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Gravitational Physics: Quantum Gravity
and Other Theoretical Aspects
Luca Bombelli
Tibor Torma
Caixia Gao
approaches to quantum gravity:
causal sets, loop quantum gravity
Arif
other projects: black-hole entropy,
star clusters and star formation
Brian Mazur
what is quantum gravity?
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General relativity: Gravity is a consequence
of the curvature of spacetime, some of whose
components obey the equation
curvature = 8pG (energy-momentum) ;
as a consequence, spacetime geometry (the
metric g) in part depends on matter, and
in part it has its own wavelike dynamics.
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Is this the final word on gravity? Almost certainly
not, because of quantum matter if nothing else.
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What about quantizing gravity itself? Ok, and we
can perhaps guess what such a theory might tell
us, but the first big question is, How? The most
developed approaches are string theory and loop
quantum gravity, but there are more radical ones.
the causal set approach
• Basic idea: A causal set is a discrete version of
spacetime, stripped of everything except for the causal
relationships x < y among its elements.
• Kinematics: To what extent is all of spacetime
geometry encoded in the relations?
• Dynamics: Use for example the action
loop quantum gravity approach
• Type of approach: Apply canonical quantization to a version
of classical general relativity in which spacetime = space  time,
and choose an appropriate set of variables.
• The variables: The metric g is split into spatial information,
encoded in a triad of vectors Eai, and its conjugate “momentum”,
a connection Aai for the rotation group. One then looks for wave
functions y(A,t) satisfying a quantum version of Einstein’s
equation. It turns out that important ones are based on graphs…
• Open questions: Many! From very technical ones to, What does
it mean for this field to be made of quanta? What is time? …
And also, … What do “semiclassical solutions” look like?
some phenomenological questions
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Quanta of gravity: In principle they are somewhat like photons with a
higher spin, but specific predictions are hard to make and we are not
close to being able to detect them as particles.
Cosmology: The big bang singularity, expansion, imprints on the CMB.
Black holes: Singularities, entropy and Hawking radiation.
Photons: Electromagnetic waves propagating in a vacuum satisfy, in
Fourier transform space, the (no-) dispersion relation
k2c2 – 2 = 0, according to which n = 1.
but quantum spacetime fluctuations are expected to change this.
Is the effect observable? From dimensional analysis, one would think
that corrections only appear at scales approaching Planck scales,
 = lP = (Gh/c3)1/2 = 2  10–33 cm
EP = (hc5/G)1/2 = 1.3  1019 GeV
But there are loopholes...