studies being done today.
Work in spin foams and LQG continues on many fronts, including
some here at Perimeter: it was spin foams, for instance, that
allowed Eugenio Bianchi to calculate the entropy of a black
hole, as outlined below. For his part, Freidel is working on a new
continuum interpretation of loop quantum gravity.
Building black holes
How do you build a black hole? Ask
Perimeter Postdoctoral
Researcher Eugenio Bianchi
. Taking a loop quantum gravity
approach, Bianchi recently re-derived a famous equation for the
entropy of black holes from first principles.
A formula for the entropy of a black hole may seem like an
obscure result, but it’s actually an important signpost on the
road to quantum gravity. The formula – which is called the
Bekenstein-Hawking equation – is one of the very few in physics
that contains constants from both quantum mechanics and
Einstein’s gravitation. This tantalizing intersection between the
two great physics theories of the 20
th
century has long fascinated
researchers who are struggling to unify them into a 21
st
century
theory of quantum gravity.
Quantum gravity is concerned with unifying Einstein’s general theory of relativity and quantum
theory into a single theoretical framework. At Perimeter Institute, researchers are actively
pursuing a number of approaches to this problem, including loop quantum gravity, spin foam
models, asymptotic safety, emergent gravity, string theory, and causal set theory. The search
for quantum gravity overlaps with other areas such as cosmology, particle physics, and the
foundations of quantum theory.
Quantum
Gravity