Approaches to Quantum Gravity

578 Questions and answersAs a result, while I admire the beautiful work that friends and colleagueshave done with spin foam models with representations of the Lorentz or evenPoincaré groups I do not believe that ultimately this will be the choice thatcorresponds to nature.One might of course, take the other view, which is that the spin foam modelis to be invented independently of any quantization from a classical theory.I am sympathetic to this as quantum physics must be prior logically to classicalphysics, but in this case also I have two arguments against using therepresentations of the Lorentz or Poincaré group in a spin foam model.The first argument starts with the observation that Lorentz and Poincarémust in the quantum theory be considered global symmetries. Someone mightclaim that they are local symmetries, but the equivalence principle is limitedin quantum theory because the wavelength of a state is a limit to how closelyyou can probe geometry. When the curvature is large, the equivalence principlemust break down, and thus it cannot be assumed in formulating the pathintegral, which will be dominated by histories with large curvatures. Thus,you cannot assume the equivalence principle for the quantum theory and as aconsequence I dont think you can regard local symmetries derived from theequivalence principle as fundamental. On the other hand, global symmetriesare not fundamental in General Relativity – because the generic solution hasno symmetries at all and there are – as Kuchar showed – no symmetries onthe configuration space of GR. Any appearance of a global symmetry in GRis either imposed by boundary conditions or a symmetry only of a particularsolution.Thus, the Lorentz and Poincaré groups are not fundamental to GR, they areinstead symmetries only of a solution of the theory. Hence I cannot believethat a spin foam model using labels from Lorentz or Poincaré reps can befundamental.My second argument is that I believe that physics at the smallest possiblescale should be simple and involve only finite calculations. I cannot believethat the universe must do an infinite amount of computation in a Planck timein each Planck volume just to figure out what happens next. I would thus proposethat the computation required in the smallest unit of time in the smallestpossible volume of space must be elementary and must require only a minimalnumber of bits of information and a minimal number of steps. My ownbet would then be that at the Planck scale the graphs which label quantumgeometry are purely combinatorial, in which case there are no representationlabels at all.You could push me by arguing that this is quantum theory and a minimalprocess should involve a small number of q-bits and not classical bits. This