Einstein's theory of general relativity is based on the premise that the
physical laws take the same form in all coordinate systems. However, it still
presumes a preferred decomposition of the total kinematic Hilbert space into
local kinematic Hilbert spaces. In this paper, we consider a theory of quantum
gravity that does not come with a preferred partitioning of the kinematic
Hilbert space. It is pointed out that, in such a theory, dimension, signature,
topology and geometry of spacetime depend on how a collection of local clocks
is chosen within the kinematic Hilbert space.