  Despite considerable progress in several approaches to quantum gravity, there
remain uncertainties on the conceptual level. One issue concerns the different
roles played by space and time in the canonical quantum formalism. This issue
occurs because the Hamilton-Jacobi dynamics is being quantised. The question
then arises whether additional physically relevant states could exist which
cannot be represented in the canonical form or as a partition function. For
this reason, the author has explored a statistical approach (NDA) which is not
based on quantum dynamical assumptions and does not require space-time
splitting boundary conditions either. For dimension 3+1 and under thermal
equilibrium, NDA simplifies to a path integral model. However, the general case
of NDA cannot be written as a partition function. As a test of NDA, one
recovers general relativity at low curvature and quantum field theory in the
flat space-time approximation. Related paper: arxiv:1505.03719.
