The Trinity of Relational Quantum Dynamics

Understand

The problem of time in quantum gravity calls for a relational solution.

• Using quantum reduction maps, we establish a previously unknown equivalence between three approaches to relational quantum dynamics: 1) relational observables in the clock-neutral picture of Dirac quantization, 2) Page and Wootters' (PW) Schr\"odinger picture formalism, and 3) the relational Heisenberg picture obtained via symmetry reduction.
• Constituting three faces of the same dynamics, we call this equivalence the trinity.
• We develop a quantization procedure for relational Dirac observables using covariant POVMs which encompass non-ideal clocks.