Approaches to Quantum Gravity

Questions and answers 575– A - J. Kowalski-Glikman:1. You are certainly right that one could use any objects: photons, protons,or potatoes to synchronize two identical clocks placed at two distinct points,at rest with respect to each other. Yet it would be extremely odd to do thatby means of anything but light in view of the Einstein postulate: “Clocks canbe adjusted in such a way that the propagation velocity of every light ray invacuum – measured by means of these clocks – becomes everywhere equal toa universal constant c, provided that the coordinate system is not accelerated.”Such clocks provide Einstein synchronization.2. I do not know exactly, but a general idea is that in momentum space, insteadof clocks and rulers you will have a device measuring energy and momentum.If I have an observer independent fundamental scale of energy, carried byan object, which I call planckion, it would be convenient to synchronize theenergy meters in such a way that “the energy of every planckion – measuredby means of these meters – becomes everywhere equal to a universal constantκ, provided that the coordinate system is not accelerated.”3. If the GZK anomaly indeed is there (which means that we see 10 2 1eVprotons,whose source is at the cosmological distance, and all the astrophysicaldata used to calculate the mean free path of such protons are correct) then Ido not see any other explanation.4. We obviously cannot do phenomenology if we do not understand it. Howeverwe already have some generic understanding of DSR formalism whichleads to at least two robust predictions: there is no energy dependence of thespeed of light, and, as I argued in my contribution, it is extremely unlikelythat there are any sizable DSR corrections to GZK threshold.• Q-L.Crane:I think your explanation of the origin of the deformation of Lorentz transformationsis very interesting. But wouldn’t it then depend on the size and distance ofthe system and the state of motion of the observer?– A - F. Girelli:The deformation can be read out from the dispersion relation encoding theparticle dynamics. This dispersion relation can be particle dependent, that isthe extra terms encoding the deformation could depend on the helicity, spin,intrinsic properties of the particle. In this sense the deformation would bereally particle dependent. Then the deformation depends also on the factorM P , the Planck scale. This parameter is a priori universal. However, I arguedthat for many particles one should allow a rescaling of the maximum mass,in order to avoid the soccer ball problem, that is, the emergence problemof macroscopic objects. Indeed the maximal mass as a Scharwschild massshould rescale linearly in terms of its typical length. If we agree on that, if we