Are the different relational descriptions of quantum time equivalent?
In plain words
One proposal measures time through correlations with a physical clock inside the system; others use special combinations of variables that do not change. These approaches agree in simple models, but whether they agree in general is open.
Precise statement
For a constrained quantum system with Hamiltonian constraint H|psi> = 0, compare (i) the Page-Wootters conditional-state formalism, (ii) relational Dirac observables on the physical Hilbert space, and (iii) reduced quantization deparametrized with respect to a chosen clock. Determine conditions under which they give unitarily equivalent predictions, including clocks with degenerate or bounded spectra and clocks that interact with the rest of the system. An answer is an equivalence theorem with explicit conditions or a counterexample.
What would settle it
An equivalence theorem covering interacting and non-ideal clocks, or a model where the formalisms give different measurable predictions.
Status in the literature
Unverified note
Equivalence was shown for ideal, non-interacting clocks (Hohn, Smith, Lock 2021); interacting and non-ideal clocks remain open as of 2026.