Noncausal Page-Wootters circuits

One of the most fundamental open problems in physics is unification general relativity and quantum theory to a gravity. An aspect that might become relevant such dynamical nature causal structure present displays uncertainty. This may lead phenomenon known as indefinite or structure, captured by process matrix formalism. Due generality framework, however, for many matrices there no clear physical interpretation. A popular approach towards gravity Page-Wootters formalism, which associates time Hilbert space similar spatial position. By explicitly introducing clock, it allows describe time-evolution systems via correlations between this clock said encoded history states. In paper we combine framework with generalization formalism one considers several agents, each their own discrete clock. We how extract from scenarios involving agents clocks, analyze properties. The description state multiple clocks imposes constraints on implementation perspectives described reference frames. While where different definite orders are coherently controlled, explain why certain noncausal processes not be implementable within setting.