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6.4 Quantum gravity - phenomenology

Over the last few years a widespread consensus has emerged that observational tests of quantum gravity are for the foreseeable future likely to be limited to precision tests of dispersion relations and their possible deviations from Lorentz invariance [261Jump To The Next Citation Point]. The key point is that at low energies (well below the Planck energy) one expects the locally Minkowskian structure of the spacetime manifold to guarantee that one sees only special relativistic effects; general relativistic effects are negligible at short distances. However as ultra high energies are approached (although still below Planck scale energies) several quantum gravity models seem to predict that the locally Euclidean geometry of the spacetime manifold will break down. There are several scenarios for the origin of this breakdown ranging from string theory [214109] to brane worlds [54] and loop quantum gravity [134]. Common to all such scenarios is that the microscopic structure of spacetime is likely to show up in the form of a violation of Lorentz invariance leading to modified dispersion relations for elementary particles. Such dispersion relations are characterised by extra terms (with respect to the standard relativistic form) which are generally expected to be suppressed by powers of the Planck energy. Remarkably the last years have seen a large wealth of work in testing the effects of such dispersion relations and in particular strong constraints have been cast by making use of high energy astrophysics observations (see for example [382195194196197261355] and references therein).

Several of the analogue models are known to exhibit similar behaviour, with a low-momentum effective Lorentz invariance eventually breaking down at high momentum once the microphysics is explored.26 Thus some of the analogue models provide controlled theoretical laboratories in which at least some forms of subtle high-momentum breakdown of Lorentz invariance can be explored. As such the analogue models provide us with hints as to what sort of modified dispersion relation might be natural to expect given some general characteristics of the microscopic physics. Hopefully investigation of appropriate analogue models might be able to illuminate possible mechanisms leading to this kind of quantum gravity phenomenology, and so might be able to provide us new ideas about other effects of physical quantum gravity that might be observable at sub-Planckian energies.


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