In the Page-Wooters formalism, time is treated as a position observable of a reference clock system, so that states are double-kets $|\Psi\rangle\rangle \in \mathcal{H}_{t} \otimes \mathcal{H}_{S}$ where $S$ is the system under analysis and $t$ is the time-degree of freedom, which is just the position of a particle constrained on a line.
Then, it can be shown that the dynamics (that is, time evolution) of the sub-system $S$ is recovered from a constraint, similar to the Wheeler-De-Witt equation: $\mathbb{J}|\Psi\rangle\rangle = 0$, it is then easy to show that if $\mathbb{J} = \hat{p}_{t} \otimes 1 + 1 \otimes \hat{H}_{S}$ where $\hat{p}_{t}$ is the momentum of the clock particle, then the constraint equation in the eigenbasis $|t\rangle$ is just the Schrodinger equation.
It seems that even tough we are treating time and space on equal footing, we reach a non-relativistic equation in the end, my question is: what constraint operator $\mathbb{J}$ can one choose to get a relativistic evolution for system $S$ in this formalism?
