a more primitive noninvariant theory.

For some type II models, another problem can occur. While such models involve emergent space, some (e.g., [@Marko; @Lloyd]) include a time parameter to describe the evolution of the underlying degrees of freedom. In such cases, one must worry about the relationship between this fundamental time and the emergent time in the description of gravity. This is another decoupling problem: the time in which the fundamental degrees of freedom evolve is a background structure, and any coupling to the emergent degrees of freedom would define a preferred time and break diffeomorphism invariance.

Diffeomorphism invariance II
----------------------------

Diffeomorphism invariance plays another key role in general relativity: it eliminates the spin zero and spin one degrees of freedom, leaving only spin two modes. In the ADM formalism, the spatial metric and its conjugate momentum form six independent canonical pairs $(q_{ij},\pi^{ij})$, but the four diffeomorphism constraints eliminate four pairs. It is crucial that the constraints are first class (i.e., that the commutator of two constraints is itself proportional to the constraints); a first class constraint eliminates two phase space degrees of freedom, while a second class constraint eliminates only one [@HenneauxTeitelboim]. While the presence of additional degrees of 