Observables in Quantum Gravity

1. Observables in Quantum Gravity Observables in QM are Measured by Semi-classical Machines Current Understanding: Pointer Variables are Averages of Local Operators over Volumes >> Micro length Scales. Tunneling Between Pointer Positions ~ e- cS : c order 1 S pointer entropy In QG Too Much Localized Entropy - Black Hole. BH has no Pointers except total M, Q etc. This is the basic constraint on local observables. To me, it doesn’t make much sense to try to understand QG observables in Field Theory terms. Eventual formalism will not resemble field theory at all (e.g. NOT String Field Theory).

2. Observables in QG • Challenge will be to rederive field theory rules as approximation to new formalism. • Hints from “Holographic Space-Time” • Basic Variables Are Like Detector Elements in a Collider Expt. • Particles Will Exist and Have Properties Attributed to Them by Field Theory, Only in Situations Where Detector is Sparsely Excited. Particle trajectories will be patterns of excitation in nested detectors. • Derive Feynman rules directly from holographic formalism. Non-perturbative formulation of field theory in fixed geometry will be more complicated and of limited utility????? • dS space: Finite N precludes precise definition of observables but ambiguities of order e-K K ~ (RMP)3/2

3. Landscapes in String Theory? • Effective action in String Theory is Wilsonian, not 1PI. All confirmed uses of it involve computing “scattering” in given asymptotic space-time background • Attempts to create regions of other “vacua” fail and result in black holes. Generically create small regions (“Lee-Wick abnormal nuclei”) if potential is small enough, or black holes. Exception: can explore region in field space of order mPd-2/2 on moduli space

4. Landscapes of Vacua or a Vacuous Landscape • No “short distance regime” where “different vacua” agree. All kinematic regimes (eikonal, stringy, black hole) of high energy scattering are sensitive to low energy spectrum. Essence of superselection sectors in QFT is UV/IR SEPARATION. In QG, UV/IR CONNECTION via black holes.

5. Coleman DeLucia: Only guide to transitions in QG • Great Divide (co-d 1) in the Space of Potentials • Lowest positive c.c. min. is stable/unstable as L  0 (Is/Isn’t + E Thm. At L = 0 ) • Boundary: V Has Static Domain Wall at L = 0 • Above Great Divide: Calculable Transitions Consistent w Detailed Balance in System With a Finite # of States • Speculation that reverse transition from L < 0 Crunch to Lowest dS relatively rapid: consistent with covariant entropy bound for observers in crunching bubble. • Below the Great Divide: Only Questions. Can the observable universe be consistent with our min being below the great divide?

6. The String Landscape Potential • Doesn’t fit above classification because of 0 c.c. locally SUSic regions • Attempts at interpretation focus on “final scattering states in census taker bubble”. If right, definitely infinite # of states. All but a finite number extrapolate back to space-like singularity intervening between census taker and CDL tunneling into census taker bubble. • Further confusion: Many different census taker bubbles (different positive c.c. minima tunneling into different asymptotically locally SUSY (IIA, IIB, M, Het A,B etc) regions). In QFT all Hilbert spaces unitarily inequivalent under maps which preserve locality of asymptotic fields. • IMHO Need a definition of what the observables are and an in principle computational scheme before one can take the String Landscape seriously. • Would also be nice to have a prescription for computing physics of our world in terms of these well defined observables.