Approaches to Quantum Gravity

434 G. Amelino-Camelia22.2.2 Planck-scale departures from CPT symmetryPerhaps the most intelligible evidence of a Planck-scale effect would be a violationof CPT symmetry. CPT symmetry is in fact protected by a theorem in our current(Minkowski-limit) theories, mainly as a result of locality and Poincaré symmetry.The fact that the structure of the Quantum Gravity problem invites us to considerspacetimes with some element of nonlocality and/or departures from Poincaré symmetryclearly opens a window of opportunity for Planck-scale violations of CPTsymmetry.22.2.3 Distance fuzziness and spacetime foamThe fact that the structure of the Quantum Gravity problem suggests that the classicaldescription of spacetime should give way to a nonclassical one at scales of orderof the Planck scale has been used extensively as a source of inspiration concerningthe proper choice of formalism for the solution of the Quantum Gravity problem,but for a long time (decades) it had not inspired ideas relevant for phenomenology.The description that came closer to a physical intuition for the effects induced byspacetime nonclassicality is Wheeler’s “spacetime foam”, which however does notamount to a definition (at least not a scientific/operative definition). A few yearsago I proposed a physical/operative definition of (at least one aspect of) spacetimefuzziness/foam, which makes direct reference to interferometry. According to thisdefinition, the fuzziness/foaminess of a spacetime is established on the basis ofan analysis of strain noise in interferometers set up in that spacetime. In achievingtheir remarkable accuracy modern interferometers must deal with several classicalphysicsstrain noise sources (e.g. thermal and seismic effects induce fluctuations inthe relative positions of the test masses). And, importantly, strain noise sourcesassociated with effects due to ordinary Quantum Mechanics are also significantfor modern interferometers (the combined minimization of photon shot noise andradiation pressure noise leads to a noise source which originates from ordinaryQuantum Mechanics). The operative definition of fuzzy/foamy spacetime which Iadvocate characterizes the corresponding Quantum Gravity effects as an additionalsource of strain noise. A theory in which the concept of distance is fundamentallyfuzzy in this operative sense would be such that the read-out of an interferometerwould still be noisy (because of Quantum Gravity effects) even in the idealizedlimit in which all classical-physics and ordinary-quantum-mechanics noise sourcesare completely eliminated.22.2.4 DecoherenceFor approaches to the Quantum Gravity problem which assume that, in mergingwith General Relativity, Quantum Mechanics should revise one of the most