Quantum Gravity as Escher ’ s Dragon

The main obstacle in attempts to construct a consistent quantum gravity is the absence of independent flat time. This can in principle be cured by going out to higher dimensions. The modern paradigm assumes that the fundamental theory of everything is some form of string theory living in space of more than four dimensions. We advocate another possibility that the fundamental theory is a form of D = 4 higher–derivative gravity. This class of theories has a nice feature of renormalizability so that perturbative calculations are feasible. There are also finite N = 4 supersymmetric conformal supergravity theories. This possibility is particularly attractive. Einstein’s gravity is obtained in a natural way as an effective low–energy theory. The N = 1 supersymmetric version of the theory has a natural higher–dimensional interpretation due to Ogievetsky and Sokatchev, which involves embedding of our curved Minkowsky space-time manifold into flat 8-dimensional space. Assuming that a variant of the finite N = 4 theory also admit a similar interpretation, this may eventually allow one to construct consistent quantum theory of gravity. We argue, however, that even though future gravity theory will probably use higher dimensions as construction scaffolds, its physical content and meaning should refer to 4 dimensions where observer lives. Invited talk at the conference “Modern trends in classical approaches” devoted to the 80-th birthday of K.A. Ter–Martirosyan, Moscow, September 2002. On leave of absence from ITEP, Moscow, Russia.