  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.
