New research challenges the conditional interpretation of the Page-Wootters (PW) proposal, a theoretical framework that aims to recover the notion of time and dynamics in timeless formulations of quantum theory. The PW proposal conceives the total timeless system as a clock entangled with the world, where states with a definite clock reading appear to restore the temporal states of the world as relative states, allowing dynamics to emerge. However, the study points out a fundamental inconsistency in how the time operator is chosen within this framework.

The core problem lies in the fact that an entangled state admits infinitely many decompositions as a superposition of product states. Each of these decompositions corresponds to a different, but equally valid, time operator for the same clock system. Choosing different time operators for the same clock leads to diverging physical histories, where the world states in one history are superpositions of the world states from another history. Fixing one operator as "the" clock time reintroduces the notion of time that the Page-Wootters proposal precisely aims to explain intrinsically.

This inconsistency suggests that the interpretation of PW, according to which the world state is passively conditioned on the clock state, cannot hold. Instead, the timeless state must be resolved into time-dependent states by intrinsic pointer observables of the world itself, without outsourcing the role of the time operator to a separate clock. Despite this criticism of the conditional interpretation, the formalism of the Page-Wootters proposal remains valid, provided it is interpreted in terms of intrinsic pointer observables of the world itself, opening new avenues for understanding the emergence of time in quantum physics.