The Observer as a Local Breakdown of Atemporality

This project investigates the emergence of time from a fundamentally timeless description of the universe. Rather than assuming time as a primitive background parameter, we study the physical and informational conditions under which temporal ordering, dynamics, and irreversibility appear for an observer embedded in the system. The core of the framework is a unified relational formula—extending the Page–Wootters mechanism—that shows how three traditionally distinct aspects of the “problem of time” arise from the same operational structure: (i) quantum dynamics from conditioning on physical clock states, (ii) the thermodynamic arrow from partial access to environmental degrees of freedom, and (iii) observer-dependent time from the locality of the clock subsystem. Crucially, the framework does not modify unitary quantum mechanics, introduce collapse postulates, or assume a fundamental flow of time. All temporal features emerge from projection, partial trace, and normalization applied to a single global atemporal state satisfying a Hamiltonian constraint. The project includes analytical results, numerical simulations (implemented in QuTiP), pedagogical companion notes, and philosophical analysis. Together, these components support a central claim: time is not a property of the universe itself, but a property of restricted descriptions generated by physical observers with limited informational access. This OSF repository serves as a living container for the formal development, conceptual interpretation, and future extensions of this observer-dependent approach to temporal emergence.